Computational Intelligence in Reliability Engineering: New Metaheuristics, Neural and Fuzzy Techniques in Reliability

427 Pages·2007·13.413 MB·English

by  Yun-Chia Liang, Alice E. Smith (auth.), Dr. Gregory Levitin (eds.)

Gregory Levitin (Ed.)
Computational Intelligence in Reliability Engineering
Studies in Computational Intelligence, Volume 40
Editor-in-chief
Prof. Janusz Kacprzyk
Systems Research Institute
Polish Academy of Sciences
ul. Newelska 6
01-447 Warsaw
Poland
E-mail:: [email protected]
Further volumes of this series Vol. 32. Akira Hirose
can be found on our homepage: Complex-Valued Neural Networks, 2006
springer.com ISBN 3-540-33456-4
Vol. 33. Martin Pelikan, Kumara Sastry, Erick
Vol. 23. M. Last, Z. Volkovich, A. Kandel (Eds.) Cant(cid:22)ú-Paz (Eds.)
Algorithmic Techniques for Data Mining,2006 Scalable Optimization via Probabilistic

ISBN 3-540-33880-2 Modeling,2006
ISBN 3-540-34953-7
Vol. 24. Alakananda Bhattacharya, Amit Konar,
Ajit K. Mandal Vol. 34. Ajith Abraham, Crina Grosan, Vitorino
Parallel and Distributed Logic Programming, Ramos (Eds.)
2006 Swarm Intelligence in Data Mining,2006
ISBN 3-540-33458-0 ISBN 3-540-34955-3
Vol. 25. Zolt n Ésik, Carlos Martn-Vide, Vol. 35. Ke Chen, Lipo Wang (Eds.)
Victor Mitrana (Eds.) Trends in Neural Computation,2007
Recent Advances in Formal Languages ISBN 3-540-36121-9
and Applications,, 2006
ISBN 3-540-33460-2 Vol. 36. Ildar Batyrshin, Janusz Kacprzyk, Leonid
Sheremetor, Lotfi A. Zadeh (Eds.)
Vol. 26. Nadia Nedjah, Luiza de Macedo Mourelle Perception-based Data Mining and Decision
(Eds.)
Making in Economics and Finance,2006
Swarm Intelligent Systems, 2006
ISBN 3-540-36244-4
ISBN 3-540-33868-3
Vol. 37. Jie Lu, Da Ruan, Guangquan Zhang (Eds.)
Vol. 27. Vassilis G. Kaburlasos
E-Service Intelligence,2007
Towards a Unified Modeling and Knowledge-
ISBN 3-540-37015-3
Representation based on Lattice Theory, 2006
ISBN 3-540-34169-2 Vol. 38. Art Lew, Holger Mauch
Dynamic Programming,2007
Vol. 28. Brahim Chaib-draa, Jörg P. Müller (Eds.) ISBN 3-540-37013-7
Multiagent based Supply Chain Management,2006
ISBN 3-540-33875-6 Vol. 39. Gregory Levitin (Ed.)
Computational Intelligence in Reliability
Vol. 29. Sai Sumathi, S.N. Sivanandam
Engineering, 2007
Introduction to Data Mining and its
Applications, 2006 ISBN 3-540-37367-5
ISBN 3-540-34689-9
Vol. 40. Gregory Levitin (Ed.)
Vol. 30. Yukio Ohsawa, Shusaku Tsumoto (Eds.) Computational Intelligence in Reliability
Chance Discoveries in Real World Decision Engineering, 2007
Making, 2006
ISBN 3-540-37371-3
ISBN 3-540-34352-0

