Structural reliability analysis: A Bayesian perspective



Dang, Chao, Valdebenito, Marcos A, Faes, Matthias GR, Wei, Pengfei and Beer, Michael ORCID: 0000-0002-0611-0345
(2022) Structural reliability analysis: A Bayesian perspective. STRUCTURAL SAFETY, 99. p. 102259.

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Failure probability, Bayesian inference, Gaussian process, Numerical uncertainty, Parallel computing
Divisions: Faculty of Science and Engineering > School of Engineering
Depositing User: Symplectic Admin
Date Deposited: 08 Aug 2022 12:45
Last Modified: 18 Jul 2023 01:30
DOI: 10.1016/j.strusafe.2022.102259
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3160705