结构/机构可靠设计基础
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作者吕震宙，员婉莹，冯凯旋，李璐?t
出版社科学出版社
ISBN9787030773784
出版时间2024-01
装帧平装
开本16开
定价450元
货号29681084
上书时间2024-11-15
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导语摘要
本书较为系统地介绍了随机不确定性下静态及时变结构可靠性分析与结构优化设计的基本理论和高效算法。主要内容包括：（1）可靠性和可靠性灵敏度分析的矩方法；（2）可靠性和可靠性灵敏度分析的数值模拟法；（3）可靠性和可靠性局部灵敏度分析的代理模型法；（4）时变结构可靠性分析的数值模拟法、极值法、跨越率法、包络函数法和代理模型法；（5）失效概率函数的高效求解法；（7）可靠性全局灵敏度分析的新方法；（8）可靠性优化设计概念、单层法、双层法、解耦法和完全解耦法。
目录
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 Carlo-based subset simulation method 151
5.1.1 Introduction of intermediate failure events and expression of failure probability based on intermediate failure events 151
5.1.2 Generation of conditional samples and estimation of conditional failure probabilities 153
5.1.3 Adaptive stratification strategy for determining the intermediate failure events in subset simulation and solution of failure probability 155
5.1.4 Subset simulation for local reliability sensitivity analysis 158
5.2 Importance sampling-based subset simulation method 160
5.2.1 Importance sampling-based subset simulation for reliability analysis 161
5.2.2 Adaptive stratification strategy for failure domain and solution of failure probability in importance sampling-based subset simulation 162
5.2.3 Convergence analysis of failure probability estimate obtained by importance sampling-based subset simulation 163
5.2.4 Importance sampling-based subset simulation for local reliability sensitivity analysis 166
5.3 Examples 169
5.4 Summary 181
Bibliography 181
Chapter 6 Line sampling method 182
6.1 Line sampling method for the problem with single failure mode 182
6.1.1 Definition and determination of important direction 183
6.1.2 Failure probability estimation by line sampling for problem with single failure mode 186
6.1.3 Detailed implementation of line sampling reliability analysis method for problem with single failure mode 187
6.1.4 Examples 188
6.2 Line sampling method for the problem with multiple failure modes in series 192
Contents ix
6.2.1 Reliability analysis with non-overlapping failure regions among the multiple failure modes 192
6.2.2 Reliability analysis with overlapping failure regions among the multiple failure modes 192
6.2.3 Examples 198
6.3 Line sampling method for the problem with correlated normal input variables 202
6.3.1 Transformation of correlated normal input variables into independent ones 202
6.3.2 Line sampling method for the problem with correlated normal input variables and single failure mode 203
6.3.3 Line sampling method for the problem with correlated normal inputs variables and multiple failure modes 204
6.3.4 Examples 207
6.4 Summary 211
Bibliography 211
Chapter 7 Directional sampling method 212
7.1 Directional sampling method for the problem with single failure mode 212
7.1.1 Basic idea of directional sampling method for the problem with single failure mode 213
7.1.2 Convergence analysis of failure probability estimate obtained by directional sampling 214
7.1.3 Detailed implementation of directional sampling method for the problem with single failure mode 215
7.1.4 Generation of uniformly distributed unit direction vector sample 217
7.1.5 Examples 219
7.2 Directional sampling method for the problem with multiple failure modes 222
7.2.1 Estimation of failure probability of the problem with multiple failure modes and convergence analysis of the estimate 222
7.2.2 Detailed implementation of directional sampling reliability analysis with multiple failure modes 224
7.2.3 Examples 225
7.3 Directional sampling method for the problem with correlated normal input variables 228
7.3.1 Transformation of correlated normal input vector into independent normal one 229
7.3.2 Directional sampling method for the problem with single/multiple failure modes 229
7.3.3 Examples 230
7.4 Summary 235
Bibliography 235
Chapter 8 Response surface method and support vector machine 236
8.1 Response surface method 236
8.1.1 Weighted linear response surface method 237
8.1.2 Weighted nonlinear response surface method 243
8.2 Support vector machine 250
8.2.1 Statistical learning theory 251
8.2.2 Dual optimization 255
8.2.3 Support vector classification algorithm 257
8.2.4 Support vector regression algorithm 261
8.2.5 Evaluating the generalization capability and selecting the parameters of support vector machine 265
8.3 Summary 270
Bibliography 271
Chapter 9 Kriging model-based reliability and local reliability sensitivity analysis method 272
9.1 Kriging surrogate model and adaptive learning function for reliability analysis 273
9.1.1 Basic principles of Kriging surrogate model 273
9.1.2 Adaptive learning function of Kriging model in reliability analysis 275
9.2 Adaptive Kriging model combined with Monte Carlo simulation method for reliability analysis and local reliability sensitivity analysis 282
9.2.1 Adaptive Kriging model combined with Monte Carlo simulation method for reliability analysis 282
9.2.2 Adaptive Kriging model combined with Monte Carlo simulation method for local reliability sensitivity anal
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