Engineering risk assessment and design with subset simulation / / Siu-Kui Au, Yu Wang

• Autore: Au Siu-Kui
• Pubblicazione: Singapore : , : Wiley, , 2014; ©2014
• Descrizione fisica: 1 online resource (337 p.)
• Disciplina: 519.2
• Soggetto topico: Risk assessment - Mathematics; Engineering design - Mathematics; Set theory
• Classificazione: TEC009070
• Persona (resp. second.): WangYu
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: ENGINEERING RISK ASSESSMENT WITH SUBSET SIMULATION; Contents; About the Authors; Preface; Acknowledgements; Nomenclature; 1 Introduction; 1.1 Formulation; 1.2 Context; 1.3 Extreme Value Theory; 1.4 Exclusion; 1.5 Organization of this Book; 1.6 Remarks on the Use of Risk Analysis; 1.7 Conventions; References; 2 A Line of Thought; 2.1 Numerical Integration; 2.2 Perturbation; 2.3 Gaussian Approximation; 2.3.1 Single Design Point; 2.3.2 Multiple Design Points; 2.4 First/Second-Order Reliability Method; 2.4.1 Context; 2.4.2 Design Point; 2.4.3 FORM; 2.4.4 SORM ; 2.4.5 Connection with Gaussian Approximation 2.5 Direct Monte Carlo; 2.5.1 Unbiasedness; 2.5.2 Mean-Square Convergence; 2.5.3 Asymptotic Distribution (Central Limit Theorem); 2.5.4 Almost Sure Convergence (Strong Law of Large Numbers); 2.5.5 Failure Probability Estimation; 2.5.6 CCDF Perspective; 2.5.7 Rare Event Problems; 2.5.8 Variance Reduction by Conditioning; 2.6 Importance Sampling; 2.6.1 Optimal Sampling Density; 2.6.2 Failure Probability Estimation; 2.6.3 Shifting Distribution; 2.6.4 Benefits and Side-Effects; 2.6.5 Bias; 2.6.6 Curse of Dimension; 2.6.7 CCDF Perspective ; 2.7 Subset Simulation 2.8 Remarks on Reliability Methods; 2A.1 Appendix: Laplace Type Integrals; References; 3 Simulation of Standard Random Variable and Process; 3.1 Pseudo-Random Number; 3.2 Inversion Principle; 3.2.1 Continuous Random Variable; 3.2.2 Discrete Random Variables; 3.3 Mixing Principle; 3.4 Rejection Principle; 3.4.1 Acceptance Probability; 3.5 Samples of Standard Distribution; 3.6 Dependent Gaussian Variables; 3.6.1 Cholesky Factorization; 3.6.2 Eigenvector Factorization; 3.7 Dependent Non-Gaussian Variables; 3.7.1 Nataf Transformation; 3.7.2 Copula ; 3.8 Correlation through Constraint 3.8.1 Uniform in Sphere; 3.8.2 Gaussian on Hyper-plane; 3.9 Stationary Gaussian Process; 3.9.1 Autocorrelation Function and Power Spectral Density; 3.9.2 Discrete-Time Process; 3.9.3 Sample Autocorrelation Function and Periodogram; 3.9.4 Time Domain Representation; 3.9.5 The ARMA Process; 3.9.6 Frequency Domain Representation; 3.9.7 Remarks; 3A.1 Appendix: Variance of Linear System Driven by White Noise; 3A.2 Appendix: Verification of Spectral Formula; References; 4 Markov Chain Monte Carlo; 4.1 Problem Context; 4.2 Metropolis Algorithm; 4.2.1 Proposal PDF ; 4.2.2 Statistical Properties 4.2.3 Detailed Balance; 4.2.4 Biased Rejection; 4.2.5 Reversible Chain; 4.3 Metropolis-Hastings Algorithm; 4.3.1 Detailed Balance; 4.3.2 Independent Proposal and Importance Sampling; 4.4 Statistical Estimation; 4.4.1 Properties of Estimator; 4.4.2 Chain Correlation; 4.4.3 Ergodicity; 4.5 Generation of Conditional Samples; 4.5.1 Curse of Dimension; 4.5.2 Independent Component MCMC; References; 5 Subset Simulation; 5.1 Standard Algorithm; 5.1.1 Simulation Level 0 (Direct Monte Carlo); 5.1.2 Simulation Level (MCMC); 5.2 Understanding the Algorithm ; 5.2.1 Direct Monte Carlo Indispensible
• Sommario/riassunto: "A unique book giving a comprehensive coverage of Subset Simulation - a robust tool for general applicationsThe book starts with the basic theory 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 method 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. A number of variants of Subset Simulation that can lead to improved performance for specific classes of problems will also be covered. The second half the book introduces the reader to probabilistic failure analysis and reliability-based design, which are laid out in a context that can be efficiently tackled within the context of Subset Simulation or Monte Carlo simulation in general. The result is a general framework that allows the practitioner to investigate reliability sensitivity to uncertain parameters and to explore possible design scenarios systematically for selection of the final design in a convenient but computationally efficient manner via simulation.A unique feature of this book is that it is complemented with a VBA (Visual Basic for Applications) that implements Subset Simulation in the Excel spreadsheet environment. This allows the reader to experiment with the examples in the book and get hands-on experience with simulation. A chapter is devoted to the software framework that allows a practical solution by resolving the risk assessment problem into three uncoupled procedures, namely, deterministic modeling, uncertainty modeling and uncertainty propagation. Presents a powerful simulation method called Subset Simulation for efficient engineering risk assessment and reliability-based design Illustrates application examples with MS Excel spreadsheets allowing readers to gain hands-on experience with simulation techniques Covers theoretical fundamentals as well as advanced implementation issues in practical engineering problems A companion website is available to include the developments of the software ideas "--
• Titolo autorizzato: Engineering risk assessment and design with subset simulation
• ISBN: 1-118-39807-6; 1-118-39805-X; 1-118-39806-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910132215503321
• Lo trovi qui: Univ. Federico II