Risk and Reliability Analysis: Theory and Applications (eBook)

Preface 7
Acknowledgements 9
Contents 10
Introduction 13
1 Risk and Reliability Analysis 14
Abstract 14
1 Introduction 15
2 Armen Der Kiureghian and His Role in Modern Risk and Reliability Analysis 16
2.1 Biography 16
2.2 Role in Modern Risk and Reliability Analysis 17
2.3 Overall Goal and Contributions of the Book 19
3 Structure and Overview of the Volume 20
References 26
Reliability Analysis: Methods and Applications 36
2 Structural System Reliability, Reloaded 37
Abstract 37
1 Introduction 38
2 Methods Developed to Address Essential Needs in SSR 39
2.1 Bounds on System Reliability by Linear Programming (LP Bounds) 39
2.2 Matrix-Based System Reliability (MSR) Method 41
2.3 Sequential Compounding Method (SCM) 44
2.4 Cross-Entropy-Based Adaptive Importance Sampling (CE-AIS) 45
3 Methods Developed to Address Needs in SSR Analysis of Complex Systems 47
3.1 Selective Recursive Decomposition Algorithm (S-RDA) 47
3.2 Branch-and-Bound Method Employing System Reliability Bounds (B3 Method) 50
3.3 Genetic-Algorithm-Based Selective Search for Dominate Failure Modes 52
4 Summary and Conclusions 53
Acknowledgements 54
References 54
3 Global Buckling Reliability Analysis of Slender Network Arch Bridges: An Application of Monte Carlo-Based Estimation by Optimized Fitting 57
Abstract 57
1 Introduction 57
2 Network Arch Bridge 59
2.1 Model Uncertainty 61
2.2 Traffic Load 62
2.3 Buckling Analysis of Network Arch Bridges 63
3 Efficient System Reliability Estimation 64
3.1 Monte Carlo-Based Reliability Estimation by Optimized Fitting 65
4 The Brandanger Network Arch Bridge—A Case Study 67
4.1 Structural Response by Finite Element Analysis 68
4.2 Global System Buckling Reliability Estimation 69
5 Conclusions 75
References 75
4 Review of Quantitative Reliability Methods for Onshore Oil and Gas Pipelines 77
Abstract 77
1 Introduction 77
2 Problem Definition 78
2.1 Limit States 79
2.2 Hazards 80
3 Excavation Damage 83
3.1 Uncertainties 84
3.2 Models 85
3.2.1 Puncture 86
3.2.2 Dent-Gouge 87
3.2.3 Gouge 88
3.2.4 Rupture 88
3.3 Methods to Estimate the Probability of Failure 88
4 Corrosion 89
4.1 Uncertainties 90
4.2 Models 90
4.2.1 Occurrence Models 90
4.2.2 Growth Models 92
4.2.3 Limit States 94
4.3 Methods to Estimate the Probability of Failure 95
5 Cracks 97
6 Natural Hazards 98
7 Human Error 100
8 Conclusion 100
References 101
Stochastic Dynamics: Methods and Applications 106
5 An Intuitive Basis of the Probability Density Evolution Method (PDEM) for Stochastic Dynamics 107
Abstract 107
1 Introduction 107
2 Practical Significance of PDEM 108
2.1 Brief Theoretical Basis 108
2.2 Reliability of Complex Systems 109
3 On Application to Reliability of Complex Systems 110
4 Numerical Examples 110
5 Implications to Reliability-Based Design 115
6 Conclusions 115
Acknowledgements 115
References 116
6 The Tail Equivalent Linearization Method for Nonlinear Stochastic Processes, Genesis and Developments 117
Abstract 117
1 Introduction 118
2 The Original Time Domain TELM 119
2.1 Input Representation 119
2.2 Time-Domain Response Representation, and TELS Definition 120
3 TELM Analysis in Frequency Domain 122
3.1 Input Representation 122
3.2 Frequency-Domain Response Representation, and TELS Definition 123
4 TELM Analysis with Sinc Basis Functions 124
4.1 Numerical Example 126
5 TELM for Multiple-Supported Excitation Problems 129
5.1 Representation of Correlated Ground Motions 129
5.2 Formulation of TELS for Multiple-Support Excitation Analysis 132
5.3 Random Vibration Analysis 135
6 The Secant Hyperplane Method and the Tail Probability Equivalent Linearization Method 136
6.1 High-Dimensional Spaces 136
6.2 The Multi-variate Normal Standard Distribution 140
6.3 Structural Reliability Analysis in High Dimensions 141
6.4 Applicability of FORM in High Dimensions 142
6.5 The Secant Hyperplane Method (SHM) for Stochastic Dynamic Analysis 142
6.6 The Tail Probability Equivalent Linearization Method (TPELM) 145
