Table of Contents

Preface
Chapter 1 Introduction 1
1.1 Basic concepts in the structure and mechanism reliability analysis 2
1.2 Progress in the structure and mechanism reliability analysis 5
1.3 Main contents of this book 10
Chapter 2 Moment method for reliability and local reliability sensitivity analysis 11
2.1 First-order and second-moment method 11
2.1.1 First-order and second-moment method for reliability analysis 11
2.1.2 First-order and second-moment method for local reliability sensitivity analysis 14
2.1.3 Examples 17
2.2 Advanced first-order and second-moment method 18
2.2.1 Advanced first-order and second-moment method for reliability analysis 18
2.2.2 Advanced first-order and second-moment method for local reliability sensitivity analysis 24
2.2.3 Examples 27
2.3 Rackwitz-Fiessler reliability analysis algorithm for non-normal random variables 29
2.3.1 Basic theory and implementation of R-F algorithm 29
2.3.2 Specific implementation steps of R-F algorithm 32
2.3.3 Examples 33
2.4 Point estimation method for statistical moment of performance function 35
2.4.1 Definition of statistical moment of performance function 35
2.4.2 Two-point estimation method by Rosenblueth 35
2.4.3 Three-point estimation method by Gorman and Seo 38
2.4.4 Point estimation method by Zhou and Nowak 39
2.4.5 Point estimation method by Zhao and Ono 44
2.5 Fourth-order moment method for reliability and local reliability sensitivity analysis 46
2.5.1 Fourth-order moment method for reliability analysis 46
2.5.2 Fourth-order moment method for local reliability sensitivity analysis 47
2.5.3 Examples 51
2.6 Moment method for system reliability and local reliability sensitivity analysis 52
2.6.1 Calculation of the system moment 52
2.6.2 Examples 52
2.7 Independent transformation of correlated variables 56
2.7.1 Rosenblatt method for transforming correlated variables into the independent normal variables 57
2.7.2 Orthogonal transformation method for independent transformation of correlated normal variables 57
2.7.3 Geometric meaning of correlation coefficient of two linear performance functions in standard normal space 59
2.7.4 Examples 60
2.8 Discussion on the applicability scope of point estimation-based moment method 63
2.9 Summary 63
Bibliography 64
Chapter 3 Monte Carlo simulation method 66
3.1 Random number generator and sampling principle of random variable 66
3.1.1 Random number generator 66
3.1.2 Sampling principle of random variable 67
3.1.3 Sampling methods commonly used in reliability analysis 69
3.2 Monte Carlo simulation method for reliability analysis and its convergence 71
3.2.1 Monte Carlo simulation method for reliability analysis of single failure mode and its convergence 71
3.2.2 Monte Carlo simulation method for reliability analysis of multiple failure modes and its convergence 73
3.2.3 Steps of estimating failure probability by Monte Carlo simulation method 74
3.3 Monte Carlo simulation method for local reliability sensitivity analysis and its convergence 76
3.4 Monte Carlo simulation method for reliability and local reliability sensitivity analysis with correlated normal input variables 78
3.4.1 Independent transformation method for correlated normal variables 79
3.4.2 Direct Monte Carlo simulation method for reliability and local reliability sensitivity analysis with correlated normal variables 80
3.4.3 Transformed Monte Carlo simulation method for reliability and local reliability sensitivity analysis with correlated normal variables 82
3.4.4 Comparison between direct Monte Carlo simulation method and transformed Monte Carlo simulation method 88
3.4.5 Examples 89
3.5 Summary 96
Bibliography 96
Chapter 4 Importance sampling method 98
4.1 Most probable failure point-based importance sampling method 98
4.1.1 Importance sampling method for reliability analysis 98
4.1.2 Importance sampling method for local reliability sensitivity analysis 101
4.1.3 Mixture importance sampling under multiple failure modes 105
4.1.4 Adaptive importance sampling based on kernel density estimation 112
4.1.5 Examples 118
4.2 The truncated sampling method and truncated importance sampling method 126
4.2.1 The probabilistic characteristic in n-dimensional standard normal space 127
4.2.2 Truncated sampling method for reliability analysis 128
4.2.3 Truncated sampling method for local reliability sensitivity analysis 132
4.2.4 Truncated importance sampling method for reliability analysis 133
4.2.5 Truncated importance sampling method for local reliability sensitivity analysis 137
4.2.6 Examples 139
4.3 Adaptive truncated sampling method 143
4.3.1 Adaptive strategy for determining the hypersphere radius 144
4.3.2 Examples 147
4.4 Summary 149
Bibliography 150
Chapter 5 Subset simulation method 151
5.1 Markov chain Monte