TY - JOUR

T1 - Estimation of small failure probabilities by partially Bayesian active learning line sampling

T2 - Theory and algorithm

AU - Dang, Chao

AU - Valdebenito, Marcos A.

AU - Song, Jingwen

AU - Wei, Pengfei

AU - Beer, Michael

N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC). Jingwen Song acknowledges the financial support from the National Natural Science Foundation of China (grant no. 12202358 and 12220101002 ). Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ). 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 - 2023/7/1

Y1 - 2023/7/1

N2 - Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.

AB - Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.

KW - Active learning

KW - Bayesian inference

KW - Failure probability

KW - Gaussian process

KW - Line sampling

UR - http://www.scopus.com/inward/record.url?scp=85159208250&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2023.116068

DO - 10.1016/j.cma.2023.116068

M3 - Article

AN - SCOPUS:85159208250

VL - 412

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 116068

ER -