tenth international conference on soft computing applied in

Transkript

tenth international conference on soft computing applied in
EVROPEAN POLYTECHNIC INSTITUTE, Ltd. KUNOVICE
PROCEEDINGS
„TENTH INTERNATIONAL CONFERENCE ON
SOFT COMPUTING APPLIED IN COMPUTER
AND ECONOMIC ENVIRONMENTS“
ICSC 2012
January 20, Kunovice, Česká republika
Edited by:
Prof. Ing. Imrich Rukovanský, CSc.
Doc. Ing. Mirslav Mečár, CSc.
Prof. Ing. Pavel Ošmera, CSc.
Ing. Jaroslav Kavka
Prepared for print by:
Ing. Andrea Kubalová, DiS.
Bc. Martin Tuček
Printed by:
© European Polytechnical Institute Kunovice, 2012
ISBN 978-80-7314-279-7
INTERNATIONAL CONFERENCE ON SOFT COMPUTING
APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS
ICSC 2012
Organized by
THE EUROPEAN POLYTECHNIC INSTITUTE, KUNOVICE
THE CZECH REPUBLIC
Conference Chairman
H. prof. Ing. Oldřich Kratochvíl, Ph.D., CSc., Dr.h.c., MBA
rector
Conference Co-Chairmen
Prof. Ing. Imrich Rukovanský, CSc.
Doc. Ing. Miroslav Mečár, CSc.
INTERNATIONAL PROGRAMME COMMITEE
O. Kratochvíl – Chairman (CZ)
W. M. Baraňski (PL)
K. Rais (CZ)
M. Šeda (CZ)
J. Baštinec (CZ)
J. Brzobohatý (CZ)
J. Diblík (CZ)
P. Dostál (CZ)
U. Chakraborthy (USA)
M. Kubát (USA)
P. Ošmera (CZ)
J. Petrucha (CZ)
I. Rukovanský (CZ)
G. Vértesy (HU)
I. Zelinka (CZ)
A. M. Salem (ET)
A. Borisov (LT)
M. Wagenknecht (GE)
Session 1: ICSC – Soft Computing a jeho uplatnění v managementu,
marketingu a v moderních finančních systémech
Session 2: ICSC – Soft Computing – tvorba moderních počítačových
nástrojů pro optimalizaci procesů
Opponency Board
Doc. Wlodzimierz M. Baraňski, Wroclaw University of Technology, Wroclaw, PL
Prof. Ing. Petr Dostál, CSc., Vysoké učení technické, Brno, ČR
Doc. RNDr. Jaromír Baštinec, CSc., Vysoké učení technické, Brno, ČR
CONTENTS
ÚVODNÍ SLOVO ................................................................................................................................................. 7
PROPOSAL OF SIMULATION STUDIES FOR THE PURPOSES OF ARCHAEOLOGICAL
PREDICTIVE MODEL........................................................................................................................................ 9
Stanislava Dermeková, Dalibor Bartoněk .......................................................................................................... 9
HISTORICAL MAPS IN GIS............................................................................................................................ 17
Dalibor Bartoněk, Stanislava Dermeková, Irena Opatřilová ............................................................................ 17
THE PREDICTION OF SALE TIME SERIES BY ARTIFICIAL NEURAL NETWORK ........................ 27
Petr Dostál, Oldřich Kratochvíl ........................................................................................................................ 27
VÝKON DATABÁZOVÝCH SYSTÉMOV NA HARDVÉROVÝCH PLATFORMÁCH .......................... 31
Juraj Ďuďák, Gabriel Gašpar, Michal Kebísek ................................................................................................ 31
DATA ANALYSIS & MODELING USING OPEN SOURCE SOFTWARE R ............................................ 37
Lukáš Falát ....................................................................................................................................................... 37
OPTIMISATION OF DECOMPOSITION STRATEGIES IN PARALLEL ALGORITHMS ................... 43
Ivan Hanuliak ................................................................................................................................................... 43
PERFORMANCE OPTIMIZATION OF BROADCAST COLLECTIVE OPERATION ON MULTICORE CLUSTER ............................................................................................................................................... 51
Hudik Martin .................................................................................................................................................... 51
PERFORMANCE MODELLING OF MATRIX PARALLEL ALGORITHMS.......................................... 57
Filip Janovič ..................................................................................................................................................... 57
MATHEMATIC EVALUATION OF ECOTOXICITY TESTING ............................................................... 65
Kateřina Kejvalová ........................................................................................................................................... 65
MANAGERIAL DECISION-MAKING: MEASURING AND MANIFESTATIONS OF RISKS .............. 75
Dusan Marcek .................................................................................................................................................. 75
TESTING OF TOPCON GRS-1 INSTRUMENT USING RTK METHOD .................................................. 81
Irena Opatřilová, Dalibor Bartoněk .................................................................................................................. 81
QUANTUM MODEL OF ATOMS ................................................................................................................... 89
Ošmera Pavel.................................................................................................................................................... 89
RBF NEURAL NETWORK APPLICATIONS USING JNNS SIMULATOR .............................................. 95
Jindřich Petrucha .............................................................................................................................................. 95
OPTIMIZATION OF THE THROUGHPUT OF COMPUTER NETWORK ........................................... 101
Imrich Rukovansky ........................................................................................................................................ 101
MINISATION OF COMPLEXLOGICAL FUNCTIONS ............................................................................. 109
Miloš Šeda ...................................................................................................................................................... 109
PERFORMANCE MODELLING OF MULTIPROCESSOR PARALLEL SYSTEMS ............................ 117
Dan Slovaček.................................................................................................................................................. 117
DESIGN AND CONSTRUCTION OF EXPERT SYSTEM FOR ANALYSIS OF RECREATION
ATTRACTIVENESS ........................................................................................................................................ 123
Yaroslav Vyklyuk, Olga Artemenko .............................................................................................................. 123
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PRINCÍPY OPRIMALIZÁCIE NAVRHOVANIA ELEKTROMECHANICKÝCH AKČNÝCH ČLENOV
............................................................................................................................................................................ 127
Juraj Wagner .................................................................................................................................................. 127
JMENNÝ REJSTŘÍK ....................................................................................................................................... 137
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ÚVODNÍ SLOVO
Konference „ICSC – International konference on Soft Computing Applied in Computer and Economic
Environments“ proběhla sice již po desáté, ale poprvé ve virtuální technologii. Účastníci konference přišli z 5
univerzit a výzkumných institucí. Recenzované příspěvky v počtu 18 se věnovaly vývoji v oblasti teoretických
disciplín (Optimisation of Decomposition Strategie in paralel Algorithms atd.), především však aplikovanému
výzkumu v oblasti aplikované informatiky a elektroniky. Cílem konference bylo umožnit akademickým
pracovníkům zveřejnit výstupy jejich vědecké práce a podrobit je veřejnému posouzení.
Ve sborníku se nachází jen ty příspěvky, které prošly recenzním řízením. Nedoporučené příspěvky mohou autoři
dopracovat a navrhnout v květnové konferenci k novému hodnocení.
Sborník příspěvků bude odeslán autorům a jako povinná odevzdávka do univerzitních knihoven v ČR.
Je mně ctí poděkovat nejen všem akademickým pracovníků, recenzentům za jejich práci, ale také vědeckému
výboru konference a organizačnímu výboru konference za vynikající práci.
Oldřich Kratochvíl
Ing. ,h. prof., Ph.D., CSc., Dr.h.c., MBA
rektor EPI, s.r.o.
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PROPOSAL OF SIMULATION STUDIES FOR THE PURPOSES OF
ARCHAEOLOGICAL PREDICTIVE MODEL
Stanislava Dermeková1, Dalibor Bartoněk2
1
University of Technology, Faculty of Civil Engineering, Institute of Geodesy
2
Evropský polytechnický institut, s.r.o. Kunovice
Abstract: The process of simulation model generally represents a reconstruction of its way and
prediction of the possible existence of phenomena reflecting objects investigation. The subject of
modeling and simulation is to study objects that may already exist in reality or it could exist. The
paper deals with the existence of objects in a time long past, which can be described by the
simulation prediction model. The core modeling spatial phenomena prediction model through
simulation process is to conduct not only spatial analysis of archaeological data, but also the use of
instruments examining the characteristics of landscape elements and factors affecting the incidence
of long-past history.
Keywords: Simulation model, GIS, archaeological predictive model
INTRODUCTION
The process of simulation model building generally represents a reconstruction and its way a prediction of the
possible existence of phenomena reflecting objects investigation. The subject of modeling and simulation is to
study objects that already exist in reality or it could be. The paper deals with the existence of objects in a time
long past which can be described by the simulation model prediction. The core of the modeling of spatial
phenomena prediction model through simulation process is to conduct not only spatial analysis of archaeological
data, but also the use of tools for examining the characteristics of landscape elements and factors affecting the
occurrence of long-past history.
Results of simulation study will be complete simulation model for purposes of archaeological prediction. The
life cycle of the simulation process is composed of two stages: design and development of simulation model and
experimentation with the model. The paper also deals with the various individual stages of the simulation studies
in archaeological predictive models. Through simulation as a research technique, whose primary objective is the
substitution of simulator certain studying dynamic system. It will be predicted the abstraction of object model
solved the archaeological site. Using the simulator is experimented objectives for obtaining information on the
original scheme. From the results of simulation studies can reconstruct the appearance of the remains of human
activity from ancient times using 3D modeling and visualization.
1. MODELING AND SIMULATION
The subject of modeling and simulation is the study of the objects that may already exist in reality or it could be.
If we deal with the existence of objects in a time long past, can be described by the simulation predictive model.
In examining these objects is often not possible to describe the object rationally in all its complexity therefore
the description of the investigated object is applied an abstraction (some aspects of objects that are not important
in solving the problem, are neglected and insignificant characteristics are described in a way that leads to the
manageable solution to the problem). That can’t accurately predict the location extinct by describing the object.
On objects (parameters) to be studied is made in the modeling system definition, and one object can be defined
in different systems depending on the different angle of view under which the object is observed in various fields
of human activity. A different point of view is arising from the existence of parameters that are influenced by
various factors depending on the variables. The system, in which disregards the importance of the passing of
time, called a static system. Experiments in simulation of static system for archaeological predictive model
(APM) would represent a simple analysis only connected with the rights geological, climatic and landscape
character of the studied area. System in which we are considering the passing of time called a dynamic system.
Time instants of a dynamic system are identified as well as for the abstraction. Experiments in simulation study
of dynamic systems offer in predicting a wide range of analysis that can be combined in different options. [2]
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In a dynamic system in the modeling process and simulation is considered that the system consists of certain
elements (entities / elements). We distinguish between permanent and temporal elements. Permanent elements
occur in the system throughout its existence. The permanent elements in the archaeological prediction modeling
can sort elements: land use (landscape features - height, slope, exposure to the field), geological and climatic
nature of the territory, and others. Temporal elements can entry into the system and leaving it again. We consider
the temporal elements in APM: a factor of appropriate environmental protection, economic factor, factor of
minimum effort, defensive factor, cult factor, and other socioeconomic factors.
1.1 THE DEPENDENCE OF OBJECTS IN THE MODEL OF SIMULATION
After defining the system to the objects of the investigation are clearly insignificant properties on objects that are
subjected to closer scrutiny. In our case the objects of the investigation will be a location of the potential
archaeological site in a particular historical period. There are elements that don’t enter directly into the purpose
of the investigation but it is necessary to consider their existence because of respect to the examinee. Correlation
of elements is very important. The interdependence of different variables directs the operation of prediction in
historical documents. It can be used interaction modeling in the simulation process where each comparing
factors. These factors are dependent on variables. Interaction modeling is a strong correlation between the
individual elements that can be identified as important factors influencing on the prediction of a particular place.
Important factors occurring in the predictive model include the land use factor, the cult factor, economic factors,
social factors (socioeconomic factors), a defensive factor, factor in the minimum effort, and others.
1.2 THE PROCESS OF MODEL BUILDING
The essence of modeling is a substitute of the investigated system of the model which aim is to get information
through experiments with model on the original modeling system. Simulation is a research technique. The
essence of simulation is to substitute of the considered a dynamic system (a system in which we are considering
the passing of time) with the simulator. By experimenting with the simulator is to obtain information about the
original investigation system. Run the simulation program can be seen as carrying out a sequence of activities in
the order in which they perform their corresponding actions in simulation systems. [2].
Activities (processes) of the model can be divided according to nature:
 Discrete phenomena - the building of APM is preferable to consider discrete activities that change state
only at the time of its completion and their time existence is understood only as a single element set of
real numbers (the time by which the planned completion activities). Individual objects can be divided
into sections on the coordinates X, Y. Its have limits which are spatially defined. There are mostly
vector data model.
 Continuous phenomena – they cover continuously the whole territory, the phenomenon can not be
stopped (to find the exact limit). We determine the value of the phenomenon in the spot X, Y. It is a
raster data model usually.
The values of entity attribute change only at discrete time moments in APM. The reason is clear evaluation of
the results in parts of interaction analysis of the process simulation. Clarity is very important in archaeological
prediction because in this project is still considered only place which existence has long since disappeared.
1.3 ARCHAEOLOGICAL PREDICTIVE MODELING
The process of building of the archaeological predictive models is a specific approach and solutions. APM is a
tool that should simplify the archaeological research in the field of systems of settlement and land use in the past.
APM is a certain degree of accuracy the probable location of parts of the country which was previously used and
which can now predict the occurrence of archaeological sites. The problem of archaeological predicts is solved
by experiment sites (areas, packing areas), which typically are not usually randomly distributed, but occur with
respect to the geographical environment and settlement organization. The starting point of a correct
archaeological predictive model is to find the interdependence and carefully selected set of factors in the input
documents that affect the distribution of archaeological sites. Correct correlation of the setting parameters creates
the possibility of identifying sites in the country in which they are to find archaeological sites with high
probability. [4], [6]
Summarize of the input documents and their evaluation in the initial phase of APM is a certain amount of
attention and knowledge of archeology, Fig. 1. The expert analysis addresses the first correctness of data entry
documents where is created a database of all documents (maps and graphic materials, literary sources, material
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artifacts). Emphasis will be placed on a database of historical documents that will be used to analyze the
influence of time factor. The time factor affects on the every part of the solution prediction model. Any analysis,
each base, each output is affected by factors of time because is needed the expertise of historical objects. These
objects are changing in appearance and properties from the time. It is desirable to input documents consult with
experts. Interaction of experts is very important to address the process of model building. It represents the
experience and expertise in terms of make informed people from the fields of archeology who determined the
exact rules and parameters for prediction of term solution. Of the selected documents are creating a simulation
model to base GIS. In the process of creation is also using all the tools and modules in GIS thematic layers.
Model Builder applications, map algebra, 3D Analyst, Spatial Analyst create a full prediction model which can
be handled in different ways. [5]
Fig. 1 Scheme of different parts of archaeological predictive model
Expert system in predictive models is using settings of parameter that will be more precise each thematic layer.
Parameters that affect the location of the archaeological site are: altitude, slope of terrain, distance from
watercourse, communication, religion and others. Outside the spatial parameters can be considered a way of
behavior of people in the past. Factors that affect the way the behavior of people are as follows: cult factor,
economic factor, the factor of environmental suitability, defensive factor, factor minimum effort and others, Fig.
2.
The actual implementation of the analysis in the GIS occurs to simulate the presence of archaeological sites after
the setting of the parameters of the model arises. Spatial analysis is combined and used multi-criteria, interaction,
hydrological modeling, model of the petrology and others. All created spatial analysis should be subjected to an
influence analysis of the time factor which is used to create a database of historical documents and there is
mutual comparison of statistical and graphical output of results in different time periods. The outputs of
predictive model are the visualization of sites of archaeological locations in relation to their probability. The
formulation of outputs is specific. It depends on the solved at a site, the terrain and the presentation of
appropriate sites for archaeologists. [7]
Fig. 2 Expert system
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2 SIMULATION STUDY
The core of the whole project is the creation of simulation studies which will result in a complete simulation
model. The whole process of simulation is implemented in ArcGIS software. Basic diagram of connection is
shown in Fig. 3 where is presented each of the step in the modeling. In the first stage of the creating is
preprocessing which is usually the largest component of the process. Continuously builds an important part of
the simulation and its associated archaeological prediction. In this stage are used different types of models. For
purposes of archaeological prediction applies modeling of multi-criteria, interaction modeling, hydrologic
models, erosion models and others. Reciprocal correlation model eliminates the uncertainty of the location of
potential archaeological sites. The final part is the postprocessing which connects the individual outputs of each
simulation model.
The life cycle of the simulation process (studies) consists of 2 stages: design and simulation model development
and experimentation with the model. The procedure of making is described at each step of its implementation.
[1]
2.1 PHASE 1. – DESIGN AND DEVELOPMENT OF SIMULATION MODEL
2.1.1 INDICATION OF THE OBJECTS EXAMINATION AND THE ISSUE OF STYLIZATION
Creation of archaeological predictive model using the simulation method is a process where objects are
destroyed examining medieval settlements and their prediction. Defined object of investigation is experimented
on the research methods of simulation. Prediction of the location of the settlement will be at the core of the
project simulation model. The suitability of the site would result from different combinations of spatial analysis
undertaken, which will describe the sub-objects examination.
2.1.2 THE SETTING AIM OF PROJECT AND TIME SCHEDULE
The aim of project is using of prediction of defunct areas and their interaction modeling by spatial analysis in
ArcGIS software. Time schedule of the project requires extensive time reserve for the procurement of necessary
documentation, documentation and input data for progressive graphics verification. Part of the definition of
reserves is the control of technical and substantive correctness of input data to avoid mistaken and negative
influences. The solution for spatial analysis requires a large proportion of the total schedule of the simulation
model.
2.1.3 DETERMINATION OF THE SYSTEM
On the object of examination is applied an abstraction. Specify the simulated system (the original). It is needed
to accurately determine the correctness of input data and their thematic distribution. Suitability of the material is
achieving the objectives and solves problems without the need for further analysis and experiments.
2.1.4 CONCEPTUAL MODEL
An important part of life simulation model is the choice of appropriate methodology (concepts). In the election
play an important role in the methodological procedures that will gradually narrow range of solutions to the
problem resulting "clear" verification. The choice of types of interaction modeling will be will be a key for the
further course of archaeological predictive models.
2.1.5 COLLECTION AND ANALYSIS OF DATA CORRECTNESS
Data collection and their analysis take place parallel with the formation of the conceptual model. The process of
the data collection process is the most important part of the project. Phase of search suitable materials requires
considerable attention because of streamlining downstream spatial analysis. The input data are important for
decision-making rules relating to the issue of conflict resolution. Search for documents in them include
communication with the various institutions which represents the risk of negative feedback. It is therefore
important to ensure the correctness of received documents to prevent false information at a lower number of
input data. The process of data collection and analysis are dependent on the requirements which have been set in
the conceptual model solutions. The concept of the model will set the direction of its own collection of input
documents.
2.1.6 DEVELOPMENT OF SIMULATION MODEL
In ArcGIS software will be designed and implemented the appropriate data structures. It is necessary to
determine the main parameters of which will be based, and which will form the skeleton of model. Enter the
following parameters will be important for directing operation of the simulation model. It should be available to
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use simulation tools to the ArcGIS software offers in the archaeological predictive models. Appropriate tools can
be the 3D Analyst, Spatial Analyst, Map Algebra offers other components ArcGIS software. An interaction
between these instruments is very important.
2.1.7 VERIFICATION OF SIMULATION MODEL
Verification of functional correctness of the simulation model represents the first phase of the control
components interdependencies that were initially established in the conceptual model. Different methods for
testing the functionality of input and interaction of sub-documents have for verification of archaeological
predictive model. It will be applied the main methods of analysis using spatial interaction modeling, assessment
of multi-criteria, land use analysis and others. Testing the processes interaction requires a great deal of
knowledge to tackle (study of the historical sources, archaeological documentation, documents representing
landscape features, geological and climatic characteristics and other countries). Deficiencies found during
verification lead to legal intervention in the process of design and production simulation model.
2.1.8 VALIDATION OF SIMULATION MODEL
Validation is testing of the veracity of behavioral simulation model and the correctness of the result of processes
of spatial analysis. Implementation of validation in itself includes a variety of methods [2]:
 Method of compare with reality – using comparative methods of the dealing concept of using statistical
methods. It is using processed archaeological data of existing archaeological sites, the State
Archaeological Database System, exploring the surface collections solutions to existing sites.
 Compare with other models – validation that will be created to compare each model with a
fundamentally different structure model. Examples include models using modeling of multi-criteria on
the base of fuzzy logic, neural networks, interaction modeling using hydrological analysis, etc.
 Empirical method – using expert assessment by an independent expert. Consultation various parts of the
concept and created a simulation model with knowledgeable experts in the field of archeology.
Negative results of the validation may lead to structural changes in the conceptual phase of the simulation model
to review the correctness of input and concise treasures to repeated changes stylistics issues.
2.2 PHASE 2. – EXPERIMENTING WITH THE SIMULATION MODEL
2.2.1 THE SIMULATION TEST PLAN
The plan attempt depends on the frequency and accuracy of input documents. The proposed plan may be
modified based on the results progressively obtained. It is necessary to consider the impact of the time factor of
historical documents and their relation to the contemporary world..
2.2.2 IMPLEMENTATION OF THE PLAN AND PROCESS ANALYSIS
Using GIS software includes itself in the mathematical combination of spatial data to create derived data which
may provide new insights into natural phenomena and anthropomorphic. These can be further used in the
geological models for predicting the suitability of reverse land for agriculture or predicting erosion potential or
the potential deployment models in archaeological sites. To create the simulation model that would allow
defining, analyzing and evaluating residential development followed in the past, the selected area on the basis of
criteria determined from revised and localized archaeological data. Mathematics - simulation model for
predicting in archeology works based on the known archaeological patterns, several calculations were carried out
by the facts. The core of the process simulation model is a description and analysis of how the behavior of
people - simulating the actual behavior. Between the individual analyses I try to model the social dynamics of
the population and predict the possible occurrence of a real historical settlement.
The model uses a deliberately thought processes from individual to the general, the models, patterns, concepts of
factors that do not only features of the landscape, but also focuses on the patterns and effects resulting from the
spatial position and cross-functional compatibility of memory space. Created model simulates the dynamics of
changes in functional use of space in this area by combining the results of the analysis. Efforts to understand and
correct evaluation of often very complex behavior of a spatial system is usually difficult because of the resulting
documents, which represent an informed decision and simulation caused by the influence of individual factors in
the area.
For modeling purposes as a representation of the real (historical) world the wide range of alternative applications
Model Builder can be used. The ArcGIS software can create models of "localization" process model (variables,
parameters and their influence tackle) model description (description of issues examined). The benefits of the
Model Builder application, is creating its own sequence of functions and their parameterization (modification of
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function parameters, respectively. Instruments), modification of storage functions, scripting languages and
others. The iteration of the individual process creates detailed and final output in spatial analysis in the
application.
2.2.3 DETERMINATION OF THE FEASIBILITY OF ALTERNATIVE EXPERIMENTAL
(FEEDBACK)
When evaluating the specific factors of historical events is not enough just to work with absolute variables that
reflect the modeled variable without reference to other modeled quantity, time period and area. It is necessary to
have the values of these variables in other situations and compare their relative manner proportional method.
Comparison can be done by either absolute difference, comparative index (time index, geographic index, and
mixed material index). Confrontation of the output analyses with archaeological documents and papers state the
possibility for the alternative experiments because of the low reliability of the results for the final prediction of
perished areas. The process of deciding on the appropriateness of the models and their combination for
predicting the archaeological site potential requires a great deal of knowledge about the issue as well as
discussions with skilled and knowledgeable professionals. Although the location of archaeological prediction
may not always be complete, ambiguity and uncertainty of determining the place can be alternate with other
spatial analysis of multi-criteria modeling. Therefore it is important to confront your knowledge of simulation
modeling with experts to determine the alternative solutions.
2.2.4 DOCUMENTATION OF RESULTS
Graphic outputs of simulation model results are heterogeneous. For the purposes of archaeological prediction
models are useful mapping outputs with related factors which affect the decision-making on the suitability of
sites of potential archaeological sites. Combining the resulted layers of analysis and graphical presentation is an
excellent instrument for intuitive visualization of the possibility of settlement. Through simulation the
archeological site can be reconstructed in the form of 3D models directly applied to the solved area. For
example: making a real contemporary look of the village by using simulations according to the available
historical documents helps archaeologists in the visual orientation of the territory. 3D model of the ancient
settlements is a part of a comprehensive analysis of the simulation study. Its combination with the spatial
analysis moves simulation process to concrete results with decreasing percentage of localization uncertainty of
potential archaeological sites.
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Fig. 3 The life cycle of the simulation process
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3 CONCLUSION
The paper deals with the existence of objects in a time long past, which can be described by the simulation
model prediction. The core modeling spatial phenomena prediction model through simulation process is to
conduct spatial analysis of archaeological data only, but also the use of instruments examining the characteristics
of landscape elements and factors affecting the incidence of long-past history. The simulation model is linked to
ArcGIS software environment that offers a method of simulation by spatial modeling. In the spatial analysis are
considered factors that affect the suitability of the location of potential archaeological sites. In the simulation
study, which consists of two phases, the experiment phase is in various combinations of post processing analysis
of the results.
The simulation of the archaeological prediction provides us with the abstraction object model solved for the
archaeological site. Simulation in the GIS environment is a suitable tool for visual representation of
dependencies of the variables and factors modeled site. Through the simulation archeological site can be
reconstructed in the form of 3D models and visualization applied directly to the solved area. Combining 3D
models with spatial analysis reduces the percentage of localization uncertainty of potential archaeological site,
for better visual connection of the location with reality and its possibilities for the existence of historical
settlements.
LITERATURE
[1] KAVIČKA, A. Modelování a simulace. Pardubice : Electronic lectures of the course of Modelling and
Simulation. 2005.
[2] KŘIVÝ, I.; KINDLER, E. Simulace a modelování. Ostrava : Textbooks, University of Ostrava, 2001.
[3] CENDELÍN, J.; KINDLER, E. Simulace a modelování. Plzeň : Publishing Centre, UWB, Textbooks UWB
Plzeň, 1993. 230 s.
[4] GOLÁŇ, J. Archeologické predikativní modelování pomocí geografických informačních systémů – na
příkladu území jihovýchodní Moravy, Brno : PhD Thesis, Masaryk University, Faculty of Science,
Department of Geography. 2003.
[5] MACHÁČEK, J. Počítačová podpora v archeologii 2. Brno – Praha – Plzeň : Department of Archaeology
and Museology, MU Brno, Institute of Archaeology in Prague, Department of Archaeology ZU Plzeň,
2008.
[6] NEÚSTUPNÝ, E. Předvídání minulosti, Technical magazine 11. 58-60 s.
[7] KUNA, M. Geografický informační systém a výzkum pravěké sídelní struktury. In: Macháček, J (ed.),
Počítačová podpora v archeologii, Brno : Masaryk University, 1997. 173-194 s.
ADRESS:
Ing. Stanislava Dermeková
University of Technology,
Faculty of Civil Engineering,
Institute of Geodesy,
Veveří 95
602 00 Brno, Czech Republic
[email protected]
Assoc. prof. Dalibor Bartoněk
EPI Kunovice
Osvobození 699,
686 04 Kunovice,
Czech Republic,
phone: +420-605912767
[email protected]
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16
HISTORICAL MAPS IN GIS
Dalibor Bartoněk2, Stanislava Dermeková1, Irena Opatřilová1
1
University of Technology, Faculty of Civil Engineering, Institute of Geodesy
2
Evropský polytechnický institut, s.r.o. Kunovice
Abstract: The contribution deals with the usage of old maps in GIS for urban re-development. As a
model area the historical centre of Brno (Czech Republic) city including st. Peter-Paul’s cathedral
and Špilberk castle were selected. On the basis of historical maps, plans and documents the main
temporal points of urban development were established. The goal of this project was to attempt to
establish urban re-development in these temporal points. The project analysis was made together
with the cooperation of the experts of the middle age archaeology branch. Final output is a GIS
project in ARC/INFO created with the geo-database, which contains all temporary levels of map
sheets, significant geographical objects with the attribute data and historical and current time
photos of the interested objects. In ARC/INFO system also 3D model of Špilberk castle have been
created.
Keywords: old maps, city plans, GIS, historical data warehouse, 3D model.
1. INTRODUCTION
Historic buildings or conservation area has undergone during its history many changes. They changed not only
the appearance of the objects but also their style, layout or functionality. The aim of this project was to determine
the method of reconstruction of historic buildings on the basis of contemporary materials (documents, reports,
maps, photographs, etc.) and using GIS to determine their location or appearance at some stage of their
development (Procházka, 2007, 2009, Štěpánková, 2009).
In the region of interest were selected historical centre of Brno and Špilberk castle. Brno is the second largest
city in the Czech Republic with more than 400 000 inhabitants. It is the administrative centre of South Moravia,
and its historic district is a separate part of Brno - the city. The entire project was run in several major phases –
see Fig. 1:
1) Collection of historical materials relating to the area of interest,
2) Assessment of the materials and consultation with experts in the field of history,
3) Preparing and selecting the appropriate program; processing,
4) Data processing and analysis of appropriate software, identifying the main stages in which there were
significant changes in the region, creation of geo-database,
5) Creation and presentation of outputs.
Each phase of solutions is described in subsequent chapters.
Materials
collection
Evaluation
of materials
Data
preparation,
choice of
software
Consultation with
experts - historians
Analysis,
processing
Outputs,
presentation
s
Creation of
geo-database
Figure 1. Development of the project
2 HISTORICAL DATA COLLECTION AND EVALUATION
This phase was the most difficult of all (Hitchcock 1996). Although the center of Brno has a rich history,
historical material has been preserved relatively little. The paradox is that most of the preserved historical
documents were located outside the city of Brno, even outside the Czech Republic. In fact, some of the
organizations visited as Museum of Brno city, Archive of Brno, Moravian provincial archive, National office for
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17
preservation of historical monuments in Brno, bishopric of Brno have some materials but the quality of its was in
many cases insufficient. The most valuable items were found in the Military Archives in Vienna. It concerns the
collection of 21 plans since 1658 – 1819, 5 profile sheets and 3 sheets of construction plans. All above
mentioned materials were purchased by Institute of Geodesy, Faculty of Civil Engineering, Brno University of
Technology for the needs of this project. Current map materials necessary for the reconstruction were provided
by Facility management of Brno city and Czech Office for Surveying and Cadastre (Charvát et all, 2007).
To the oldest and the most valuable exemplary belong de Rochepien’s plan of Brno city of 1749 and the plan of
1754 - see Fig. 2. Overview of all collected historical materials is given in Table No 1. Collected data were
evaluated with the help of experts from the field history and adapted for further processing.
The collected materials collected occurred to be insufficient for processing. Above all it was necessary to look
up and determine appropriate identical points for geo-referencing of old maps. Further it was necessary to verify
current map material and compare them with a reality. For these reasons the collected data were completed with
direct geodetic measurement in field (Pundt 2002, Vivoni 2004). The actual selection of suitable materials for
reconstruction was consulted with experts at Middle age archaeology from Brno Museum. A basic document for
a choice of appropriate elements and identical points for reconstruction was present cadastral map of a given
locality. This map contained objects which can be divided into 2 categories:
1) Preserved parts of an object of late 18th century.
2) Objects with small construction works which cannot influence identification with old maps and plans
(facades adaptations, building reconstruction on an original object etc.).
Data source
(company)
Military Archive
Vienna, Austria
Archive of Brno city,
Czech Republic
Museum of Brno city,
Czech Republic
Archaia ltd., Czech
Republic
ELGEO ltd., CZ.
Facility management of
Brno city, Czech
Republic
Czech Office for
Surveying and
Cadastre
Geodis Ltd., Brno
Date
1658 - 1783
Number
of sheets
29
Content
Format
1720 – 1944
10
Plans of Špilberk castle
and Brno city
Plans, sketch of Brno city
A0 – A1, raster,
TIFF, 200 dpi
A3, raster, JPEG
1749 - 1984
4
Plans in scale 1:1000
A3, raster, JPEG,
TIFF, B/W
DGN, DWG
1997 - 2004
3
2006
2006
2
1
2002
4
Plans of Špilberk
fortification
Digital cadastral map
Building structure
investigation of Špilberk
fortification
Fundamental Base of
Geographic Data (3D)
Raster CIT, vector
SHP
2003
2
Ortho-photo 20 cm/pixel
Geo-TIFF, JPEG
DGN
Raster, JPEG
Table 1. Overview of all collected historical materials
Above mentioned objects contained localities for placement of reference points for geo-referencing of old map
documents. Other necessary identical points were obtained by geodetic surveying of south-west bastion of the
castle Špilberk which was newly reconstructed in the year 2002 in the frame of archaeological research. These
points are the most accurate (both in history and topography). On the contrary the historical maps and plans have
the lowest quality which is influenced by these factors:
 The ravages of time, causes fading of drawing which results in losing a part of a map.
 Precision of scanning in case, the map consists of several (in many cases damaged) parts.
 The exact dimension of map frame and field are unknown.
 Method of geodetic measurement and its accuracy are unknown.
 Disunited attribute style of drawing of maps and plans (various line styles and weights).
Therefore with transformation (geo-referencing) the accuracy was not determined and the whole process is only
to a certain extent informative, but the only available one.
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18
Figure 2. Plan of Brno city from 1754 year
Geo-referencing of historical maps was based on affine transformation according this equation:
 x  q x cos 
 y    q sin 
   x
where