Vol. 31. Ajith Abraham, Crina Grosan, Vitorino
Ramos (Eds.)
Stigmergic Optimization,2006
ISBN 3-540-34689-9
Gregory Levitin (Ed.)
Computational Intelligence
in Reliability Engineering
New Metaheuristics, Neural and
Fuzzy Techniques in Reliability
With 90 Figures and 53 Tables
123
Dr. Gregory Levitin
Research && Development Division
The Israel Electronic Corporation Ltd.
PO Box 10
31000 Haifa
Israel
E-mail: [email protected]
Library of Congress Control Number: 2006931548
ISSN print edition: 1860-949X
ISSN electronic edition: 1860-9503
ISBN-10 3-540-37371-3 Springer Berlin Heidelberg New York
ISBN-13 978-3-540-37371-1 Springer Berlin Heidelberg New York
This work is subjjject to copppyyyriggght. All riggghts are reserved, whether the whole or ppart of the mate-
rial is concerned, spppecificallyyy the riggghts of translation, repprintinggg, reuseof illustrations, recita-
tion, broadcastinggg, reppproduction on microfilm or in anyyy other wayyy, and storaggge in data banks.
Dupplication of this pppublicationor ppparts thereof is ppermitted onlyy under the ppprovisions of the
German Copppyyyriggght Law of Sepptember 9, 1965, in its current version, and pppermission for use
must alwayys be obtained from Springer-Verlag. Violations are liable to prosecution under the
German Copyright Law.
Springer is a part of Springer Science+Business Media
springer.com
© © Springer-Verlag Berlin Heidelberg 2007
The use of gggeneral descrippptive names, regggistered names, trademarks, etc. in this pppublication
does not imppplyyy, even in the absence of a spppecific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
Cover desiggn: deblik, Berlin
Typesetting by the editor and SPi
Printeddd on acidd-ffree paper SPIN: 11817581 89/SPi 5 4 3 2 1 0
Preface
This two-volume book covers the recent applications of computational intelli-
gence techniques in reliability engineering. Research in the area of computational
intelligence is growing rapidly due to the many successful applications of these
new techniques in very diverse problems. “Computational Intelligence” covers
many fields such as neural networks, fuzzy logic, evolutionary computing, and
their hybrids and derivatives. Many industries have benefited from adopting this
technology. The increased number of patents and diverse range of products devel-
oped using computational intelligence methods is evidence of this fact.

These techniques have attracted increasing attention in recent years for solving
many complex problems. They are inspired by nature, biology, statistical tech-
niques, physics and neuroscience. They have been successfully applied in solving
many complex problems where traditional problem-solving methods have failed.

The book aims to be a repository for the current and cutting-edge applications of
computational intelligent techniques irne liability analysis and optimization.

In recent years, many studies on reliability optimization use a universal optimiza-
tion approach based on metaheuristics. These metaheuristics hardly depend on the
specific nature of the problem that is solved and, therefore, can be easily applied
to solve a wide range of optimization problems. The metaheuristics are based on
artificial reasoning rather than on classical mathematical programming. Their im-
portant advantage is that they do not require any information about the objective
function besides its values corresponding to the points visited in the solution
space. All metaheuristics use the idea of randomness when performing a search,
but they also use past knowledge in order to direct the search. Such algorithms are
known as randomized search techniques.

Genetic algorithms are one of the most widely used metaheuristics. They were in-
spired by the optimization procedure that exists in nature, the biological phenome-
non of evolution. The first volume of this book starts with a survey of the contri-
butions made to the optimal reliability design literature in the resent years. The
next chapter is devoted to using the metaheuristics in multiobjective reliability op-
timization. The volume also contains chapters devoted to different applications of
the genetic algorithms in reliability engineering and to combinations of this algo-
rithm with other computational intelligence techniques.
VI Preface
The second volume contains chapters presenting applications of other metaheuris-
tics such as ant colony optimization, great deluge algorithm, cross-entropy method
and particle swarm optimization. It also includes chapters devoted to such novel
methods as cellular automata and support vector machines. Several chapters pre-
sent different applications of artificial neural networks, a powerful adaptive tech-
nique that can be used for learning, prediction and optimization. The volume also
contains several chapters describing different aspects of imprecise reliability and
applications of fuzzy and vague set theory.

All of the chapters are written by leading researchers applying the computational
intelligence methods in reliability engineering.

This two-volume book will be useful to postgraduate students, researchers, doc-
toral students, instructors, reliability practitioners and engineers, computer scien-
tists and mathematicians with interest in reliability.

I would like to express my sincere appreciation to Professor Janusz Kacprzyk
from the Systems Research Institute, Polish Academy of Sciences, Editor-in-Chief
of the Springer series "Studies in Computational Intelligence", for providing me
with the chance to include this book in the series.

I wish to thank all the authors for their insights and excellent contributions to this
book. I would like to acknowledge the assistance of all involved in the review
process of the book, without whose support this book could not have been suc-
cessfully completed. I want to thank the authors of the book who participated in
the reviewing process and also Prof. F. Belli, University of Paderborn, Germany,
Prof. Kai-Yuan Cai, Beijing University of Aeronautics and Astronautics, Dr. M.
Cepin, Jozef Stefan Institute, Ljubljana , Slovenia, Prof. M. Finkelstein, Univer-
sity of the Free State, South Africa, Prof. A. M. Leite da Silva, Federal University
of Itajuba, Brazil, Prof. Baoding Liu, Tsinghua University, Beijing, China, Dr. M.
Muselli, Institute of Electronics, Computer and Telecommunication Engineering,
Genoa, Italy, Prof. M. Nourelfath, Université Laval, Quebec, Canada, Prof. W.
Pedrycz, University of Alberta, Edmonton, Canada, Dr. S. Porotsky, FavoWeb, Is-
rael, Prof. D. Torres, Universidad Central de Venezuela, Dr. Xuemei Zhang, Lu-
cent Technologies, USA for their insightful comments on the book chapters.

