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Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions

Zuev, Konstantin M. and Beck, James L. and Au, Siu-Kui and Katafygiotis, Lambros S. (2012) Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions. Computers and Structures, 92-93 . pp. 283-296. ISSN 0045-7949. doi:10.1016/j.compstruc.2011.10.017.

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Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter space that is difficult to evaluate numerically. This paper focuses on enhancements to Subset Simulation (SS), proposed by Au and Beck, which provides an efficient algorithm based on MCMC (Markov chain Monte Carlo) simulation for computing small failure probabilities for general high-dimensional reliability problems. First, we analyze the Modified Metropolis algorithm (MMA), an MCMC technique, which is used in SS for sampling from high-dimensional conditional distributions. The efficiency and accuracy of SS directly depends on the ergodic properties of the Markov chains generated by MMA, which control how fast the chain explores the parameter space. We present some observations on the optimal scaling of MMA for efficient exploration, and develop an optimal scaling strategy for this algorithm when it is employed within SS. Next, we provide a theoretical basis for the optimal value of the conditional failure probability p_0, an important parameter one has to choose when using SS. We demonstrate that choosing any p_0 ∈ [0.1, 0.3] will give similar efficiency as the optimal value of p0. Finally, a Bayesian post-processor SS+ for the original SS method is developed where the uncertain failure probability that one is estimating is modeled as a stochastic variable whose possible values belong to the unit interval. Simulated samples from SS are viewed as informative data relevant to the system’s reliability. Instead of a single real number as an estimate, SS+ produces the posterior PDF of the failure probability, which takes into account both prior information and the information in the sampled data. This PDF quantifies the uncertainty in the value of the failure probability and it may be further used in risk analyses to incorporate this uncertainty. To demonstrate SS+, we consider its application to two different reliability problems: a linear reliability problem and reliability analysis of an elasto-plastic structure subjected to strong seismic ground motion. The relationship between the original SS and SS+ is also discussed.

Item Type:Article
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URLURL TypeDescription
Zuev, Konstantin M.0000-0003-2174-700X
Au, Siu-Kui0000-0002-0228-1796
Additional Information:© 2011 Elsevier Ltd. Received 26 July 2011. Accepted 20 October 2011. Available online 21 November 2011. This work was supported by the National Science Foundation, under award number EAR-0941374 to the California Institute of Technology. This support is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation. Partial support is acknowledged from the Hong Kong Research Grant Council through the General Research Fund 9041550 (CityU 110210).
Funding AgencyGrant Number
Hong Kong Research Grant Council9041550 (CityU 110210)
Subject Keywords: Reliability engineering; Stochastic simulation methods; Markov chain Monte Carlo; Subset Simulation; Bayesian approach
Record Number:CaltechAUTHORS:20120306-082708524
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Official Citation:Konstantin M. Zuev, James L. Beck, Siu-Kui Au, Lambros S. Katafygiotis, Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions, Computers & Structures, Volumes 92–93, February 2012, Pages 283-296, ISSN 0045-7949, 10.1016/j.compstruc.2011.10.017.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29584
Deposited On:13 Mar 2012 16:42
Last Modified:23 Mar 2022 19:41

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