 q y sin(   )  x  tx 

q y cos(   )   y  ty 
(1)
tx, ty is shift in the x, y axis,
qx, qy is scale factor in the x, y axis,
 is angle of rotation,
 is coefficient of non-orthogonality of both axis
3 DATA PREPARATION AND PROCESSING
For the project was selected by ESRI ArcGIS software. Before entering into ArcGIS some files had to be
adjusted. Raster data was preprocessed with Adobe Photoshop (cropping, downsizing, conversion, etc.), vector
data has been adjusted in MicroStation V8. Upon entering into the system ArcGIS had to be some layers georeferencing using identical points. In many cases, especially in historical maps, it was very difficult, because
many elements of the past disappear. For the whole project was used S-JTSK system (Datum of Uniform
Trigonometric Cadastral Network in the Czech Republic). All altitude dimensions were calculated into altimetry
system Bpv (Baltic Vertical Datum after Adjustment). There were successively inserted into the system or a
newly created 172 layers, which were grouped into 23 categories.
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19
From institutions or private entities have taken these layers:
 Historical maps,
 Ortho-photo maps,
 Geological map,
 ZABAGED (Fundamental Base of Geographic Data in the Czech Republic) – contour lines and
topography,
 State map of Brno city in the scale 1:5000,
 Utilities map of Brno city
 Zoning plan of Brno city
 Current cadastral maps of Brno municipality
Based on an analysis of existing layers were determined four periods in which were the most important urban
changes, namely:
 1750 – 1815
 1816 – 1880
 1881 – 1945
 1946 – 2010
These new layers have been created further categories or layers:
 Municipality fortification,
 Situation in 1890,
 Housing development in four above mentioned periods,
 Historical sightseeing tour in 1750 and 1890 – see fig. 4 (Štěpánková, 2009),
 Digital terrain model with layers: TIN, aspect, slope, hillshade, view, TIN-grid – see Figure 8,
Further were created followed special layers:
 Layer for WMS (Web Map Services)
 Layers of significant historical objects: st. Peter’s and Pauls’ cathedral, st. James church and German
house,
 Graph of selected profiles of Špilberk hill,
 Group layers of reconstruction of Špilberk castle.
For all newly created layers geo-database has been designed - see Figure 3 (Bartoněk et all, 2009).
As a special part of the project was create a topography and altimetry reconstruction of the castle Špilberk. Based
on historical and current maps was created 3D model of Špilberk castle during the Baroque period - see Figure 9
(Procházka, 2009).
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20
Figure 3 Geo-database of historical objects
4 RESULTS AND OUTPUTS
The main results of the project are:
 Collection of historical and contemporary material (map, documents, photographs and reports) of the
selected location,
 Classification of the material, determine the main stages of construction work - see Figure 6,
 Create new layers that show major changes in selected buildings,
 Creation of a common geo-database of historic buildings,
 Connection to the WMS services, where each user can work on-line with the selected map data,
 A special coating on the important historical places of Brno (st. Peter and Pauls’ cathedral, st. James
church and German house),
 Creation of GIS analysis in the locality - 3D Model, profiles,
 Complex process of reconstruction of the castle Špilberk in both 2D and 3D model.
All major results are presented in Figure 4 to 9. Figure 4 shows the main phase of structural changes in the centre
of Brno. There is marked historical guided tour in 1750 with outstanding stops. In Figure 5 you can see
important milestones in the development of the St. Peter’s and Paul’s cathedral, based on old maps. Fig. 6 shows
the historical centre of Brno in 1750 and Fig. 7 the same site in 1890. On both figures it is clear what significant
changes have taken place during the 140 years. Relatively stable are church buildings and squares, big changes
can be observed in transport infrastructure (rail, tram). Another figure 8 presents a 3D model of representative
sites created in the 3D Analyst module in ArcGIS. Elevations of the legend are given in altimetry system Bpv
(Baltic Vertical Datum after Adjustment).
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Figure 4. Housing development and historical sightseeing tour in Brno
The last figure represents the result of reconstruction of the castle Špilberk. This reconstruction in 3D has 2
phases (Pundt et all 2000):
1) The creation of Digital Terrain Model (DTM) of Špilberk hill – see previous Figure 8.
2) 3D model of historical reconstruction of Špilberk castle and its fortification – see Figure 9.
For making DMT these materials have been used:
 A plan of Špilberk castle of 1984 borrowed from Brno Museum in the scale 1:1000. The plan contained
contour lines with the interval 1 – 0,5 m which have been digitalized.
 Altimetry of Špilberk in ZABAGED system (Fundamental Base of Geographic Data) – see table 1.
For 3D model of historical reconstruction of Špilberk castle and its fortification these materials have been used:
 Plan of 1749 by Pierre Philippe do Beichade de Rochepine containing 15 dimensioned sections.
 Plan of 1759 with 2 sections missing in the previous plan.
 Plan of 1809 showing the fortress damaged in the period of Napoleonic wars.
 4 map sheets of 1917 containing detailed drawing of building adaptation in the years 1840 – 1880
including altimetry spots dimensioned heights of terrain and fortification.
 Contour lines ZABAGED (Fundamental Base of Geographic Data) in the locality.
 Geo-database of topography map created in a previous phase of the project.
 Current digital cadastral map of Brno centre.
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Figure 5. Significant re-building stages of st. Peter –Paul’s cathedral
Figure 6. Historical centre of Brno city in 1750
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Figure 7. Historical centre of Brno city in 1890
Figure
8. TIN model of historical centre of Brno city
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Figure 9. Extent of Špilberk fortification (3D model)
5 CONCLUSIONS
The goal of the project was documenting the historical development and changes in core of the housing city,
creation of a functioning system of historical database, serving a special interest group of users. This process was
done on the basis of maps imported into the ArcGIS program. Furthermore, it was also working with information
obtained from literature. Some materials (especially historical maps) did not meet the required accuracy,
therefore, had to be supplemented by direct measurement in field. Created project allows comparison the
development of urban historical core of Brno in various stages of the Middle Ages to the present. Layers contain
the most important of all elements ranked classified according to purpose, style and time. Further was created the
fly over the terrain by module ArcScene. The entire project was exported into a format PMF (Publish Map
Format), which can be viewed by AcrReader. This application enables users work with all layers without license
(free ware). The project was completed WMS capabilities, which allows the sharing of geographic information
in the form of raster maps on the Internet. Allows you to connect to the workflow software (GIS, CAD)
geographical data (maps, satellite images, ortho-photo, etc.) stored on other servers, in different formats (*.jpg,
*.tif, *.png). Showing thematic geographic information (layer), or composite map (overlay multiple layers). This
data is already related to a given coordinate system, which allows us to their correct interpretation.
Another contribution of this project is a creation of 3D model today non-existing baroque fortification of
Špilberk castle. It will be historically the first 3D digital model of the citadel taking original shape the one the
second half of 18th century. I believe the results of historical reconstruction of Špilberk castle and its
surroundings will become a valuable contribution not only for institutes and people working in the field of
medieval archaeology, but it will also draw attention of general public.
The project is not completely closed, maps are prepared and depends only on the ideas of more effective
treatment and complete, because each area, the building has a special history, characteristics that can be further
described.
REFERENCES
[1]
ŠTĚPÁNKOVÁ, A. 2009. Urban re-development of historical centre of Brno city. Diploma thesis,
Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, 55 pp (in Czech).
[2]
PROCHÁZKA, T. 2007. Planimetric component of a map reconstruction of historical fortification of
Špilberk castle. Bachelor thesis, Institute of Geodesy, Faculty of Civil Engineering, Brno University of
Technology, 29 pp (in Czech).
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EPI Kunovice, Czech Republic. January 20, 2012
25
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
PROCHÁZKA, T. 2009. Altimetry component of a map reconstruction of historical fortification of
Špilberk castle. Diploma thesis, Institute of Geodesy, Faculty of Civil Engineering, Brno University of
Technology, 47 pp (in Czech).
HONL, I.; PROCHÁZKA, E. 1990. Introduction into History of Surveying. Text book, Czech Technical
University, Prague, (in Czech).
CHARVÁT, K.; KOCÁB, M.; KONEČNÝ, M.; KUBÍČEK, P. 2007. Geographic Data in Information
Society. Research Institute of Geodesy, Topography and Cartography, Zdiby, Czech Republic, year 53,
no. 43, 270 pp, (in Czech).
BARTONĚK, D.; BUREŠ, J. 2009. Platform for GIS Tuition Usable for Designing of Civil
Engineering Structures at Brno University of Technology., Proceedings ICA Symposium on
Cartography for Central and Eastern Europe, Research Group Cartography, pp. 955 – 957, Vienna
University of Technology, Vienna, Austria, 2009
BARTONĚK, D.; BUREŠ, J.; DRÁB, A.; MENŠÍK, M. 2009. Usage of a Multidisciplinary GIS
Platform for the Design of Building Structures., Proceedings Professional Education – FIG International
Workshop Vienna, pp. 108 – 118, Austrian Society for Surveying and Geo-information, Vienna,
Austria.
PUNDT, H. 2002. Field Data Collection with Mobile GIS. Dependencies Between Semantics and Data
Quality. In Geoinformatica, vol. 6, no 4, pp 363 – 380. Accessible from
http://www.ingentaconnect.com/content/klu/gein/2002/00000006/00000004/05099730
[Pundt et all. 2000] Pundt, H.; Bringkotter, R-Runde, K. 2000: Visualization of spatial data for field
based GIS. In Computer & Geosciences. vol. 26, no. 1, pp 51-56. Accessible from
WWW:http:/www.iamg.org/CGEditor/cg2000.htm.
HITCHCOCK, A.; PUNDT, H.; BIRKKOTTER, R.; RUNDE, K.; STREIT, U. 1996. Data acquision
tools for geographic information system. In Geographical Information System International Group
(GISIG). (Ed.), Proceedings of the 13th WELL-GIS Workshop on technologies for land management
and data supply, RS and GPS Research and Education, June 13, Budapest, Hungary, 3rd session: GIS
and Global Positioning System. 8 s. Accessible from http://www.gisis.it/wellgis.www/Budap.htm.
VIVONI, E. R.; CAMILLI, R. 2003. Real-time streaming of environmental field data. In Computers &
Geosciences., vol. 29, no. 4, pp. 457-468. Accessible from http:///www.iamg.org/CGEditor/cg2003.htm.
ADRESS:
Ing. Stanislava Dermeková
University of Technology,
Faculty of Civil Engineering,
Institute of Geodesy,
Veveří 95
602 00 Brno, Czech Republic
[email protected]
Assoc. prof. Dalibor Bartoněk
EPI Kunovice
Osvobození 699,
686 04 Kunovice,
Czech Republic,
phone: +420-605912767
[email protected]
Ing. Irena Opatřilová
Institute of Geodesy, Faculty of Civil Engineering,
Brno University of Technology,
Veveří 331/95,
602 00 Brno, Czech Republic,
phone: +420-541147221
[email protected]
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26
THE PREDICTION OF SALE TIME SERIES BY ARTIFICIAL NEURAL NETWORK
Petr Dostál1, Oldřich Kratochvíl2
1
Brno University of Technology, Faculty of Business and Management, Department of Informatics
2
Private European Polytechnic Institute, Ltd. Kunovice
Abstract: The article presents one of the methods of prediction of time series with the support of
MATLAB program when Neural Network Toolbox is used. There are mentioned the steps of
calculation.The setup of parameters plays a key role for correct prediction. The method of
calculation can be used for any time series.
Keywords: Prediction, time series, calculation, MATLAB, Neural Network Toolbox
1. INTRODUCTION
The article presents the steps of calculation of prediction of sell time series. The Neural Network Toolbox of
MATLAB environment is used. The correct prediction is very complicated task because the components of time
series in economy and financial are quite often stochastic and random. Therefore the prediction is very difficult
and sometimes impossible, when the behaviour of time series is random. This is quite often case of time series
on the stock market. A little better situation it is with sale time series. The sale time series include also
deterministic components such asperiodicityand/or tendency that are easy recognizable. It could be mentioned
consumption or sell of some products, for example week periodicity is caused by behaviour of customers during
the week, year tendency is caused by physical phenomena, Gompertz curve is caused by saturation of market,
etc. These periodicity and tendency enable reasonable prediction. The case study is focussed on consumption of
energy.
2. USED METHODS
There are hundreds of methods for prediction of time series. The competitions are held where the best prediction
is evaluated. The program MATLAB with Neural Network Toolbox is a strong tool for prediction. The steps of
predictions are asfollows: download ofinput and output time series, choice of the type of neural network, set up
the number of layers, the number of neurons, transfer functions and some other parameters necessary for the
calculation. When the neural network is build up, the process of learning and testing is necessary to run. After
the calculation it is necessary to evaluate the results of prediction. The parameters of neural network are possible
to change in case of bad prediction. The process of learning and testing is possible repeat several times and with
changed parameters. When the prediction is correct,it could be used as a support for decision making for the
setup of production plan. The results could be exported for graphical visualisation.
3. CASE STUDY
This case study presents the prediction of consumption of energy of a town, where the day and week periodicity
is recognisable together with season tendency influence. The behaviour of people and weather could be
evaluated as a chaotic. The input data are available at input.csv and output data for learning at target.csv file.
The data are downloaded by orders
p=(load('input.csv'))';
t=(load('target.csv'))';
nntool
and the order nntool for opening neural network is called.The import of input time series is done by means of
menu Import p Input data Import OKand output data by means ofmenu Import t Target data Import OK. See
Fig.1.
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Fig. 1 Import of input and output time series
The order New Create displays the screen that enables to choose the type of neural network, the number of
layers, the number of neurons, transfer functions and some other parameters necessary for the calculation. The
process of build-up of neural network is done by order Create. See Fig.2.
Fig. 2 The build-up of neural network
The neural network named network1must be trained. The procedure starts by orderTrain-Train Network. The
process of training is presented in the window. After the process of training it is possible to use options for
display graphs to evaluate the performance. See Fig. 3.
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Fig. 3 Displaying the process of training of neural network
When the neural network is trained and successfully validated, the data could be exported by the order Export –
network1 – Export OK – Close for drawing of real and predicted values of time series. The graph is plotted by
orders
sim(network1,p);
plot(t)
hold on
plot(ans,'g').
The graph is presented at Fig.4. The graph presents a history of 350 samples and the next 50 samples of
prediction. The fig.5 presents zoomed graph of prediction.
Prediction
Fig. 4 Historical and predicted data of time series
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Fig. 5 Zoomed graph of time series
5. CONCLUSION
The sale time series usually contains recognizable tendency and periodicity trends, therefore the predictions
gives quite often useful information. The prediction supports right decision when production plan is prepared.
LITERATURE
[1]
DOSTÁL, P. Advance Decision Making in Business and Public Services. Brno : CERM Akademické
nakladatelství, 2011. 168 p. ISBN 978-80-7204-747-5.
[2]
DOSTÁL, P. Pokročilé metody analýz a modelování v podnikatelství a veřejné správě. Brno : CERM,
2008, ISBN 978-80-7204-605-8.
[3]
THE MATHWORKS. MATLAB – Neural network Toolbox - User’s Guide. The MathWorks, Inc., 2010.
ADRESS:
Prof. Ing. Petr Dostál, CSc.
Brno University of Technology,
Faculty of Business and Management,
Department of Informatics,
Kolejní 4,
612 00 Brno,
Tel. +420 541 143714, Fax. +420 541 142 692,
[email protected];
h. prof. Ing. Oldřich Kratochvíl, Ph.D., CSc., DrSc., MBA
Private European Polytechnic Institute, Ltd.
Osvobození 699,
686 04 Kunovice,
[email protected]
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VÝKON DATABÁZOVÝCH SYSTÉMOV NA HARDVÉROVÝCH PLATFORMÁCH
Juraj Ďuďák1, Gabriel Gašpar2, Michal Kebísek2
1
Evropský polytechnický institut s.r.o., Kunovice
Materiálovotechnologická fakulta so sídlom v Trnave, STU Bratislava, Slovensko
2
Abstrakt: V priemyselných senzorických systémoch sú dôležité viaceré faktory správnej a efektívnej
funkcionality. Tieto faktory môžeme rozdeliť na hardvérové a softvérové aspekty. Medzi hardvérové
aspekty patrí napríklad výber vhodného zbernicového štandardu na ktorom sú pripojené meracie
senzory. Ďalej výber dostatočne výkonnej hardvérovej platformy a zároveň nenáročnej na priestor,
inštaláciu a spravovanie a spotrebovanú elektrickú energiu. Medzi softvérové aspekty patrí
dostatočne výkonný a spoľahlivý spôsob ukladania dát. V článku bude predstavená myšlienka
senzorického systému postaveného na priemyselnom zbernicovom štandarde MODBUS. Ako
riadiaci prvok je použité priemyselné riešenie postavené na architektúre ARM - jednodoskové
počítače IGEPv2 a PandaBoard. Systém pre ukladanie dát bol zvolený databázový systém MySQL.
V článku sú prezentované výsledky záťažových testov databázových systémov na spomínaných
harvérových platfomách. Vybrané hardvérové platformy patria medzi aktuálne používané riešenia v
priemyselnej sfére.
Kľúčové slová: Senzorický systém, merací systém, databázový systém, hardvérové priemyselné
platformy
ÚVOD
Senzorický systém SenSys slúži na zber nameraných údajov. V súčasnosti je podporovaný zber teploty a
vlhkosti vzduchu. Výnimočnosť tohto systému je v jeho architektúre. Pri vývoji systému bol kladený veľký
dôraz na jednoduchosť implementácie a minimálnu cenu systému. Ďalším aspektom pri vývoji boli funkčné
požiadavky. Na systém SenSys sú kladené nároky na rozľahlosť systému (dĺžka zbernice do 2km), mohutnosť
systému (počet senzorov do 1000) a rýchlosť odozvy (odozva v rádoch ms). Vďaka použitým technológiám,
senzorický systém SenSys tieto požiadavky spĺňa. Základom celého systému je zbernicový štandard MODBUS v
úprave uBUS [1] a zbernicový systém 1-Wire. Na Obr. 1 je znázornená principiálna schéma senzorického
systému SenSys. Zariadenia DCB sú “Dual Channel Booster”, teda zariadenie, ktoré slúži ako 2-kanálový most
medzi zbernicovým systémom uBUS a 1-Wire. Si sú senzory teploty, resp. vlhkosti. Problematike funkcionality
blokov DCB a protokolu uBus sa venuje článok [2].
Obrázok 1 Principiálna schéma senzorického systému SynSys
Pre správnu funkcionalitu systému SenSys je potrebný počítač, ktorý v celom systéme je v úlohe riadiaceho
bloku. Blok PC nemusí byť štandardný osobný počítač, postačí aj priemyselné 1-doskové riešenie ako napríklad
IGEP V2 alebo PandaBoard.
Pre možnosť neskoršej analýzy nameraných dát, sa tieto dáta ukladajú v bloku PC. Na ukladanie údajov je
použitý databázový systém. Ako vhodní kandidáti boli zvolené databázové systémy MySQL a SQLite.
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HARDVÉROVÉ RIEŠENIE
V tejto kapitole budú predstavené viaceré hardvérové riešenia pre blok PC (z Obr. 1). Ako vhodné riešenia pre
použitie v priemysle boli vybrané také architektúry a vyhotovenia, ktoré majú malé fyzické rozmery a nízku
spotrebu elektrickej energie.
Ako testovacie zostavy poli použité nasledovné riešenia:
 IGEPv2
 PandaBoard
 Asus EeeBox B202
Procesor
Počet jadier
Taktovanie
RAM
Architektúra
RS 232
Ethernet
WiFi
USB
Rozširujúce
karty
Power
IGEP v2
ARMv7 Processor rev
2
1
1000 MHz
512 MB
ARM Cortex A8
Ano
10/100 eth
802.11b/g
1x
MicroSD
PandaBoard
ARMv7 Processor rev
2
2
1000 MHz
1024 MB
ARM Cortex A9
Ano
10/100 eth
802.11b/g
4x
SD/MMC
Asus EeeBox B202
Intel(R) Atom(TM)
CPU N270
2
1600 MHz
1024 MB
i686
Nie
10/100 eth
802.11.b/g
4x
SD/MMC
5 VDC
5 VDC
19 VDC
Tabuľka 1: Hardvérové parametre riadiaceho počítača
Na uvedených hardvérových riešeniach bol nainštalovaný databázový server mysql v akruálnych stabilných
verziách. Následne bola vytvorená testovacia databáza a naimportované existujúce namerané údaje. Štruktúra
testovacej databázy je na obrázku 2.
Obrázok 2 Štruktúra testovacej databázy
Do tabuliek boli naimportované už namerané dáta: 29722 záznamov v tabuľke sensor_dates a 142709 záznamov
v tabuľke sensor_values, čo predstavuje 4 mesiace nepretržitého snímania teplotných hodnôt s intervalom
snímania 5 minút s 5-timi teplotnými senzormi.
Kernel
OS
MySQL
SQLite
IGEP v2
2.6.35.7-16
Ubuntu 10.04
5.1.58-1ubuntu1
sqlite3 3.7.7
PandaBoard
3.0.0-1206-omap4
Ubuntu 11.10
5.1.58-1ubuntu1
sqlite3 3.7.7
Asus EeeBox B202
3.0.0-12-generic-pae
Ubuntu 11.10
5.1.58-1ubuntu1
sqlite3 3.7.7
Tabuľka 2 Softvérová konfigurácia použitých riadiacich počítačov
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TESTOVANIE VÝKONNOSTI DATABÁZOVÝCH SERVEROV
Pri tvorbe databázových testov sa vychádzalo z budúceho použitia systému. Pri prevádzke systému sa budú
namerané hodnoty do databázy zapisovať v dostatočne veľkých intervaloch (niekoľko minút). Bude nás
zaujímať rýchlosť operácie vloženia údajov, teda počet operácií INSERT za jednu sekundu a taktiež rýchlosť
operácie výberu dát. Pre potreby vyhodnocovania údajov sa budú tieto vyberať z databázy pomocou príkazu
SELECT. Pre príkaz výberu SELECT bolo pripravených viacero testov, ktorých úlohou je zistiť výkon
databázového servera na danej architektúre pre rôzne typy výberov.
Pre testovanie výkonnosti databázových serverov bol vytvorený testovací skript v jazyku Python. Test bol
rozdelený na niekoľko častí:
 test výkonnosti príkazu SELECT:
 výber hodnôt z jednej tabuľky,
 použitie agregačných funkcií.
V nasledujúcom výpise je skript napísaný v jazyku Python pre meranie času vykonávania pripravených SQL
dotazov.
def executeQuery(sql):
start = time.time()
cur.execute(sql)
stop=time.time()
rows = cur.fetchall()
elapsed = (stop - start)
return elapsed1,len(rows)
Konkrétne SQL dotazy uvádzame priamo v opisoch jednotlivých testov.
TESTY S DATABÁZOU MYSQL
Na Obr. 2 je logická štruktúra databázových tabuliek nad ktorými budeme robiť testy, ktoré budú zamerané na
výkonnosť pri výbere údajov.
Test 1:
Ako prvý test bude jednoduchý výber údajov nad tabuľkou sensor_values, v ktorej je 140 000 záznamov. Tento
test bol realizovaný jednoduchým SQL príkazom:
SELECT * FROM sensor_values LIMIT 0,N;
kde N bola hodnota od 10000 do 140000 s krokom 10000. Na nasledujúcom grafe (Obr. 3) je znázornená
závislosť času vykonania výberu od počtu vyberaných údajov.
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Obrázok 3 Výsledok testu 1
Z grafu na Obr. 3 je vidieť, že najrýchlejší výber bol na platforme Atom. Tento výsledok bol zčasti očakávaný,
pretože po hardvérovej stránke je táto platforma najvýkonnejšia. Porovnateľnými platformami sú IGEP v2 a
PandaBoard. V tomto prípade je rýchlejšie riešenie PandaBoard. V priemere je výber údajov na platforme
PandaBoard o 50 % rýchlejší ako na platforma IGEP v2. Treba poznamenať, že PandaBoard je taktovaná skoro s
dvojnásobným taktom oproti IGEP v2.
Test 2:
V druhom teste boli nad celou tabuľkou sensor_values použité agregačné funkcie AVG, MIN, MAX a STD.
Zápis v jazyku SQL:
SELECT AVG(value),MIN(value), MAX(value), STD(value) FROM sensor_values;
Obrázok 4 Výsledok testu 2
Pre testovanie agregačných funkcií bola použitá tabuľka sensor_values. Výsledkom dotazu boli 4 hodnoty
vypočítané ako priemerná hodnota (AVG), minumum (MIN), maximum (MAX) a štandardná odchýlka (STD) z
hodnôt uložených v stĺpci value. Tieto 4 hodnoty boli vypočítané zo všetkých údajov v tabuľke sensor_values.
Na Obr. 4 sú výsledky tohto testu. Opäť je najrýchlejšie na tom platforma Atom, kde bol celkový čas 32ms.
Prekvapením tu bol výsledok platformy Igep, na ktorej požadovaný výpočet trval 100ms. Čas pre platformu
PandaBoard je o 14% vyšší, teda 114ms.
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ZÁVER
Cieľom článku bolo zistiť výkonnosť rôznych hardvérových platforiem pre špecifické úlohy. V tomto prípade to
bol výkon databázového systému MySQL. Vo všetkých testoch sa pracovalo s rovnakou verziou tohto softvéru.
Aby sa dali výsledky vzájomne porovnávať, boli testy vykonávané na rovnakom operačnom systéme. V našom
prípade to bol Ubuntu server 11.10, okrem platformy Igep, kde bola k dispozícii len verzia 10.04. Aby sa
eliminovali ďalšie vplyvy, daný operačný systém bol nainštalovaný bez grafickej nadstavby a všetky testy boli
vykonávané z konzoly.
V testoch sa ukázali najväčšie rozdiely medzi hardvérovou architektúrou medzi ARM a x86 v prospech
architektúry x86. Rozdiely vo výkone pri architektúre ARM mohli byť spôsobené samotným počtom jadier CPU
(1 pri IGEP v2 a 2 pri PandaBoard), avšak zistené výsledky sú porovnateľné.
REFERENCIE
[1]
DUDAK, J. The Contribution to Industrial Communication Standards. In: INFORMATION SCIENCES
AND TECHNOLOGIES BULLETIN OF THE ACM SLOVAKIA. - ISSN 1338-1237. - Vol. 2, No. 1
(2010), p. 34-41.
[2]
DUDAK, J.; GASPAR, G.; KEBISEK, M. APPLICATION OF MODIFIED MODBUS PROTOCOL
FOR THE NEEDS OF MODERN MEASUREMENT SYSTEMS, In: Proceedings of the International
Conference on Advances in Mechatronics 2011 (AIM’11), University of Defence, Faculty of Military
Technology, Brno, 2011, ISBN 978-80-7231-848-3, pp. 9-14
[3]
ISEE : IGEPv2 Board, online: http://www.igep.es/index.php?option=com_content &view
=article&id=46&Itemid=55.
[4]
pandaboard: online:<http://pandaboard.org/>
[5]
MAGA, D.; WAGNER, J. Ultra High Torque SRM - Measurement and Computer Design. Compel –
The International Journal for Computation and Mathematics in Electrical and Electronic Engineering.
1998, Volume 17, Number 1/2/3, s. 364 – 368. ISSN 0332-1649.
[6]
SLOVÁČEK, D.; JANOVIČ, F. Efficiency Network Regulated By Linux. In ICSC 2010. Kunovice :
EPI, s.r.o, 2010. ISBN 978-80-7314-201-8.
ADRESA:
Ing. Juraj Ďuďák, PhD.
Evropský polytechnický institut , s.r.o.
Osvobození 699
686 04 Kunovice, Česká republika
[email protected]
Gabrie Gašpar
Materiálovotechnologická fakulta so sídlom v Trnave
STU Bratislava, Slovensko
Michal Kebísek
Materiálovotechnologická fakulta so sídlom v Trnave
STU Bratislava, Slovensko
[email protected]
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DATA ANALYSIS & MODELING USING OPEN SOURCE SOFTWARE R
Lukáš Falát
University of Žilina, Faculty of Management Science & Informatics, the Slovak Republic
Abstract: This paper deals with data analysis and modelling of Open Source Software R. Firstly, R
software is generally presented as a free alternative to commercial programs such as SPSS or SAS.
Later main features of R Project and main advantages of this program are also discussed. Finally,
a financial application of exchange rate is performed in order to illustrate work with this software
as well as the wide range of R usability.
Keywords: R, Open Source, packages, data analysis, financial analysis, data mining, data
modelling, ARIMA, GARCH, ARCH, time series
1 INTRODUCTION
Nowadays, to be able to analyse huge amount of data, find there interesting information and then construct a
model is very important and demanding from many scientists, engineers and statisticians from all over the world,
no matter what a real problem is. It can include how to distinct spam from normal message, how to find out the
development of human population or set the tomorrow’s price of corn on world markets. These examples have
something in common. In all cases one has to create a right model before knowing answer to these questions. As
the problems of real world are quite complex, data analysis as well as constructing models is sometimes not as
simple and it often demands lot of time and number of tests to find out something important or to declare the
model is correct. And as we are living in the information era, computers come in handy in this case.
However, today there exists a huge number of special programs for data modelling. They can differ in what area
of modelling they are used in but very often, what they differ in is mainly price for the software. It is true that
commercial programs such as SPSS, SAS or Eviews dispose by a large number of functions, they are very user
friendly, they have beautiful graphs and outputs, the documentation is also on high level. But the main
disadvantage of these programs is their price. They cost very much money and even if it is not a big deal for an
IT company, there is only small amount of schools, universities and other non-profit institutions that can afford
to buy this kind of software.
2 R PROJECT
Fortunately, for those kind of people, open source programs exist. One open source software for data mining,
modelling and analysis is called R. Project R is very popular among lots of universities all over the world.
Moreover, as data mining has entered a golden age, R has become a major tool for plenty of statisticians,
engineers or mathematicians, whether being used to set ad prices, find new drugs more quickly or fine-tune
financial models. Companies as diverse as Google, Pfizer, Merck, Bank of America, the InterContinental Hotels
Group and Shell use it, too.
R first appeared in 1996, when the statistics professors Ross Ihaka and Robert Gentleman of the University of
Auckland in New Zealand released the code as a free software package. They both wanted technology better
suited for their statistics students, who needed to analyze data and produce graphical models of the information.
The software itself can be downloaded on the webpage http://www.r-project.org. This tool is also great for
statisticians and mathematicians as it contains lots of build in statistical functions. The main advantages of this
software include:
 Easy accessibility. The program is for free as it belongs to the Open Source software.
 Active user support all over the world.
 It runs on various platforms including Windows, Linux and MacOS.
 Wide range of constructed functions. There exists hundreds of packages (more than 1600), each of them
specializing in some specific area (machines, genome analysis, financial analysis,…).
 A large, coherent, integrated collection of intermediate tools for data analysis.
 Great plots and graphical facilities for data analysis.
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As stated above, a thing what makes R so useful — and helps explain its quick acceptance — is that statisticians,
engineers and scientists can improve the software’s code or write variations for specific tasks. Packages written
for R add advanced algorithms, colored and textured graphs and mining techniques to dig deeper into databases.
For example, a package, called BiodiversityR, offers a graphical interface aimed at making calculations of
environmental trends easier. Another package, called Emu, analyzes speech patterns, while GenABEL is used to
study the human genome. The financial services community has also demonstrated a particular affinity for R;
dozens of packages exist for financial analysis alone.
3 APPLICATION
The strengths of R project will be illustrated on financial modelling of time series of AUD/USD exchange rate,
to see wide range of specialized applications where this software can be applied. The packages which have been
used for this illustrative application include: FinTS, fGARCH, tseries, zoo, stats.
The data include exchange rate data of AUD/USD from November 2005 to November 2010. The aim was to
analyse the data, then model this exchange rate and finally verify if our model was constructed correctly.
The first step was to load appropriate libraries and load our data:
library(xlsReadWrite)
library(stats)
my_data = read.xls("D:\\AU.xls", colNames=TRUE, type="double",
sheet=1, from=1)
3.1 DATA ANALYSIS AND MODEL CONSTRUCTION
Next step in modelling a specific problem is to have correct data. Very often real data are biased; it means that
they are influenced by some external factors and therefore cannot be used alone without being dependent on
something else. In other word we want the data or the time series be independent or stationary. Otherwise, the
results of analysis and the constructed models would not be considered to be right and correct. There exists
various options how to determine the stationarity of time series, probably the most popular are stationarity tests
such as ADF test or Ziwhat-Andrew. It is no surprise that R financial packages support also this feature. KPSS
test which is the same type of test and which can be found in tseries package is great for findind this out:
Kpss.test(my_data)
The KPSS test confirmed that the series was not stationary and therefore must be transformed into stationary
series. This was done by data differentiating. Analysing of this data was performed using knowledge from
specific area (financial econometrics). Knowing from econometrics area, the tools for autocorrelation function
(ACF) and partial autocorrelation function (PACF) and Akaike Information Criteria (AIC) are excellent aid in
this case. No surprise R has all this stuff. In R, ACF is defined as
acf( x, lag.max = NULL,
type = c("correlation", "covariance", "partial"),
plot = TRUE, na.action = na.fail, demean = TRUE, ...)
For our purposes, it is enough to use only our data series variable. As seen from the command, the ACF can be
also presented into graph. PACF function is defined in a similar way. However, by analysing the differentiated
versions of our data, we were not able to determine any trend in the series. AIC criteria which is a penalty
function may come in handy in this case. In R, for specific model, it is defined as a negative number and can be
found in the model summary. The more negative the number is, the better the model is. For example, for a model
arima (2,2,2), which is a typical econometric model, the AIC is in the figure 1
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Figure 5 The Summary of ARIMA (2,2,2)
By analysing AIC of several models, we found out that ARIMA (1,2,1) was the best model.
Table 1 AIC values of tested models
We determined the model for AUD/USD exchange rate in R as ARIMA (1,2,1). The next step was to verify this
model.
3.2 MODEL VERIFICATION
The verification of the model include verification of residuals of the model. This can be done by ARCH test:
ArchTest(residuals$arima11, lags = 1)
ArchTest(residuals$arima11, lags = 5)
ArchTest(residuals$arima11, lags = 12)
On base of small value of p-value it was clear that residuals were not independent and there existed some ARCH
effect. This could be removed by incorporating ARCH into our model. In our case, this model definition looked
like this:
model = garchFit(~arma(1,2,1)+garch(1, 1), data =my_data)
summary(model)
We hence edited the model by adding the GARCH(1,1) part into the default model. As previously, residuals of
this model must have been checked too.
GarchRezidua = model@residuals/[email protected]
ArchTest(GarchRezidua, lags = 1)
ArchTest(GarchRezidua, lags = 5)
ArchTest(GarchRezidua, lags = 12)
On base of p-value larger than significance level, one could say the residuals were now independent and the
model was correct. The correctness of this model could be also checked graphically.
x11()
plot(density(Garch Residuals),main="Distribution of Garch reziduals")
curve(dnorm(x,m=-0.001742,sd=0.9966694),from=-5,to=5,
main="Normal
distribution", col="red", add=TRUE)
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Figure 6
Density Distribution of Residuals of Model
Graphical control was also all right and therefore we could say that final financial model for AUD/USD
exchange rate was ARIMA (1,2,1) + GARCH (1,1).
Finally, figure 3 shows the historical values of time series (green colour) and model-estimated values (red
colour) for graphical control.
Figure 7
Historical values (green) of time series and estimated values (red) of the model
4 CONCLUSION
In this paper the Open Source Software for data analysis and modelling was presented. The main advantages of
this program were discussed, among other it is mainly a huge number of packages with very wide range of
special usability. This feature has been illustrated with a financial modelling example. The AUD/USD exchange
rate was analysed, then the model was created and verified. Commands in R have been presented, too. As seen
above, the commands must be typed into the console and there is no clicking interface. However, R commands
are usually very user-friendly oriented and simple. Moreover, usually there are lots of manuals of packages and
even plenty of examples which can be used in your R analysis and modelling.
REFERENCES
[1]
FALÁT, L. Econometric Modelling on Forex Market: Application of ARIMA and GARCH Models to
Specific Exchange Rates Data, International Masaryk Conference for Doctoral Students and Young
Scientists, Hradec Králové, the Czech Republic, 2011.
[2]
FALÁT, L.; LAŠTÍK, T.; TKÁČ P. FRI R Manual, 2011, 44p [online]
ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS”
EPI Kunovice, Czech Republic. January 20, 2012
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[3]
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[6]
[7]
[8]
MARČEK, M. Viacnásobná štatistická analýza dát a modely časových radov v ekonómii, Opava :
Silesian University, 2009. 242 p.
MARČEK, D.; MARČEK, M.; PANČÍKOVÁ, L. Econometrics and Soft Computing, Žilina : EDIS,
University of Žilina, 2008. 272 p.
MONTGOMERY, D. C.; JENNINGS, C. L.; KULAHCI, M. Introduction to Time Series Analysis and
Forecasting, New Jersey : John Wiley & Sons, Inc, 2008.
VANCE, A. Data Analysts Captivated by R’Power, [online], 07/01/2009, NYTimes.com
The R Project Homepage [online], 11/14/2011, www.r-project.org
ZIVOT, E.;, WANG, J. Modelling Financial Time Series with S Plus, Springer, 2003, 632 p.
ADDRESS
Ing. Lukáš Falát
University of Žilina
Faculty of Management Science & Informatics
the Slovak Republic
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OPTIMISATION OF DECOMPOSITION STRATEGIES IN PARALLEL ALGORITHMS
Ivan Hanuliak
European polytechnic institute, Kunovice
Abstract: The article is devoted to the important role of decomposition strategy in parallel
computing. This influence is illustrated on the example of very frequently used parallel algorithm
and that is matrix multiplication. On the basis of the done analysis of the used parallel computers in
the world these are divided to the two basic groups which are from the programmer-developer point
of view very different. They are also introduced the typical principal structures for both these
groups of parallel computers and also their models. The paper then in an illustrative way describes
development of concrete parallel algorithm for matrix multiplication on various parallel systems.
For each individual practical implementation of matrix multiplication there is introduced the
derivation of its calculation complexity. The described individual ways of developing parallel
matrix multiplication and their implementations are compared, analysed and discussed from sight
of programmer-developer and user in order to show the very important role of decomposition
strategies mainly at the class of asynchronous parallel computers.
Keywords: parallel computer, synchronous and asynchronous parallel system, systolic system,
matrix multiplication, decomposition method
1. INTRODUCTION
It is very difficult to classify the existed parallel system. From the point of programmer-developer I divide, after
the done analysis [2, 3], parallel computers to the following two different groups
 synchronous parallel architectures. They are typical through the handling mutually independent or noninteracted processes. These are used for performing the same computation on different sets of data.
They can be used under central control, that means under the global clock synchronisation (vector, array
system etc.) or a distributed local control mechanism (systolic computer etc.). The dominant system
property is the concentration to data parallelism. The typical example of synchronous parallel computer
illustrates Fig. 1.
 asynchronous parallel computers. They are composed of a number of independent processors or
computers. From the point of programmer it is typical for their application using (co-operation and
synchronisation of processes) mutual inter process communications (IPC). To this group belong mainly
computer networks based on network of workstation (NOW|) according Fig. 2.
Host
computer
Shared
memory
Control computer
…
…
…
Array of processors
(compute nodes)
…
Fig. 1. Typical synchronous parallel system.
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There has been an increasing interest in the use of networks (Cluster) of workstations connected together by high
speed networks for solving large computation intensive problems. This trend is mainly driven by the cost
effectiveness of such systems as compared to massive multiprocessor systems with tightly coupled processors
and memories (Supercomputers). Parallel computing on a cluster of workstations connected by high speed
networks has given rise to a range of hardware and network related issues on any given platform. Load
balancing, inter processor communication (IPC), and transport protocol for such machines are being widely
studied [9, 11,]. With the availability of cheap personal computers, workstations and networking devises, the
recent trend is to connect a number of such workstations to solve computation intensive tasks in parallel on such
clusters.
Network of workstations (NOW) [13, 16, 18] has become a widely accepted form of high performance
computing (HPC). Each workstation in a NOW is treated similarly to a processing element in a multiprocessor
system. However, workstations are far more powerful and flexible than processing elements in conventional
multiprocessors (Supercomputers). To exploit the parallel processing capability of a NOW, an application
algorithm must be paralleled. A way how to do it for an application problem builds its decomposition strategy.
This step belongs to a most important step in developing parallel algorithm [8, 10, 14] and their performance
modelling and optimization (Effective parallel algorithm).
Local
memory
Processor
Processor
Local
memory
Processor
Local
memory
Communication
network
Local
memory
Processor
Fig. 2. Typical asynchronous parallel system.
2. PARALLEL ALGORITHMS
The role of programmer is for the given parallel computer and for the given application task (Complex
application problem) to develop the effective parallel algorithm. This task is more complicated in those cases, in
which he must create the conditions for the parallel activity, that is through dividing the input algorithm to many
mutual independent parts (Decomposition strategy), which are named processes or threads. In general
development of the parallel algorithms include the following activities [4, 5, 6]
 decomposition - the division of the application into a set of parallel processes and data
 mapping - the way how processes and data are distributed among the nodes of a parallel system
 inter process communication (IPC) - the way of cooperation and synchronization
 tuning – performance optimisation of a developed parallel algorithm.
The most important step is to choose the best decomposition method for given application problem [3, 12]. To
do this it is necessary to understand the concrete application problem, the data domain, the used algorithm and
the flow of control in given application. When designing a parallel program the description of the high level
algorithm must include, in addition to design a sequential program, the method you intend to use to break the
application into processes or threads (Decomposition strategy) and distribute data to different nodes (Mapping).
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The chosen decomposition method drives the rest of program development.
Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for
the delivery of high performance. Performance studies apply to initial design phases as well as to procurement,
tuning, and capacity planning analysis. As performance cannot be expressed by quantities independent of the
system workload, the quantitative characterization of resource demands of application and of their behaviour is
an important part of any performance evaluation study. Among the goals of parallel systems performance
analysis are to assess the performance of a system or a system component or an application, to investigate the
match between requirements and system architecture characteristics, to identify the features that have a
significant impact on the application execution time, to predict the performance of a particular application on a
given parallel system, to evaluate different structures of parallel applications. To the performance evaluation we
briefly review the techniques most commonly adopted for the evaluation of parallel systems and its metrics.
3. THE ROLE OF PERFORMANCE
Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for
the delivery of high performance. Performance studies apply to initial design phases as well as to procurement,
tuning and capacity planning analysis. As performance cannot be expressed by quantities independent of the
system workload, the quantitative characterisation of resource demands of application and of their behaviour is
an important part of any performance evaluation study [1, 15]. Among the goals of parallel systems performance
analysis are to assess the performance of a system or a system component or an application, to investigate the
match between requirements and system architecture characteristics, to identify the features that have a
significant impact on the application execution time, to predict the performance of a particular application on a
given parallel system, to evaluate different structures of parallel applications. In order to extend the applicability
of analytical techniques to the parallel processing domain, various enhancements have been introduced to model
phenomena such as simultaneous resource possession, fork and join mechanism, blocking and synchronisation.
Modelling techniques allow to model contention both at hardware and software levels by combining
approximate solutions and analytical methods. However, the complexity of parallel systems and algorithms limit
the applicability of these techniques. Therefore, in spite of its computation and time requirements, simulation is
extensively used as it imposes no constraints on modelling.
Evaluating system performance via experimental measurements is a very useful alternative for parallel systems
and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim
at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all
types of performance studies, their main field of application is competitive procurement and performance
assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by
providing a wider a wider set of suites that exercise each system component targeted workload.
4. SYNCHRONOUS MATRIX MULTIPLICATION
4.1. A SYSTOLIC MATRIX MULTIPLIER
We now consider an example of the systolic multiplication of two matrices A (km) and B (mn). The algorithm
for matrix multiplication that is most suited is based on outer products rather than the conventional inner product
method. Here we evaluate
k
N  A.B   C ( p).R( p)
p 1
where
C( p) R( p)  c pj rpj
p  1,2,...,k ,
and j=1,2,...,n. Here C(p) is a k~n matrix with all the
columns identical with the p-th column of A and R(p) is a k~n matrix with all the rows identical with the p-th
row of B. For example if:
 a11 a12 a13 
A