I would like to thank the Springer editor Dr. Thomas Ditzinger for his professional
and technical assistance during the preparation of this book.

Haifa, Israel, 200 6 Gregory Levitin
Contents

1 The Ant Colony Paradigm for Reliable Systems Design
Yun-Chia Liang, Alice E. Smith...............................................................................1
1.1 Introduction..................................................................................................1
1.2 Problem Definition......................................................................................5
1.2.1 Notation................................................................................................5
1.2.2 Redundancy Allocation Problem..........................................................6
1.3 Ant Colony Optimization Approach............................................................7
1.3.1 Solution Encoding................................................................................7
1.3.2 Solution Construction...........................................................................8
1.3.3 Objective Function...............................................................................9
1.3.4 Improving Constructed Solutions Through Local Search..................10
1.3.5 Pheromone Trail Intensity Update......................................................10
1.3.6 Overall Ant Colony Algorithm...........................................................11
1.4 Computational Experience.........................................................................11
1.5 Conclusions................................................................................................16
References........................................................................................................18
2 Modified Great Deluge Algorithm versus Other Metaheuristics
in Reliability Optimization
Vadlamani Ravi.....................................................................................................21
2.1 Introduction................................................................................................21
2.2 Problem Description..................................................................................23
2.3 Description of Various Metaheuristics......................................................25
2.3.1 Simulated Annealing (SA).................................................................25
2.3.2 Improved Non-equilibrium Simulated Annealing (INESA)...............26
2.3.3 Modified Great Deluge Algorithm (MGDA).....................................26
2.3.3.1 Great Deluge Algorithm..........................................................27
2.3.3.2 The MGDA..............................................................................27
2.4 Discussion of Results.................................................................................30
2.5 Conclusions................................................................................................33
References........................................................................................................33
Appendix.........................................................................................................34
VIII Contents
3 Applications of the Cross-Entropy Method in Reliability
Dirk P. Kroese, Kin-Ping Hui...............................................................................37
3.1 Introduction...............................................................................................37
3.1.1 Network Reliability Estimation..........................................................37
3.1.2 Network Design.................................................................................38
3.2 Reliability..................................................................................................39
3.2.1 Reliability Function............................................................................42
3.2.2 Network Reliability............................................................................44
3.3 Monte Carlo Simulation............................................................................45
3.3.1 Permutation Monte Carlo and the Construction Process....................46
3.3.2 Merge Process....................................................................................48
3.4 Reliability Estimation using the CE Method.............................................50
3.4.1 CE Method.........................................................................................52
3.4.2 Tail Probability Estimation................................................................53
3.4.3 CMC and CE (CMC-CE)...................................................................54
3.4.4 CP and CE (CP-CE)...........................................................................56
3.4.5 MP and CE (MP-CE).........................................................................57
3.4.6 Numerical Experiments......................................................................59
3.4.7 Summary of Results...........................................................................62
3.5 Network Design and Planning...................................................................62
3.5.1 Problem Description...........................................................................63
3.5.2 The CE Method for Combinatorial Optimization...............................64
3.5.2.1 Random Network Generation..................................................64
3.5.2.2 Updating Generation Parameters.............................................65
3.5.2.3 Noisy Optimization.................................................................66
3.5.3 Numerical Experiment.......................................................................66
3.6 Network Recovery and Expansion............................................................68
3.6.1 Problem Description...........................................................................68
3.6.2 Reliability Ranking............................................................................69
3.6.2.1 Edge Relocated Networks.......................................................69
3.6.2.2 Coupled Sampling...................................................................70
3.6.2.3 Synchronous Construction Ranking (SCR).............................71
3.6.3 CE Method.........................................................................................74
3.6.3.1 Random Network Generation..................................................74
3.6.3.2 Updating Generation Parameters.............................................74
3.6.4 Hybrid Optimization Method.............................................................77
3.6.4.1 Multi-optima Termination.......................................................77
3.6.4.2 Mode Switching.......................................................................78
3.6.5 Comparison Between the Methods.....................................................79
References.......................................................................................................80
4 Particle Swarm Optimization in Reliability Engineering
Gregory Levitin, Xiaohui Hu, Yuan-Shun Dai......................................................83
4.1 Introduction...............................................................................................83
4.2 Description of PSO and MO-PSO.............................................................84
4.2.1 Basic Algorithm.................................................................................85
Contents IX
4.2.2 Parameter Selection in PSO................................................................86
4.2.2.1 Learning Factors......................................................................86
4.2.2.2 Inertia Weight..........................................................................87
4.2.2.3 Maximum Velocity..................................................................87
