Computational Intelligence in Reliability Engineering - Evolutionary Techniques in Reliability Analysis and Optimization

Gregory Levitin (Ed.)

Contents
Way Kuo, Rui Wan ................................................................................................... 1
1.1 Introduction................................................................................................... 3
1.2 Problem Formulations .................................................................................. 6
1.3 Brief Review of Advances In P 1 -P 4 .............................................................. 8
1.3.1 Traditional Reliability-Redundancy Allocation Problem (P 1 ).............. 8
1.3.1.1 Active and Cold-Standby Redundancy ...................................... 9
1.3.1.2 Fault-Tolerance Mechanism..................................................... 10
1.3.2 Percentile Life Optimization Problem (P 2 ) ......................................... 11
1.3.3 MSS Optimization (P 3 ) ....................................................................... 12
1.3.4 Multi-Objective Optimization (P 4 )...................................................... 16
1.4.1 Meta-Heuristic Methods ..................................................................... 19
1.4.1.1 Ant Colony Optimization Method ........................................... 19
1.4.1.2 Hybrid Genetic Algorithm ....................................................... 20
1.4.1.3 Tabu Search.............................................................................. 21
1.4.1.4 Other Meta-Heuristic Methods ................................................ 22
1.4.2 Exact Methods..................................................................................... 22
1.4.3 Other Optimization Techniques .......................................................... 23
1.5 Comparisons and Discussions of Algorithms Reported in Literature........ 25
1.6 Conclusions and Discussions...................................................................... 27
References......................................................................................................... 29
2 Multiobjective Metaheuristic Approaches to Reliability Optimization
Sadan Kulturel-Konak, Abdullah Konak, David W. Coit....................................... 37
2.1 Introduction................................................................................................. 37
2.2 Metaheuristics and Multiobjective Optimization ....................................... 39
2.2.1 Metaheuristics ..................................................................................... 39
2.2.2 Metaheuristic Approaches to Multiobjective Optimization................ 41
2.3 Multiobjective Tabu Search and Reliability Optimization......................... 42
2.3.1 The Multinomial Tabu Search Algorithm to Solve Redundancy
Allocation Problem ............................................................................. 42
2.3.1.1 Multiobjective System Redundancy Allocation Problem........ 42
2.3.1.2 Multinomial Tabu Search Algorithm ....................................... 43
2.3.1.3 Computational Experiments..................................................... 45
2.4 Multiobjective Genetic Algorithms ............................................................ 47
2.4.1 Multiobjective GA Approaches to Reliability Optimization.............. 48
1 Recent Advances in Optimal Reliability Allocation
1.4 Developments in Optimization Techniques ............................................... 18 2.5 Multiobjective Optimization of Telecommunication Networks
Considering Reliability .............................................................................. 50
2.5.1 Network Survivability and Reliability................................................ 50
2.5.2 Multiobjective Elitist GA with Restricted Mating.............................. 52
2.5.2.1 Problem Encoding.................................................................... 52
2.5.2.2 Crossover Operator .................................................................. 52
2.5.2.3 Mutation ................................................................................... 53
2.5.2.4 Overall Algorithm .................................................................... 53
2.5.3 Computational Experiments................................................................ 55
2.6 Other Metaheuristic Techniques to Multiobjective Reliability
Optimization............................................................................................... 56
2.6.1 Ant Colony Optimization.................................................................... 56
2.6.2 Simulated Annealing........................................................................... 57
2.6.3 Conclusions......................................................................................... 57
References ........................................................................................................ 58
3 Genetic Algorithm Applications in Surveillance and Maintenance
Optimization
Sebastián Martorell, Sofía Carlos, José F. Villanueva, Ana Sánchez................... 63