a 21 a 22 a 23 
b11 b12 


B  b21 b22 
b31 b32 
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then N=A.B=C(1).R(1)+C(2).R(2)+ C(3).R(3)
N
 a11b11

a 21b11
a11b12   a12 b21

a 21b12  a 22 b21
a12 b22  a13 b31

a 22 b22  a 23 b31
a13b32 

a 23b32 
A systolic matrix multiplier is shown in Figure 3. The input streams of the rows of A arrive from the left , and
the input streams of columns of B arrive from the top of nodes N 11,N12,N21 and N22. Each of these nodes has the
capability of multiplying two inputs numbers and holding the result until the next set of inputs arrives for
multiplication; then the sum is accumulated and the process is repeated.
Note that the product matrix N is finally available at the nodes N 11,N12,N21 and N22. Thus in this case the matrix
is entirely mapped in one-to-one correspondence to the processor array.
The time taken to multiply two matrices of size k  m and m  n with using k x n processors is m+(k-1)+(n-1)
time units. This result is easily proved using the fact that the last computation are carried out after a lapse of (k1)+(n-1) units, because of the skewing of the matrices, and it takes m units of time to multiply two vectors of
size m.
Note that a conventional single-processor matrix multiplication requires k.m.n operational time units; in the case
of the systolic multiplier we use k x n processors (or more space) to reduce the time to m+n+k-2.
Fig. 3. Systolic matrix multiplier.
5. THE ASYNCHRONOUS MATRIX MULTIPLICATION
Principally development of the asynchronous parallel algorithm include the following activities [7, 17]
3) Decomposition - the division of the application into a set of parallel processes and data. This is the most
important step at developing asynchronous parallel algorithm.
4) Mapping - the way how processes and data are distributed among the nodes of used parallel systems
(processors or working stations)
5) Interprocess communication - the way of corresponding and synchronisation among individual processes
6) Tuning - alternation of the working application to improve performance (performance optimisation)
5.1. DECOMPOSITION STRATEGIES
To choose the best decomposition method for any application, we have to understand the concrete application
problem, the data domain, the used algorithm and the flow of control in given application. Therefore we can use
according the concrete character of given task the following decomposition models [3, 12]
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



perfectly parallel decomposition
domain decomposition (suitable for matrix multiplication)
control decomposition:
 functional
 manager/workers
object-oriented programming OOP ( modern object oriented programming technology)
5.2. DOMAIN DECOMPOSITION METHODS FOR MATRIX MULTIPLICATION
We will illustrate the role of right decomposition strategies just on matrix multiplication. The principle of matrix
multiplication we illustrate for simplicity for the matrixes A, B with numbers of rows and columns k=2. The
result matrix C=A x B is:
 a11
a
 21
a12  b11 b12   a11  b11  a12  b21


a22  b21 b22  a21  b11  a22  b21
a11  b12  a12  b22   c11

a21  b12  a22  b22  c21
c12 
c22 
The way of sequential calculation is following
Step 1: Calculate all the values of the result matrix C for the first row of matrix A and for all columns of the
matrix B
Step 2: Take the next row of matrix A and repeat step 1.
In this procedure we can see the potential possibility of parallel calculation, that is the repetition of activities in
the step 1 always with the another row of matrix A. Let consider the calculation example of matrix multiplication
on parallel system. The basic idea of the possible decomposition procedure illustrates Fig.4.
A´i

B´i
=
C´i i
Fig. 4. Decomposition of matrix multiplication through the rows of the first matrix.
The procedure is as following:
Step 1: Give to the i-th node horizontal column of the matrix A with the names A´i and i-th vertical column of
the matrix B named as B´i
Step 2: Calculate all values of the result matrix C for A´i and B´i and named them as C´ii
Step 3: I-th node give its value B´i to the node i-1 and get B´i+1 value from i+1-th node.
Repeat the steps 2 and 3 to the time till i-th node does not calculate C´i,i-1 values with B´i-1 columns and row
A´i. Then i-th node calculated i-th row of the matrix C (Fig. 5.) for the matrix B with the number k-columns. The
advantage of such chosen decomposition is the minimal consume of memory cells. Every node has only three
values (rows and columns) from every matrix.
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C´i , 1
...
C´i , i - 2
C´i , i - 1
C´i , i
C´i , i + 1 C´i , i + 2
...
C´i , k
.
Fig. 5. Illustration of the gradually calculation of matrix C.
This method is also essential fast as the second possible way of decomposition according Fig. 6.
A´i
B´i


C´
Fig. 6. Decomposition of matrix multiplication with using the rows of first matrix.
The procedure is following:
Step 1: Give to the i-th node vertical column of the matrix A (A´i) and the horizontal row of the matrix B (B´i).
Step 2: Perform the ordinary matrix calculation A´i and B´i. The result is the matrix C´i of type n x n. Every
element from C´i is the particular element of the total sum which corresponds to the result matrix C.
Step 3: Call the function of parallel addition GSSUM for the creating of the result matrix C from the corresponds
elements C´i. This added function causes increasing of the calculation time, which strong depends on the
magnitude of the input matrixes (Fig. 7.).
n
C´3(1,1) C´3(1,2)
C´2(1,1)
C´2(1,2)
C´3(2,1)
C´1(1,1) C´1(1,2)
C´1(2,1)
ad
dit
io
C(1,1) C(1,2)
C(2,1)
=
C´1(2,1)
Fig. 7. Illustration of the gradually calculation of the elements C´i,j.
Let k be the magnitude of the rows or columns A, B and U defines the total number of nodes. Then:
C1 1,1  a1,1  b1,1  a1, 2  b1, 2  . . .  a1,k  b1,k
C2 1,1  a1,k 1  b1,k 1  a1,k  2  b1,k  2  . . .  a1, 2k  b1, 2k
.
.
.
.
CU 1,1  a1,(U 1) k 1  b1,(U 1) k 1  . . .  a1, Mk  b1, Mk
and the finally element of matrix C
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U
C 1,1   Ci 1,1
i 1
50,0
D e c o m p o s i t i o n1
D e c o m p o s i t i o n2
Time [s]
40,0
30,0
20,0
10,0
0,0
5,0
10,0
15,0
Number of compute nodes
Figure 8. Optimisation of decomposition methods at matrix multiplication.
6. THE RESULTS
The comparison on both decomposition strategies for various number of compute node illustrates Fig. 9. The
first chosen decomposition method go straightforward to the calculation of the individual elements of the result
matrix C through multiplication of the corresponds matrix elements A and B. The second decomposition method
for the getting the final elements of the matrix C besides multiplication of the corresponded matrix elements A
and B demand the additional addition of the particular results, which causes the additional time complexity in
comparison to the first used method. This additional time complexity depends strong on the magnitude of the
input matrixes as you can see from the Figure 8.
7. CONCLUSIONS AND PERSPECTIVES
On the given simple example of matrix multiplication I demonstrated the great influence of optimisation of
decomposition strategies to the whole complexity of parallel algorithms. The using of parallel systems to this
time showed unambiguous that the parallel architectures of the computer systems belong to the most effective
and rational ways of increasing the computer system performance also in the future time. The various in the
world successful widespread synchronous parallel architectures have not been expanded in our country from the
various causes and in relation to the latest trends in the world they will not be expanded in the future.
In spite of it the dynamic growth in our country we can see just in the asynchronous parallel architectures and
specially symmetrical multiprocessors and local area networks of personal computers. The last one are
independent from the still very low technical level of the remote telecommunication lines in our country.
Therefore we are also using to the practical implementations of parallel algorithms the build integrated
heterogeneous computer network of personal computers at my working place. One node of our computer
network is also the powerful multiprocessor parallel system (symmetrical multiprocessor).
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HANULIAK, I. Paralelné architektúry – multiprocesory, počítačové siete, Žilina : Vyd.: Knižné
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EPI Kunovice, Czech Republic. January 20, 2012
49
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TRANSCOM 2011 - section 3, Žilina : 2011. pp. 213 – 216
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ADDRESSEE
Prof. Ing. Ivan Hanuliak, CSc.
European Polytechnic Institute
Osvobozeni 699
686 04, Kunovice
[email protected]
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PERFORMANCE OPTIMIZATION OF BROADCAST COLLECTIVE OPERATION ON
MULTI-CORE CLUSTER
Hudik Martin
University of Zilina, Faculty of Control and Informatics, Zilina, Slovana
Abstract: Current trends in high performance computing (HPC) and grid computing (Grid) are to use
networks of workstations (NOW) as a cheaper alternative to traditionally used massively parallel
multiprocessors or supercomputers. Today computers consist of processor which has more than one core.
Is not unusual to have computer with a processor with four and more cores in combination with SMP. For
effective use of such a parallel machines it is crucial to know it limitations (bottlenecks). This paper
analyses "broadcast" a basic cooperative communication operation in light of using multi-core cluster.
The focus is put in its bottlenecks as they are in many parallel systems the limiting factor of the maximum
rate of parallelization.
In this paper, analysis focus on performance difference when normal MPICH2 broadcast is used with
different processes scheduling strategies. In the end customized broadcast is revealed as best solution for
multi-core environment. This customized broadcast distinguishes between intra-node and inter-node
communication and so it divide one communication domain into sub-domains.
Keywords: parallel computer, parallel algorithm, performance modeling, multi-core, broadcast, collective
operation
1 INTRODUCTION
Nowadays if we look on small cheap cluster solutions or big clusters rated by Top500.org we can say that for these
platforms multi-core processor architecture is dominant. Performance of multi-core computers dramatically increases
compare to single processor computer [1, 12]. Combination with fast interconnection network with high bandwidth and
low latency will create cluster with massive computational power. Multi-core cluster can speed up application
performance and scalability [11, 13]. This massive computational power needs deep understanding of multi-core
characteristic and their influence in application behavior.
To exploit the parallel processing capability of a cluster, an application algorithm must be paralleled. The role of
programmer is to develop the effective parallel algorithm [3, 5] for the given parallel computer and for the given
application task. In general development of the parallel algorithms include the following activities
 decomposition - the division of the application into a set of parallel processes and data [2, 4, 6]
 mapping - the way how processes and data are distributed among the computational nodes [7]
 inter process communication (IPC) - the way of cooperation and synchronization [10]
 tuning – performance optimization of a developed parallel algorithm.[3, 8]
The most important step is to choose the best decomposition method for a given application problem [9].
MPI become a primary programming paradigm for writing parallel algorithms. It provides building blogs for
developing parallel algorithms such as methods for point-to-point communication and cooperative communication.
There are many implementations of MPI standard one of them is MPICH [15]. This implantation takes into account
shared-memory architecture in sense of choosing appropriate communication method.
1.1 BACKGROUND
In this paper we assuming that every node in cluster is a multi-core computer with only one network adapter (NIC).
Computers in the cluster are connected together with high-performance switch so that all nodes in a single cluster can
communicate with each other without performance degradation [12]. We use MPICH2 as the MPI implantation.
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1.2 MPICH2
The communication portion of MPICH2 is implemented in several layers, as shown in Figure 1, and provides two ways
to port MPICH2 to a communication subsystem. The ADI3 layer presents the MPI interface to the application layer
above it, and the ADI3 interface to the device layer below it. MPICH2 can be ported to a new communication
subsystem by implementing a device. The CH3 device presents the CH3 interface to the layer below it, and provides
another way for MPICH2 to be ported to a new communication subsystem: by implementing a channel.
Fig. 1. Layers of MPICH2
1.3 CH3: NEMESIS
The Nemesis communication subsystem was designed to be a scalable, high-performance, shared-memory,
multinetwork communication subsystem for MPICH2. This communication channel offers universal solution for
intranode and internode communication. Its universality lays in automatic choosing appropriate method for sending a
message. To achieve the high scalability and low intranode overhead, Nemesis communication channel was designed
using lock-free queues in shared memory. Thus, each process needs only one receive queue, onto which other processes
on the same node can enqueue messages without the overhead of acquiring a lock.
2 MPI BROADCAST
MPICH2 uses different collective algorithms for small and large messages [15]. For sending small messages MPICH
uses binominal tree algorithm (Fig 2.) and for large messages van de Geijn Algorithm (Fig 3.).
3
6
7
2
4
5
3
2
3
1
3
2
0
1
3
Fig. 2. Binominal tree algorithm on hypercube
Fig. 3. Van de Geijn algorithm
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Binomial Tree.
Figure 2 shows hypercube structure. In the first step, the root sends the whole message to node which is half of
the maximum distance (p=4). Next, the root and p=4 send the message to next half node p=6 and (0=2)p,
respectively. Then the algorithm is continued recursively.
While this algorithm is preferred for small messages, it is not suitable for large messages. This is because some
nodes send the whole message several times.
van de Geijn Algorithm
As described in Figure 3, this algorithm consists of two phases. The first phase is scatter when the message is
divided and scattered among all nodes by using a binomial tree. The second phase is allGather when divided
messages are collected by using recursive doubling technique. Then the whole message becomes available in
every node.
Algorithm
Time complexity
Binominal tree
van de Geijn
Table 1. Summary of communication times for discussed broadcast algorithms. The message size is m and the number of nodes is p. ts
constant is start time for sending message and tw is constant representing sending one word of message.
3 CASE STUDY: MPI BROADCAST ON CLUSTERS WITH MULTI-CORE-PROCESSOR NODES
For clusters that consist only from single-core-processor nodes table 1 shows the summary of estimated cost of
broadcast algorithms. Assuming that the cluster is centralized this estimated cost are not dependent on process
scheduling or location of root process. On the other hand on cluster that consist from multi-core or SMP nodes
the estimated cost are dependent on process scheduling and location of root process. This is valid under the
assumption that each node has only one network adapter.
Fig. 4. Case study of broadcast operation on multi-core nodes cluster with use of round robin process scheduling
We present a case study of binominal tree algorithms on multi-core cluster. Figure 4 shows a steps of this
algorithm. Every node consist of computer with dual core processor. The processes are scheduled with round
robin algorithm. As we can see with this algorithm (described in section 3) some steps are done dually from one
node, trough one network adapter. The estimate cost almost doubles compare to single-core configuration of
cluster. To avoid this slow down the block scheduling method can be used.
Measurements for this case study was done on cluster which consists of 8 computers and each of them has quad
core processor. They were connected together according Fig.4. From the Figure 5 we can see the difference
between two scheduling methods. The preliminary conclusion can be made, that for the clusters with multi-core,
SMP computers the block scheduling method is more efficient than the round robin. It’s because the messages
within one computer are send through shared memory using Nemesis module. The block method make explicitly
use of multi-core, SMP environment. Sending-receiving time of broadcast stays approximately constant.
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Processes
Scheduling method
8
----
Data out
[MB]
---
Data in
[MB]
---
Packet out
Packet in
---
---
Time
[s]
31,6
16
Round Robin
4591
3260
285912
544760
53,6
16
Block
3071
1650
155194
344917
31,7
32
Round Robin
8146
6810
561392
921838
93,4
32
Block
3251
1706
153896
345428
35,2
Table 2. Measurement result from case study
Fig. 5. Broadcast time comparison between round robin and block scheduling
4 CONCLUSION
Today, most supercomputers and clusters are based on multi-core processors or SMP, but not all applications
benefit from them[14]. The current version of MPICH2 isn't fully adopted for multi-core, SMP supercomputer
environment. There were made some improvements, on communication layer focusing on point to point
communication, when nemesis communication subsystem module was presented. Collective operation stays
unaware of multi-core, SMP environment. Lot of exiting parallel applications can benefit from improved
collective operations that are aware of multi-core environment.
In this paper we present a analysis of broadcast collective operation in multi-core environment. We compared
two different scheduling methods for assigning processes to processors, round robin and block scheduling
method. From our research and measurements we can say that the more efficient is the block scheduling method.
Some existing applications can benefit from using block scheduling method, specially applications in which the
root sending process doesn't change during the computation. If we want more universal solution for all sorts of
application, customized broadcast need to be presented. Figure 6 shows customized broadcast operation in which
one broadcast domain is divided according physical computer parameter to small broadcast domains. This
customized broadcast isn't dependent on any scheduling method or root sender location.
Fig. 6. Customized Broadcast with divide communication domains
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54
REFERENCES
[1]
GELENBE, E. Computer system performance modeling in perspective, 288 pages, published
September 2006, Imperial College Press
[2]
HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, Kybernetes,
Volume 39, No.1, United Kingdom : 2010, pp. 107- 126
[3]
HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011, sekcia
č. 2, pp 125 - 132, Kunovice, Czech republic
[4]
HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, section 2, pp
1 - 8, Kunovice, Czech republic (in print)
[5]
HANULIAK, P.; SLOVÁČEK, D. To performance modelling of virtual computers, In Proc.:
TRANSCOM 2011 - section 3, pp. 213 – 216, 2011, Žilina
[6]
HUDIK, M. HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System
Equations, In Proc.: GCCP 2011, October 24-26, pp. 70-77, 2011, SAV Institute of Informatics,
Bratislava
[7]
JANOVIČ, F.; HOLÚBEK, A. Load balance and data decomposition for distributed prime number
algorithm, In Proc.: TRANSCOM 2011, pp. 99 - 101, 2011, Žilina, Slovakia
[8]
JANOVIČ, F. Modelovanie výkonnosti distribuovaných paralelných algoritmov, ICSC Leden 2012,
Kunovice, Czech republic (in print)
[9]
KIRK, D. B.; HWU, W. W. Programming massively parallel processors, Morgam Kaufmann, 280
pages, 2010
[10]
KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking , 750 pp., 2004, Morgan
Kaufmann
[11]
LILJA D. J., Measuring Computer Performance, 280 pages, 2005, University of Minnesota, Cambridge
University Press, United Kingdom
[12]
PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan
Kaufmann, 2009
[13]
SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, pp. 42-51,
2010, 6.-10 Prosinec, Hradec Králové, Czech republic
[14]
SLOVÁČEK, D. Modelovanie výkonnosti viacprocesorových paralelných systémov , ICSC Leden
2012, Kunovice, Czech republic (in print)
[15]
THAKUR, R.; RABENSEIFNER, R.; GROPP, W. "Optimization of Collective Communication
Operations in MPICH," Int'l Journal of High Performance Computing Applications, (19)1:49-66,
Spring 2005
ADDRESS
Ing. Martin Húdik
Žilinská univerzita v Žiline
Fakulta riadenia a informatiky, katedra technickej kybernetiky
Univerzitná 8215/1
010 26 Žilina
e-mail: [email protected]
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PERFORMANCE MODELLING OF MATRIX PARALLEL ALGORITHMS
Filip Janovič
Žilinská Univerzita
Abstract: With the availability of powerful personal computers, workstations and networking
devices, the recent trend in parallel computing is to connect a number of individual workstations
(PC, PC SMP) to solve computation intensive tasks in parallel way on connected class of
workstations (NOW, SMP, Grid). Current trends in high performance computing (HPC) are to use
networks of workstations (NOW, SMP) or a network of NOW networks (Grid) as a cheaper
alternative to traditionally used massively parallel multiprocessors or supercomputers. The
individual workstations could be so single PC (Personal computer) as parallel computers based on
modern symmetric multicore or multiprocessor systems (SMP) implemented within workstation.
Such actual parallel systems (NOW, Grid) are connected through widely used communication
standard networks and cooperate to solve one large problem. Each workstation is threatened
similarly to a processing element as in a conventional multiprocessor system. To make the whole
system appear to the applications as a single parallel computing engine (virtual parallel system),
run time environments such as OpenMP, MPI, Java are used to provide an extra layer of
abstraction.
To exploit the parallel processing capability of such cluster, the application program must be
paralleled. To behaviour analysis we have to take into account most important overheads that have
the influence to performance of parallel algorithms (architecture, computation, communication
etc.). On real application example we demonstrate the various influences in process of modelling
and performance evaluation and the consequences for real parallel implementations.
Keywords: complexity, parallel algorithm, performance modelling, network of
analytical model, communication system, decomposition strategy
workstations,
1. INTRODUCTION
There has been an increasing interest in the use of networks of workstations (Cluster) connected together by high
speed networks for solving large computation intensive problems. This trend is mainly driven by the cost
effectiveness of such systems as compared to parallel computer with massive number of tightly coupled
processors and memories. Parallel computing on a cluster of powerful workstations (NOW, SMP, Grid)
connected together by high speed networks have given rise to a range of hardware and network related issues on
any given platform.
Network of workstations (NOW) has become a widely accepted form of high-performance parallel computing.
As in conventional multiprocessors, parallel programs running on such a platform are often written in an SPMD
form (Single program – multiple data) to exploit data parallelism or in an improved SPMD form to take into
account also the potential of functional parallelism of a given application. Each workstation in a NOW is treated
similarly to a processing element in a multiprocessor system. However, workstations are far more powerful and
flexible than processing elements in conventional multiprocessors. From the point of system classification we
can divide parallel systems to the two mutual very different groups
 synchronous parallel architectures [4, 14, 16]. To this group belong practically all known parallel
architectures except computer networks. The basic system properties are given through the existence of
some kind of the common shared memory M by parallel processors P i.
 asynchronous parallel architectures [4, 16]. This group covers field of various forms of computer
networks. Their basic property is the mutual interconnection both in the remote form of the distributed
memory modules Mk and the parallel processors Pi with using the existed telecommunication lines
(WAN networks) and in the local form in reaching range of the used fixed lines (LAN networks),
respectively.
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2. PROPERTIES OF PARALLEL ALGORITHMS
The load balancing, inter process communication and transport protocol for such machines are being widely
studied [4, 9, 10]. With the availability of cheap personal computers, workstations and networking devises, the
recent trend is to connect a number of such workstations to solve computation intensive tasks in parallel on such
clusters. To exploit the parallel processing capability of a NOW, the application program must be parallelised.
The effective way how to do it for a particular application problem (Decomposition strategy) belongs to the most
important step in developing a effective parallel algorithm [5, 7, 15].
To choose the best decomposition method for these applications, it is necessary to understand the particular
application problem, the data domain, the used algorithm and the flow of control in given application. Therefore,
according to the character of given task the following decomposition models are used
 perfectly parallel decomposition
 domain decomposition
 control decomposition
 object oriented programming (OOP).
3. PERFORMANCE EVALUATION
Quantitative evaluation and modelling of hardware and software components of the parallel systems are critical
for the delivery of high performance. Performance studies apply to initial design phases as well as to
procurement, tuning, and capacity planning analysis. As performance cannot be expressed by quantities
independent of the system workload, the quantitative characterisation of application resource demands and their
behaviour is an important part of any performance evaluation study. Among the goals of parallel systems
performance analysis is to estimate the performance of a system or a system component or an application, to
investigate the match between requirements and system architecture characteristics, to identify the features that
have a significant impact on the application execution time, to predict the performance of a particular application
on a given parallel system, to evaluate different structures of parallel applications. To the performance evaluation
we briefly review the techniques most commonly adopted for the evaluation of parallel systems and its metrics.
To the performance evaluation we can use following methods
 analytical methods [6, 8, 9, 10]
 application of queuing theory [3]
 Petri nets [11]
 order analysis [1, 2]
 simulation methods [11]
 simulation experiments
 benchmarks [12, 13]
 direct measuring of particular developed parallel application [4, 5, 6].
In order to extend the applicability of analytical techniques to the parallel processing domain, various
enhancements have been introduced to model phenomena such as simultaneous resource possession, fork and
join mechanism, blocking and synchronisation. Hybrid modelling techniques allow to model contention both at
hardware and software levels by combining approximate solutions and analytical methods. However, the
complexity of parallel systems and algorithms limits the applicability of these techniques. Therefore, in spite of
its computation and time requirements, simulation is extensively used as it imposes no constraints on modelling.
3. 1. EVALUATION METRICS
To evaluating parallel algorithms there have been developed several fundamental concepts. Tradeoffs among
these performance factors are often encountered in real-life applications.
3.1.1. SPEED UP
Let O(s, p) be the total number of unit operations performed by p processor system, s defines size of the
computational problem and T(s, p) be the execution time in time units. Then speedup factor is defined as
S ( s, p ) 
T ( s, 1)
T ( s, p )
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3.1.2. EFFICIENCY
The system efficiency for a p processor system is defined by
E ( s, p ) 
S ( s, p )
T ( s, 1)