6.7 Numerical Example 145
7 Conclusions 148
References 148
7 Estimate of Small First Passage Probabilities of Nonlinear Random Vibration Systems 151
Abstract 151
1 Introduction 151
2 Brief Description of the SGLD 153
3 Small Probabilities of First-Passage Failure 157
4 Extreme Value Distributions of Nonlinear Random Responses 158
4.1 Marginal Distribution and Its Parameter Estimate 158
4.2 Joint Distribution and Its Parameter Estimate 159
5 Procedure for the Estimation of Small Probabilities of Failure 160
6 Numerical Examples 161
6.1 Investigation of the Efficiency of the 2-Level Method for Estimating the Parameters of the SGLDs 161
6.2 Hysteretic Oscillator Excited by a Stationary Gaussian Process 163
6.3 Mechanical Model of Two Connected Electric Substation Equipment Items 165
6.4 Network Seismic Reliability of a Lifeline Engineering 170
7 Conclusions 175
References 175
8 Generation of Non-synchronous Earthquake Signals 177
Abstract 177
1 Introduction 178
2 Random Field Propagation Model and Definition of Earthquakes that Vary in Space 181
2.1 Spatial Model of the Earthquakes 182
2.2 Case Study: Generation of Surface Asynchronous Signals at the Foundations of a Bridge Located in the Aterno Valley Near L’Aquila, Italy 187
2.3 Random Field Generation Procedure PR1 and PR2 189
2.4 Comparison of the Generated Signals by Procedure PR1 and PR2 at Surface 191
2.4.1 Comparison Among FFT Amplitude Spectra 192
2.4.2 Comparison Among Signals Coherences at Different Surface Points 192
2.4.3 Comparison Among the Acceleration Response Spectra Sa 197
3 Conclusion 203
Acknowledgements 204
References 204
9 Seismic Response Analysis with Spatially Varying Stochastic Excitation 207
Abstract 207
1 Introduction 208
2 Modeling of Ground-Motion Spatial Variability 209
2.1 The Coherency Function 209
2.2 Estimation of the Coherency Modulus 211
2.3 The Case of the UPSAR Array 212
3 Simulation of Spatially Varying Ground Motions 215
3.1 The Unconditioned and Conditioned Approaches 215
3.2 Discrete Representation of an Array of Gaussian Processes 216
3.3 Simulation of Stationary Motions with the Unconditioned Approach 217
3.4 Simulation of Stationary Motions with the Conditioned Approach 218
3.5 Extension to Non-stationary Motions 219
3.6 Example Application 220
4 Structural Response to Differential Support Excitation 222
4.1 Linear Response Analysis with Response-Spectrum Methods 222
4.2 The Generalized MSRS Rule 224
4.3 The Extended MSRS Rule 226
4.4 Non-linear Response: The ‘Equal Displacement’ Rule 229
5 Conclusions and Perspectives 231
Acknowledgements 231
References 232
Sensitivity Analysis and Optimization 234
10 Application of CQC Method to Seismic Response Control with Viscoelastic Dampers 235
Abstract 235
1 Introduction 235
2 Review of a Developed VED 238
2.1 Mechanical Characteristics of VE Material 238
2.2 NLF Model of VE Material 241
2.3 Dynamic Loading Tests of VED 243
3 Maximum Earthquake Response of a Building with VEDs 245
3.1 Equivalent Linearization of VED 245
3.2 Modal Analysis by the Expanded CQC Method 246
4 Performance-Based Placement-Design Procedure of VED 248
5 Design Examples 249
5.1 High-Rise Building Models with Optimally Placed VED 250
5.2 Verification by Time-History Response Analyses 254
6 Conclusions 255
Acknowledgements 256
Appendix I 256
Earthquake Interstory Drifts of Hypothetical 15- and 24-story Buildings 256
Appendix II 257
Voigt Model of VED Considering the Stiffness of the Mounting Component 257
References 258
11 Optimal Design of Reinforced Concrete Section Under Combined Dynamic Action 261
Abstract 261
1 Foreword 261
2 Scope 262
3 Reinforced Concrete Section Analysis 263
3.1 Assumptions 263
3.2 Discretization 264
3.3 Constitutive Relations of Materials 265
4 Relations Between Distributor of Longitudinal Strains and the Vector of Reduced Forces 267
5 Limit States 269
6 Interaction Curves 270
7 Aerodynamic and Seismic Forces 271
