Structural reliability analysis

A Bayesian perspective

authored by: Chao Dang, Marcos A. Valdebenito, Matthias G.R. Faes, Pengfei Wei, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Universidad Adolfo Ibanez
TU Dortmund University
Northwestern Polytechnical University
University of Liverpool
Tongji University
Type: Article
Journal: Structural safety
Volume: 99
ISSN: 0167-4730
Publication date: 11.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Building and Construction, Safety, Risk, Reliability and Quality
Electronic version(s): https://doi.org/10.1016/j.strusafe.2022.102259 (Access: Closed)