p
p T ( s, p )
3.1.3. ISOEFFICIENCY CONCEPT
We denote the workload w = w (s) as a function of size of the problem s. For parallel algorithms we define an
isoefficiency function relating workload to machine size p needed to obtain a fixed efficiency E when
implementing a parallel algorithm on a parallel computer. Let h (s, p) be the total overhead function involved in
the parallel algorithm implementation. The efficiency of a parallel algorithm is defined as
E ( s, p ) 
w( s)
w( s)  h( s, p)
The workload w (s) corresponds to useful computations while the overhead function h (s, p) represent useless
overheads times (communication delays, synchronisation, control of processes etc.). With a fixed problem size
(Fixed workload), the efficiency decreases as p increase. The reason is that the overhead h(s, p) increases with p.
With a fixed machine size, the overhead function h (s, p) grows slower as workload w does. Thus the efficiency
increases with increasing problem size for a fixed-size machine. Therefore, one can expect to maintain a constant
efficiency if the workload w is allowed to grow properly with increasing machine size (Scalability).
4. COMPLEXITY OF FUNCTIONS AND ORDER ANALYSIS
Order analysis and the asymptotic complexity of functions are used extensively in practical applications to
analyse the performance of algorithms. When analysing parallel algorithms in this book, we use the following
three types of functions
1. Exponential functions: A function f from reals to reals is called an exponential function in x if it can be
expressed in the form f (x) = ax for x, a  (the set of real numbers) and a > 1. Examples of exponential
functions are 2x, 1.5x+2, and 31.5x.
2. Polynomial functions: A function f from reals to reals is called a polynomial function of degree b in x if it
can be expressed in the form f (x) = x b for x, b  and b > O. A linear function is a polynomial function of
degree one and a quadratic function is a polynomial function of degree two. Examples of polynomial functions
are 2, 5 x, and 5.5 x2.3.
A function f that is a sum of two polynomial functions g and h is also a polynomial function whose degree is
equal to the maximum of the degrees of g and h. For example, 2x + x 2 is a polynomial function of degree two.
3. Logarithmic functions: A function I from reals to reals that can be expressed in the form f (x) = log b x for b
 and b > 1 is logarithmic in x. In this expression, b is called the base of the logarithm. Examples of
logarithmic functions are log1.5 x and log2 x. Unless stated otherwise, all logarithms in this book are of base two.
We use log x to denote log2 x, and log2 x to denote (log2 x)2.
Most functions in this book can be expressed as sums of two or more functions. A function f is said to dominate
a function g if f (x) grows at a faster rate than g(x). Thus, function f dominates function g if and only if f (x) / g
(x) is a monotonically increasing function in x. In other words, f dominates g if and only if for any constant c >
0, there exists a value xo such that f (x) > c g (x) for x > xo. An exponential function dominates a polynomial
function and a polynomial function dominates a logarithmic function. The relation dominates is transitive. If
function f dominates function g, and function g dominates function h, then function f also dominates function h.
Thus, an exponential function also dominates a logarithmic function.
4.1. ORDER ANALYSIS OF FUNCTIONS
In the analysis of algorithms, it is often cumbersome or impossible to derive exact ex¬pressions for parameters
such as run time, speedup, and efficiency. In many cases, an approximation of the exact expression is adequate.
The approximation may indeed be more illustrative of the behaviour of the function because it focuses on the
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critical factors influencing the parameter.
The  Notation:
Formally, the  notation is defined as follows: given a function g(x), f(x) =  (g(x) if and only if for any
constants c1, c2 > 0, there exists an x0 such that c1 f(x) g(x)  c2 f(x) for all x  x0.
The O Notation: Formally, the O notation is defined as follows: given a function g(x), f(x) = O(g(x) if and only
if for any constant c > 0, their exists an x0  0 such that f (x)  c g (x) for all x  x0. From this definition we
deduce that DA(t) = O(t2) and DB(t) = O(t2). Furthermore, D A (t) = O (t) also satisfies the conditions of the O
notation.
The  Notation: The O notation sets an upper bound on the rate of growth of a function. The  notation is the
converse of the O notation; that is, it sets a lower bound on the rate of growth of a function. Formally, given a
function g (x), f (x) =  (g (x) if and only if for any constant c > 0, there exists an x0  0 such that f(x)  c g(x)
for all x  x0.
5. MODELLING OF COMPLEXITY IN PARALLEL ALGORITHMS
To this time known results in complexity modelling on the in the world used classical parallel computers with
shared memory (supercomputers, SMP and SIMD systems) or distributed memory (Cluster, NOW, Grid) mostly
did not consider the influences of the parallel computer architecture and communication overheads supposing
that they are lower in comparison to the latency of executed massive calculations [12].
In this sense analysis and modelling of complexity in parallel algorithms (PA) is rationalised to the analysis of
complexity of own calculations, that mean that the function of control and communication overheads are not a
part of derived relations for execution time T (s, p). In this sense the function in the relation for isoefficiency
suppose, that dominate influence to the overall complexity of the parallel algorithms has complexity of
performed massive calculations. Such assumption has proved to be true in using classical parallel computers in
the world (Supercomputers, massively multiprocessors – shared memory, SIMD architectures etc.). To map
mentioned assumption to the relation for asymptotic isoefficiency w(s) means that


 
w ( s)  max Tcomp , h ( s, p)  Tcomp  max Tcomp
In opposite at parallel algorithms for the actually dominant parallel computers on the basis NOW (including
SMP systems) and Grid is for complexity modelling necessary to analyse at least most important overheads from
all existed overheads which are [5, 6, 8]
 architecture of parallel computer
 own calculations (Tcomp)
 communication latency (Tcomm)
 start - up time
 data transmission
 routing
 parallelisation latency (Tpar)
 synchronisation latency (Tsyn).
Taking into account all this kinds of overheads the total parallel execution time is
T ( s, p) complex   Tcomp  Tpar  Tcomm  Tsyn 
where Tcomp, Tpar, Tcomm, Tsyn denote the individual overheads for calculations, parallelisation overheads,
communication and synchronisation overheads. The more important overhead parts build in the relation for
isoefficiency the used the overhead function h (s, p), which influence in general is necessary to take into account
in performance modelling of parallel algorithms. In general nonlinear influence of h (s, p) could be at
performance parallel algorithm modelling dominant (Fig. 2.). Then for asymptotic isoefficiency analysis is true
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
w ( s)  max Tcomp , h ( s, p)

where the most important parts for dominant parallel computers (NOW, Grid) in overhead function h (s, p) is the
influence of Tcomm (Communication overheads).
Calculation time T (s, p)comp of parallel algorithm is given through quotient of sequential running time
(Complexity product of sequential algorithm Zsa and a constant tc as a average value of performed calculation
operations) through number of used calculation nodes of the given parallel computer. Parallel calculation
complexity of T(s,p) as a limit of a theoretical unlimited number of calculation nodes is given as
T ( s, p )comp  lim p  
Z sa . tc
0
p
Communication time T (s, p)comm is given through the number of performed communication operations in
concrete parallel algorithm and depends from used decomposition model. To the practical illustration of
communication overheads we used the possible matrix decomposition models.
5.1. DECOMPOSITION MATRIX MODELS
In general we are considering the typical possible decomposition strategies in following matrix
A=
a11, a12, . . . , a 1n
a21, a22, . . . , a 2n
.
.
.
.
.
.
.
.
.
am1, am2, . . . , a mn
In order to achieve effective parallel algorithm it is necessary to map every parallel process more than one matrix
element. Then for mapping a cluster of matrix elements there are in principal two ways
 mapping of square blocks to every parallel process as illustrated at Fig. 1 a)
 mapping of p columns or rows (for example according Fig. 1 b).
Depending of used decomposition methods there are derived needed communication activities. In general square
matrix in two dimensions in halts n2 elements (complexity for sequential algorithm, which are equally divided to
p build parallel processes, that means every parallel process gets n2 / p elements. Communication consequences
for mentioned decomposition methods illustrate Fig. 1.
5.1.1. MATRIX DECOMPOSITION TO BLOCKS
For mapping matrix elements in blocks a inter process communication is performed on the four neighbouring
edges of blocks, which it is necessary in computation flow to exchange. Every parallel process therefore sends
four messages and in the same way they receive four messages at the end of every calculation step supposing
that all needed data at every edge are sent as a part of any message). Then the requested communication time for
this decomposition method is given as
Tcomb  8 (ts 
n
tw )
p
This equation is correct for p ≥ 9, because only under this assumption it is possible to build at least one square
because only then is possible to build one square block with for communication edges.
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n
...
...
...
...
...
...
n/ p
b)
a)
Fig. 1. Communication consequences a) blocks b) strips
Using these variables for the communication overheads in decomposition method to blocks is correct
T ( s, p )comm  Tcomb  h ( s, p )  8 (ts 
n
tw )
p
5.1.2. MATRIX DECOMPOSITION TO STRIPS
Decomposition method to rows or columns (Strips) are algorithmic the same and for their practical using is
critical the way how are the matrix elements putting down to matrix. For example in C language are array
elements put down from right to left and from bottom to top (Step by step building of matrix rows). In this way it
is possible send very simple through specification of the beginning address for a given row and through a
number of elements in row (Addressing with indexes). Let for every parallel process (strips) two messages are
send to neighbouring processors and in the same way two messages are received from neighbouring processors
supposing that it is possible to transmit for example one row to one message. Communication time for a
calculation step Tcoms is then given as
Tcoms  4 ts  n tw 
Using these variables for the communication overheads in decomposition method to strips is correct
T ( s, p)comm  Tcoms  h ( s, p)  4 (ts  n t w )
5.1.3. ANALYSIS OF COMMUNICATION PARAMETERS
Based on performed analysed used parallel computers in the world comes out that values t s have one or two
ranks higher values as tw and essentially higher values as tc (for example for NOW type IBM SP-2 ts =35 µs, tw
=230 ns, tc = 4,2ns). If for these values (IBM SP-2) we normalise a value tc (tc =1 time unit), then ts has a value
8 333 and tw 55 time units. From this comes out that ts>> tw > tc, that is a dominant influence of value ts of the
given parallel computer.
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n=256
500
T
[µs] 450
400
350
300
D1
250
D2
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180
200
220
240
p
260
Fig. 2. The role of decomposition method.
5.2. DECOMPOSITION METHOD SELECTION
For comparison based on derived relations for communication complexity decomposition method to blocks
demands higher communication time as decomposition to strips (more effective decomposition to strips) if
8 (t s 
n
tw )  4 (t s  n tw )
p
or after adjusting (for p ≥ 9)
ts  n (1 
2
) tw .
p
Fig. 2. illustrates choice optimisation of suitable decomposition method based on derived dependences to
establishing ts for n = 256 and values tw for NOW type IBM SP-2 (tw = 230 ns = 0,23 µs) and for one rank higher
value tw = 2,4 µs (NCUBE-2) according Fig. 2. For higher values ts as at given tw (tw = 0,23 µs), tw = 2,4 µs)
from a appropriate curve line for n = 256 is more effective decomposition method to strips. Limited values in
choice optimal decomposition strategy are at given n for higher values t w higher. Therefore in general
decomposition to strips is more effective for higher values of ts.
6. CONCLUSIONS
The paper deals with the role of parallel complexity in parallel algorithms. Due to the dominant using of parallel
computers based on the standard PC in form of NOW and Grid, there has been great interest in performance
modelling of parallel algorithms in order to achieve optimised parallel algorithms (Effective parallel algorithms).
Therefore this paper summarises the used methods for complexity analysis which can be applicable to all types
of parallel computers (supercomputer, NOW, Grid). Although the use of NOW and Grid parallel computers
should be in some parallel algorithms less effective than the used of massively parallel architectures in the world
(Supercomputers) the parallel computers based on NOW and Grid belong nowadays to dominant parallel
computers.
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REFERENCES
[1]
ARORA, S.; BARAK, B. Computational complexity - A modern Approach, Cambridge University
Press, 573 pp., 2009.
[2]
GOLDREICH, O. Computational complexity, Cambridge University Press, 632 pages, 2010.
[3]
GELENBE, E. Computer system performance modeling in perspective, 288 pages, published
September 2006, Imperial College Press.
[4]
HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, Kybernetes,
Volume 39, No.1, United Kingdom : 2010, pp. 107- 126.
[5]
HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011, sekcia
č. 2, Kunovice : pp 125 - 132, Czech republic.
[6]
HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, Kunovice :
section 2, Czech republic (in print).
[7]
HANULIAK, P.; SLOVÁČEK, D. To performance modeling of virtual computers, In Proc.:
TRANSCOM 2011 - section 3, Žilina : pp. 213 – 216, 2011.
[8]
HUDIK, M. Performance optimization of broadcast collective operation on multi-core cluster, ICSC
Kunovice : Leden 2012, Czech republic (in print).
[9]
HUDIK, M.; HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System
Equations, In Proc.: GCCP 2011, October 24-26, Bratislava : pp. 70-77, 2011, SAV Institute of
Informatics.
[10]
HUDIK, M.; HANULIAK, P. Parallel complexity of linear system equation, In Proc.: TRANSCOM
2011 - section 3, Žilina : pp. 107-110, 2011.
[11]
KOSTIN, A.; ILUSHECHKINA, L. Modeling and simulation of distributed systems, 440 pages, Jun
2010, Imperial College Press.
[12]
KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking, 750 pp., 2004, Morgan
Kaufmann.
[13]
LILJA, D. J. Measuring Computer Performance, United Kingdom : 280 pages, 2005, University of
Minnesota, Cambridge University Press.
[14]
PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan
Kaufmann, 2009.
[15]
SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, Hradec
Králové : pp. 42-51, 2010, 6.-10 Prosinec, Czech republic.
[16]
SLOVÁČEK, D. Modelovanie výkonnosti viacprocesorových paralelných systémov, ICSC Kunovice :
Leden 2012, Czech republic (in print).
ADDRESS
Ing. Filip Janovič,
Fakulta riadenia a informatiky,
Žilinská Univerzita
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64
MATHEMATIC EVALUATION OF ECOTOXICITY TESTING
Kateřina Kejvalová
Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology
Abstract: This article deals with problem of mathematic reliability of ecotoxicity testing. It
describes reasons and methods of testing substances on live organisms and process of its
evaluating. The main chapters are dedicated to one real test evaluated by standard methodand
thenby an advanced statistic process. Conclusion of this article deals with comparison of those two
methods
.
Key words: Ecotoxicity testing, EC50, inhibition, mathematic evaluation.
INTRODUCTION
Ecotoxicity testing is used to verify efficiency or dangerousness of those substances and agent, which can get
into to environment – intentionally or by an accident. Methodology of the testing is described in various Czech,
European or international standards (ČSN, EN, ISO). These standards are obligatory to obtain reliable results
and to prevent redundant testing on animals and other live organisms [1].
There aretwo possibilities of testing according to the prescribed methodology. The first one is to state stimulation
or inhibition of the agent diluted according to the recommended dosage. The second one is to find the value EC 50
- concentration or dosage of the agent that kills, immobilizes or reduces growth (inhibits) 50 % of organisms
compared to the control sample (without any agent) [4].
The standards also prescribed organisms, which are used for testing. There are 4 basic organisms (daphnia
magna, unicellular and fiber algae and sinapsisalba) and some others (fish, mouse, rat …).
The methodology includes some basic mathematic operations but without any accuracy calculations or statistic
testing. This article deals with statistic evaluation of EC 50 determination. For that are used real data from testing
of influence of STOP-ALGIN (new developed algaecide agent) on sinapsisalba germination.
STOP-ALGIN
STOP-ALGIN is a new developed biocide agent produced by the company RAWAT consulting s.r.o. It is
designated for extermination and prevention of algae, cyanobacteria and other undesirable organisms in
industrial and technological systems and retention basins (e.g. water systems in power stations).
METHODOLOGY OF TESTING ON THE SINAPSISALBA
Sinapsisalba is an usual plant planted as “green fertilizer” or as the base ingredient for mustard. Also it is one of
the organisms required for biocide agent testing. Its main advantage is very quick germination. For testing is
necessary to use seed with certificated germination.
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Fig. 1.
Sinapsis alba (http://www.biopix.info/white-mustard-sinapis-alba_photo-35560.aspx)
The test is done in 5-grade diluting series (100 µl/l, 50 µl/l, 10 µl/l, 5 µl/l, 1 µl/l) corresponding with the
recommended dosage in 3 or 5 repetitions. Constant volume (3 to 5 ml) of precisely diluted agent (diluted with
special solution of nutrients in distilled water) is dropped on filtration paper in Petri dish. On that are exactly 20
seeds of sinapsisalba placed. The seeds germinate 72 hours in the dark (under aluminum foil) and then the length
of all their roots is measured. In cause of 3 repetitions and 5-grade diluting series with 3 control samples it means
360 measurements. This high number guarantees satisfactory credibility of the testing.
STANDARD DATA PROCESSING
Is it to mention, that the methodology of testing is verified by many years of using so no statistic testing is
required. Data processing is usually done by laboratory technicians and any “advanced statistic calculations”
only increase professional image of the project.
AVERAGE LENGTH OF THE ROOTS
When all the roots are measured it is to calculate value of their average length in each concentration (average
from 60 values). The results in single Petri dishes with the same concentration of the agent are not compared.
Three of them are used only because of danger thatthe filtration paper in one of them would dry out.
INHIBITION
Inhibition describes how much some substance, agent etc. kills, immobilizes or reduces growth of tested
organism compared to the control sample (without any tested substances). The opposite of inhibition is
stimulation, when tested substance or agent helps to the organism to grow or reproduce.
The inhibition is calculated with following formula
(1)
where
is inhibition for the concentration
,
is the average root length in control solution,
is average
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root length for the concentration
solution
.
100 µl/l
50 µl/l
10 µl/l
5 µl/l
1 µl/l
control
4,1
9,5
24,2
28,2
28,3
32,3
87,29%
70,59%
25,01%
12,51%
12,35%
0,00%
average root length [mm]
inhibition
Tab. 1.
Average length root length in single solutions and their inhibition
EC50
As written above, the value EC50 is the concentration of the agent that kills or immobilizes 50 % of tested
organism or reduces their growth by 50 % compared to the control sample (inhibition is 50 %) [10]. It is almost
impossible to hit that concentration during testing so it is calculated by linear interpolation from two neighboring
values.
or
(2)
where
is the calculated concentration (EC50),
and
are lower and higher concentrations in diluting
series matching to
and
, which are inhibitions lower and higher than
(required inhibition, in this case
50 %). The interpolation can be used only in case that concentrations and inhibitions of tested samples
approximately linearly depend on each other, what can be calculated or verified by graph.
Fig. 2.
Linearity of inhibition
(3)
(4)
STATISTIC VALUATION
Although the methodology of ecotoxicity testing is verified by years of using is interesting to do some statistic
calculation to get some knowledge about its accuracy and reliability.
AVERAGE LENGTH OF THE ROOTS
It is very easy to calculate the average value. But does it really represent the most probable value of all possible?
And how accurate is it? The easiest way how to get some information about tested data is to state their standard
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deviation. Than is possible to compare intervals of the most probable occurrence or to test the hypothesis, if
those data belongs to the universe with expected distribution.
single Petri dishes
average standard
relative
length deviation
deviation
(mm)
(mm)
100 µl/l
50 µl/l
10 µl/l
5 µl/l
1 µl/l
2,9
2,4
85%
5,5
5,5
101%
4,0
3,6
91%
10,6
8,4
79%
7,5
6,2
83%
10,4
7,5
73%
25,5
12,3
48%
25,4
9,1
36%
21,7
6,5
30%
29,5
14,7
50%
24,5
9,8
40%
30,7
14,8
48%
29,1
14,1
48%
20,3
15,9
78%
35,4
15,9
45%
32,9
16,7
51%
37,6
26,3
control
17,4
8,9
Tab. 2.
46%
34%
average
length
(mm)
Combined data
standard
relative
deviation
deviation
(mm)
4,1
4,1
99%
9,5
7,4
79%
24,2
10,5
43%
28,2
14,2
50%
28,3
16,9
60%
32,3
16,3
50%
Standard deviation of the average root length
NORMALITY OF MEASURED DATA
To verify that measured data belong to aggregate with defined distribution is used Pearson’s test of goodness to
fit. This test can be used only for combined data, because needs “enough large” number of values. We suppose
that the length of roots of sinapsis alba germinated in same conditions (same concentration of tested agent) has
normal distribution with mean value equal to the average value and standard deviation equal to the estimated
one.
100 µl/l
j
tj nj
1
1 17 -0,76 0,2226 0,2226 13,35
0,995
2
3 21 -0,27 0,3932 0,1707 10,24
11,310
3
5
8
0,22 0,5877 0,1945 11,67
1,154
4
7
3
0,71 0,7625 0,1748 10,49
5,344
5
∞ 11
sum
60
kj
∞
fj
pj
npj
1,0000 0,2375 14,25
0,742
1
19,544
60
T= 5,991
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50 µl/l
j
tj
1
6 26 -0,47 0,3200 0,3200 19,20
2,406
2
12 14 0,34 0,6322 0,3122 18,73
1,195
3
18 12 1,14 0,8735 0,2413 14,48
0,424
4
24 5
0,182
5
∞
sum
nj
3
kj
fj
pj
npj
1,95 0,9743 0,1008 6,05
∞
1,0000 0,0257 1,54
60
1
60
pj
npj
1,383
5,590
T= 5,991
10 µl/l
j
tj
1
10 6 -1,35 0,0883 0,0883 5,30
0,995
2
20 19 -0,40 0,3451 0,2568 15,41
11,310
3
30 22 0,55 0,7102 0,3651 21,91
1,154
4
∞ 13
60
∞
5,344
j
tj
kj
1
12 5 -1,14 0,1265 0,1265 7,59
0,884
2
24 19 -0,30 0,3832 0,2566 15,40
0,842
3
36 21 0,55 0,7084 0,3252 19,51
0,113
4
48 10 1,39 0,9184 0,2100 12,60
0,537
5
∞
0,002
sum
nj
kj
fj
1,0000 0,2898 17,39
1
60
19,544
T= 3,841
5 µl/l
sum
nj
5
∞
fj
pj
npj
1,0000 0,0816 4,90
60
1
60
pj
npj
2,380
T= 5,991
1 µl/l
j
tj
nj
1
13 14 -0,90 0,1828 0,1828 10,97
0,837
2
26 15 -0,13 0,4466 0,2637 15,82
0,043
3
39 13 0,64 0,7376 0,2910 17,46
1,140
4
52 15 1,41 0,9202 0,1826 10,95
1,494
5
3
sum
60
kj
∞
fj
1,0000 0,0798 4,79
1
60
0,668
4,182
T= 5,991
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control
j
tj
1
13 9 -1,18 0,1184 0,1184 7,10
0,507
2
26 13 -0,38 0,3504 0,2321 13,92
0,061
3
39 18 0,41 0,6609 0,3105 18,63
0,021
4
52 12 1,21 0,8876 0,2267 13,60
0,189
5
∞
0,234
sum
nj
8
kj
∞
fj
pj
npj
1,0000 0,1124 6,74
60
1
Tab. 3.
60
T= 5,991
1,013
Use of the Pearson’s test
Legend
j
number of the interval
tj
high extreme of the interval j
nj
number of values belonging to the class j
kj
fj
pj
n
T
, where is average length for the concentration C and is estimated standard deviation
value of distribution function of normal normalized distribution for kj
probability of occurrence of measured value in interval (t j-1; tj)
total number of measured values
testing criterion,
, where m is number of classes
From those results can be seen, that except of the first solution (100 µl/l) the values have the predicted
distribution with risk of mistake 5 %. It is understandable that lengths close to zero can’t have normal
distribution, because they can’t be symmetric. For that reason was histogram constructed and distribution
function estimated as
(5)
Fig. 3.
Histogram of the root length in the most concentrated solution
Suitability of this function was verified again using Pearson’s test of goodness to fit.
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100 µl/l
j
1
2
3
4
5
sum
tj nj
1
3
5
7
∞
17
21
8
3
11
60
fj
pj
npj
0,2485
0,5756
0,7603
0,8647
1,0000
0,2485
0,3271
0,1847
0,1043
0,1353
1
14,91
19,63
11,08
6,26
8,12
60
Tab. 4.
0,293
0,096
0,858
1,697
1,021
3,965
T= 5,991
Use of the Pearson’s test
COMPATIBILITY OF MEASURED DATA
Next testing was processed to verify, that length of roots germinating in different Petri dishes but with came
concentration of the agent are same or at least similar. For that were two methods used. The first one was using
of the interval estimation the second one the Two-sample T2 test. The same testswere used to verify that results
in single Petri dish and in combination of the three of them are compatible.
INTERVAL ESTIMATION
In this were intervals
, where l is the average length of roots and s the standard deviation of this value,
compared. The confidence coefficient 2 was used to keep the 95 % dependability.
Fig. 4.
Interval estimation
As seen in the graph, except of the two solutions with the lowest concentration, the results between single Petri
dishes are comparable. All single samples are comparable with their combination.
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TWO-SAMPLE T2 TEST
This test is used to verify difference between mean values of two aggregates with normal distribution. The test
uses following figure:
(6)
where and are the average values of the two aggregates, s their standard deviations, n and m numbers of
values and d the difference. In this case we suppose that the difference is zero for both comparisons: two Petri
dishes and single Petri dish and combination of three of them. If the absolute value of the parameter T is lower
than
, we can with α % dependability say that the two aggregates are comparable.
1–2
T (two P.D.), t=2,02 T (sing. P.D. and comb.), t=1,99
-1,933
1,3
100 µl/l 2 – 3
0,982
-1,2
3–1
1,177
0,1
1–2
50 µl/l 2 – 3
1,325
-0,6
-1,305
1,07
3–1
-0,099
-0,4
1–2
10 µl/l 2 – 3
0,029
-0,5
1,506
-0,5
3–1
-1,238
1,01
1–2
1,253
-0,3
2–3
-1,565
1,09
3–1
0,268
-0,7
1–2
1,855
-0,2
2–3
-3,000
1,85
3–1
1,325
-1,7
1–2
control 2 – 3
-0,864
-0,2
2,578
-1,2
3–1
-1,561
1,55
5 µl/l
1 µl/l
Tab. 5.
Two sample T2-test
Results got from the Two-sample T2 test are, as seen in the table, completely comparable with thosefrom interval
testing. Only two problems appear between Petri dishes 2 and 3 with the two lowestconcentrations.
ACCURACY OF THE INHIBITION
As written above the inhibition depends on the ratio between average root lengths in tested and control solution.
(7)
From this formula can be the standard deviation if the inhibition expressed as
(8)
Where mC and mO are the standard deviations of the average root lengths in solution with the concentration C
and control solution.
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100 µl/l
lC - average
root length
(mm)
4,1
50 µl/l
9,5
7,4
70,59 %
27 %
10 µl/l
24,2
10,5
25,01 %
50 %
5 µl/l
28,2
14,2
12,51 %
62 %
1 µl/l
28,3
16,9
12,35 %
69 %
control
32,3
16,3
0,00 %
71 %
Cconcentration
Tab. 6.
mC(mm)
I
mI
4,1
87,29 %
14 %
Standard deviation of the average root length and Inhibition
Those results are very interesting and hard to be interpreted. It seems that the inhibition accuracy decreases with
the decreasing concentration. But how can be the standard deviation of control inhibition 71 %, when this value
is set to be exactly zero? This question requires future sophisticated solution.
ACCURACY OF THE EC50
As written above, the value EC50 is such a concentration of tested agent that inhibits 50 % of organisms in
relation to the control solution. It is interpolated from the closest higher and lower values, if they comply with
some specific conditions.
(9)
For easier calculation we set following.
and
(10), (11)
(12)
(13)
With our data we obtain
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
This result shows high unreliability of the value EC50 calculated from this data set.
CONCLUSION
Statistic methods can be used in many fields either scientific or not. In case of biotechnology or biology at all it
is necessary to treat them with caution, because the biological material (organisms or their parts) is more variable
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than any other. Results of bio-testing are reliable when all standards during its processing were abided. On the
other hand this article shows that sometimes is usefulto verify data and the method of their processing to avoid
their incorrect interpretation.
ACKNOWLEDGEMENTS
The author thanks to the company RAWAT consulting s.r.o. for space and material for proceeding of the ecotesting and especially to Ing. Petra Hemzová for valued advices and help.
REFERENCE
[1]
376/2001 Sb. - Vyhláška Ministerstva životního prostředí a Ministerstva zdravotnictví o hodnocení
nebezpečných vlastností odpadů
[2]
ČSN EN ISO 6341 Jakost vod – Zkouška inhibice pohyblivosti Daphnia magna Straus (Cladocera,
Crustacea) - Zkouškaakutní toxicity
[3]
ČSN EN 28692 Jakostvod – Zkouška inhibicerůstu sladkovodních řas Scenedesmussubspicatus a
Selenastrumcapricornutum (ISO 8692; 1989)
[4]
MŽP (2007): Metodický pokyn ke stanovení ekotoxicky odpadů, věstník MŽP 4/2007 [Citováno 200811-24].
[5]
KOUTKOVÁ, H. Pravděpodobnost a matematická statistika: základy teorie odhadu. Vyd. 1. Brno :
Akademické nakladatelství CERM, 2007. 50 s. ISBN 978-807-2045-273.
[6]
KOUTKOVÁ, H. Pravděpodobnost a matematická statistika: základy testování hypotéz. Vyd. 1. Brno :
Akademické nakladatelství CERM, 2007. 50 s. ISBN 978-807-2045-280.
[7]
KOUTKOVÁ, H.; MOLL, I. Úvod do pravděpodobnosti a matematické statistiky. 1. vyd. Brno : VUT,
1990. 140 s.
[8]
http://www.zupraha.cz/cs/Ekotoxicita-21.htm[cit.: 18. 1. 2011, 14:00]
[9]
http://www.mzp.cz/osv/edice.nsf/390334EFF595E8B9C1256FC000440F3C/$file/Z_12ekotoxicita.html
[cit.: 18. 1. 2011, 14:00]
[10]
http://en.wikipedia.org/wiki/EC50[cit.: 18. 1. 2011, 14:00]
[11]
http://www.enviwiki.cz/wiki/Ekotoxicita [cit.: 18. 1. 2011, 14:00]
ADDRESS
Ing. Kateřina Kejvalová
Institute of Geodesy
Faculty of Civil Engineering
Brno University of Technology
Veveří 331/95
602 00 Brno
Czech Republic
[email protected]
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MANAGERIAL DECISION-MAKING: MEASURING AND MANIFESTATIONS OF
RISKS
Dusan Marcek
Research Institute of the IT4 Innovations Centre of Excellence The Silesian University Opava, Bezruc
Abstract: The paper is concerned with measuring and assessment of risk scenes in managerial
decision-making. It builds upon the uncertainty of economic information, which is converted into
the concept of risk scene expressed in terms of probability and using confidence intervals of the
predicted quantities. The paper explains the relation of a degree of risk expressed by the classical
information measure, bit, by the concept of confidence intervals, or possibly by the standard
deviation.
Key words: confidence interval, uncertainty, entropy, prediction models, neural networks,
managerial decision, risk scene assessment
1 INTRODUCTION
Managerial decision-making is a complex issue, the complexity of which is caused by many factors. One of the
factors is the way of obtaining information and its credibility for decision-making and operating with them.
Every piece of information which the manager has at their disposal is overcast with uncertainty or entropy, as
rooted in information sciences. This phenomenon is present throughout the whole process of managerial
decision-making. Managers often find themselves in difficult situation due to uncertainty in the decision-making
process. They realize the responsibility they have for the consequences of their decisions. The only way of
reducing uncertainty of the whole decision-making process is making the information which serves as the basis
for making decisions more precise. There is no need to emphasise the fact that using suitable means of making
information more precise facilitates decision-making. An important sphere of information necessary for
management of economic processes on all managerial levels is the information about the future development of
quantities expressed quantitatively, which is used to characterise the state and the development of the object or
process. Evidence shows that it is possible to make this information more precise by a suitable choice and use of
forecasting models based on statistical methods, soft computing and artificial intelligence methods. In
comparison with the manager's expert estimates, these models based on statistical and soft computing methods or
artificial intelligence methods are capable of providing information in the form of forecasts of quantities with an
acceptable degree of uncertainty. The manager using these forecasts is able to make better decisions, i.e. such
decisions whose risks in achieving targets are minimized.
Mathematical statistics [6, 23] offers the theory of point estimates and confidence intervals. The manager can set
and influence the span of these confidence intervals. The confidence interval indicates the span of possible
values into which falls the future estimate of the forecasted quantity with the chosen probability defined by the
manager. This way the limits of the possible future values are set. Point or interval estimates of the future values
of various economic indicators are important for the strategic manager's decision-making. When determining
information entropy in decision-making, it is useful to focus on how the confidence interval for the forecasted
economic quantity can be made more precise, i.e. narrowed by using the forecasting model. A significant
prerequisite for the application of such a model in management is that apart from the increased reliability of
decision-making, the model output results in uncertainty reduction, which makes decision-making easier and less
weighted with risk. The fact or statement that uncertainty reduction facilitates the manager's decision-making is
not sufficient. The crucial factor is how specifically the entropy change manifests itself in the consequences of
the decision. Not only will it be “easier” to make the decision, but more importantly the decision will be more
effective in the long run.
One of the approaches to understanding uncertainty in forecasting models is understanding it as the standard
deviation σ of the forecasted quantity or process [16, 17]. The standard deviation as a degree of uncertainty, or
risk, of forecasted quantity values estimates is equivalent to the statistical degree of accuracy of the forecast
defined as Root Mean Square Error of the forecast [14 – 16]. This approach is used with measuring risks of
prognoses of many economic and financial forecasting models, and in forecasting models of economic time
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series, models for managing financial risk [11, 25, 26], methods based on the extreme value theory [19], and
Lévy models [1, 2], methods to assess and control financial risk [12], methods based on time intensity models,
usage copulas and implementing risk systems [3].
For management, the approach based on the statistical analysis of the dispersion of the quantity values, or on the
standard deviation analysis, is the most comprehensible way of representing uncertainty. It need to be stated that
the standard deviation does not reflect entropy in its true substance as uncertainty which is indicated in bits
(binary digits). On the other hand, uncertainty is closely related to how precise are the estimates of the future
values of quantities that managers have at their disposal. The less precise the estimate, the larger the standard
deviation, and the higher the uncertainty that the information is weighted with. This view of uncertainty does not
articulate it in its true sense, however, it expresses very well its inner essence and the mutual relation of entropy
and decision-making.
The objective of the paper is to point out specific outlines of uncertainty and risk categories, determine their
content in managerial decision-making as a category which conditions the ways and methods of management not
only at the stage of decision-making but also the impacts at the stage of implementation of the decision, where
the consequences of these decisions (effects or losses) will manifest themselves. The aim of the paper is also to
point out the direct relation between the amount of the removed uncertainty and the quality of the manager's
decision.
The issue of measuring risk in management and its accompanying phenomena is divided into four chapters in the
present paper. Chapter two is devoted to characterizing risk and its manifestation in decision-making in
uncertainty conditions. In the third chapter, a diagram of an uncertainty reduction procedure in the manager's
decision-making is designed and characterized. In the fourth chapter, risk reduction with the use of forecasting
models based on the classical (statistical) methods and models based on artificial intelligence is documented and
assessed. Chapter five summarizes the main topics and results.
2 THE RLATION BETWEEN DECISION-MAKING WITH UNCERTAINTY AND DECISIO-MAKING
WITH RISK
Specific choice of tools and models for decision-making depends on whether the manager has precise and
complete or imprecise and incomplete information at their disposal. The complexity of managerial decisionmaking relates to decision-making with incomplete information. Most of the real systems can only be described
incompletely, i.e. with information which cannot be formally expressed by unequivocally set parameters. This is
uncertain information then. In practice, according to [20], there are mainly two types of such information:
According to the first type, uncertain information makes it impossible to exactly determine the future behaviour
of the examined system. This type of uncertainty is called stochastic, and it can usually be modelled using the
probability theory.
Stochastic uncertainty is concerned with the category of the probability risk, which is determined as a scene in
the future associated with the specific adverse incident that we are able to predict it using probability theory and
a lot of data [10]. In this manuscript, we will concern with this type models, which may be described as follows.
Let D be a managerial prediction system including explanatory variables V to explain the behaviour of the
variable to be forecast, and faults represented as forecast errors et in time t = 1, 2,…n. A risk function R in term
of the conceptual model D for having a risk scene can be represented as
R  D(V , et ),
t  1, 2,...n
(1)
To assess the managerial prediction risk R we apply different forecasting models which parameters are estimated
by statistical tools.
The second type of uncertainty is connected with the description or formulation of the actual meaning of the
phenomena or statements about them. This is semantic uncertainty. Natural language words semantics with
uncertainty, i.e. with meanings of words and individual statements not being exact, is typical of natural language.
This uncertainty has the character of possibility rather than probability, and it is most often modelled by fuzzy
systems [5, 9, 13, 22, 24]. As far as decision-making with risk is concerned, this is the case of decision-making
where actual information about real systems is uncertain, and it is not important if the uncertainty is caused by
incomplete information about the system's behaviour, or if it is semantic uncertainty. In the further text, in
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accordance with, the risk connected with managerial decision-making will be modelled using probability models
and understood as a statistical term of the expected value between two extreme states of decision, i.e. with full
uncertainty and decision with certainty.
3 THE ASSESSMENT OF UNCERTAINTY USING THE CONFIDENCE INTERVALS APPROACH
As it was mentioned in the preceding chapter, within the managerial decision-making process uncertainty
indicates the degree of risk of achieving targets. Information serves to the manager as the basis for their
decisions-making. To minimize the decision risk, i.e. to minimize the negative impacts of the decision and to
maximize the benefits of the individual decisions, it is extremely important to get to know the future state of the
economic environment. Economic environment on the micro level is characterized by different economic. There
are two ways in which the value of information for the manager is significantly increased. The first way is
obtaining the sufficient amount of information in time and with the content that the manager can use for their
decision-making. The second way is increasing the precision of the estimates of the future values of quantities
and of the output of processes occurring in economy. Before making the decision itself, the manager must select
a suitable forecasting model for determining the forecast. By selecting a suitable forecasting model according to
the character of the monitored process, the manager can positively influence the quality of the forecast e.g. by
increasing the precision of the prognosis. Because the classical forecasting models are based on the probability
theory, it is obvious that these models are affected by stochastic uncertainty. It is natural that mangers try to
obtain maximum utilizable information, i.e. the most precise values of the future estimate possible. For the
assessment of the estimate uncertainty degree, the method of confidence intervals for point forecasts can be used.
With determining forecast confidence intervals based on the classical forecasting models such as the models of
regression analysis, exponential smoothing, and Winter's seasonal models is concerned e.g. A more complicated
situation is in case of models based on artificial intelligence such as GMDH (Group Method of Data Handling)
or the classical neural networks with adaptation of parameters by the gradient method using Back-propagation
algorithm. In this case it is possible to test the H0 hypothesis of the expected type of probability distribution to
determine confidence intervals provided that residuals have a normal probability distribution according to [7] ,
and this hypothesis can be verified using χ2 test of good fit on levels of significance set in advance. It is a wellknown, widely used and relatively universal method of mathematical statistics [6]. To obtain the correct result, it
is necessary for the statistical data file to have at least 50 values. The H0 hypothesis, verified by applying the χ 2
test of good fit on the level of significance α = 0,01, claims that the residuals of the forecasted values from the
actual values can be considered as a data file with a normal probability distribution.
The span of the confidence interval is related to the estimate precision. The more precise the input from the
forecasting model, the more precisely it is possible to set the span of the confidence interval, and the larger part
of uncertainty is removed. Using the χ2 test of good fit, the H0 hypothesis can be verified on the level of
significance α = 0.05 and α = 0.01, and this hypothesis claims that the residuals of the forecasted values from the
actual values can be considered as a data file with a normal probability distribution. The confidence interval can
be then calculated according to the following expression
x  x  k .
where
k
α
n
x

