TY - JOUR

T1 - Structural reliability analysis

T2 - A Bayesian perspective

AU - Dang, Chao

AU - Valdebenito, Marcos A.

AU - Faes, Matthias G.R.

AU - Wei, Pengfei

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, PR China under grant number M-0175 .
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2022/11

Y1 - 2022/11

N2 - Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.

AB - Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.

KW - Bayesian inference

KW - Failure probability

KW - Gaussian process

KW - Numerical uncertainty

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=85134368709&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2022.102259

DO - 10.1016/j.strusafe.2022.102259

M3 - Article

AN - SCOPUS:85134368709

VL - 99

JO - Structural Safety

JF - Structural Safety

SN - 0167-4730

M1 - 102259

ER -