3.1 Introduction ................................................................................................ 63
3.2 Analysis of Published Research ................................................................. 67
3.3 Overview of Testing and Maintenance ...................................................... 71
3.3.1 RAMS and the role of T&M at NPP................................................... 71
3.3.2 Failure types and T&M activities ....................................................... 77
3.4 Decision-making Based on RAMS+C ....................................................... 78
3.4.1 Basis for the RAMS+C informed decision-making............................ 78
3.4.2 Quantification models of RAMS+C ................................................... 80
3.5.1 Problem Formulation ..........................................................................
3.5.2 Solution Approaches........................................................................... 84
3.6 Genetic Algorithms .................................................................................... 86
3.6.1 Origin, fundamentals and first applications........................................ 86
3.6.2 Pioneering GA..................................................................................... 87
3.7 Research Areas ........................................................................................... 91
References ........................................................................................................ 94
4 Genetic Algorithms and Monte Carlo Simulation for the Optimization of
System Design and Operation
Marzio Marseguerra, Enrico Zio, Luca Podofillini............................................. 101
4.1 Introduction .............................................................................................. 101
4.1.1 Motivations for the GA-MC Approach ............................................ 102
4.1.1.1 Use of Monte Carlo Simulation for the System Modeling .... 102
4.1.1.2 Use of Multi-Objective Genetic Algorithms for the System
Optimization .......................................................................... 103
4.1.1.3 Combination of GA-MC ........................................................ 104
3.5 Optimization Problem ................................................................................
84
84
3.6.3 Development of multi-objective GA .................................................. 89
4.1.2 Application to System Optimization Under Uncertainty.................. 105
4.1.3 Structure of the Chapter .................................................................... 106
4.2 Fundamentals of Monte Carlo Simulation ............................................... 106
4.2.1 The System Transport Model............................................................ 107
4.2.2 Monte Carlo Simulation for Reliability Modeling............................ 107
4.3 Genetic Algorithms................................................................................... 112
4.3.1 Introduction ....................................................................................... 112
4.3.2 The Standard GA Procedure ............................................................. 115
4.4 Embedding the Monte Carlo Simulation in the Genetic Algorithm
Search Engine........................................................................................... 117
4.5 Optimization of the Design of a Risky Plant............................................ 118
4.5.1 Problem Statement ............................................................................ 118
4.5.2 Applying the GA-MC Approach....................................................... 121
4.6 Multi-objective Genetic Algorithms......................................................... 127
4.7 Optimizing the Technical Specifications of the Reactor Protection
Instrumentation System of a PWR ........................................................... 129
4.7.1 System Description ........................................................................... 130
4.7.2 Testing Procedures and TSs of the RPIS .......................................... 131
4.7.3 Modeling Assumptions ..................................................................... 132
4.7.4 Multiobjective Optimization ............................................................. 140
4.8 Conclusions............................................................................................... 145
References....................................................................................................... 147
5 New Evolutionary Methodologies for Integrated Safety System Design and
Maintenance Optimization
B. Galván, G. Winter, D. Greiner, D. Salazar, M. Méndez ................................. 151
5.1 Introduction............................................................................................... 151
5.2 Evolutionary Algorithms (EA) ................................................................. 155
5.2.1 Multiple Objective Evolutionary Algorithms ................................... 155
5.2.2 Evolutionary Algorithms with Mixed Coding Schemes:
A Double Loop Approach................................................................. 157
5.2.3 Flexible Evolutionary Algorithms .................................................... 163
5.3 Integrated Safety Systems Optimization .................................................. 167
5.3.1 The System Model ............................................................................ 167
5.3.2 Components Unavailability and Cost Models .................................. 169
5.3.3 Computing the System Model Using Restricted Sampling .............. 171
5.3.4 Coding Schemes................................................................................ 172
5.4 Application example: The Containment Spray System of a
Nuclear Power Plant ................................................................................. 173
5.4.1 System Description ........................................................................... 173