n
, x  k .

n
(2)
– the critical value of the standardized normal probability distribution,
– the level of significance, σ is the standard deviation,
– the length of the sample,
– the expected value.
Interesting about the support of the preference of forecasting models based e.g. on neural networks to managers'
expert estimates in managerial decision-making is the information about the probability change. The calculation
of this probability is possible from expression (2) as the level of significance k
k  x a
n 1
 est
(3)
where
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α is the lower limit of the forecast interval of the prognosis calculated by forecasting model
 est is the estimate of the standard deviation
According to the critical values of the standardized normal distribution, to k appertains a new  . This implies
that the probability that the mean value will fall into the narrower (more precise) interval will change from (1 –
 ).
This begs the question, how will the entropy change if the estimate is more precise? The basic relation for
entropy calculation is
H (X) = − log2 P (X)
(4)
At present, one bit (binary digit) is used most often as the information unit. The information achieved in one
information step, indicated in bits, means the choice of one of two possibilities, i.e. one step of a bivalent
decision.
The probability used in the relation for the calculation of entropy (4) is the probability that the estimate value
will fall into the narrower 95% confidence interval.
4 ENTROPY AND STANDARD DEVIATIONS AS THE MEASURE OF UNCERTAINTY
As we mentioned early, another measure of uncertainty used in the theory of information is entropy. According
to [21] entropy and also uncertainty is expressed by the amount of information that we get after performing an
experiment. For example, if we get a message that an event A has occurred with probability P(A), we also get
information I(A) equal  log 2 P( A) bit.
In case the event A consists of a finite amount of measured events, i.e. subsets of probabilistic space  while
Ai  A for i  1, 2,...n ,  
n
i 1
Ai and Ai
Aj  0 for i  j is valid, then the entropy expressed by Sannon´s
definition is [21]
n
n
i 1
i 1
H ( P)   I ( Ai ).P( Ai )    I ( Ai ).log 2 P( Ai )
(5)
In the introductory chapter, we mentioned the possibility of expressing or measuring uncertainty using the
standard deviation. The standard deviation is used in literature as the degree of uncertainty and risk [4, 14]. As
far as relevancy is concerned, it is probably the easiest and, for managerial practice, the most comprehensible
way of expressing and quantification of uncertainty. While the entropy indicated in the information unit bit is at
present a still relatively abstract and almost non-used measure for expressing risk in the sphere of managerial
decision-making. Uncertainty in the sense of the standard deviation has a higher informative value for managers.
Uncertainty expressed by the standard deviation has one drawback, which is unit incompatibility. Entropy is
indicated in bits. Despite this fact, as we could see in the given examples, it is easier to work with entropy as the
standard deviation. It is possible to state that reduction of entropy of the forecast system was achieved when its
standard deviation of forecast errors was reduced. It can be clearly seen in expression (1). In technical systems,
rule 3 σ is used which in the figurative meaning provides information about which interval the forecast will
almost certainly fall into. Therefore, it provides certainty instead of uncertainty. But it is a certainty which will
not push the manager forward with his decision-making if there is a big standard deviation. The real solution
leading to the support of decision-making is reducing uncertainty of the forecast system by using a better
forecasting model which will achieve lesser variability of prognosis errors. Described in [18], on the basis of
prognosis errors analysis, is a method of searching for such a forecast horizon for which entropy and thus also
prognosis risk is minimal.
5 CONCLUSION
In managerial decision-making, risk is the central category based on which the effects of individual variants are
assessed, and subsequently the final decision is chosen from several variants. In the present paper we showed the
procedure of quantitative assessment of risk scene based on probability terms using confidence intervals for
point estimates of economic quantities. We build upon measuring uncertainty based on information entropy
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indicated in bits and on measuring based on prognosis confidence interval, where uncertainty is expressed in
terms of the span of the confidence interval and the probability that by using forecasting model the set prognosis
limits around the expected value will not be exceeded. Both approaches to measuring uncertainty were assessed
from the viewpoint of utilization in managerial decision-making using forecasting models based on an expert
estimate, statistical models, and neural networks models.
In [8], the theory of this study is applied to forecasting models which are based on an expert estimate and a
statistical theory, and the risk scenes are assessed in forecasting models based on neural networks. We showed
that there are more ways of approaching the issue of measuring risk in managerial decision-making in
companies. In [8] it was also proved that it is possible to achieve significant risk reduction in managerial
decision-making by applying modern forecasting models based on information technology such as neural
networks developed within artificial intelligence.
Acknowledgement. This paper has been elaborated in the framework of the IT4Innovations Centre of
Excellence project, reg. no. CZ.1.05/1.1.00/02.0070 supported by Operational Programme 'Research and
Development for Innovations' funded by Structural Funds of the European Union and state budget of the Czech
Republic.
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ADRESS:
Prof. Ing. Dušan Marček, CSc.
Research Institute of the IT4
Innovations Centre of Excellence The Silesian University Opava,
Bezruc Square 13,
746 01 Opava, Czech Republic
e-mail: [email protected]
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TESTING OF TOPCON GRS-1 INSTRUMENT USING RTK METHOD
Irena Opatřilová1, Dalibor Bartoněk2
1
Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology,
2
Evropský polytechnický institut, s.r.o., Kunovice
Abstract: The paper deals with testing of Topcon GRS-1 instrument, specifically with evaluating of the
position and height of a point in the good horizon, i.e. better than 75 %. The GRS-1 device is GNSS
receiver, which is especially designed for GIS applications that are usually associated with single
frequency code measurements using an internal antenna. In this case, we expect dm accuracy associated
with the method of DGNSS. Nevertheless, the usage of this device is wider, because we can use an external
antenna for determining the spatial position and use dual-frequency phase RTK measurements with cm
accuracy. RTK method may be associated with the use of networks of permanent reference stations and
this method.
The article describes the preparation for testing in the form of reconnaissance and selection 10 points for
measurement. Then it evaluates the testing method of RTK, in which the services of a Czepos network of
permanent stations (RTK, MAX, RTK-PRS) and the services of a TopNET network (RTK, VRS-NVR3) have
been used.
The test results in this paper are interpreted using the graphs for some selected points, and also the tables
with the average results of measurement for each service. Then there is the expected accuracy declared by
the manufacturer that is compared with the obtained precision by testing and comparing the accuracy of
services of a Czepos network.
Keywords: Testing of GNSS receiver, RTK, network of permanent reference stations
INTRODUCTION
Nowadays there are many instruments for various applications related to satellite determining of the spatial position.
The range of these devices can be divided for example to their accuracy. On the one hand there are instruments to
evaluate the position with cm accuracy; on the other hand, there are devices with accuracy in the order of several
meters. The instruments for surveying purposes belong to the first group of devices. These instruments may determine
the points with mm accuracy using long observation and the subsequent post-processing. RTK method is used for of
determining of the position in real time and this method is widely used in geodesy, in civil engineering and in other
applications. The accuracy of this method is in the order of centimeters and a great advantage over the static method is
immediate information about the position of the point. The static and RTK method determinate the position of point
using the phase measurement.
The devices used for GIS applications are another group of GNSS instruments. The position of points is usually
determined using code measurement based on DGNSS method, which achieves dm accuracy. Phase and code
measurements evaluate so-called the relative position of the point. It means that first a spatial vector is evaluated
between the determined and known point and then the spatial coordinates of determined point are calculate from this
vector. This method is more accurate than the so-called autonomous determination of position, in which the coordinates
of points are derived only from the measured data using device itself. So the reference station is needed for relative
determination of point. This station has the known coordinates of the point and measures at the same time as the device
on the determined point (the rover).
Such a reference station can be either our other apparatus, or the data from networks of permanent reference stations
can be use. Nowadays three such networks are in the Czech Republic, which cover the whole territory of our country. It
is a Czepos network operated by the Czech Office for Surveying, Mapping and Cadastre (COSMC) [3], a TopNET
network by Geodis Brno [4] and a Trimble VRS Now Czech network [5], which is managed by Geotronics Praha.
These networks provide more services. Either there are data from a particular station for subsequent post-processing, or
services used for the RTK and DGNSS method. In the second case you need a mobile internet connection for receiving
of correction data provided by individual services. The services for RTK are as follows. Either a customer chooses a
particular reference station, from which it receives of correction data during measurement, or this station is searched
itself. There are for example services called Czepos RTK and TopNET RTK. The second group is so-called the network
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solution, in which mostly a virtual reference station is generated. The necessary corrections are subsequently received
from this station. This group includes services called Czepos PRS, TopNET VRS and other. For example a list of
services provided by a Czepos network is in Figure 1.
Fig. 2 Topcon GRS-1[7]
Fig. 1 The services provided by a Czepos network [6]
The paper deals with testing of Topcon GRS-1 instrument, specifically with evaluating of the position and height of a
point in the good horizon, i.e. better than 75 %. RTK method was used for the testing of instrument. It was worked with
an external PG-A1 antenna during measuring, thanks to which we can determine the spatial position using dualfrequency measurements with cm accuracy. The device further includes an internal antenna for code measurements with
dm accuracy, an internal GSM/GPRS modem, 2.0 Mpix digital camera, a electronic compass and is equipped with
TopSURV software. More information about the device GRS-1 is shown for example in [7].
Fig. 3 The scheme of workflow during the testing of instrument
The scheme of whole work progress during the testing of device is suggested in Figure 3. The services of a Czepos
network (RTK, MAX, RTK-PRS) and a TopNET network (RTK VRS-NVR3) were used for the RTK measurement.
The main goal of this work was not only the testing of selected device but also to familiarize with a particular type of
GNSS receiver, with select services of networks of permanent reference stations, then to design the methodology of
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measurement, to evaluate the accuracy of the instrument from measurement results, to compare it with the expected
accuracy and to assess the use of this instrument in practice.
TESTING OF INSTRUMENT
SELECTION OF SUITABLE POINTS FOR TESTING
At the beginning to select appropriate geodetic points for testing was necessary. 46 points of fundamental horizontal
control were reconnaissanced. These points have known coordinates in S-JTSK system (Datum of Uniform
Trigonometric Cadastral Network), altitude in Bpv system (Baltic Vertical Datum - After Adjustment) and also ETRS
coordinates and ellipsoidal height. 41 points were found. 10 point from these were chosen for testing purposes so that
they were evenly distributed throughout the Brno city, they had a horizon greater than 75 %, they were at different
distances from the reference stations and an easily accessible by public transport was to them. Figure 4 shows the
location of selected points within the city of Brno.
Fig. 4 The selected geodetic points for testing
RTK MEASUREMENT
The external Topcon PG-A1 antenna (Fig. 5) was used for RTK testing. This antenna was placed on a tripod so that the
influence of centering was as low as possible. The sample of measurement is in Figure 6. PG-A1 antenna is a dualfrequency and dual-constellation. It means that antenna receives signals from GPS and also from GLONASS. It was
designed with the technology to eliminate errors caused by multipath [8].

Fig. 5 Dual-frequency and dual-constellation Topcon PG-A1antenna [9]
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Fig. 6 The sample of RTK testing
The measurement was done on a 10 selected points in two periods. A point was measured at one period 30 times
for each service separately. One measurement was imposed as the average of the 5 epochs. One epoch had a
length of 1 second. It means that 150 measurements were made on every point during one period (5 services over
a 30 measurement).
Services used for RTK measurements were as follows:
1 - Czepos RTK
2 - TopNET RTK
3 - Czepos PRS
4 - TopNET VRS-NVR3
5 - Czepos VRS-MAX.
The periods were separated from each other so that repeated measurements on individual points have been
distinguished from each other at least 3 hour interval. The first period took place 9/26/11 and 9/28/11, the
average number of satellites was 7+6 (GPS+GLONASS) and it was cloudy and about 23° C. The second period
was 09/28/11 and 30/09/11, while the average number of satellites was 8+6, it was clear weather again about 23°
C. The mask angle was 12° in both cases.
PROCESSING OF RTK
S-JTSK coordinates and Bpv elevation were exported into TXT format. All other measurement was processed in
Microsoft Office Excel software. The measurements are processed separately for each point and for each period
and formulas from [1] and [2] were used for computing. The average coordinates of a point in S-JTSK for
individual
services were calculated by the (1), and these were compared with coordinates given by the (2).

30
lj 
l
i 1
i
30
 j  X lj
,
l is measured quantity, it means x and y coordinates and elevation of point
i (number of measurement) = 1, 2, …, 30,
j (number of service) = 1, 2, 3, 4, 5
(1)
,
X is given coordinate, possibly elevation of point
(2)
The measured and given coordinates were entered into the graph (Fig. 7), as well as the average values of
measured coordinates for each service. Graphs have mm resolution.
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Fig. 7 The graph with results of 1st and 2nd period of RTK measurement on point 1 for individual services, the positional component
Fig. 8 The graph with results of 1st and 2nd period of RTK measurement on point 8 for individual services, the height component
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Similarly the height variations were calculated, which were represented for better clarity in the graphs (Fig. 8).
Then mean errors of the differences of the measured coordinates from given coordinates (m) were calculated for
individual service, again for both periods separately.
30

mj
(3), (4)


