Preface Chapter 1 Introduction 1.1 Basic concepts in the structure and mechanism reliability analysis 1.2 Progress in the structure and mechanism reliability analysis 1.3 Main contents of this book Chapter 2 Moment method for reliability and local reliability sensitivity analysis 2.1 First-order and second-moment method 2.1.1 First-order and second-moment method for reliability analysis 2.1.2 First-order and second-moment method for local reliability sensitivity analysis 2.1.3 Examples 2.2 Advanced first-order and second-moment method 2.2.1 Advanced first-order and second-moment method for reliability analysis 2.2.2 Advanced first-order and second-moment method for local reliability sensitivity analysis 2.2.3 Examples 2.3 Rackwitz-Fiessler reliability analysis algorithm for non-normal random variables 2.3.1 Basic theory and implementation of R-F algorithm 2.3.2 Specific implementation steps of R-F algorithm 2.3.3 Examples 2.4 Point estimation method for statistical moment of performance function 2.4.1 Definition of statistical moment of performance function 2.4.2 Two-point estimation method by Rosenblueth 2.4.3 Three-point estimation method by Gorman and Seo 2.4.4 Point estimation method by Zhou and Nowak 2.4.5 Point estimation method by Zhao and Ono 2.5 Fourth-order moment method for reliability and local reliability sensitivity analysis 2.5.1 Fourth-order moment method for reliability analysis 2.5.2 Fourth-order moment method for local reliability sensitivity analysis 2.5.3 Examples 2.6 Moment method for system reliability and local reliability sensitivity analysis 2.6.1 Calculation of the system moment 2.6.2 Examples 2.7 Independent transformation of correlated variables 2.7.1 Rosenblatt method for transforming correlated variables into the independent normal variables 2.7.2 Orthogonal transformation method for independent transformation of correlated normal variables 2.7.3 Geometric meaning of correlation coefficient of two linear performance functions in standard normal space 2.7.4 Examples 2.8 Discussion on the applicability scope of point estimation-based moment method 2.9 Summary Bibliography Chapter 3 Monte Carlo simulation method 3.1 Random number generator and sampling principle of random variable 3.1.1 Random number generator 3.1.2 Sampling principle of random variable 3.1.3 Sampling methods commonly used in reliability analysis 3.2 Monte Carlo simulation method for reliability analysis and its convergence 3.2.1 Monte Carlo simulation method for reliability analysis of single failure mode and its convergence 3.2.2 3.4.1 Independent transformation method for correlated normal variables 3.4.2 Direct Monte Carlo simulation method for reliability and local reliability sensitivity analysis with correlated normal variables 3.4.3 Transformed Monte Carlo simulation method for reliability and local reliability sensitivity analysis with correlated normal variables 3.4.4 Comparison between direct Monte Carlo simulation method and transformed Monte Carlo simulation method 3.4.5 Examples 3.5 Summary Bibliography …… Chapter 4 Importance sampling method Chapter 5 Subset simulation metho Chapter 6 Line sampling method Chapter 7 Directional sampling method Chapter 8 Response surface method and support vector machine. Chapter 9 Kriging model-based reliability and local reliability sensitivity Chapter 10 The theory and algorithms of time-dependent reliability analysis Chapter 11 Failure probability function Chapter 12 Failure probability-based global sensitivity measure Chapter 13 Classical methods for reliability-based design optimization Chapter 14 Kriging model-based single-loop approaches for reliability-based design optimization Chapter 15 Kriging model-based decoupling reliability-based design optimization methods Bibliography
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