LEADER 07327nam 2200709 450 001 9910829294603321 005 20230803202129.0 010 $a1-118-39807-6 010 $a1-118-39805-X 010 $a1-118-39806-8 035 $a(CKB)3710000000096947 035 $a(EBL)1658802 035 $a(SSID)ssj0001132109 035 $a(PQKBManifestationID)11666553 035 $a(PQKBTitleCode)TC0001132109 035 $a(PQKBWorkID)11146894 035 $a(PQKB)10910933 035 $a(OCoLC)869552734 035 $a(MiAaPQ)EBC1658802 035 $a(DLC) 2014004007 035 $a(Au-PeEL)EBL1658802 035 $a(CaPaEBR)ebr10855756 035 $a(CaONFJC)MIL586315 035 $a(OCoLC)875098579 035 $a(EXLCZ)993710000000096947 100 $a20140412h20142014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEngineering risk assessment and design with subset simulation /$fSiu-Kui Au, Yu Wang 210 1$aSingapore :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (337 p.) 300 $aDescription based upon print version of record. 311 $a1-118-39804-1 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aENGINEERING 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 327 $a2.4.5 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 327 $a2.7 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 327 $a3.8 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 327 $a4.2.2 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 327 $a5.2.1 Direct Monte Carlo Indispensible 330 $a"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 "--$cProvided by publisher. 606 $aRisk assessment$xMathematics 606 $aEngineering design$xMathematics 606 $aSet theory 615 0$aRisk assessment$xMathematics. 615 0$aEngineering design$xMathematics. 615 0$aSet theory. 676 $a519.2 686 $aTEC009070$2bisacsh 700 $aAu$b Siu-Kui$0969663 702 $aWang$b Yu 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829294603321 996 $aEngineering risk assessment and design with subset simulation$93945040 997 $aUNINA