i 1
2
i
,
i  li  X
where
30
Later the average value of the differences of the measured coordinates from given coordinates were calculated.
They were determined for each service from all points and results are listed in the following table. ΔY,X was
calculated using the formula:
Y , X  2X  2Y
(5)
Average of the 1st period
Average of the 2nd period
Average of periods
S-JTSK coordinate a Bpv elevation
S-JTSK coordinate a Bpv elevation
S-JTSK coordinate a Bpv elevation
ΔY [m]
ΔX [m]
ΔH [m]
ΔY [m]
ΔX [m]
ΔH [m]
ΔY [m]
ΔX [m]
ΔY,X [m]
ΔH [m]
1
0,005
-0,006
0,016
0,003
-0,007
0,014
0,004
-0,006
0,007
0,015
2
0,008
-0,006
0,015
0,010
-0,008
0,014
0,009
-0,007
0,011
0,015
3
0,005
-0,007
0,019
0,002
-0,010
0,019
0,004
-0,008
0,009
0,019
4
0,004
-0,005
-0,003
0,007
-0,009
0,016
0,005
-0,007
0,009
0,006
5
0,003
-0,007
0,014
0,001
-0,008
0,016
0,002
-0,007
0,008
0,015
Service
Tab. 1 Testing of RTK – The average values of the differences between measured and given coordinates of points for individual services
Then the average values of mean errors of these differences were calculated, i.e. the differences between the
measured and given coordinates of points for each service (see Table 2).
Average of the 1st period
Average of the 2nd period
Average of periods
S-JTSK coordinate a Bpv elevation
S-JTSK coordinate a Bpv elevation
S-JTSK coordinate a Bpv elevation
mY [m]
mX [m]
mH [m]
mY [m]
mX [m]
mH [m]
mY [m]
mX [m]
mY,X [m]
mH [m]
1
0,010
0,010
0,026
0,010
0,010
0,032
0,010
0,010
0,010
0,029
2
0,011
0,010
0,031
0,012
0,013
0,031
0,012
0,011
0,012
0,031
3
0,011
0,013
0,040
0,011
0,018
0,038
0,011
0,015
0,013
0,039
4
0,018
0,011
0,046
0,011
0,013
0,033
0,015
0,012
0,013
0,039
5
0,009
0,010
0,029
0,011
0,013
0,031
0,010
0,012
0,011
0,030
Service
Tab. 2 Testing of RTK – The average values of the mean errors of the differences between measured and given coordinates of points for
individual services
Here mY,X indicates the mean coordinate error calculated by the formula:
mY , X 
mX2  mY2
2
(6)
The accuracy of phase RTK measurement is stated by the manufacturer for the Topcon GRS-1 device as value
My,x 10 mm+1,0 ppm (* base length) for the positional component and Mh 15 mm+1,0 ppm (* base length) for
the height component [7]. These values were compared with average values of mY,X and mH for individual
services at all points. The base length between the permanent station and the point (above which the device was)
had to be determined. The length was calculated from given coordinates in the case of Czepos RTK a TopNET
RTK services, for other services the length was selected as permanent value of 5 km.
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
Tab. 3 Comparison of the achieved accuracy of phase RTK measurement with the accuracy provided by the manufacturer (for one multiple
of M error)
The results are in Table 3. The achieved accuracy was satisfactory for one multiple of mean error (M) in 66 % of
the results for the positional component and in 30 % of the results for height component. 3 multiple of the error
(M) was exceeded in three cases, namely by the height component.
COSMC indicates on its website an overview of the results of testing the accuracy of the Czepos services and
products [10, 11]. The mean errors of one measurement calculated from the differences of measured and given
coordinates are given in Table 4.
Czepos Service
mxy [m]
mh [m]
RTK
RTK-PRS
VRS-MAX
0,014
0,013
0,010
0,045
0,044
0,039
Tab. 4 Czepos services – The mean errors of one measurement calculated from the differences of measured and given coordinates
It is clear by comparing of these values with the values given in Table 2 that our measurement reached
satisfactory accuracy. Unfortunately a TopNET network do not have any such specific information about the
accuracy of their services on its website.
CONCLUSIONS
This paper describes testing of GNSS instrument, Topcon GRS-1, and some selected services provided by
networks of permanent reference stations. The work is divided into three steps. In the first part a reconnaissance
of terrain was done in which it was selected 10 points suitable for subsequent testing of device.
The second part deals with the measurement using the RTK method, in which benefited from the services of a
Czepos network (RTK, MAX, RTK-PRS) and services of a TopNET network (RTK, VRS-NVR3). There were
no major complications during the measurements.
The last part concerns the processing of measurements, from which the following results are known. All services
achieve similar results, which are listed in Tables 1 and 2. Tables describe the average results of all ten points for
the differences between measured and given coordinates and their mean errors. From these tables can be
evaluated that Czepos RTK service had the best overall results in comparison with other services. Czepos MAX
got an imaginary second place, TopNET RTK was the third, TopNET VRS-NVR3 reached the forth place and
Czepos PRS had the worst results in comparison with other services. For all that the differences between the
results of these services were not particularly significant.
The achieved accuracy for mean errors of differences between measured and given the coordinates of points was
compared with the accuracy provided by the manufacturer for RTK measurements (Table 3). The evaluation
showed that 66 % of the measurement results for the positional component and 30 % of the results for the height
component are in interval of one multiple of expected accuracy. 3 multiple of the expected accuracy was
exceeded in three cases out of a hundred, namely all for the height component.
The results for services of a Czepos network from Table 2, i.e. the results for the mean error of differences
between measured and given coordinates, were compared with the accuracies, which Czepos introduces on its
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87
website. Our measurements amounted to an overall better accuracy.
The Topcon GRS-1 device is especially designed for GIS applications. For work, in which the user would be
sufficient to determine the spatial position of the point with dm accuracy, can clearly recommend using code
measurements taken by the internal antenna + a correction data from a network of permanent reference stations.
This may include for example evidence of object for database of municipal offices (containers, bus stops, poster
areas, etc.). If the user wants to determine the points with cm accuracy must already use an external antenna.
Using it may be for example for mapping purposes in geodesy, in cadastre of real estate’s for renewal of cadastre
documentation, in engineering surveying for quick setting-out, etc. Another great area of use is also forestry,
water management, traffic engineering, archeology and more. In simple terms, the area of applications for this
device is wide.
REFERENCES
[1]
HAMPACHER, M.; RADOUCH, V. Teorie chyb a vyrovnávací počet 10. Praha : Vydavatelství ČVUT.
2003. 159 pages. ISBN 80-01-02833-X.
[2]
VILÍMKOVÁ, M. Testování sítě CZEPOS (Master thesis). Praha : České vysoké učení technické
v Praze, Fakulta stavební. 2006. 109 pages.
[3]
http://czepos.cuzk.cz/_index.aspx, 4.12.2011
[4]
http://topnet.geodis.cz/topnet/, 4.12.2011
[5]
http://www.geotronics.cz/trimble-vrs-now-czech, 4.12.2011
[6]
http://czepos.cuzk.cz/_servicesProducts.aspx, 3.12.2011
[7]
http://obchod.geodis.cz/geo/grs-1-dualni-gis-prijimac, 3.12.2011
[8]
http://obchod.geodis.cz/geo/antena-pg-a1, 3.12.2011
[9]
http://www.topconuniversity.com/hardware/gnss-antennas/pga-1/, 3.12.2011
[10]
http://czepos.cuzk.cz/_vysledky.aspx, 3.12.2011
[11]
http://czepos.cuzk.cz/_vysledkyNS.aspx, 3.12.2011
ADRESS:
Ing. Irena Opatřilová,
Institute of Geodesy,
Faculty of Civil Engineering,
Brno University of Technology,
Veveří 331/95,
602 00, Brno, Czech Republic,
phone: +420-541147221,
[email protected]
Assoc. prof. Dalibor Bartoněk,
EPI, s.r.o. Kunovice,
Osvobození 699,
686 04 Kunovice, Czech Republic,
phone: +420-605912767,
[email protected]
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88
QUANTUM MODEL OF ATOMS
Ošmera Pavel
EPI, s.r.o. Kunovice
Brno University of Technology, Czech Republic
Abstract: This paper is an attempt to attain a better model of the atomic nucleus using vortex-ringfractal models. The aim of this paper is the vortex-ring-fractal modelling of atoms, which is not in
contradiction to the known laws of nature. We would like to find some acceptable models of the
atomic nucleus. Our imagination is that the atomic nucleus consists from the ring protons and the
ring neutrons. We present here computer calculations and pictures.
Keywords: vortex-ring-fractal modelling, hydrogen atom, quantum, ring structures, vortex, fractal
1. INTRODUCTION
The electrical force decreases inversely with the square of distance between charges. This relationship is called
Coulomb’s law. There are two kinds of “matter”, which we can call positive and negative. Like kinds repel each
other, while unlike kinds attract – unlike gravity, where only attraction occurs. When charges are moving the
electrical forces depend also on the motion of charges in a complicated way (Feynman et al., 1977).
Most of our knowledge of the electronic structure of atoms has been obtained by the study of the light given out
by atoms when they are exited. The light that is emitted by atoms of given substance can be refracted or
diffracted into a distinctive pattern of lines of certain frequencies and create the line spectrum of the atom. The
careful study of line spectra began about 1880. The regularity is evident in the spectrum of the hydrogen atom.
The interpretation of the spectrum of hydrogen was not achieved until 1913. In that year the Danish physicist
Niels Bohr successfully applied the quantum theory to this problem and created a model of hydrogen. Bohr also
discovered a method of calculation of the energy of the stationary states of the hydrogen atom, with use of
Planck’s constant h. Later in 1923 it was recognized that Bohr’s formulation of the theory of the electronic
structure of atoms to be improved and extended. The Bohr’s theory did not give correct values for the energy
levels of helium atom or the hydrogen molecule-ion, H2+, or of any other atom with more than one electron or
any molecule. During the two-year period 1924 to 1926 the Bohr description of electron orbits in atoms was
replaced by the greatly improved description of wave mechanics, which is still in use and seems to be
satisfactory. The discovery by de Broglie in 1924 that an electron moving with velocity v has a wavelength
λ=h/mev. The theory of quantum mechanics was developed in 1925 with the German physicist Werner
Heisenberg. Early in 1926 an equivalent theory, called wave mechanics, was independently developed by
Austrian physicist Ervin Schroedinger. Important contributions to the theory were also made by the English
physicist Paul Adrien Maurice Dirac. The most probable distance of the electron from the nucleus is thus just the
Bohr radius rB; the electron is, however, not restricted to this distance. The electron is not to be thought of as
going around the nucleus, but rather as going in and out, in varying directions, so as to make the electron
distribution spherically symmetrical (Pauling,1988). Basic vortex-ring structures ware described in: (Osmera,
2006, 2007a, 2007b, 2008a, 2008b, 2009, 2010, and 2011). The “ring theory” is supported by experiments in
(Lim, 2011).
Fractals seem to be very powerful in describing natural objects on all scales. Fractal dimension and fractal
measure are crucial parameters for such description. Many natural objects have self-similarity or partial-selfsimilarity of the whole object and its parts.
Fractal analysis has become one of the fundamental methods of the image analysis. Fractal dimension D and
fractal measure K are the two characteristic values, which can be determined by fractal analysis. Fractal measure
characterize the properties of surfaces and edges of image structure, whereas the fractal dimension shows the
trends of surfaces and edges changes in relation to the details of structures themselves.
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2. THE MODEL OF HYDROGEN WITH A LEVITATING ELECTRON
The new model of the hydrogen atom with a levitating electron was introduced in (osmera, 2008b). There is
attractive (electric) force F+ and (magnetic) repellent force F- :
F  F  F 
e2
4 o
 1 d o2 
 2  4 
d 
d
(1)
electron
proton
d
Fig.1. The levitating electron in the field of the proton (the fractal structure model of hydrogen H is simplified (Osmera, 2010).
The hydrogen atom can have the electron on left side or on right side (Osmera, 2007a). The attractive force F+ is
Coulomb’s force. The repellent force F- is caused with magnetic fields of the proton and the electron (see Fig.1).
A distance between the electron and the proton is d. The electron moves between point d1 and point d2 .The
energy Ei required to remove the electron from the ground state to a state of zero total energy is called ionization
energy. The energy of the hydrogen atom in the ground state is E= – 13.6 eV. The negative sign indicates that
the electron is bound to the nucleus and the energy 13.6 eV must be provided from outside to remove the
electron from the atom. Hence 13.6 eV is ionization energy Ei for hydrogen atom. Calculation of ionization
energy was introduced in (Osmera 2008b):
proton
covalent bond
2 electrons
Fig. 2. Vortex-fractal ring structure of the hydrogen molecule
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subelectron
Fig. 3. Vortex-fractal ring structure of neutron (the electron is inside of the proton)
neutron
electron
proton
Fig.4. Vortex-fractal ring structure of the helium atom
Electric lines are perpendicular to magnetic lines. Electric lines create complex coil structure. Electric lines
create coil-ring structures that consist from coil sub-structures. It is coil-semi-fractal structure. Every neighbour
coil structure consists from opposite rotated electric lines that repel each other. They are created from electron or
positron ring-sub-structures (-3e, -3υ) (Osmera, 2006). The proton has coil-semi-fractal structure and the electron
has ring-semi-fractal structure.
mg. line
el. line
Fig.5 One coil layer of the electromagnetic field of the electron
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91
proton
electron
Fig.6 The structure of hydrogen with one layer of the electromagnetic field.
It is necessary to use several simple rules. Only two protons and two electrons can be on the same axis inside the
atom. Every proton can have only one levitating electron. Electrons on one axis have opposite spin. It is Pauli’s
exclusion principle. To add new proton with different axis we use neutrons which hold protons in one structure.
Protons and neutrons are connected with nuclear bond.
Acknowledgements. This work has been supported by EPI Kunovice
3. CONCLUSIONS
The exact analysis of real physical problems is usually quite complicated, and any particular physical situation
may be too complicated to analyze directly by solving the differential equations or wave functions. Ideas as the
field lines (magnetic and electric lines) are for such purposes very useful. A physical understanding is a
completely nonmathematical, imprecise, and inexact, but it is absolutely necessary for a physicist (Feynman at
al., 1977). It is necessary combine an imagination with a calculation in the iteration process. Our approach is
given by developing gradually the physical ideas – by starting with simple situations and going on more and
more complicated situations. But the subject of physics has been developed over the past 200 years by some very
ingenious people, and it is not easy to add something new that is not in discrepancy with them. The vortex model
of the electron was inspired by vortex structure in the PET-bottle experiment with one hole connector ($3
souvenir toy, Portland, Oregon 2004), our connector with 2 or 3 holes, and levitating magnet “levitron” (physical
toy). The “ring theory” is supported by experiments in (Lim, 2011). Now we realize that the phenomena of
chemical interaction and, ultimately, of life itself are to be understood in terms of electromagnetism, which can
be explain by vortex-ring-fractal structure in different state of self-organization inside gravum (Osmera, 2009).
Mass and energy are a form of the matter. They differ in the topology structures. Energy can be transformed, not
created or destroyed. Dark energy is spread uniformly through space. It is everywhere. A variety of sources
suggests that energy contributing to this flatness may be divided as follows: ordinary matter, 4 %; dark matter 23
%; dark energy 73 percent. Nature prefers simplicity, symmetry and “beauty”. Arrangement of electrons in the
atom must reply the structure of nucleus. The electron in the classical theory is described by its mass, charge,
flavor, and spin. There is no size and no structure for electrons and quarks. The fundamental laws of the
subatomic world are laws of probability, not laws of certainty. Electrons occupy “shells” in atoms and do not
cluster together in the lowest-energy state. This conclusion is required to account for the periodic table. Classical
theory does answer the question: Why do antiparticles have to be counted as negative particles. In vortex-fractalring structures of antiparticles all their substructures rotate in opposite direction. Conservation laws are
connected to principles of symmetry.
The electron structure is a semi-fractal-ring structure with a vortex bond between rings. The proton structure is a
semi-fractal-coil structure. The proton is created from electron subsubrings e -2 and positron subsubrings υ-2
which can create quarks u and d (Osmera, 2010). This theory can be called shortly “ring” theory. It is similar
name like string theory.
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In the covalent bond is a pair of electrons which oscillate and rotate around a common axis. There are two
arrangements of hydrogen: with a left and a right side orientation of the electron in their structure. Very
important is symmetry and self-organization of real ring structures.
4. REFERENCES
[1]
FEYNMAN, R. P.; LEIGHTON, R. B.; SANDS, M. (1977). The Feynman Lectures on Physics,
volume I, II, III Addison-Wesley publishing company.
[2]
LIM, T. T. (2011) archived at serve.me.nus.edu.sg/limtt/
[3]
OSMERA, P. (2006). Vortex-fractal Physics, Proceedings of the 4th International Conference on Soft
Computing ICSC2006, January 27, Kunovice, Czech Republic, 123-129.
[4]
OSMERA, P. (2007a). Vortex-ring Modelling of Complex Systems and Mendeleev’s Table,
WCECS2007, proceedings of World Congress on Engineering and Computer Science, San Francisco,
152-157.
[5]
OSMERA, P. (2007b). From Quantum Foam to Vortex-ring Fractal Structures and Mendeleev’s Table,
New Trends in Physics, NTF 2007, Brno, Czech Republic, 179-182.
[6]
OSMERA, P. (2008a). The Vortex-fractal-Ring Structure of Electron, Proceedings of MENDEL2008,
Brno, Czech Republic, 115-120.
[7]
OSMERA, P. (2008B). Vortex-fractal-ring Structure of Molecule, Proceedings of the 4th Meeting
Chemistry and Life 2008, September 9-11, Brno, Czech Republic, Chemické listy (ISSN 1803-2389),
1102-1108.
[8]
OSMERA, P.; RUKOVANSKY, I. Magnetic Dipole Moment of Electron, Journal of Electrical
Engineering, No 7/s, volume 59, 2008, Budapest, Hungary, 74-77Osmera P. (2009). Vortex-ring
fractal Structures of Hydrogen Atom, WCECS2009, proceedings of World Congress on Engineering
and Computer Science, San Francisco, 89-94.
[9]
OSMERA, P. (2010). Vortex-ring-fractal Structure of Atoms, journal IAENG, Engineering Letters,
Volume
18
Issue
2,
107-118,
Advance
Online
Version
Available:http://www.engineeringletters.com/issues_v18/issue_2/index.html
[10]
OSMERA, P. (2011). archived at http://www.pavelosmera.cz
[11]
PAULING, L. (1988). General Chemistry, Dover publication, Inc, New York.
ADRESS:
Prof. Ing. Pavel Ošmera, CSc.
EPI Kunovice
Osvobozeni 699,
686 04 Kunovice
Brno University of Technology,
Technicka 2,
Brno, Czech Republic
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RBF NEURAL NETWORK APPLICATIONS USING JNNS SIMULATOR
Jindřich Petrucha
Evropský polytechnický institut, s.r.o. Kunovice
Abstract: The paper deals about using artificial neural network and the architecture RBF for time
series data. The process of set up architecture is explai, the first part describes RBF function. . In
the second part is explaining.
Keywords: Neural network, JNNS, RBF architecture, time series, , neural simulator, training neural
networks
1. INTRODUCTION
The simulators of neural networks represent one of the options for the application of artificial intelligence for
decision making. There is very often necessary to observe phenomena in the economic area , that are stochastic
in nature, and it is very difficult to find exact solutions for the mathematical expression of the phenomena. For
these areas are artificial neural network simulators suitable tool. Simulators with a variant of RBF (Radial Basis
fuction) in the hidden layer, are suitable for use in the prediction of time series and other economic phenomena.
Use in practice shows very good results in their application. The application requires to set certain parameters to
during training process and during building the neural network architecture.
Differences between the type of neural network MLP and RBF
Similarities
1. They are both non-linear feed-forward networks.
2. They are both universal approximators.
3. They are used in similar application areas in practice.
Differences between MLP and RBF
1) An RBF network has a single hidden layer, whereas MLPs can have any number of hidden layers.
2) RBF networks are usually fully connected, whereas it is common for MLPs to be only partially connected.
3) In MLPs the computation nodes (processing units) in different layers share a common neuronal model,
though not necessarily the same activation function. In RBF networks the hidden nodes (basis functions)
operate very differently, and have a very different purpose, to the output nodes.
4) In RBF networks, the argument of each hidden unit activation function is the distance between the input and
the “weights” (RBF centres), whereas in MLPs it is the inner product of the input and the weights.
5) MLPs are usually trained with a single global supervised algorithm, whereas RBF networks are usually
trained one layer at a time with the first layer unsupervised.
6) MLPs construct global approximations to non-linear input-output mappings with distributed hidden
representations, whereas RBF networks tend to use localised non-linearities (Gaussians) at the hidden layer
to construct local approximations.
2. PRINCIPLE RBF ARCHITECTURE
RBF neural networks using three-layers architecture, where the first layer is used for data input and hidden layer
contains nodes that have a transfer function with radial bases. During training the neural network is necessary
for these nodes to find the centers and width, which affect the output value of the function. Very often used is
used method K-means clustering to find the centers for centroids of the individual functions of neurons in the
hidden layer. The output layer contains one neuron that represents the desired output function.
The simulators uses the these steps for k-means algorithm:
Random initialize centers of RBF function
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a/ Create groups of data to each function centers
b/ Input data Xi belongs cluster j
ll Xi-Cj ll = min ll Xi-Cj ll
c/ Find function centers
d/ Repeat step 2, until there is no more changes in each cluster
This method of processing for RBF neural network simulator SNNS is implemented by using the transfer
function of neurons with RBF. For the processing of time series of input patterns is necessary to prepare these
patterns into a text file and use this data in neural networks. Finding centers each RBF function is a matter of
software simulator. When properly designed architecture achieves this type of neural network very good results.
The parameters that should be made in the design of architecture are:
Number of neurons in the hidden layer
Number of neurons in the input layer
Both these parameters affect the speed indications. When a large number of neurons in the input layer increases
the complexity of the calculation of the centers of RBF naleení functions with the use clastrování. When large
numbers of neurons in the input layers will become much more complicated pattern and is lost genralizace neural
networks. Also there is a shortening of the length of time series on the size of neurons in the input vrsvě. These
parameters should be tested by experience podobých examples in practice.
Description of the experimental test
To experiment with the type of RBF neural network we use economic time series, where each value will be the
final hodnnoty shares. This data on the x axis represent individual days and the y-axis value of the shares from
the date 12. 1. 2011 to 11. 1. 2012. Each value shares of ORCL (Oracle) are listed in Table 1.
Date
Open
High
Low
Close
Volume
Adj
Close
12.1.2011
31,22
31,23
30,94
30,95
33962200
30,66
13.1.2011
30,97
31,39
30,9
31,18
43411700
30,89
14.1.2011
31,02
31,34
30,94
31,25
37933800
31,01
18.1.2011
31,26
31,55
31,23
31,53
26972100
31,29
…
…
…
…
…
…
…
9.1.2012
26,9
27,12
26,66
27,03
38476800
27,03
10.1.2012
27,18
27,6
26,85
26,97
48974800
26,97
11.1.2012
26,99
27,1
26,75
26,89
30832300
26,89
Table 1. input raw data fo experiment
Graphical representation of 249 stocks closing values is shown below figure 1.
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96
40
35
30
25
20
Řada1
15
10
5
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
9
106
101
116
111
126
121
136
131
146
141
156
151
166
161
176
171
186
181
196
191
206
201
216
211
226
221
236
231
246
241
256
1
0
Figure 1. closing data of shares ORCL
For experiments with a neural network simulator SNNS was chosen variant Java (JNNS), which allows
modifying the transfer function of the type of neuron RBF and implemented variants of calculations. This
simulator is very detailed in the text file for patterns and can be created by external programs to handle this file.
This method greatly simplifies the creation of an input file for testing, because each time you change the size of
the input layer is to change patterns. In the case of a manual would be necessary to carry out a large number of
operations due to human factors may carry error in the calculation.
Figure 2. RBF architecture of neural networks
The text file was created patterns using the PHP language and the input text file. This text file was created from
the excel saving only close values
After the connection we are able to browse table for the quote that we choose at the component yahoo. These
data we use for learning neural networks. The same component we have to use at the end of architecture of
neural network as a desired output.
One of the most important parts is to create temporary window as a delayed layer with delayed inputs and we
have to set up number of these inputs. Typically we choose from 4 to 15, but it depends on our experience with
time series. In the example we used 5 neurons, but the parameter of the number of neuron we can change and try
to optimize learning process. All components we ca see on the figure 2.
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Figure 3. sets of paterns in external file
Figure 4. window of process training rbf neural network
Other options for how learning RBF networks
Another option is learning RBF networks using genetic optimization methods in the first learning phase, during
which changes the layout of the center of each RBF functions. This can replace the K-means clustering
algorithm genetic and increase the speed of learning in the first phase of training RBF neural networks.
3. CONCLUSION
Using features in the architecture of RBF neural networks allows to improve the learning process, and these
networks achieve betterresults in the approximation of time series. Using the simulatorrequires setting certain
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parameters before the learning process,especially in terms of set the length of the input layer neural
network architecture. This process is linked to external programsthat generate the input patterns into text files.
LITERATURE:
[1]
MARRONE, P. JOONE JavaObject Oriented Neural Engine, The Complete Guide [online]. 2007 [cit.
2009-01-20].
Dostupný
z
WWW:
<http://heanet.dl.sourceforge.net/sourceforge/joone/JooneCompleteGuide.pdf>.
[2]
A
GUI
Example
[online].
2005
[cit.
2009-01-20].
Dostupný
z
WWW:
<http://www.jooneworld.com/docs/sampleEditor.html>.
[3]
DOSTÁL, P. Pokročilé metody analýz a modelování v podnikatelství a veřejné správě. Akademické
nakladatelství CERM: Brno, 2008, ISBN 978-80-7204-605-8.
[4]
DOSTÁL, P. Neural Network and Stock Market, In Nostradamus Prediction Conference, UTB Zlín,
1999, s8-13, ISBN 80-214-1424-3.
ADRESS:
Ing. Jindřich Petrucha, PhD.
Evropský polytechnický institute, s.r.o.
Osvobození 699
686 04 Kunovice
[email protected]
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100
OPTIMIZATION OF THE THROUGHPUT OF COMPUTER NETWORK
Imrich Rukovansky
European Polytechnical Institute Kunovice
Abstract: This paper describes the application of Two-Level Transplant Evolution (TE) in computer
network optimization. TE combines Grammatical Evolution (on the genotype level) with Genetic
Programming (tree structures on the phenotype level). To increase the efficiency of Transplant
Evolution (TE) the parallel Differential Evolution was added.
Keywords: computer network; optimization of throughput; two-level trans- plant evolution
1. INTRODUCTION
Modern methods to increase efficiency of computer networks comprise two main attributes, i.e. time needed for
solution finding and number of suitable variants of topology. The limit of the throughput of computer network is
based on the principles of clustering and using parallel evolutionary algorithms (PEA) [2], [8] –[10].
Cluster Analysis:
 different approaches (hierarchical and relational clustering, EM clustering, objective function based
clustering, fuzzy clustering, density based clustering, special techniques)
 choice of a suitable distance measures,
 cluster validity for determining the number of clusters and for checking the consistency of clustering
results,
 visualization techniques for clustering results,
 specific problems with high-dimensional data
Methods of (evolutionary techniques) can also be used on the synthesis and optimal setting of an appropriate
topology of computer networks. In the case of softcomputing methods (or more generally artificial intelligence)
they can be applied on a few major levels of research and application like: All these problems can be defined like
problems of optimization.
The aim of this paper is to describe a new optimization method that can optimize the throughput of computer
network. For this type of optimization a new method was created and we call it Two-Level Transplant Evolution
(TLTE). This method allowed us to apply advanced methods of optimization, for example direct tree reducing of
tree structure of control equation. The reduction method was named Arithmetic Tree Reducing (ART). For the
optimization of control equations of general controllers it is suitable to combine two evolutionary algorithms.
The main goal in the first level of TLTE is the optimization of the structure of general controllers. In the second
level of TLTE the concrete parameters are optimized and the unknown abstract parameters in the structure of
equations are set. The method TLTE was created by the combination of the Transplant Evolution method (TE)
and the Differential Evolution method (DE). The Transplant Evolution (TE) optimizes the structure of the
solution with unknown abstract parameters and the DE optimizes the parameters in this structure. The
parameters are real numbers. The real numbers are not easy to find directly in TE without DE. Some new
methods for evaluation of the quality of the found control equation are described here, which allow us evaluate
their quality. These can be used in the case when the simulation of the computer network cannot be finished.
The PGE is based on the grammatical evolution GE [5], where BNF grammars consist of terminals and nonterminals. Terminals are items, which can appear in the language. Non-terminals can be expanded into one or
more terminals and non-terminals. Grammar is represented by the tuple {N,T,P,S}, where N is the set of nonterminals, T the set of terminals, P a set of production rules which map the elements of N to T, and S is a start
symbol which is a member of N. For example, the BNF used for our problem is below:
N = {expr, fnc}
T = {sin, cos, +, -, /, *, X, 1, 2, 3, 4, 5, 6, 7, 8, 9}
S = <expr>
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and P can be represented as 4 production rules:
1. <expr> := <fnc><expr>
<fnc><expr><expr>
<fnc><num><expr>
<var>
2. <fnc> :=
sin
cos
+
*
U3. <var> := X
4. <num> := 0,1,2,3,4,5,6,7,8,9
The production rules and the number of choices associated with them are in Table 1. The symbol U- denotes an
unary minus operation.
rule no
1
2
3
4
choices
4
6
1
10
Table 1: The number of available choices for every production rule
There are notable differences when compared with [1]. We don’t use two elements <pre_op> and <op>, but
only one element <fnc> for all functions with n arguments. There are not rules for parentheses; they are
substituted by a tree representation of the function. The element <num> and the rule <fnc><num><expr> were
added to cover generating numbers. The rule <fnc><num><expr> is derived from the rule <fnc><expr><expr>.
Using this approach we can generate the expressions more easily. For example when one argument is a number,
then +(4,x) can be produced, which is equivalent to (4 + x) in an infix notation. The same result can be received
if one of <expr> in the rule <fnc><expr><expr> is substituted with <var> and then with a number, but it would
need more genes.
There are not any rules with parentheses because all information is included in the tree representation of an
individual. Parentheses are automatically added during the creation of the text output.
If the GE solution is not restricted anyhow, the search space can have infinite number of solutions. For example
the function cos(2x), can be expressed as cos(x+x); cos(x+x+1-1); cos(x+x+x-x); cos(x+x+0+0+0...) etc. It is
desired to limit the number of elements in the expression and the number of repetitions of the same terminals and
non-terminals.
2. BACKWARD PROCESSING OF THE GE
The chromosome is represented by a set of integers filled with random values in the initial population. Gene
values are used during chromosome translation to decide which terminal or nonterminal to pick from the set.
When selecting a production rule there are four possibilities, we use gene_value mod 4 to select a rule. However
the list of variables has only one member (variable X) and gene_value mod 1 always returns 0. A gene is always
read; no matter if a decision is to be made, this approach makes some genes in the chromosome somehow
redundant. Values of such genes can be randomly created, but genes must be present.
The Fig. 1 shows the genotype-phenotype translation scheme. The individual body is shown as a linear structure,
but in fact it is stored as a one-way tree (child objects have no links to parent objects). In the diagram we use
abbreviated notations for nonterminal symbols: f - <fnc>, e - <expr>, n - <num>, v - <var>.
3. TRANSPLANT EVOLUTION
Transplant Evolution (TE) was inspired by biological transplantation. It is an analogy to the transplant surgery of
organs. Every transplanted organ was created by DNA information but some parts of an ill body can be replaced
by a new organ from the database of organs [3]. The description parts of individual (organs) in the database are
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not stored on the level DNA (genotype). In Transplant Evolution (TE) every individual part (organ) is created by
the translation of grammar rules similar to Grammatical Evolution (GE), but Transplant Evolution (TE) does not
store the genotype and the grammatical rules are chosen randomly. The newly created structure is stored only as
a tree. This is like Genetic Programming (GP).
The Transplant Evolution algorithm (TE) combines the best properties of Genetic Programming (GP) [1] and
Grammatical Evolution (GE) [4], [5], [8], [9], and [10]. The Two-Level Transplant Evolution (TLTE) in addition
to that uses the Differential Evolution algorithm (DE). Optimization of the numerical parameters of general
controllers in recurrent control equations of general controllers is a very difficult problem. We applied the
second level of optimization by the Differential Evolution method (DE). The individuals in TE and TLTE are
represented only by a phenotype in the shape of an object tree. During the initialization of population and during
the creation of these phenotypes, similar methods are used as in GE. In Grammatical Evolution the numerically
represented chromosomes are used. The codons of these chromosomes are used for the selection of some rule
from a set of rules. In Transplant Evolution the chromosomes and codons are not used, but for the selection of
some rule from a set of rules randomly generated numbers are used. These numbers are not stored in the
individual chromosome. The new individuals in the population are created with the use of analytic and
generative grammar and by using crossover and mutation operators. These operators are projected for work with
the phenotype of an individual, similarly as in GP. Because the individuals of TE and TLTE are represented only
by phenotype, it was possible to implement these advanced methods in the course of evolution:
 an effective change of the rules in the course of evolution, without the loss of generated solutions,
 a difference of probability in the selection of rules from the set of rules and the possibility of this
changing during the evolutionary process,
 the possibility of using methods of direct reduction of the tree using algebraic operations,
 there is a possible to insert some solutions into the population, in the form of an inline entry of
phenotype,
 new methods of crossover are possible to use, (for example crossover by linking trees)
A. Initialization of individual
The Original initialization algorithm GE uses forward processing of grammatical rules. In the Grammatical
Evolution the method of crossover and mutation are made on the genotype level. The phenotype is created by a
later translation of this genotype. This way of mutation and crossover does not allow the using of advanced
method in crossover and mutation operators, which does not destruct the already created parts of the individual
[3]. During the evolution of this algorithm the Backward Processing of Rules (BPR) [2] arose [4]. The BPR
method uses gene marking.
This approach has the hidden knowledge of tree structure. Due to the BPR the advanced and effective methods
of crossover and mutation can be used. Anyhow the BPR method has some disadvantages. Due to these
disadvantages the new method Transplant Evolution (TE) was created. The TE method does not store genotype
information. The equation (1) is used for the selection of a rule from rules base. The advantage of TE is the
possibility to use both types of grammatical processing (forward and backward) with the same results, because
TE works only with the phenotype and the procedure of phenotype creation is not important. Some examples of
forward and backward initializations are shown in Fig.1 and Fig.2.
In column A are shown the randomly generated gene values. These values are not stored anywhere! The values
are generated only when is necessary to select from more grammatical rules. In column B is shown the
arithmetic operation. In column C is shown a state of rules translation, but it must be remembered that the
translation rules is done at the tree (in the nodes of the phenotype). In column F is the order of operations. These
numbers are used for a description of the tree nodes initialization order. The tree initialization is shown at
column G. Each node of the tree in column G is described by a number in the form Step X-Y. In the Step X-Y, X
represents the step in which the node was created. Y represents the step in which the node was fully initialized
(after initialization all of its subnodes).
As you can see, the finite tree structures are the same, but they have a different order of fully initialization. The
generated numbers in column A were changed too.
B Presentation of tree structures
The phenotype representation of the individual is stored in the object tree structure. Each of nodes in the tree
structure, including the sub-nodes, is an object that is specified by a terminal symbol and the type of terminal
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symbols. All nodes are independent and correctly defined mathematical functions that can be calculated, e.g. the
function x-3, is a tree structure containing a functional block (sub-tree).
Creating the object tree is a key part of TE, which this method differs from other evolutionary algorithms. When
the object tree is generated, similar methods to a traditional grammatical evolution are used. But the TE does not
store the genotype, because the production rules are selected by randomly generated genes that are not saved in
chromosomes of individuals. The final TE’s individual contains only phenotype expressed in an object tree
structure.
The algorithm of TE uses a generative grammar [4], [5], [6] whose translation process starts from the initial
symbol S and continues randomly with using the rules of defined grammar [2]. The basic procedure of the
translation algorithm is shown on Fig. 4 where is explain to why is unnecessary to store the genotype.
C Crossover
The crossover is a distinctive tool for genetic algorithms and is one of the methods in evolutionary algorithms
that are able to acquire a new population of individuals. For crossover of object trees can be used following
methods:
 crossover the parts of object trees
 crossover by linking trees or sub-trees
The method of crossover object trees is based on the selection of two parents from the population and changing
each other part of their sub-trees. For each of the parents cross points are randomly selected and their nodes and
sub-trees are exchanged. This is the principle of creating new individuals into subsequent population as is shown
on Fig. 1.

