Parallel adaptive Bayesian quadrature for rare event estimation

被引:51
作者
Dang, Chao [1 ]
Wei, Pengfei [2 ]
Faes, Matthias G. R. [3 ]
Valdebenito, Marcos A. [4 ]
Beer, Michael [1 ,5 ,6 ,7 ]
机构
[1] Leibniz Univ Hannover, Inst Risk & Reliabil, Callinstr 34, D-30167 Hannover, Germany
[2] Northwestern Polytech Univ, Sch Power & Energy, Xian 710072, Peoples R China
[3] TU Dortmund Univ, Chair Reliabil Engn, Leonhard Euler Str 5, D-44227 Dortmund, Germany
[4] Univ Adolfo Ibanez, Fac Sci & Engn, Av Padre Hurtado 750, Vina Del Mar 2562340, Chile
[5] Univ Liverpool, Inst Risk & Uncertainty, Liverpool L69 7ZF, Merseyside, England
[6] Tongji Univ, Int Joint Res Ctr Resilient Infrastruct, Shanghai 200092, Peoples R China
[7] Tongji Univ, Int Joint Res Ctr Engn Reliabil & Stochast Mech, Shanghai 200092, Peoples R China
基金
中国国家自然科学基金;
关键词
Reliability analysis; Gaussian process; Numerical uncertainty; Bayesian quadrature; Parallel computing; STRUCTURAL RELIABILITY-ANALYSIS; SMALL FAILURE PROBABILITIES; LEARNING-FUNCTION; DYNAMIC-RESPONSE; ENTROPY;
D O I
10.1016/j.ress.2022.108621
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilistic integration (ALPI) method offers a principled approach to quantify, propagate and reduce the numerical uncertainty via computation within a Bayesian framework, which has not been fully investigated in context of probabilistic reliability analysis. In this study, a novel method termed `Parallel Adaptive Bayesian Quadrature' (PABQ) is proposed on the theoretical basis of ALPI, and is aimed at broadening its scope of application. First, the Monte Carlo method used in ALPI is replaced with an importance ball sampling technique so as to reduce the sample size that is needed for rare failure event estimation. Second, a multi-point selection criterion is proposed to enable parallel distributed processing. Four numerical examples are studied to demonstrate the effectiveness and efficiency of the proposed method. It is shown that PABQ can effectively assess small failure probabilities (e.g., as low as 10(-7)) with a minimum number of iterations by taking advantage of parallel computing.
引用
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页数:13
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