4.2.2.4 Neighborhood Size..................................................................87
4.2.2.5 Termination Criteria................................................................88
4.2.3 Handling Constraints in PSO..............................................................88
4.2.4 Handling Multi-objective Problems with PSO...................................89
4.3 Single-Objective Reliability Allocation.....................................................91
4.3.1 Background........................................................................................91
4.3.2 Problem Formulation..........................................................................92
4.3.2.1 Assumptions............................................................................92
4.3.2.2 Decision variables....................................................................92
4.3.2.3 Objective Function..................................................................93
4.3.2.4 The Problem............................................................................94
4.3.3 Numerical Comparison.......................................................................95
4.4 Single-Objective Redundancy Allocation..................................................96
4.4.1 Problem Formulation..........................................................................96
4.4.1.1 Assumptions............................................................................96
4.4.1.2 Decision Variable....................................................................96
4.4.1.3 Objective Function..................................................................97
4.4.2 Numerical Comparison.......................................................................98
4.5 Single Objective Weighted Voting System Optimization..........................99
4.5.1 Problem Formulation..........................................................................99
4.5.2 Numerical Comparison.....................................................................101
4.6 Multi-Objective Reliability Allocation....................................................105
4.6.1 Problem Formulation........................................................................105
4.6.2 Numerical Comparison.....................................................................106
4.7 PSO Applicability and Efficiency............................................................108
References......................................................................................................109
5 Cellular Automata and Monte Carlo Simulation for Network Reliability
and Availability Assessment
Claudio M. Rocco S., Enrico Zio.........................................................................113
5.1 Introduction..............................................................................................113
5.2 Basics of CA Computing.........................................................................115
5.2.1 One-dimensional CA........................................................................116
5.2.2 Two-dimensional CA.......................................................................118
5.2.3 CA Behavioral Classes.....................................................................118
5.3 Fundamentals of Monte Carlo Sampling and Simulation........................119
5.3.1 The System Transport Model...........................................................119
5.3.2 Monte Carlo Simulation for Reliability Modeling...........................120
5.4 Application of CA for the Reliability Assessment of Network Systems.122
5.4.1 S-T Connectivity Evaluation Problem..............................................123
5.4.2 S-T Network Steady-state Reliability Assessment...........................124
5.4.2.1 Example.................................................................................125
X Contents
5.4.2.2 Connectivity Changes............................................................125
5.4.2.3 Steady-state Reliability Assessment......................................126
5.4.3 The All-Terminal Evaluation Problem.............................................127
5.4.3.1 The CA Model.......................................................................127
5.4.3.2 Example.................................................................................128
5.4.3.3 All-terminal Reliability Assessment: Application.................128
5.4.4 The k-Terminal Evaluation Problem................................................130
5.4.5 Maximum Unsplittable Flow Problem.............................................130
5.4.5.1 The CA Model.......................................................................130
5.4.5.2 Example.................................................................................132
5.4.6 Maximum Reliability Path...............................................................134
5.4.6.1 Shortest Path..........................................................................134
5.4.6.2 Example.................................................................................135
5.4.6.3 Example.................................................................................136
5.4.6.4 Maximum Reliability Path Determination.............................136
5.5 MC-CA network availability assessment.................................................138
5.5.1 Introduction......................................................................................138
5.5.2 A Case Study of Literature...............................................................140
5.6 Conclusions.............................................................................................141
References.....................................................................................................142
Appendix.......................................................................................................143
6 Network Reliability Assessment through Empirical Models Using
a Machine Learning Approach
Claudio M. Rocco S., Marco Muselli..................................................................145
6.1 Introduction: Machine Learning (ML) Approach to Reliability
Assessment....................................................................................................145
6.2 Definitions...............................................................................................147
6.3 Machine Learning Predictive Methods....................................................149
6.3.1 Support Vector Machines.................................................................149
6.3.2 Decision Trees..................................................................................154
6.3.2.1 Building the Tree...................................................................156
6.3.2.2 Splitting Rules.......................................................................157
6.3.2.3 Shrinking the Tree.................................................................159
6.3.3 Shadow Clustering (SC)...................................................................159
6.3.3.1 Building Clusters...................................................................162
6.3.3.2 Simplifying the Collection of Clusters..................................164
6.4 Example...................................................................................................164
6.4.1 Performance Results.........................................................................166
6.4.2 Rule Extraction Evaluation..............................................................169
6.5 Conclusions.............................................................................................171
References.....................................................................................................172
7 Neural Networks for Reliability-Based Optimal Design
Ming J Zuo, Zhigang Tian, Hong-Zhong Huang.................................................175
7.1 Introduction.............................................................................................175