Crossover the parts of object trees (sub-trees)
Node of
crossing
Parrents
–
–
num
Node of
crossing
×
+
num
Uk
Uk
U-
DEk
num
Offsprings
–
Crossed
nodes
U-
num
×
Crossed
nodes
–
+
num
Uk
DEk
num
Uk
Fig. 1 Classical Crossover (CC)
This method, as well as the previous one, is based on the crossover of two parents who are selected from the
previous population. But the difference is in the way how the object trees are crossed. This method, unlike the
previous one, does not exchange two randomly selected parts of the parents but parts of individuals are linked
together with new and randomly generated node. This node will represent a new root of the tree structure of the
individual. This principle is shown on Fig. 2.
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Node of
crossing
Parrents
–
–
num
Uk
–
DEk
num
Randomly
generated
node
/
U-
–
U-
num
Uk
U-
Offsprings
–
num
+
num
Uk
Randomly
generated
node
Node of
crossing
×
num
num
Uk
Fig. 1. Crossover by linking method (LC Linking Crossing)
Fig. 2 Crossover by linking method
D Mutation
Mutation is the second of the operators to obtain new individuals. This operator can add new structures, which
are not included in the population so far. Mutation is performed on individuals from the old population. In the
selected individual are randomly chosen nodes which are then subjected to mutation. The mutation operator can
be subdivided into two types:
 Non-structural Mutation (NM)
 Structural Mutation (SM)
 Non-structural Mutation (NM)
Non-structural mutations do not affect the structure of already generated individual. In the individual who is
selected for mutation, chosen nodes of object sub-tree are further subjected to mutation. The mutation will
randomly change chosen nodes, whereas used grammar is respected. For example it means that mutated node,
which is a function of two variables (i.e. + - × ÷) cannot be changed by node representing function of one
variable or only a variable, etc. (see Fig. 3).
Node for
mutation
–
×
Ek-1
–
+
num
Uk
Mutated node
Non structural
mutation
Ek-1
num
Uk
Fig. 3 Nonstructural mutation
 Structural Mutation (SM)
Structural mutations, unlike non-structural mutations, affect the tree structure of individuals. Changes of the subtree by extending or shortening its parts depend on the method of structural mutations. Structural mutation can
be divided into two types: Structural mutation which is extending an object tree structure (ESM) and structural
mutation which is shortening a tree structure (SSM). This type of mutation operator can be subdivided into two
types:
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Structural
mutation
–
Ek-1
–
–
num
Uk-1
num
Ek
Shortening
Extending
Fig. 4 Structural mutation
 Extending Structural Mutation (ESM)
In the case of the extending mutation, a randomly selected node is replaced by a part of the newly created subtree that respects the rules of defined grammar (see Fig. 3). This method obviously does not always lead to the
extension of the sub-tree but generally this form of the mutation leads to extension of sub-tree. (see Fig. 4).
In view of the object tree complexity of the individual and also for subsequent crossover is preferable to have a
function in the form x = 3a than x = a + a + a, or more generally x = n × A. Another example is the shortening of
the function x = ─ (─ a), where is preferable to have the form x = a (it is removing redundant marks in the object
tree individual). The introduction of algebraic modifications of individual phenotype leads to the shorter result of
the optimal solution and consequently to the shorter presentation of the individual, shortening the time of
calculation of the function that is represented in object tree and also to find optimal solutions faster because of
higher probability of crossover in the suitable points with higher probability to produce meaningful solutions.
The essential difference stems from the use of direct contraction of trees, which leads to significantly shorter
resulting structure than without using this method.
E Hierarchical structure of TE for optimisation of the controller
The hierarchical structure of the transplant evolution can be used for optimisation of the structure and parameters
of a general controller. This structure contains three layers. First two layers (GE + DE) are contained in TE.
Those two layers are used for optimisation of the structure and parameters of general controller. The third layer
which is named layer of controller is used for computation of fitness in TE.
At the beginning of TE an initial population is created and then fitness of individuals is calculated. In the case of
finding the optimal solution in the first generation, the algorithm is terminated, otherwise creates a new
population of individuals by crossover and mutation operators, with the direct use of already created parent’s
object tree structures (it is analogy as transplantation of already created organs, without necessary know-ledge of
DNA – “Transplant Evolution (TE)”). If the result of TE needs some numerical parameters (for example num in
[10], the second level with Differential Evolution (DE) is used for optimization their parameter setting. The DE
gives better results in finding optimal values of unknown numerical parameters that are expressed in the form of
real numbers, then in the GE. Due to the use of TE for optimization of controllers in the next stage of calculation
of fitness is model of controller used which is represented by the equation in incremental form (recurrent
algorithm). Quality of controller is determined depending on the type of object function (3). For fitness
calculation are various object functions used. Basic criterion is linear control area, quadratic control area, linear
or quadratic control area extended with overshoot, oscillation of action value of the controller. We used are two
types of fitness evaluation. First is used at the beginning for creation of computer network structure and second
for optimization of parameters this structure.
4. CONCLUSION
The Two-Level Transplant Evolution (TLTE) was successfully use for automatic generation of optimal computer
network structure with the high through put. We tested this algorithm on many networks. We hope that this new
method of network design will be use in practice, not only for simulation.
The transplant evolution can be used with clustering to optimize the throughput of computer network We are far
from supposing that all difficulties are removed but first results with TEs are very promising. We have prepared
and tested optimization tools for increasing quality of computer networks
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REFERENCES
[1]
KOZA, J. R. 1992: Genetic Programming: On the Programming of Computers by Means of Natural
Selection, The MIT Press
[2]
KRATOCHVÍL, O.; OŠMERA, P.; POPELKA, O. 2009: Parallel grammatical evolution for circuit
optimization, in Proc. WCECS, World Congress on Engineering and Computer Science, San
Francisco, 1032-1040.
[3]
LI, Z.; HALANG, W. A.; CHEN, G. 2006: Integration of Fuzzy Logic and Chaos Theory; paragraph:
Osmera P.: Evolution of Complexity, Springer, pp. 527 – 578.
[4]
O’NEILL, M.; RYAN, C. 2003: Grammatical Evolution: Evolutionary Automatic Programming in an
Arbitrary Language Kluwer Academic Publishers.
[5]
O’NEILL, M.; BRABAZON, A.; ADLEY, C. 2004: The Automatic Generation of Programs for
Classification Problems with Grammatical Swarm, Proceedings of CEC, Portland, Oregon, pp. 104 –
110.
[6]
PIASECZNY, W.; SUZUKI, H.; SAWAI, H. 2004: Chemical Genetic Programming – Evolution of
Amino Acid Rewriting Rules Used for Genotype-Phenotype Translation, Proceedings of CEC,
Portland, Oregon, pp. 1639 - 1646.
[7]
PRICE, K. 1996. Differential evolution: a fast and simple numerical optimizer, Biennial Conference of
the North American Fuzzy Information Processing Society, NAFIPS, IEEE Press, New York, NY, pp.
524-527.
[8]
RUKOVANSKÝ, I. Optimization of the throughput of Computer Network Based on Parallel EA. In
Proceedings of the World Congress on Engineering and Computer Science WCECS 2009, San
Francisco, CA, Oct. 20-22, 2009, Vol. II, pp. 1038-1043
[9]
WEISSER, R.; OŠMERA, P.; MATOUŠEK, R. Transplant Evolution with Modified Schema of
Differential Evolution: Optimization Structure of Controllers. In International Conference on Soft
Computing MENDEL. Brno : MENDEL, 2010, pp.113 - 120
[10]
WEISSER, R.; OŠMERA, P.; ŠEDA, M.; KRATOCHVÍL, O. Transplant Evolution for Optimization
of General Controllers. In European Conference on Modelling and Simulation. 24th. Kuala Lumpur
(Malaysia) : ECMS 2010, pp. 250 -- 260.
ADRESS:
Prof. Ing. Imrich Rukovanský, CSc.
Evropský polytechnický institute, s.r.o.
Osvobození 699
686 04 Kunovice
[email protected]
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MINISATION OF COMPLEXLOGICAL FUNCTIONS
Miloš Šeda
European Polytechnical Institute, Ltd. Kunovice
Abstract: Finding the minimal logical functions has important applications in the design of logical
circuits. This task is solved by many different methods but, frequently, they are not suitable for a
computer implementation. We briefly summarise the well-known Quine-McCluskey method, which
gives a unique procedure of computing and thus can be simply implemented, but, even for simple
examples, does not guarantee an optimal solution. Since the Petrick extension of the QuineMcCluskey method does not give a generally usable method for finding an optimum for logical
functions with a high number of values, we focus on interpretation of the result of the QuineMcCluskey method and show that it represents a set covering problem that, unfortunately, is an NPhard combinatorial problem. Therefore it must be solved by heuristic or approximation methods.
We propose an approach based on genetic algorithms and show suitable parameter settings.
Keywords: Boolean algebra, Karnaugh map, Quine-McCluskey method, set covering problem,
genetic algorithm.
1. INTRODUCTION
For minimisation of logical functions, laws of the Boolean algebra and the Karnaugh maps are mostly used. The
Karnaugh maps represent a very efficient graphical tool for minimising logical functions with no more than 6
variables. However, their use is based on visual recognition of adjacent cells and, therefore, the method is not
suitable for automated processing on computers. A direct application of the Boolean algebra laws is not
restricted in this way, but there is no general algorithm defining the sequence of their application and thus this
approach is not suitable for computer implementation either.
With the growing strength of computational techniques, further investigations were focused on an algorithmbased technique for simplifying Boolean logic functions that could be used to handle a large number of
variables.
The well-known method usable on computers is the algorithm proposed by Edward J. McCluskey, professor of
electrical engineering at University of Standford, and philosopher Willard van Orman Quine from Harvard
University [13], [18].
We will assume that the number of variables n may be high but restricted in the sense that all 2n rows of the
corresponding truth table may be saved in a memory and thus may be processed. If this condition is not satisfied,
then we could only work with a selected number of truth table rows. This approach is possible, e.g., in image
filters [19]. Of course, this is inacceptable in real logic control applications where all input combinations must be
tested. In the next considerations we will assume the full truth table.
2. QUINE-MCCLUSKEY METHOD
The Quine-McCluskey method [13], [17], [18] is an exact algorithm based on systematic application of the
distributive law (1), complement law (2) and idempotence law (3), i.e. the laws as follows:
x.( y  z )  xy  xz
(1)
x  x  1 (2)
x  x  x (3)
From (1) and (2), we can easily derive the uniting theorem (4)
xy  x y  x.( y  y)  x.1  x (4)
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In general, this means that two expressions with the same set of variables differing only in one variable with
complementary occurrence may be reduced to one expression given by their common part, e.g.
f  xyzw  xyzw  xzw( x  x)  xzw.1  xzw
For next considerations we will need the following notions:
Literal is a variable or its negation.
Term is a conjunction (= product) of literals.
Minterm is a conjunction of literals including every variable of the function exactly once in true or
complemented form.
For example, if , then and are terms and minterms are represented by conjunctions and because .
Disjunctive normal form (DNF) of a formula f is a formula f’ such that f’ is equivalent to f and f’ has the form of
a disjunction of conjunctions of literals.
Canonical (or complete) disjunctive normal form (CDNF) is a DNF where all conjunctions are represented by
minterms.
Now we can describe a skeleton of the Quine-McCluskey method:
1.
Minterms of a given Boolean function in CDNF are divided into groups such that minterms with the
same number of negations are in the same group.
2.
All pairs of terms from adjacent groups (i.e. groups whose number of negations differ by one) are
compared.
3.
If compared terms differ only in one literal (and the uniting theorem may be applied) then these terms
are removed and a term reduced to a common part is carried to the next iteration.
4.
All terms are used only once, i.e. if necessary the idempotence law is applied.
5.
If the number of terms in the new iteration is nonzero, then steps 2-5 are repeated, otherwise the
algorithm finishes.
The result of the algorithm is represented by the terms that were not removed, i.e. that could not be simplified.
Now, we will apply the Quine-McCluskey method to a simple logical function from [5] and, by means of the
Karnaugh map, we will show that it will not find its minimal form.
Example 1 Minimise the following logical function in CDNF.
f  x yzw  x y zw  xyz w 
 x yz w  x y z w  xyz w  x y zw  x y z w 
 x y zw
Solution: If we divide the minterms into groups by the number of their negations, then we get this initial
iteration:
(0)
xyzw ; x yzw ; xyzw ;
xyzw ; x y zw ; xyz w ; x y zw ; x y z w ;
x y zw
If we compare all pairs of terms from adjacent groups in the initial iteration (0) and place in frames terms that
can be simplified and divide the resulting terms in the next iteration (1) into groups again, then we get:
(0)
xyzw ; x yzw ; xyzw ;
xyzw ; x y zw ; xyz w ; x y zw ; x y z w ;
x y zw
(1)
x yz ; x zw ; x y z ; y zw ; x y w ; xyz ; xz w ;
xzw ; y zw ; x y z ;
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Applying the previous steps to iteration (1), we get:
(1)
xyz ; xzw ; x y z ; y zw ; x yw ; xyz ; xzw ;
xzw ; y zw ; x y z ;
(2)
xz ; y z
In iteration (2) we have only one group of terms and thus no simplified terms can be generated and the algorithm
finishes. Its result fm is given by a disjunction of those terms that cannot be simplified.
f m  xz  y z  x yw  xyz  xzw
Let us consider the same example and solve it using the Karnaugh map. For the given Boolean function f, we get
the following map
x
w
1
1
1
1
1
1
1
1
1
y
z
Fig. 1 Karnaugh map
From this map, we get two possible solutions of a minimal logical function depending on the way of covering
the first two cells with logical 1 in the last columns.
a) f1min  xz  yz  xyw  xyz
b) f 2 min  xz  yz  xzw  xyz
We can see that the result gained using Karnaugh map includes a lower number of terms than the result of
computation by means of Quine-McCluskey method.
S. R. Petrick proposed a modification of Quine-McCluskey method that tries to remove the resulting redundancy
[16]. The Quine-McCluskey simplification technique with special modifications is presented in [21].
Before describing the second phase of computation, we will define several notions.
(i)
A Boolean term g is an implicant of a Boolean term f if:
 each literal in g is also obtained in f (i.e. if g has the form g(x1, ... , xn) then f has the form f(x1, ... , xn,
y1, … , ym)), and
 for all combinations of literals the implication g  f has a value of True.
We know that the implication is defined by Table 1. From this definition, we get that g is an implicant of f if and
only if g  f.
In our case, that means that the second property is satisfied if g(x1, ... , xn)  f(x1, ... , xn, y1, … , ym) for each
selection of x1, ... , xn and each selection of y1, … , ym.
g
0
0
1
1
TABLE 1
IMPLICATION
f
0
1
0
1
g f
1
1
0
1
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Therefore, we can consider only those values of variables at which g is true and, for all these cases, f must also
be true.
(ii)
The terms resulting from the Quine-McCluskey method are called prime implicants.
In the Petrick modification of the Quine-McCluskey method, a table of prime implicants given by the results of
the first phase is built. It has prime implicants in the heads of columns, minterms from a given CNDF are in the
heads of rows and, in cells representing intersection
the prime implicant in question is a subset of a corresponding minterm. We say that prime implicants cover
minterms.
In our example then we get Table 2 as follows.
Although the prime implicants cannot be simplified, some of them can be redundant and thus may be omitted.
disjunction of prime implicants would not express the initial canonical (complete) disjunctive normal form, i.e.,
there would be a non-covered minterm.
omitted. Such implicants are called essential prime implicants. In our example there are three essential prime
implicants: , and .
symbols. We get Table 3.
TABLE 2
COVERING OF MINTERMS BY PRIME IMPLICANTS
xz
xyzw
yz
xy w


xyzw



xyz w



xy zw
x y zw


x y zw
x y zw
xz w

x y zw
xyzw
xy z



TABLE 3
xy zw
xy w
xz w


It can be easily seen that, in simplified Table 3, the minterm x y z w may be covered by the prime implicant
x y w or by xzw . Hence we get two minimal disjunctive forms:
f1min  xz  yz  xyw  xyz and
f 2 min  xz  yz  xzw  xyz ,
which agrees with the previous solution by the Karnaugh map.
Although computations by the Quine-McCluskey method with the Petrick modification have a wider use than the
approach based on the Karnaugh map, however, this improved method has also its restrictions. The main
problem is in the procedure of covering minterms by prime implicants. It can be easily found if the number of
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the essential prime implicants is high and thus the table of prime implicants will be very reduced. In general, we
cannot expect this, and it is even possible that none of the prime implicants is essential. From the combinatorial
optimisation theory, it is known that the set covering problem is NP-hard and its time complexity grows
exponentially with the growing input size.
It can be shown that, for a CNDF with n minterms, the upper bound of the number of prime implicants is 3n/n. If
n=32, we can get more than 6.5 * 1015 prime implicants. To solve such a large instance of the set covering
problem is only possible by heuristics (stochastic or deterministic) [1], [2], [4], [6], [10], [11], [14], [15], [20],
[22] or by approximation [7], [8] methods. However, they do not guarantee an optimal solution.
A formal definition of the problem and possible solution by a genetic algorithm is proposed in the next section.
3. SET COVERING PROBLEM (SCP)
The set covering problem (SCP) is the problem of covering the rows of a m-row, n-column, zero-one matrix (aij)
by a subset of columns at a minimal cost. Defining xj1 if column j (with cost cj0) is in the solution and xj0
otherwise, the SCP is:
n
Minimise
cjxj
(5)
j 1
subject to
n
 aij x j  1, i  1, 2,..., m, (6)
j 1
x j {0,1}, j  1, 2,..., n
(7)
Constraints (6) ensure that each row is covered by at least one column and (7) is a constraint guaranteeing
integers.
In general, the cost coefficients cj are positive integers. Here, in the application of the SCP for the second phase
of the Quine-McCluskey method, we assume all cj equal to 1 because we try to minimise the number of the
covering columns. This special case of SCP is called a unicost SCP. 
SCP has, besides Quine-McCluskey method, a wide range of applications, for example vehicle and crew
scheduling [12], facilities location [1], assembly line balancing and Boolean expression simplification. There are
number of other combinatorial problems that can be formulated as, or transformed to, SCP such as the graph
colouring problem [1] and the independent vertex set problem [7].
A fuzzy version of SCP is studied in [3] and [9].
Since we use, for solving the SCP, a modified version of the genetic algorithm (GA) proposed by Beasley and
Chu [2], [4] for the non-unicost SCP, we summarise the basic properties of GAs.
4. GENETIC ALGORITHM
The skeleton for GA can be described as follows:
generate an initial population ;
evaluate fitness of individuals in the population ;
repeat
select parents from the population;
recombine (mate) parents to produce children ;
evaluate fitness of the children ;
replace some or all of the population by the children
until a satisfactory solution has been found ;
Since the principles of GAs are well-known, we will only deal with GA parameter settings for the problems to be
studied. Now we describe the general settings.
Individuals in the population (chromosomes) are represented as binary strings of length n, where a value of 0 or
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1 at the i-th bit (gene) implies that xi = 0 or 1 in the solution respectively.
The population size N is usually set between n and 2n. Many empirical results have shown that population sizes
in the range [50, 200] work quite well for most problems.
Initial population is obtained by generating random strings of 0s and 1s in the following way: First, all bits in all
strings are set to 0, and then, for each of the strings, randomly selected bits are set to 1 until the solutions
(represented by strings) are feasible.
The fitness function corresponds to the objective function to be maximised or minimised.
There are three most commonly used methods of selection of two parent solution for reproduction: proportionate
selection, ranking selection, and tournament selection. The tournament selection is perhaps the simplest and most
efficient among these three methods. We use the binary tournament selection method where two individuals are
chosen randomly from the population. The more fit individual is then allocated a reproductive trial. In order to
produce a child, two binary tournaments are held, each of which produces one parent.
The recombination is provided by the uniform crossover operator, which has a better recombination potential
than do other crossover operators as the classical one-point and two-point crossover operators. The uniform
crossover operator works by generating a random crossover mask B (using Bernoulli distribution) which can be
represented as a binary string B = b1b2b3 ··· bn-1bn where n is the length of the chromosome. Let P1 and P2 be the
parent strings P1[1], ... ,P1[n] and P2[1], ... ,P2[n] respectively. Then the child solution is created by letting:
C[i] = P1[i] if bi = 0 and C[i] = P2[i] if bi = 1. Mutation is applied to each child after crossover. It works by
inverting M randomly chosen bits in a string where M is experimentally determined. We use a mutation rate of
5/n as a lower bound on the optimal mutation rate. It is equivalent to mutating five randomly chosen bits per
string.
When v child solutions have been generated, the children will replace v members of the existing population to
keep the population size constant, and the reproductive cycle will restart. As the replacement of the whole parent
population does not guarantee that the best member of a population will survive into the next generation, it is
better to use steady-state or incremental replacement which generates and replaces only a few members
(typically 1 or 2) of the population during each generation. The least-fit member, or a randomly selected member
with below-average fitness, are usually chosen for replacement.
Termination of a GA is usually controlled by specifying a maximum number of generations tmax or relative
improvement of the best objective function value over generations. Since the optimal solution values for most
problems are not known, we choose tmax  5000.
5. GENETIC ALGORITHM FOR SCP
The chromosome is represented by an n-bit binary string S where n is the number of columns in the SCP. A
value of 1 for the j-th bit implies that column j is in the solution and 0 otherwise.
Since the SCP is a minimisation problem, the lower the fitness value, the more fit the solution is. The fitness of a
chromosome for the unicost SCP is calculated by (8).
n
f ( S )   S[ j ] (8)
j 1
The binary representation causes problems with generating infeasible chromosomes, e.g. in initial population, in
crossover and/or mutation operations. To avoid infeasible solutions a repair operator is applied.
Let
I = {1, … , m} = the set of all rows;
J = {1, … , n} = the set of all columns;
 i = {jJ | aij 1}
= the set of columns that cover row i, iI;
 j = {iI | aij 1}
= the set of rows covered by column j, jJ;
S = the set of columns in a solution;
U = the set of uncovered rows;
wi = the number of columns that cover row i, iI in S.
The repair operator for the unicost SCP has the following form:
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initialise wi : = | S   i | , i  I ;
initialise U : = { i | wi = 0 , i  I } ;
for each row i in U (in increasing order of i) do
begin find the first column j (in increasing order of j)
in  i that minimises 1/ |U   j | ;
S:=S+j;
wi : = wi + 1, i  j ;
U:=Uj
end ;
for each column j in S (in decreasing order of j) do
if wi  2 , i  j
then
begin S : = S  j ;
wi : = wi  1, i  j
end ;
{ S is now a feasible solution to the SCP and contains no redundant columns }
Initialising steps identify the uncovered rows. For statements are “greedy” heuristics in the sense that in the 1 st
for, columns with low cost-ratios are being considered first and in the 2nd for, columns with high costs are
dropped first whenever possible.
6. CONCLUSION
In this paper, we studied the problem of minimising the Boolean functions with a rather high number of
variables. Since traditional approaches based on the Boolean algebra or Karnaugh maps have restrictions in the
number of variables and the sequence of laws that could be applied is not unique, we focus on the well-known
Quine-McCluskey method. Since it does not guarantee the finding of an optimal solution, we must apply a
postprocessing phase. Unfortunately, the data resulting from the Quine-McCluskey method are in the form of a
unicost set covering problem, which is NP-hard. Therefore, for logical functions, the obvious Petrick’s extension
of the Quine-McCluskey method cannot be applied, and heuristic or approximation method must be used instead.
We proposed a genetic algorithm-based approach and discussed problem-oriented parameter settings.
In the future, we are going to implement also other stochastic heuristics, such as simulated annealing and tabusearch, and compare them with the genetic algorithm.
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ADRESS:
Prof. RNDr. Miloš Šeda, Ph.D.
European Polytechnical Institute, Ltd.
Osvobození 699,
686 04 Kunovice, Czech Republic
e-mail: [email protected], [email protected]
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PERFORMANCE MODELLING OF MULTIPROCESSOR PARALLEL SYSTEMS
Dan Slovaček
European polytechnic institute, Kunovice
Abstract: The using of parallel principles is the most effective way how to increase the performance
of applications (parallel computers and algorithms). In this sense the paper is devoted to
performance modelling of parallel computers. Therefore the paper describes the typical parallel
computers and then he summarised the basic concepts performance modelling of them. Current
trends in high performance computing (HPC) and grid computing (Grid) are to use networks of
workstations (NOW) as a cheaper alternative to traditionally used massively parallel
multiprocessors or supercomputers. There has been an increasing interest in the use of networks of
workstations connected together by high speed networks (Fig.2) for solving large computation
intensive problems. This trend is mainly driven by the cost effectiveness of such systems as
compared to massive multiprocessor systems with tightly coupled processors and memories
(Supercomputers). Parallel computing on a cluster of workstations connected by high speed
networks has given rise to a range of hardware and network related issues on any given platform.
Keywords: parallel computer, virtual parallel system, network of workstations, performance
modelling
1. INTRODUCTION
Principal example of networks of workstations also for solving large computation intensive problems is at Fig. 1.
The individual workstations are mainly extreme powerful personal workstations based on multiprocessor or
multicore platform. Parallel computing on a cluster of workstations connected by high speed networks has given
rise to a range of hardware and network related issues on any given platform.
PC 1
PC 2
PC 3
...
PC n
- Myrinet switch
- Myrinet ports
- 1G Ethernet (10G Ethernet) ports
Fig.1. Architecture of NOW (Myrinet, Ethernet, Infiniband etc.).
With the availability of cheap personal computers, workstations and networking devises, the recent trend is to
connect a number of such workstations to solve computation intensive tasks in parallel on various integrated
forms of NOW. Fig. 2 illustrates typical complex integrated module of NOW networks.
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GRID Modul
(SMP, NOW)
Laboratory 1
1
Switch 1
i
1
2
Laboratory 2
1
Switch 2
i
Switch n
(central)
.
.
.
Laboratory n -1
1
Switch n -1
i
Router
i
Fig.2. Integration of NOW networks.
2. THE ROLE OF PERFORMANCE
Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for
the delivery of high performance. Performance studies apply to initial design phases as well as to procurement,
tuning and capacity planning analysis. As performance cannot be expressed by quantities independent of the
system workload, the quantitative characterisation of resource demands of application and of their behaviour is
an important part of any performance evaluation study [1, 2, 3]. Among the goals of parallel systems
performance analysis are to assess the performance of a system or a system component or an application, to
investigate the match between requirements and system architecture characteristics, to identify the features that
have a significant impact on the application execution time, to predict the performance of a particular application
on a given parallel system, to evaluate different structures of parallel applications. In order to extend the
applicability of analytical techniques to the parallel processing domain, various enhancements have been
introduced to model phenomena such as simultaneous resource possession, fork and join mechanism, blocking
and synchronisation. Modelling techniques allow to model contention both at hardware and software levels by
combining approximate solutions and analytical methods. However, the complexity of parallel systems and
algorithms limit the applicability of these techniques. Therefore, in spite of its computation and time
requirements, simulation is extensively used as it imposes no constraints on modelling.
Evaluating system performance via experimental measurements is a very useful alternative for parallel systems
and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim
at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all
types of performance studies, their main field of application is competitive procurement and performance
assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by
providing a wider a wider set of suites that exercise each system component targeted workload.
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3. PERFORMANCE MODELLING
To evaluating parallel algorithms there have been developed several fundamental concepts. Tradeoffs among
these performance factors are often encountered in real-life applications. To the performance evaluation we can
use following methods
 analytical methods
 application of queuing theory results [1 4, 14]
 asymptotic analyses [7, 8, 9]
 simulation methods [12]
 benchmarks [5, 10, 13]
 direct measuring (parallel computers and algorithms) [6, 12].
Evaluating system performance via experimental measurements is a very useful alternative for parallel systems
and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim
at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all
types of performance studies, their main field of application is competitive procurement and performance
assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by
providing a wider a wider set of suites that exercise each system component targeted workload.
3.1. THE ANALYTICAL APPROACH
For the mathematical model of the computer networks it is necessary to specify
 statistical character of the input demand stream (the input stream of data unities, number and length of
data unities etc.)
 servicing network (the servicing nodes, topology of servicing network, number of servicing devices,
servicing types, servicing character etc.)
 servicing times
 a way of servicing (FIFO – First In First Out, LIFO – Last In First Out, servicing with priorities)
 limited or unlimited number of buffers for sorting the transmitted data unities and the algorithms of
their assigning.
To the most existed mathematical models we do not know their exact analytical solution. The main causes which
complicate of analytical solution are
 the specific distribution of real data flows
 the complicated servicing structures
 the mutual dependencies of the wanted values and control data flows
 the complications in the control activities of the real system (priorities, physical limitations of the used
system components as for example of the used system components as for example waiting queues,
interrupted activities of the devices etc.).
For the analytical solutions they are from the point of solution complexity the most suitable the models with
exponential random distribution (for example the inter arrival input times or servicing time etc.) In the cases in
which we are not able to approximate the real variables with no defined random distributions the analytical
solution is unable even in the simplest cases.
3.2 THE SIMULATION METHOD
This method is based on the simulation of the basic characteristics that are the input data stream and their
servicing according the measured and analyzed probability values simulate the behaviour model of the analyzed
system. Its part is therefore the time registration of the wanted interested discrete values. The result values of
simulation model have always their discrete character (discrete numerous values), which do not have the
universal form of mathematical formulas to which we can set when we need the variables of the used
distributions as in the case of analytical models. The accuracy of simulation model depends therefore on the
accuracy measure of the used simulation model for the given task.
It is very important to find the suitable dividing line of the application using of both methods. For the application
area of the distributed computer system it is very effective their mutual interlace and complementation. For
example for the behaviour analyze of the independent queuing theory system is in principal simpler to use the
derived analytical results. In case of serially connected queuing theory systems the outgoing method is the
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simulation because the application of the analytical methods is very problematic. In common the using of
simulation method is mainly in following cases
 models have large number of variables and function, which are changing in time intervals
 variables are influenced through various disturbing influences of random character with various
distributions and with many mutual structures
 models are mutual connected with particular models of various operations and the possibility of
outstanding intervention
 existence of limitations in trajectories of model variables an limits in model combinations
 no existence of any suitable analytical method and therefore the using of simulation method is the only
analyzing tool.
Even if the discrete simulation can contribute to the behaviour analyze of the distributed computer network for
the analysis of the large complex computer networks is very unpractical and unusable. His disadvantage is also
that the achieved results are not universal. But it is very useful in these cases in which we are not able apply any
analytical method and so the simulation methods is the only analytical tool or in cases in which exist only
approximate analytical methods and the simulation became the verification tool of achieved analytical results.
4. PERFORMANCE CRITERIONS
4.1. PERFORMANCE TESTS
 Classical
 Peak performance