8 Standard Practice for the Design of a Reinforced Concrete Section 272
9 Improvement of the Design Method—Transformation to the Standard Normal Space 275
10 Search for a Design Point and Safety Margin 276
11 Optimization of a Reinforced Concrete Section 278
12 Conclusion 280
References 281
FORM Sensitivities to Distribution Parameters with the Nataf Transformation 282
1 Introduction 282
2 Nataf Transformation 284
3 Sensitivities to Distribution Parameters 287
3.1 Sensitivity to Correlation 288
3.2 Sensitivity to Parameters of Marginal Distributions 289
4 Application Examples 290
4.1 Example 1: CalRel Example 291
4.2 Example 2: Load-Resistance Problem with Correlated Lognormal R and S 292
4.3 Example 3: A Three-Span, Five-Story Linear Elastic Frame Structure Subjected to Lateral Loads 295
4.4 Example 4: Crack Propagation Based on the Virkler Data 298
5 Concluding Remarks 304
References 305
13 Using FORM for Minimizing the Uncertain Cost of Structural Designs 308
Abstract 308
1 Introduction 308
2 Methodology 309
3 Cost Thresholds 311
4 Warm Starts in FORM 313
5 Exact Gradients 314
6 Demonstration Example 316
7 Conclusions and Ongoing Studies 318
References 319
Statistical Analysis and Probabilistic Models 320
14 Model Checking After Bayesian Inference 321
Abstract 321
1 Introduction 321
2 Model Checking Using Bayesian Inference 323
2.1 Inference Within a Single Model 323
2.2 Comparison of Models 324
2.3 Rejecting a Model by Computing Its Posterior Probability 325
3 Prior and Posterior Model Checking Using p-Value Analysis 325
4 Bayesian Selection of Test Statistic 327
4.1 Bayesian Model Comparison Versus p-Value Analysis 327
4.2 Selection of Test Statistics 329
4.3 Selecting Test Statistics for Linear Gaussian Models 330
5 Illustrative Examples of Linear Gaussian Models 332
5.1 Toy Example in Data Analysis 332
5.2 Identification of the Stiffness of a Cantilever 334
6 Numerical Investigation of a Non-gaussian Model 335
7 Conclusions 338
Appendix A: Gaussian Linear Models 339
Appendix B: Monte Carlo Scheme for Numerical Investigation of the P-Value 341
References 342
15 Batch and Recursive Bayesian Estimation Methods for Nonlinear Structural System Identification 344
Abstract 344
1 Introduction 345
2 Bayesian FE Model Updating 346
2.1 Batch Bayesian Estimation Method 348
2.2 Recursive Bayesian Estimation Method 350
2.2.1 Extended Kalman Filter (EKF) 350
2.2.2 Unscented Kalman Filter (UKF) 352
3 Application Example 353
3.1 Bayesian FE Model Updating 356
3.1.1 Discussion of Parameter Estimation Results 359
3.2 Computational Cost 364
4 Conclusions 364
Acknowledgements 365
References 365
16 Reliability Updating in the Presence of Spatial Variability 368
Abstract 368
1 Introduction 368
2 Methodology 370
2.1 Random Field Discretization 370
2.2 Reliability Analysis 372
2.3 Bayesian Analysis and Reliability Updating 375
2.4 Reliability Updating with Random Fields 376
3 Numerical Investigations 378
3.1 Problem Description 378
3.2 Results and Discussion 380
4 Concluding Remarks 384
References 385
17 Bayesian Networks and Infrastructure Systems: Computational and Methodological Challenges 387
Abstract 387
1 Introduction 388
2 BN Model of Seismic Hazard 389
3 MLS-Based Approach 391
3.1 Compression Algorithm 395
3.2 Application to a Water Supply Network 396
4 Simulation-Based Approach 400
4.1 The Thrifty Naïve (t-Naïve) Formulation 400
4.2 The Object-Oriented Platform for Infrastructure Systems Modeling and Simulation (OOFIMS) 401
4.3 Kang and Lee Water Supply System by the t-Naïve Formulation 404
4.4 A Larger, Realistically Sized Example 409
5 Conclusions and Future Work 415
Acknowledgements 415
References 416
18 Bayesian Network Methods for Modeling and Reliability Assessment of Infrastructure Systems 418
Abstract 418
1 Introduction 418
2 Bayesian Networks (BNs) 419
2.1 Advantages of BNs 420
2.2 Limitations of BNs 421
2.3 BNs for Analyzing System Reliability 421
2.4 Conditional Probability Tables (CPTs) 421
2.5 BN Formulation for Infrastructure Systems 422
