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Informationen zum Autor Siu-Kui Au, University of Liverpool, UK Yu Wang, City University of Hong Kong, China Klappentext Engineering Risk Assessment with Subset Simulation This book starts with the basic ideas in uncertainty propagation using Monte Carlo methods and the generation of random variables and stochastic processes for some common distributions encountered in engineering applications. It then introduces a class of powerful simulation techniques called Markov Chain Monte Carlo method (MCMC), an important machinery behind Subset Simulation that allows one to generate samples for investigating rare scenarios in a probabilistically consistent manner. The theory of Subset Simulation is then presented, addressing related practical issues encountered in the actual implementation. The book also introduces the reader to probabilistic failure analysis and reliability-based sensitivity analysis, which are laid out in a context that can be ef ciently tackled with Subset Simulation or Monte Carlo simulation in general. The book is supplemented with an Excel VBA code that provides a user-friendly tool for the reader to gain hands-on experience with Monte Carlo simulation. Presents a powerful simulation method called Subset Simulation for ef cient engineering risk assessment and failure and sensitivity analysis Illustrates examples with MS Excel spreadsheets, allowing readers to gain hands-on experience with Monte Carlo simulation Covers theoretical fundamentals as well as advanced implementation issues Developments of the software ideas in the book available from the author This book is essential reading for graduate students, researchers and engineers interested in applying Monte Carlo methods for risk assessment and reliability based design in various fields such as civil engineering, mechanical engineering, aerospace engineering, electrical engineering and nuclear engineering. Project managers, risk managers and financial engineers dealing with uncertainty effects may also find it useful. Zusammenfassung This book starts with the basic ideas in uncertainty propagation using Monte Carlo methods and the generation of random variables and stochastic processes for some common distributions encountered in engineering applications. Inhaltsverzeichnis About the Authors xiii Preface xv Acknowledgements xvii Nomenclature xix 1 Introduction 1 1.1 Formulation 2 1.2 Context 5 1.3 Extreme Value Theory 5 1.4 Exclusion 6 1.5 Organization of this Book 7 1.6 Remarks on the Use of Risk Analysis 7 1.7 Conventions 8 References 8 2 A Line of Thought 9 2.1 Numerical Integration 10 2.2 Perturbation 10 2.3 Gaussian Approximation 12 2.3.1 Single Design Point 12 2.3.2 Multiple Design Points 14 2.4 First/Second-Order Reliability Method 14 2.4.1 Context 15 2.4.2 Design Point 16 2.4.3 FORM 17 2.4.4 SORM 18 2.4.5 Connection with Gaussian Approximation 22 2.5 Direct Monte Carlo 24 2.5.1 Unbiasedness 25 2.5.2 Mean-Square Convergence 25 2.5.3 Asymptotic Distribution (Central Limit Theorem) 28 2.5.4 Almost Sure Convergence (Strong Law of Large Numbers) 31 2.5.5 Failure Probability Estimation 32 2.5.6 CCDF Perspective 34 2.5.7 Rare Event Problems 38 2.5.8 Variance Reduction by Conditioning 41 2.6 Importance Sampling 44 2.6.1 Optimal Sampling Density 45 2.6.2 Failure Probability Estimation 45 2.6.3 Shifting Distribution 46 2.6.4 Benefits and Side-Effects 48 2.6.5 Bias 50 2.6.6 Curse of Dimension 53 2.6.7 CCDF Perspective 56 2.7 Subset Simulation 58 2.8 Remarks on Reliability Methods 60 2A.1 Appendix: Laplace Type Integrals 61 References 62...
