TY - JOUR

T1 - Parallel adaptive Bayesian quadrature for rare event estimation

AU - Dang, Chao

AU - Wei, Pengfei

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Beer, Michael

N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC) . Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ). Marcos Valdebenito acknowledges the support by ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271 . Chao Dang, Pengfei Wei and Michael Beer also would like to appreciate the support of Sino-German Mobility Program under grant number M-0175 .

PY - 2022/6/2

Y1 - 2022/6/2

N2 - 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.

AB - 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.

KW - Bayesian quadrature

KW - Gaussian process

KW - Numerical uncertainty

KW - Parallel computing

KW - Reliability analysis

UR - http://www.scopus.com/inward/record.url?scp=85131434113&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2022.108621

DO - 10.1016/j.ress.2022.108621

M3 - Article

AN - SCOPUS:85131434113

VL - 225

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 108621

ER -