5.4.2 Models and Parameters Selected....................................................... 175
5.4.3 System Model.................................................................................... 176
5.5 Results....................................................................................................... 177
5.6 Conclusions............................................................................................... 184
References....................................................................................................... 186
6 Optimal Redundancy Allocation of Multi-State Systems with Genetic
Algorithms
Zhigang Tian, Ming J Zuo, Hong-Zhong Huang ................................................. 191
6.1 Introduction .............................................................................................. 191
6.1.1 Optimal Redundancy Allocation of Multi-state Systems ................. 191
6.1.2 Optimal Redundancy Allocation of Multi-state Systems with
Genetic Algorithms........................................................................... 193
6.1.3 Content of this Chapter ..................................................................... 195
6.2 System Utility Evaluation......................................................................... 195
6.2.1 Multi-state Series-parallel Systems by Barlow and Wu (1978) ....... 196
6.2.2 The Multi-state Load Sharing Series-parallel Systems by Levitin
et al (1998) ........................................................................................ 198
6.2.3 Multi-state k-out-of-n Systems ......................................................... 200
6.2.4 General Comments............................................................................ 201
6.3 Optimization Models for Multi-state Systems ......................................... 201
6.3.1 Single-objective Optimization Models ............................................. 202
6.3.2 The Multi-objective Optimization Model......................................... 203
6.4 Implementation of Genetic Algorithms.................................................... 206
6.4.1 General Framework of GA ............................................................... 206
6.4.2 Encoding and Decoding.................................................................... 207
6.4.3 Fitness Function Value ..................................................................... 208
6.4.4 Fitness Function Value ..................................................................... 208
6.5 An Application Example .......................................................................... 208
6.6 Concluding Remarks ................................................................................ 211
References ...................................................................................................... 212
7 Intelligent Interactive Multiobjective Optimization of System
Reliability
Hong-Zhong Huang, Zhigang Tian, Ming J Zuo ................................................. 215
7.1 Introduction .............................................................................................. 215
7.2 Multiobjective Optimization Problem...................................................... 217
7.2.1 Problem Formulation ........................................................................ 217
7.2.2 Pareto Solution.................................................................................. 217
7.3 Designer’s Preference Structure Model ................................................... 219
7.3.2 General Multiobjective Optimization Procedure.............................. 219
7.3.3 Designer’s Preference Structure Model............................................ 221
7.3.4 Preference Information Elicitation.................................................... 222
7.4 IIMOM Procedure .................................................................................... 222
7.5 Application of IIMOM to Reliability Optimization Problem .................. 225
7.5.1 Problem Definition............................................................................ 225
7.5.2 The Mapping from Weight Vector to Preference Value .................. 227
7.5.3 Results and Discussions.................................................................... 228
7.5.4 Discussion on the Performances of IIMOM ..................................... 234
7.2.3 Weighted-sum Method...................................................................... 218
7.2.4 Augment Weighted Tchebycheff Programs ..................................... 218
7.3.1 Model Parameter Vector ................................................................... 219 7.6 Conclusions............................................................................................... 235
References....................................................................................................... 236
8 Reliability Assessment of Composite Power Systems Using Genetic
Algorithms
Nader Samaan, Chanan Singh ............................................................................. 237
8.1 Introduction............................................................................................... 237
8.2 Reliability Evaluation of Composite Generation-Transmission Systems 239
8.3 Genetic Algorithms Approach for the Assessment of Composite
Systems Annualized Indices..................................................................... 241
8.3.1 Construction of System State Array.................................................. 244
8.3.2 Evolution of a New Generation ........................................................ 246
8.3.3 Stopping Criterion............................................................................. 247
8.3.4 State Evaluation Model..................................................................... 249
8.3.5 Assessment of Composite System Adequacy Indices ...................... 251
8.3.6 Case Studies for the Assessment of Annualized Indices .................. 252