3 Compression Algorithm 423
3.1 Run-Length Encoding 424
3.2 Lempel-Ziv 424
3.3 Developed Compression Algorithm 425
3.4 Application to an Example System 427
3.4.1 Construction of Compressed CPT 428
4 Inference Algorithm 430
4.1 Variable Elimination (VE) 430
4.2 Junction Tree (JT) 431
4.3 Developed Inference Algorithm 432
4.4 Example System 434
4.4.1 Results of Implementing Inference Algorithm 436
5 Performance of Algorithms 437
5.1 Test Example Systems 438
5.2 Memory Storage 438
5.3 Computation Time 440
6 Heuristic Augmentations 442
6.1 Heuristic for Compression Algorithm 442
6.2 Heuristic for Inference Algorithm 444
6.3 Algorithm for Supercomponents 445
7 Application: Power System 447
7.1 Inference 448
7.2 Performance of New Algorithms 449
8 Conclusions 451
Acknowledgements 451
References 452
Kriging Interpolation Strategy for Finite-Element-Based Surrogate Responses of DCB Delamination Tests 454
1 Introduction 454
2 Mode-I Delamination Test Parameter Identification 456
3 Kriging Interpolation 458
4 Parameter Calibration and Numerical Application 459
4.1 Discussion 460
5 Conclusions 461
References 461
Life-cycle and Resilience Analysis and Financial Tools 463
20 Life-Cycle Analysis of Engineering Systems: Modeling Deterioration, Instantaneous Reliability, and Resilience 464
Abstract 464
1 Introduction 465
2 Life-Cycle Analysis 467
2.1 Availability 469
2.2 Cost of Operation, Failure Losses, and Benefit 469
3 Performance Analysis 470
3.1 Modeling of Deterioration Processes 470
3.1.1 State Change Due to Deterioration 471
3.1.2 Stochastic Capacity and Demand Models 473
3.2 Modeling of the Recovery Process 473
3.2.1 State Change Due to Recovery 474
3.2.2 Stochastic Capacity and Demand Models 475
4 Reliability Analysis 475
5 Resilience Analysis 476
6 Illustrative Example 478
6.1 Modeling of Deterioration of RC Bridges Due to Corrosion and Seismic Excitations 479
6.1.1 Deterioration Due to Corrosion 479
6.1.2 Deterioration Due to Seismic Excitations 481
6.2 Modeling of Recovery Process 482
6.3 Results and Discussion 485
6.3.1 Instantaneous Reliability and Resilience 485
6.3.2 Life-Cycle Performance Measures 486
7 Conclusions 490
Acknowledgements 491
References 491
Fragility Curves of Restoration Processes for Resilience Analysis 494
1 Introduction 494
1.1 State of the Art 495
2 Restoration Fragility Functions 496
3 Methodology 496
4 Case Study: The Mauriziano Hospital in Turin 497
4.1 Hospital Performance and Restoration Functions (rf) 499
4.2 Numerical Results 499
4.3 RFF Comparison Between ED with and Without Emergency Plan Applied 505
5 Conclusions 505
References 506
22 A Decision Support Tool for Sustainable and Resilient Building Design 507
Abstract 507
1 Introduction 508
2 Multi Criteria Decision-Making Under Uncertainty 510
2.1 MAUT 510
2.2 Probabilistic MAUT 511
2.3 Expected Utility and Risk Measures for a Single Criterion 513
2.4 Decision Analysis Using Target 516
3 Evaluation of the Distribution of the Utility Functions 517
4 Joint Distribution of the Uncertain Parameters 519
4.1 PBE Approach 519
4.2 Unified Reliability Approach 520
4.3 Probability Distributions 521
5 Bayesian Networks for Sustainable and Resilient Building Design 521
6 Lifecycle Sustainability Analysis of Sinberbest Office Space in the Create Building, Singapore 527
6.1 Decision Criteria 527
6.2 Definition of the Alternatives and BN Model for Lifecycle Analysis 529
6.3 PBE-MAUT 529
7 Concluding Remarks 531
Acknowledgements 532
References 532
23 Innovative Derivatives to Drive Investment in Earthquake Protection Technologies 535
Abstract 535
1 Introduction 535
2 Basic Scheme 537
2.1 General View of Regular Cat Bond 537
2.2 New Derivatives to Promote Earthquake Protection 539
2.3 Derivatives Price 542
3 Pricing Formula 542
4 Case Study 545
4.1 An Actual Cat Bond 545
4.2 Earthquake Models 548
4.3 Benchmarking 552
4.4 Pricing 553
5 Conclusions 555
References 556
24 Erratum to: Model Checking After Bayesian Inference 558
Erratum to:& #6