Dhrystone

Whetstone

LINPAC

Khornestone
 Problem oriented tests (Benchmarks)
 SPEC tests
4.2. SPEC TESTS
4.2.1. SPEC RATIO
SPEC (Standard performance evaluation corporation - www.spec.org) defined one number to summarise all
needed tests for integer number. Execution times are at first normalised through dividing execution time by value
of reference processor (chosen by SPEC) with execution time on measured computer (user application program).
The achieved ratio is labelled as SPEC ratio, which has such advantage that higher numerical numbers represent
higher performance, that means that SPEC ratio is an inversion of execution time. INT 20xx (xx means year of
latest version) or CFP 20xx result value is produced as geometric average value of all SPEC ratios.
The relation for geometric average value is given as
n
n
 normalised execution time
i 1
i
, where normalised execution time is the execution time normalised by reference computer for i – th tested
program from whole tested group n (all tests) and
n
a
i 1
i
 product of individual ai .
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4.2.2. SPEC INT RESULTS
SPEC INT results for AMD Operon X4 model are in Tab.1. 1.
Description
Name
Instr. count CPI
[10 9]
String processing Perl
2 188
0,75
Clock
cycle
time
[ns]
0,4
637
9 770
15,3
Block-sorting
compression
GNU
C compiler
Combinatorial
optimisation
Go game
bzip2
2 389
0,85
0,4
817
9 650
11,8
Gcc
1 050
1,72
0,4
724
8 050
11,14
mcf
336
10,00
0,4
1 345
9 120
6,8
go
1 658
1,09
0,4
721
10 490
14,6
Search
gene hmmer
sequence
Chess game (AI) sjeng
2 783
0,80
0,4
890
9 330
10,5
2 176
0,96
0,4
837
12 100
14,5
Quantum
Libquantum
computer
simulation
Video
h264avc
compression
Discrete
event omnetpp
simulation library
Games/path
astar
finding
XML parsing
xalancbmk
1 623
1,61
0,4
1 047
20 720
19,8
3 102
0,80
0,4
993
22 130
22,3
587
2,94
0,4
690
6 250
9,1
1 082
1,79
0,4
773
7 020
9,1
1 058
2,70
0,4
1 143
6 900
Geometric mean
Execution
time
[s]
Reference
time
[s]
SPEC
ratio
6,0
11,7
Tab.1.1. SPEC INT results for AMD Opteron X4 model 2356.
5. REAL MODELS
Generally model is the abstraction of the system. The functionality of the model represents the level of the
abstraction applied. That means, if we know all there is about the system and are willing to pay for the
complexity of building a true model, the role of abstraction is near nil. In practical cases we wish to abstract the
view we take of a system to simplify the complexity of the real system. We wish to build a model that focuses on
some basic elements of our interest and leave the rest of real system as only an interface with no details beyond
proper inputs and outputs. Real system is a real process or system that we wish to model. In our case it is the
process of performance of parallel algorithms (PA) for used parallel computers (SMP, NOW, GRID).
The basic conclusion is that a model is a subjective view of modeller’s subjective insight into modelled real
system. This personal view defines what is important, what the purposes are, details, boundaries, and so one.
Therefore the modeller must understand the system in order to guarantee useful features of the created model.
6. CONCLUSIONS
In our home conditions we have been intensively dealing with virtual parallel systems based on network of
personal computers (SMP, NOW) for many years and in later four years also with more complex Grid system.
Based on mentioned virtual parallel architectures we developed real models according Fig.3. to analyse their
complexity and performance. We will referee to them in next articles. Now according current trends in virtual
parallel computers (SMP, NOW, Grid), based of powerful personal computers and also Internet computing
(Cloud computing), we are looking for a flexible model of virtual parallel computer that supports both parallel
and distributed computers. In such unified model we would like to study load balancing, inter-process
communication (IPC), transport protocols, performance prediction etc. We would refer to results later in
scientific journals.
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Fig. 3. Real performance modelling.
The intent of this paper is to evolve the important role of performance modelling for actual parallel computer
(NOW, Grid) for solving complex problems, which are widely present also in other scientific areas than only in
to this time mainly analysed complex problems from application informatics.
REFERENCES
[1]
GELENBE, E. Computer system performance modeling in perspective, 288 pages, published September
2006, Imperial College Press.
[2]
HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, United
Kingdom : Kybernetes, Volume 39, No.1, 2010, pp. 107- 126.
[3]
HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011,
Kunovice : sekcia č. 2, pp 125 - 132, Czech republic
[4]
HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, Kunovice :
Czech republic (in print).
[5]
HANULIAK, P.; SLOVÁČEK, D. To performance modeling of virtual computers, In Proc.:
TRANSCOM 2011 - section 3, Žilina : pp. 213 – 216, 2011.
[6]
HUDIK, M. Performance optimization of broadcast collective operation on multi-core cluster, ICSC
Leden 2012, Kunovice : Czech republic (in print).
[7]
HUDIK, M.; HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System
Equations, In Proc.: GCCP 2011, October 24-26, Bratislava : pp. 70-77, 2011, SAV Institute of
Informatics.
[8]
HUDIK, M.; HANULIAK, P. Parallel complexity of linear system equation, In Proc.: TRANSCOM
2011 - section 3, Žilina : pp. 107-110, 2011.
[9]
JANOVIČ, F. Modelovanie výkonnosti distribuovaných paralelných algoritmov, ICSC Leden 2012,
Kunovice : Czech republic (in print)
[10]
KIRK, D. B.; HWU, W. W. Programming massively parallel processors, Morgam Kaufmann, 280
pages, 2010
[11]
KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking , 750 pp., 2004, Morgan
Kaufmann
[12]
LILJA, D. J.; Measuring Computer Performance, United Kingdom : 2005, University of Minnesota,
Cambridge University Press. 280 p.
[13]
PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan
Kaufmann, 2009.
[14]
SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, Hradec
Králové : pp. 42-51, 2010, 6.-10 Prosinec, Czech republic
ADDRESS:
Mgr. Dan Slovaček
European Polytechnic Institute
Osvobozeni 699
686 04, Kunovice
[email protected]
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DESIGN AND CONSTRUCTION OF EXPERT SYSTEM FOR ANALYSIS OF
RECREATION ATTRACTIVENESS
Yaroslav Vyklyuk, Olga Artemenko
Bucovinian University, Ukraine
This paper describes designing and developing an expert system for analysis of territory
recreational attractiveness. An analysis of recent researches was done to find an optimal
combination of intelligent methods of modeling to meet the capabilities of geographic information
systems to support decisions and forecasting in tourism.
Keywords: fuzzy logic, expert system, recreation attractiveness.
INTRODUCTION
Tourism can be a major push factor for socio-economic development. After all, tourism is not only provides a
large number of jobs in services, but also affects the development of such industries as transportation,
construction, trade, communications and entertainment industry. In addition, tourism has a high profitability, and
is less capital-intensive than other types of business activity [1].
Tourism includes many species and fields. The combination in time and space tourist related services,
recreational resources, and infrastructure is a difficult task. Therefore, predicting the spatial location, operation
and development of tourism and recreation systems using mathematical and intelligent methods of data analysis
is one of the important directions of research.
Among other things, information about promising for the creation and development of tourism infrastructure
area, are interested not only investors but also state and local authorities. It can identify promising areas of
recreation will find attractive for investment objects, as well as in scientific basis for the strategy of economic
development of tourism in the regions.
PURPOSE AND RESEARCH ACTUALITY
A research purpose was to build a conceptual model of expert system analysis of recreational attractiveness of
the area, allowing an analysis of attractiveness for tourism business and tourism and recreation systems in the
region to the scientific study of their development strategy.
Research actuality was to explore the possibilities of using information technology for solving the problem of
assessment, optimization and forecasting in tourism.
The practical value of the study: the structure of expert system is built and types and directions of information
flows are defined. We also show how to implement such an expert system.
DEVELOPMENT OF A CONCEPTUAL MODEL OF EXPERT SYSTEM
Analysis of information technology used in the world to study and optimization of Tourism shows that most
research focuses on modeling and optimization of existing tourist and recreation systems. The problem of
modeling of the origin and dynamics of development of new tourism and recreation systems is not solved. The
main objective is to choose the optimal location for building, structure prediction of tourist flows, the choice of
optimal strategy performance, forecasting and management of spatial development of urban areas. So, based on
analysis of collected data can be considered tasks that need to be addressed through the development and
improvement of information technology for tourism are: calculation of attractiveness of the territory and spatial
distribution of urbanization.
The attractiveness of the area for tourists is determined by many factors, including qualitative and often
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subjective. In order to analyze the attractiveness of large areas statistical information should be collected.
Geographical characteristics of the territory can be obtained from databases of geographic information systems.
Unlike the widely used classical methods of modeling attractiveness of the area, the apparatus of fuzzy logic not
only allows you to work with parameters, in which there is linguistic ambiguity, but also greatly simplifies the
process of getting a result [2].
A number of studies on tourism, also used fuzzy modeling. For example, the definition of tourist flows in the
U.S. [3], a site selection expert system [4]. Determining the optimal location of international hotels have made
on the basis of fuzzy logic in [5]. Building models that describe aspects of the functioning of the tourism
industry and forecasting processes in her devoted work [6-8]. In addition, forecasting under uncertainty (eg, the
demand for tourist services) can be implemented using fuzzy models [9]. Cellular automata are used to predict
the development of urban infrastructure in the software iCity [10].
A research purpose was to create software that will allow the user to make informed and effective decisions on
tourism businesses. Users are creating an expert system should become entrepreneurs, tourism industry experts
and officials of regional governments and local authorities, whose job in some way connected with tourism.
Analysis of the domain allowed a list of tasks that should solve the effective expert system analysis of the
attractiveness of the area. Developed by the expert system should solve the problem:
 Decisions about the advisability of investing in tourism in the area;
 Making decisions for optimizing the list of travel services for some existing tourist and recreational
facility (TRO);
 Evaluation of recreational resources and decision-making regarding the possibility of their use;
 Localization of areas with the most favorable conditions for building tourist facilities;
 Making decisions on the development of transport and social infrastructure to facilitate the development
of tourist business.
The external environment
The simulation
results
Problems to be
solved
Statistical data
User
Expert
Knowledge
Spot territory
attractiveness
Decisions on
investment
5
Territory parameters
GIS
Roads, water, slope height,
forests, urbanization,
geographic coordinates of
objects
Population
Territory parameters
The amount of
services provided
3
DB
Integral territory
attractiveness
Optimization of the
list of tourist
services
Territiry
2
Rules
Modeling of territory
attractiveness
1
Convert geodata in the
matrix of input
parameters
knowledge
training
Spatial distribution
of recreational
attractiveness
Spot recreational
potential
Matrixes of
attractiveness
Estimation of
recreational
resources
Determination of
optimal areas for
development
Rules
Modeling of
recreational potential
Territory
Transport and accommodation
infrastructure
Integral recreational
potential
Decisions on
development of
transport and social
infrastructure
The existing infrastructure,
limitation
Expert system
Forecast maps of
the spatial
distribution round.
infrastructure
4
Modeling of the
development of tourism
infrastructure
Terrytory, forcast time
horizon
Picture 1. The conceptual model of expert system
CONCLUSIONS
This paper describes the structure of an expert system for calculation and analysis of recreational attractiveness
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of territory. This expert system enable to define perspective places for developing tourist infrastructure. The
maps of spatial distribution of territory attractiveness, produced with our expert system, allow monitoring the
change of territory’s attractiveness during a year.
First of all, the offered method will allow the tourist industry investors to elect more effectively direction and
dimensions of capital investments in planning their strategy, arranging PR-actions.
Secondly, the regional government gets a scientific base which allows to make effective strategy for regional
development and to optimize activity of tourist industry in the region.
The offered system allows building the maps of recreation attractiveness for any territory. The used method for
calculation the potential attractiveness of territory takes into account various parameters; therefore the received
results give a complex representation of territory’s perspectives for tourist business.
REFERENCES
[1]
YAKIN, V.; RUDENKO, V.; KOROLJ, O.; KRACHILO, M.; GOSTYUK, M.; OTHERS (2006).
Problems of geography and tourism management. Chernivtsi: Chernivtsi national university.
[2]
LEONENKOV, A. (2005). Fuzzy modelling in MATLAB and fuzzyTECH. St. Petersburg.: БХВПетербург.
[3]
CATHY, H. C.; HSU, KARA WOLFE, SOO K. KANG. Image assessment for a destination with
limited comparative advantages // Tourism Management, 2004. - #25., p.121–126
[4]
NGAI, E. W. T.; WAT, F. K. T. Design and development ofa fuzzy expert system for hotel selection //
Omega, 2003. - #31, p.275 – 286
[5]
TSUNG-YU CHOU, MEI-CHYI CHEN, CHIA-LUN HSU. A fuzzy multi-criteria decision model for
international tourist hotels location selection // International Journal of Hospitality Management 2007.
[6]
CHAO-HUNG WANG, LI-CHANG HSU. Constructing and applying an improved fuzzy time series
model: Taking the tourism industry for example // Expert Systems with Applications, 2007.
[7]
WEN-BAO LIN An empirical of service quality model from the viewpoint of management // Expert
Systems with Applications, 2007. - #32, p.364–375
[8]
WEN-BAO LIN The exploration of customer satisfaction model from a comprehensive perspective //
Expert Systems with Applications, 2007. - #33, p.110–121
[9]
CHAO-HUNG WANG. Predicting tourism demand using fuzzy time series and hybrid grey theory //
Tourism Management, 2004. - #25, p. 367–374
[10]
STEVENS, D. iCity: A GISeCA modelling tool for urban planning and decision making / D. Stevens,
S. Dragicevic, K. Rothley // Environmental Modelling & Software. – 2007 – №22 – p. 761-773.
ADRESS:
Yaroslav Vyklyuk
Bucovinian University,
Simovich str. 21,
Chernictsi, 58000, Ukraine
E-mail: [email protected]
Olga Artemenko
Bucovinian University,
Simovich str. 21,
Chernictsi, 58000, Ukraine
E-mail: [email protected]
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PRINCÍPY OPRIMALIZÁCIE NAVRHOVANIA ELEKTROMECHANICKÝCH AKČNÝCH
ČLENOV
Juraj Wagner
Evropský polytechnický institut, s.r.o.
Abstrakt: Príspevok sa zaoberá teoretickými základmi optimalizačných metód s dôrazom na
uplatnenie metód statickej optimalizácie pri optimalizácii návrhu elektromechanických akčných
členov mechatronických systémov s využitím počítačových metód navrhovania.
Kľúčové slová: optimalizácia, optimalizačná metóda,
mechatronické systémy, počítačové metódy navrhovania
elektromechanické
akčné
členy,
ÚVOD
Pri návrhu každého elektromechanického akčného člena, jeho elektromagnetickom výpočte (návrhu elektrického
a magnetického obvodu) a pri návrhu hlavných rozmerov, vychádzame zvyčajne zo zadania, ktoré definuje
hlavné vstupné parametre (napájacie napätie, prúd, frekvencia, rozmery atď.) a hlavné výstupné parametre
(výkon, moment, otáčky, momentová preťažiteľnosť, krok krokového motora a podobne).
Zvyčajne je súbor údajov, ktoré definujú zadanie preurčený, to znamená, že dodržiavanie parametrov jednej
triedy je podmienené inou triedou zadaných parametrov, respektíve absolútne dodržanie jedných, vylučuje
dodržanie druhých. Jednoducho povedané, jednotlivé parametre uvedené v zadaní sú na sebe navzájom závislé.
Robiť výpočet skusmo je zdĺhavé a neefektívne. Dlhoročná prax pri navrhovaní elektrických strojov a získané
vedomosti viedli ku spracovaniu postupov a odporúčaní formou empirických vzťahov, tabuliek a grafov, ktoré
rešpektujú rôzne parametre strojov, použité materiály, typy elektromechanických aktuátorov podľa ich
fyzikálneho princípu pôsobenia, použitia a prevádzkových pomerov strojov, konštrukciu, s cieľom nájsť spôsob
a postup, ktorý bude najrýchlejšie a najpravdepodobnejšie viesť k cieľu, k návrhu aktuátora, ktorý vyhovuje
zadaniu a normami odporúčaným hodnotám strát, tepelných pomerov a pod. V mnohých prípadoch sú
definované rôzne limitujúce podmienky, ktoré treba pri návrhu akceptovať, napr. minimálna cena motora,
maximálne možné rozmery, maximálna hmotnosť, definovaná dedičnosť vybraných konštrukčných prvkov pri
návrhu radu aktuátorov a pod. V takých to prípadoch je výhodné využiť možnosti výpočtovej techniky.
Spracovať návrh aktuátora vo forme programu s využitím princípov metód statickej optimalizácie.
1. OPTIMALIZÁCIA NÁVRHOVÝCH METÓD
1.1 PRINCÍP OPTIMALIZÁCIE
Pri formulácii optimalizácie možno vychádzať z teoretického základu, ktorý je napr. uvedený v 1. Pod úlohou
optimalizácie rozumieme výber najlepšieho variantu podľa určitého kritéria z množiny možných alebo
dovolených variantov. Pri riešení úlohy optimalizácie treba vo všeobecnosti určiť z danej množiny  prvkov 
taký prvok
 *, v ktorom kritérium optimalizácie vyjadrené účelovou funkciou
J  J  
(1)
nadobúda extrémnu hodnotu, a to minimum alebo maximum, podľa požiadavky úlohy.
Ďalšia konkretizácia všeobecnej úlohy optimalizácie sa zakladá na konkretizácii opisu množiny  a účelovej
funkcie J.
Množina  vyjadruje podmienky optimalizácie, obmedzenia kladené na výber prvkov
množina prípustných konštrukčných variantov nejakého zariadenia a pod.
 . Môže to byť napr.
 z množiny  , je
zároveň mierou optimálnosti výberu tohto prvku. Hodnoty účelovej funkcie pre rôzne prvky  umožňujú tieto
Účelová funkcia vyjadruje cieľ optimalizácie a jej hodnota, vypočítaná pre konkrétny prvok
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prvky porovnávať, určovať, ktorý z nich sa viac približuje k optimálnemu.
Pri statickej optimalizácii ide o určovanie optimálnych hodnôt určitých meniteľných veličín (parametrov), pri
ktorých účelová funkcia nadobúda extrémnu hodnotu. Účelová funkcia sa dá v tomto prípade vyjadriť ako
funkcia týchto parametrov.
Optimalizačná úloha bude úlohou statickej optimalizácie, ak kritérium optimalizácie je funkcia závislá od hodnôt
parametrov
J  J (a1 , a2 ,...an )  J (a)
kde a sme označili vektor parametrov
(2)
a1 , a2 ,...an .



Úlohou statickej optimalizácie je určiť také hodnoty parametrov a1 , a 2 ,...a n alebo súhrnne vektor a*
z dovolenej množiny  , pri ktorom bude účelová funkcia nadobúdať extrémnu hodnotu, napr. minimum
 
J  a   min J a : a  
Keďže
(3)
max J a   min  a
môžeme v ďalších úvahách vždy predpokladať minimalizáciu kriteriálnej funkcie.
Stručne môžeme charakterizovať metódy riešenia úloh statickej optimalizácie nasledovne:
1.1.1 ANALYTICKÉ METÓDY RIEŠENIA ÚLOH STATICKEJ OPTIMALIZÁCIE
Riešime úlohu
min J a 
a  
(4)
Podľa spôsobu zadania množiny dovolených vektorov parametrov  môžeme úlohy statickej optimalizácie a
metódy ich riešenia rozdeliť na tri skupiny:
1. Množina  obsahuje všetky reálne vektory. To znamená, že na parametre, od ktorých závisí účelová
funkcia, sa nekladú žiadne obmedzenia.
2. Množina  je daná systémom rovníc
(5)
g j a   0,
j  1,2,...m n
3.
Množina  je daná systémom nerovníc (prípadne aj rovníc)
g j a   0
j  1,2,...m
(6)
kde m je ľubovoľné číslo.
V prvom prípade ide o bežnú matematickú úlohu nájsť extrém reálnej funkcie n premenných.
Nevyhnutnou (ale nie postačujúcou) podmienkou, aby v bode a* bol extrém funkcie
stacionárnym bodom, pre ktorý sú splnené rovnice:
J a 
 0,
ai
alebo
i=1,2,...n
J a , je, aby bod a* bol
(7)
grad J a  0 .
V prípade obmedzení v tvare rovníc (4) každej rovnici v n-rozmernom priestore parametrov zodpovedá
hyperplocha. Extrém funkcie J a hľadáme v prieniku týchto hyperplôch. Počet rovníc m nemá byť väčší ako
počet parametrov n. V opačnom prípade úloha buď nemá riešenie, alebo má riešenie len pre špeciálne prípady.

Takto formulovanú úlohu nazývame úloha s viazaným extrémom a možno ju riešiť metódou Lagrangeových
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funkcií. Pôvodnú účelovú funkciu
J a  nahradíme novou –Lagrangeovou funkciou.
m
Qa,    J a    i gi a 
(8)
i 1
kde λj sú dodatočné parametre – Lagrangeove multiplikátory.

Platí, že extrém funkcie J a na množine  danej rovnicami (5) je totožný so sedlovým bodom Lagrangeovej
funkcie (8). Pre sedlový bod platia rovnice
Qa,  
 0,
ai
i  1,2,..., n
(9)
Qa,  
 0,
 j
j  1,2,..., m
(10)
Rovnice (9) a (10) vyjadrujú nevyhnutné podmienky, ktorým má vyhovovať optimálny vektor parametrov a* a
vektor Lagrangeových multiplikátorov  pri riešení úlohy statickej optimalizácie s obmedzeniami v tvare
rovníc (5).
Podstatne zložitejšou je úloha statickej optimalizácie pri obmedzeniach v tvare nerovníc (6). Riešenie takýchto
úloh vyžaduje osobitné metódy. Pre ne sa zaužíval názov metódy matematického programovania.
Najjednoduchšie sa rieši úloha matematického programovania vtedy, ak má účelová funkcia
J a  absolútny
extrém, a to v bode a*, ktorý je z dovolenej množiny  . V takom prípade riešenie hľadáme riešením rovníc (7).
J a  je v bode mimo dovolenej oblasti 
alebo ak účelová funkcia nemá absolútny extrém, treba hľadať riešenie na hranici množiny  . Pre hľadaný
optimálny bod a*, v ktorom nadobúda účelová funkcia extrémnu hodnotu na hranici množiny  budú splnené
V ostatných prípadoch, t. j. ak absolútny extrém účelovej funkcie
niektoré z rovníc:
g j a *  0
(11)
Keby sme vopred vedeli, ktoré sú to rovnice, mohli by sme úlohu riešiť ako v prípade obmedzení v tvare rovníc
optimalizáciou Lagrangeovej funkcie (8).
Úlohu s obmedzeniami tvaru nerovníc môžeme transformovať na úlohu s obmedzeniami v tvare rovníc aj tak, že
namiesto nerovníc
(12)
g j a   0,
j  1,2,..., m
definujeme obmedzujúce podmienky rovnicami
G j a, u   g j a  u 2j  0,
j  1,2,..., m
(13)
Taký postup je značne neefektívny, lebo príliš zväčšuje počet neznámych parametrov, a tým aj objem výpočtov.
Všeobecný prístup k riešeniu úloh matematického programovania môže vychádzať z poznatkov Kuhna a
Tuckera, ktorí zovšeobecnili metódu Lagrangeových funkcií na úlohy s obmedzeniami v tvare nerovníc.
Definujeme funkcie
G j a   0
G j a   g j a
pre g j  0
(14)
pre g j  0
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Platí, že extrém účelovej funkcie
bodom Lagrangeovej funkcie
J a  na hranici množiny  danej nerovnicami (6) je totožný so sedlovým
m
Qa,    J a     j G j a 
(15)
j 1
Analytické riešenie úlohy je však teraz sťažené spôsobom definovania funkcií G j a .
1.1.2
METÓDY
RIEŠENIA
ÚLOHY
STATICKEJ
OPTIMALIZÁCIE
POSTUPNÝM
PRIBLIŽOVANÍM K EXTRÉMU
Rovnice, ktoré dostávame pri analytických metódach statickej optimalizácie, nie vždy možno riešiť v uzavretom
tvare. V praxi sa stretávame aj s takými úlohami optimalizácie, keď je možné určiť len realizovanú hodnotu
účelovej funkcie J a , ale nepoznáme jej závislosť od parametrov, alebo sa táto závislosť s časom mení.

Vo všetkých týchto prípadoch sa úloha statickej optimalizácie rieši metódami postupného približovania
k optimálnemu riešeniu postupnou zmenou vektora parametrov a pri rešpektovaní obmedzení a súčasnom
vyhodnocovaní výsledkov.
Metódy postupného približovania k extrému rozlišujeme podľa spôsobu určovania smeru, ktorým sa má meniť
vektor parametrov a tak, aby sa približoval k optimálnemu a podľa spôsobu realizácie týchto zmien.
Podľa spôsobu realizácie zmien vektora parametrov rozlišujeme spojité a diskrétne metódy statickej
optimalizácie.
Pri spojitých metódach sa vektor parametrov mení spojite. Zaujíma nás, ako určovať, alebo voliť rýchlosť zmeny
vektora parametrov
da
 v,
dt
(16)
aby proces optimalizácie bol stabilný a ustálil sa v stacionárnom bode a*, v ktorom je extrém účelovej funkcie
Ja .

Pre účelovú funkciu, ktorá má v bode a* extrém minima, zvoľme Ľapunovovu funkciu
L a  J a  J a* ,


 
(17)
ktorá má byť kladne definitná pre celú množinu  , s výnimkou stacionárneho bodu.
Aby bol proces asymptotický stabilný, musí byť derivácia Ľapunovovej funkcie, podľa času, záporne definitná
s výnimkou stacionárneho bodu. To znamená, že v procese optimalizácie má byť stále splnená podmienka
pre
dJ a 
T da
T
 grad J a 
 grad J a  v0
dt
dt
(18)
a  a*
(19)
Voľbou spôsobu určenia vektora v v každom bode priestoru parametrov a v každom časovom okamihu môžeme
vytvárať rôzne algoritmy statickej optimalizácie. Základnou metódou je spojitá gradientová metóda, pri ktorej
vektor rýchlosti zmeny parametrov volíme úmerný gradientu účelovej funkcie. Pri hľadaní minima účelovej
funkcie vektor rýchlosti zmeny parametrov má opačnú orientáciu ako gradiet účelovej funkcie.
da
  K grad J a 
dt
(20)
V procese optimalizácie, podľa vzťahu (20), sa bod a v priestore parametrov pohybuje po trajektórii
najstrmšieho klesania účelovej funkcie.
Gradientovú metódu môžeme použiť na riešenie úlohy statickej optimalizácie s obmedzeniami v tvare nerovníc
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g j a   0,
Pôvodnú účelovú funkciu
j  1,2,..., m
(21)
Ja  rozšírime o pokutové funkcie, čím dostaneme novú kriteriálnu funkciu
m
Qa   J a     j g j a 
(22)
j 1
kde
pre g j a   0
j  0
pre g j a  0 .
j 1
Kladné znamienko vo vzťahu platí pre minimalizáciu a záporné pre maximalizáciu účelovej funkcie
Rovnica najrýchlejšieho klesania (stúpania), podľa ktorej má prebiehať proces optimalizácie je:
m
da
  K grad Qa    K grad Qa     j grad g j a 
dt
j 1
J a  .
(23)
Horné znamienka sú pre úlohu minimalizácie a dolné pre úlohu maximalizácie.
Statická optimalizácia, pri použití číslicových počítačov, prebieha ako diskrétny proces. Vektor parametrov sa
mení diskrétne v jednotlivých krokoch
a k  1  a k  a k
(24)




Stabilita diskrétneho procesu optimalizácie vyžaduje, aby sa v každom kroku realizovali len také zmeny
parametrov, pre ktoré bude splnená podmienka
J a k 1  J a k  0
(25)


  
ak sa určuje minimum účelovej funkcie, alebo
J ak  1  J ak  0
(26)
ak sa určuje maximum účelovej funkcie.
Na stabilitu diskrétneho procesu má vplyv tak voľba smeru zmeny vektora parametrov, ako aj veľkosť tejto
zmeny v každom kroku.
Stručne uvediem niektoré základné metódy diskrétnej statickej optimalizácie.
Algoritmus diskrétnej gradientovej metódy je daný vzťahom
ak 1  ak   K grad J ak 
(27)
Vzťah (27) platí pre minimalizáciu účelovej funkcie. Smer zmeny vektora parametrov je v opačnom smere
gradientu účelovej funkcie v príslušnom k-tom bode. Veľkosť zmeny je daná absolútnou hodnotou gradientu a
koeficientom K. Od voľby koeficientu K závisí rýchlosť konvergencie a stabilita procesu optimalizácie.
Pri Gaussovej – Seidelovej metóde meníme postupne jeden parameter, obyčajne o konštantnú hodnotu, kým
hodnoty ostatných parametrov zostávajú nezmenené. Parameter meníme dovtedy, kým platí vzťah (25). Potom
meníme tým istým spôsobom ďalší parameter. Proces cyklicky opakujeme pre všetky parametre. V okolí
optimálneho bodu môžeme krok zmenšovať, aby sa zvýšila presnosť priblíženia k optimálnemu riešeniu.
Prednosti gradientovej a Gaussovej – Seidelovej metódy spája metóda najrýchlejšieho štartu. V začiatočnom
bode sa určí smer gradientu. Vektor parametrov sa mení po krokoch v opačnom smere gradientu určeného
v začiatočnom bode dovtedy, kým platí vzťah (25). V poslednom bode sa určuje opäť gradient účelovej funkcie.
Tým bude daný nový smer zmien vektora parametrov. Proces sa cyklicky opakuje.
Ďalšou metódou je metóda náhodných pokusov, ktorá nevyžaduje určovať gradient účelovej funkcie.
V začiatočnom bode zmeníme vektor parametrov a k pripočítaním náhodne zvoleného vektora a k :
 
 
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ak 1  ak   ak  .
(28)
Zistíme, ako sa zmenila účelová funkcia
J k   J ak  1  J ak .
Pri hľadaní minima účelovej funkcie, ak rozdiel
(29)
J k 
je záporný, budeme vektor parametrov ďalej meniť
ak  . Ak je rozdiel J k  kladný, budeme meniť vektor parametrov
odpočítavaním náhodného vektora ak  . V každom kroku zisťujeme platnosť podmienky (25) a vektor
postupným pripočítavaním vektora
parametrov meníme dovtedy, kým podmienka platí. Keď podmienka (25) neplatí, zmeníme posledný vektor
parametrov pripočítaním iného náhodného vektora a postup opakujeme.
1.1.3 LINEÁRNE PROGRAMOVANIE
Špeciálnym typom statickej optimalizácie je lineárne programovanie. Vyznačuje sa tým, že účelová funkcia je
lineárnou funkciou parametrov
n
J x   c T x   ci xi (30)
i 1
a množina dovolených parametrov je daná systémom lineárnych nerovníc
n
a
i n
ij
xi  a Tj x  b j , j= 1,2, ..., m
x j  0,
(31)
i = 1,2, ..., n
(32)
Alebo vyjadrené súhrnne vo vektorovom tvare
Ax  b  0 .
(33)
Lineárna funkcia (30) nemá lokálny extrém, preto extrém musí v tomto prípade byť na hranici množiny Ω.
Množina má tvar mnohostenu a n – rozmernom priestore a je ohraničená rovnicami
a Tj x  b j
j = 1, 2, ..., m
(34)
Úloha lineárneho programovania predstavuje špecifický typ úlohy statickej optimalizácie, ktorá bola
sformulovaná Kolmogorovom. Na jej riešenie môžeme využiť všeobené metódy statickej optimalizácie.
Niektoré problémy sa vyznačujú veľkým počtom neznámych veličín a veľkým počtom nerovníc, vyjadrujúcich
obmedzenia. Aplikácia všeobecných metód statickej optimalizácie v takých prípadoch nie je efektívna.
Lineárnosť úloh umožnila vypracovať špeciálne metódy, ktoré vedú rýchlejšie k výsledku. Najznámejšou je
simplexová metóda.
Konečným počtom nerovníc je v priestore neznámych veličín vymedzená množina prípustných riešení v tvare
mnohostenu a konečným počtom hrán a vrcholov.Metóda spočíva na postupnom pohybe po hranách mnohostena
od vrcholu k vrcholu tak, že každé nasledujúce riešenie z hľadiska účelovej funkcie je lepšie ako
predchádzajúce. Optimálne riešenie sa dosiahne za konečný počet krokov.
Iný variant metódy spočíva v kombinácii gradientovej metódy statickej optimalizácie a pohybu po stenách
množiny dovolených riešení. Z určitého východiskového stavu x(0) sa mení vektor x v smere gradientu účelovej
funkcie ( ak hľadáme maximum účelovej funkcie), ktorým je vektor c
x(1) = K(1) c
(35)
postupným zväčšovaním kroku K(1), pri ktorej sa jedna z nerovníc zmení na rovnicu. Ostatné nerovnice musia
byť splnené. Tak bod x(1) dosiahol prvú stenu dovolenej množiny opísanú niektorou z rovníc
a Tj x  b j (36)
kde j znamená j-tú rovnicu vyplývajúcu zo vzťahu (31), resp.(34). Z dosiahnutého stavu x(1) sa opäť bude meniť
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vektor x v smere gradientu účelovej funkcie, ale po stene, ktorá je opísaná rovnicou (36) až kým sa ďalšia
nerovnica nezmení na rovnicu. Gradient účelovej funkcie premietnutý do roviny opísanej vzťahom (36) je
grad jJ  c(1)  c 
aTjca j
aTja j
(37)
Nové hodnoty premenných sa budú počítať podľa vzťahu
 aTjca j 
x(2)  x(1)  K (2)c(1)  x(1)  K (2) c  T  (38)
a j a j 

postupným zväčšovaním kroku K(2) až sa zastupujúci bod x(2) dostane na ďalšiu stenu opísanú rovnicou (36),
ale pre iné j. Druhý krok opakujeme až po dosiahnutí extrému účelovej funkcie na dovolenej množine. Pre počet
neznámych veličín väčší ako dva, je potrebné metódu modifikovať tak, aby každý pohyb zastupujúceho bodu bol
po hranách množiny, to znamená, aby postupne súčasne bolo splnených viac rovníc, až po n rovníc.Gradient po
hrane určujeme viacnásobným použitím vzťahu (38) tak, že za vektor c dosadíme vždy novú hodnotu c(k) a za aj
vektor poslednej dosiahnutej plochy. Po n krokoch sa dosiahne niektorý vrchol mnohostenu. Tomuto vrcholu
zodpovedá bázické riešenie. Ďalší pohyb pri splnení vždy n-1 rovníc bude po hranách od vrcholu k vrcholu až po
výsledné riešenie. Tento postup zodpovedá simplexovej metóde. Riešenie sa získa za konečný počet krokov.
2. ROVNICE OPTIMALIZÁCIE
Keďže návrh aktuátora vedie k opakovanému výpočtu závislostí medzi hlavnými ukazovateľmi danými formou
vzťahov, empirických koeficientov a grafických závislostí, optimálny návrh elektrických strojov je možné
chápať ako nájdenie optimálnych parametrov riešením danej sústavy. Výber kritérií optimálnosti závisí od toho,
na čo je stroj určený a na požiadavkách, ktoré sú naň kladené. Voľba optimalizačnej funkcie závisí od tých
požiadaviek, ktoré pri dodržaní ostatných požadovaných parametrov sú rozhodujúce.
Úlohu optimálneho návrhu elektromechanického aktuátora je teda možné si predstaviť ako všeobecnú úlohu
statickej optimalizácie, ktorá vedie k nájdeniu minima zvolenej optimalizačnej funkcie pri danom počte
nezávisle premenných a funkcií limitujúcich faktorov a obmedzení.
2.1PRÍKLADY OPTIMALIZAČNÝCH FUNKCIÍ
2.1.1PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE TUBULÁRNY KROKOVÝ MOTOR
Napríklad pri návrhu tubulárneho krokového motora, ak vychádzame z toho, že kritériom optimálneho riešenia
návrhu aktuátora, pri dodržaní ostatných zadaných parametrov, sú minimálne rozmery - vonkajší priemer
motora Dea dĺžka aktívnej časti aktuátora le, tak môžeme odvodiť nasledovné optimalizačné funkcie:
1.) závislosť počtu zubov pólu na dĺžke aktívnej časti aktuátora le
nz= f(le),
(39)
ktorej tvar je
nz 
l
e
 l p  K 
,
(40)
2.) závislosť priemeru kotvy od počtu zubov pólu
dt = f(nz),
ktorej tvar je
(41)
K 
d t2  Ld t  M  0 ,
(42)
3.) závislosť počtu závitov budiacej cievky od priemeru kotvy
N = f(dt),
ktorej tvar je
(43)
N
Fm k3
,
k4 Ik5 Bt dt2  k2 dt  k6


(44)
4.) závislosť šírky cievky od priemeru kotvy a počtu zubov jedného pólu
bc = f(dt, nz),
ktorej tvar je
(45)
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bc  k12 n z  N  
D
,
D
(46)
5.) závislosť vonkajšieho priemeru od priemeru kotvy výšky budiacej cievky
De = f(dt,hc),
ktorej tvar je
(47)
De  G  F  2k0 ,
(48)
kde D, D’, F, G, K’, K’’, L, M, N’, k0, k2, k4 , k5 , k6 , k12sú parametrezávislé na rozmeroch aktuátora.
2.1.2 PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE INDUKČNÉ MOTORY
Pri návrhu indukčných motorov môžeme za kritériá optimalizácie zvoliť, podľa požiadaviek na vlastnosti motora
napríklad požadovaný menovitý moment motora MN, minimálny možný moment zotrvačnosti J. Potom
optimalizačná funkcia má tvar
T = f(kD;λ;DE),
ktorej tvar je
(49)
k D6 DE6 K 1 s  K 2 s 3 
prípadne môže mať
Mtvar
(50)
F k D ,s n  
(51)
TN 
Tn k D , s n .k M k D , s n 
.
J k D 
2.1.3 PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE VYSOKO MOMENTOVÝ KROKOVÝ MOTOR
Pri návrhu vysoko momentového krokového motora môžeme za kritériá optimalizácia za predpokladu potreby
dosiahnutia maximálneho momentu motora T, vziať vŕrtanie motora D, veľkosť vzduchovej medzery
a dĺžku
motora l. Formálny tvar optimalizačnej funkcie potom je T = f(D,δ,l) a tvar rovnice je nasledovný
1 ce f  D , ,l  dG f  D , ,l 

.
.k 2 .
2
2 Gmax
d
f  D , ,l 
2
Ts , f  D , ,l 
(52)
3. ZÁVER
V predloženom príspevku sú zhrnuté poznatky a skúsenosti autora získané v rámci prác súvisiacich s
vypracovaním princípov optimalizácie návrhových metód elektromechanických akčných členov s využitím
informačných technológií.
4. LITERATÚRA
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2001, 300 pp, ISBN 80-88914-48-5 (in Slovak)
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WAGNER, J. Design of chosen electromechanical actuators, Kunovice : Publisher EPI, Ltd., 2008, 133
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[3]
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LOPUCHINA, E. M.; SEMENČUKOV, G. A. Projektirovanije asinchronnych mikrodvigatelej
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International Conference „Design to manufacture in Modren Industry“, Bled – Maribor, University of
Maribor, 1995, pp. 600 – 611.
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ADRESS:
Dr. h. c., doc. Ing. Juraj Wagner, PhD.
Evropský polytechnický institute, s.r.o.
Gallayova 1,
841 02 Bratislava,
tel.: 00421/918884637,
fax: 00421/2/64362340,
e-mail:[email protected]
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EPI Kunovice, Czech Republic. January 20, 2012
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EPI Kunovice, Czech Republic. January 20, 2012
136
JMENNÝ REJSTŘÍK
A
ARTEMENKO, O. .................. 123
M
MARČEK, D. ............................ 75
B
BARTONĚK, D. ............. 9, 17, 81
O
OPATŘILOVÁ, I. ............... 17, 81
OŠMERA, P............................... 89
D
DERMEKOVÁ, S. ................ 9, 17
DOSTÁL, P. ............................... 27
P
PETRUCHA, J. .......................... 95
Ď
ĎUĎÁK, J. ................................. 31
R
RUKOVANSKÝ, I. ................. 101
F
FALÁT, L. .................................. 37
S
SLOVÁČEK, D ....................... 117
G
GAŠPAR, G. .............................. 31
Š
ŠEDA, M. ................................ 109
H
HANULIAK, I. ......................... 43
HUDIK, M. ................................ 51
V
VYKLYUK, Y. ........................ 123
W
WAGNER, J. .......................... 127
J
JANOVIČ, F. .............................. 57
K
KEBÍSEK, M. ............................ 31
KEJVALOVÁ, K. ...................... 65
KRATOCHVÍL, O. ................... 27
ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS”
EPI Kunovice, Czech Republic. January 20, 2012
137
ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS”
EPI Kunovice, Czech Republic. January 20, 2012
138
Title:
ICSC 2012 – Tenth International Conference on Soft Computing Applied in Computer and Economic
Environments
Author:
Team of authors
Publisher, copyright holders, manufactured:
European Polytechnic Institute, Ltd.
Osvobození 699, 686 04 Kunovice, Czech Republic
Load:
100 pcs
Number of pages:
138
Edition:
first
Release Year:
2012
ISBN 978-80-7314-279-7

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