8.4 Reliability Indices Considering Chronological Load Curves................... 254
8.4.1 Modeling of Chronological Load Curve........................................... 255
8.4.2 Genetic Algorithms Sampling with m Cluster Load Vectors ........... 257
8.4.2.1 Genetic Algorithms Parallel Sampling................................... 257
8.4.2.2 Genetic Algorithm Sampling for Maximum Cluster Load
Vector with Series State Revaluation .................................... 258
8.4.3 State Evaluation Model..................................................................... 260
8.4.4 Case Studies for the Assessment of Annual Indices......................... 262
8.4.4.1 Fully Correlated Load Buses.................................................. 262
8.4.4.2 Partially Correlated Load Buses............................................. 264
8.5 Calculation of Frequency and Duration Indices....................................... 266
8.5.1 Modeling of the Chronological Load................................................ 267
8.5.1.1 Calculating Transition Rates between Load Clusters ............ 268
8.5.2 Calculating Failure State Contribution to System
Failure Frequency ............................................................................. 269
8.5.3 Non-Sequential Monte Carlo Sampling............................................ 271
8.5.4 Genetic Algorithm Sampling for Maximum Load State with
Series State Reevaluation.................................................................. 272
8.5.5 Case Studies for the Assessment of Frequency and Duration
Indices ............................................................................................... 273
8.6 Consideration of Multi-State Components............................................... 276
8.6.1 Representation of Generating Unit Derated States ........................... 276
8.6.2 Consideration of Common Mode Failures in Transmission Lines ... 278
8.6.3 Case Studies with Multi-State Components ..................................... 279
8.6.3.1 Generating Unit Derated States.............................................. 279
8.6.3.2 Common Mode Outage .......................................................... 281
8.7 Summary and Conclusions ....................................................................... 282
References....................................................................................................... 283
Appendix: The RBTS Test System Data........................................................ 285
9 Genetic Optimization of Multidimensional Technological Process
Reliability
Alexander Rotshtein, Serhiy Shtovba ................................................................... 287
9.1 Introduction .............................................................................................. 287
9.2 Statements of the Problems ...................................................................... 288
9.3 Models of Multidimensional Technological Process Reliability ............. 289
9.4 Basic Notions of Genetic Algorithms ...................................................... 291
9.5 Genetic Algorithm for Multidimensional Technological Process
Optimization............................................................................................. 291
9.5.1 Genetic Coding of Variants .............................................................. 292
9.5.2 Initial Population............................................................................... 292
9.5.3 Crossover and Mutation.................................................................... 293
9.5.4 Fitness Function ................................................................................ 294
9.5.5 Fast Calculation of the Reliability .................................................... 295
9.5.6 Selecting Schemes ............................................................................ 295
9.6 Computational Experiments ..................................................................... 295
9.7 Conclusions .............................................................................................. 300
References ...................................................................................................... 300
10 Scheduling Multiple-version Programs on Multiple Processors
...................................................................... 301
10.1 Introduction ............................................................................................ 301
10.2 Scheduling Multiprocessor Tasks – Case of the Statistically
Independent Failures .............................................................................. 304
10.2.1 Problem Formulation ...................................................................... 304
10.2.2 Computational Complexity of Multiprocessor Task Scheduling
Problems ......................................................................................... 306
10.2.3 Approximation Algorithms for Solving Multiprocessor Task
Scheduling Problems in the m-p Mode .......................................... 307
10.2.3.1 Tabu Search Algorithm Implementation.............................. 307
10.2.3.2 Population Learning Algorithm Implementation................. 309
10.2.4 Computational Experiment Results ................................................ 312
10.3 Scheduling Multiprocessor Tasks in the Presence of Correlated
Failures................................................................................................... 313
10.3.1 Multiprocessor Task Reliability Model .......................................... 313
10.3.2 Approximation Algorithms for Solving Multiprocessor Task
Scheduling Problems in the Presence of Correlated Failures ........ 316
10.3.2.1 Island Based Evolution Algorithm – IBEA ......................... 317
10.3.2.2 Neural Network Algorithm – NNA ..................................... 319
10.3.2.3 Hybrid 3opt-tabu Search Algorithm – TSA......................... 321
10.3.2.4 Population Learning Scheme – PLS .................................... 322
10.3.3 Numerical Example and the Results of the Computational
Experiment...................................................................................... 323
10.4 Conclusions ............................................................................................ 325
References ...................................................................................................... 326
Piotr Jędrzejowicz, Ewa Ratajczak 11 Redundancy Optimization Problems with Uncertain Lifetimes
Ruiqing Zhao, Wansheng Tang ............................................................................ 329
11.1 Introduction............................................................................................. 329
11.2 Uncertain Variables ................................................................................ 331
11.2.1 Fuzzy Variable ................................................................................ 331
11.2.2 Fuzzy Random Variable.................................................................. 336
11.2.3 Random Fuzzy Variable.................................................................. 338
11.3 Redundancy Optimization Problem ....................................................... 340
11.4 System Performances ............................................................................. 341
11.4.1 Fuzzy Simulations........................................................................... 342
11.4.1.1 Fuzzy Simulation for )] , ( [ ξ x T E ....................................... 342
11.4.1.2 Fuzzy Simulation for } ) , ( { Cr
0
T x T ≥ ξ ........................... 344
11.4.1.3 Fuzzy Simulation for T ...................................................... 345
11.4.2 Fuzzy Random Simulation.............................................................. 347
11.4.2.1 Fuzzy Random simulation for )] ξ ,x( [T E ......................... 347
11.4.2.2 Fuzzy Random Simulation for T ........................................ 348
11.4.2.3 Fuzzy Random Simulation for System Reliability .............. 348
11.4.3 Random Fuzzy Simulation.............................................................. 351
11.4.3.1 Random Fuzzy simulation for )] ξ ,x( [T E ......................... 351
11.4.3.2 Random Fuzzy Simulation for T ........................................ 351
11.4.3.3 Random Fuzzy Simulation for System Reliability .............. 352
11.5 Redundancy Optimization Models ......................................................... 354
11.5.1 Redundancy EVMs ......................................................................... 354
11.5.2 Redundancy CCP ............................................................................ 356
11.5.3 Redundancy DCP ............................................................................ 357
11.6 Genetic Algorithm Based on Simulation................................................ 359
11.6.1 Structure Representation ................................................................. 359
11.6.2 Initialization Process ....................................................................... 360
11.6.3 Evaluation Function ........................................................................ 360
11.6.4 Selection Process............................................................................. 361
11.6.5 Crossover Operation ....................................................................... 361
11.6.6 Mutation Operation ......................................................................... 362
11.6.7 The Genetic Algorithm Procedure .................................................. 363
11.7 Numerical Experiments .......................................................................... 364
References....................................................................................................... 372
12 Computational Intelligence Methods in Software Reliability Prediction
Liang Tian, Afzel Noore ....................................................................................... 375
12.1 Introduction............................................................................................. 375
12.2 Dynamic Evolutionary Neural Network (D–ENN) Learning ................ 380
12.3 Recurrent Neural Network with Bayesian Regularization (RNN–BR) 382
12.3.1 Recurrent Neural Network .............................................................. 382
12.3.2 Bayesian Regularization ................................................................. 385
12.3.3 Modeling Rationale......................................................................... 386

12.4 Adaptive Support Vector Machine (A–SVM) Learning ........................ 387
12.4.1 SVM Learning in Function Approximation.................................... 387
12.4.2 Lagrange Multipliers....................................................................... 389
12.4.3 Kernel Function .............................................................................. 389
12.4.4 Formulation of the SVM-Predictor................................................. 390
12.5 Validation of New Approaches .............................................................. 390
12.5.1 Data Sets Description and Pre-processing ...................................... 391
12.5.2 Experimental Results ...................................................................... 391
12.6 Discussions and Future Work................................................................. 393
12.6.1 Data Type Transformation.............................................................. 394
12.6.2 Modeling Long-Term Behavior...................................................... 394
12.6.3 Assessment of Predictive Accuracy................................................ 395
12.6.4 Incorporating Environmental Factors ............................................. 395
References ...................................................................................................... 396

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