Bayesian active learning line sampling with log-normal process for rare-event probability estimation

authored by

Chao Dang, Marcos A. Valdebenito, Pengfei Wei, Jingwen Song, Michael Beer

Abstract

Line sampling (LS) stands as a powerful stochastic simulation method for structural reliability analysis, especially for assessing small failure probabilities. To further improve the performance of traditional LS, a Bayesian active learning idea has recently been pursued. This work presents another Bayesian active learning alternative, called ‘Bayesian active learning line sampling with log-normal process’ (BAL-LS-LP), to traditional LS. In this method, we assign an LP prior instead of a Gaussian process prior over the distance function so as to account for its non-negativity constraint. Besides, the approximation error between the logarithmic approximate distance function and the logarithmic true distance function is assumed to follow a zero-mean normal distribution. The approximate posterior mean and variance of the failure probability are derived accordingly. Based on the posterior statistics of the failure probability, a learning function and a stopping criterion are developed to enable Bayesian active learning. In the numerical implementation of the proposed BAL-LS-LP method, the important direction can be updated on the fly without re-evaluating the distance function. Four numerical examples are studied to demonstrate the proposed method. Numerical results show that the proposed method can estimate extremely small failure probabilities with desired efficiency and accuracy.

Organisation(s)

Institute for Risk and Reliability

External Organisation(s)

TU Dortmund University
Northwestern Polytechnical University
University of Liverpool
Tongji University

Type

Article

Journal

Reliability Engineering and System Safety

Volume

246

No. of pages

11

ISSN

0951-8320

Publication date

04.03.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

ASJC Scopus subject areas

Safety, Risk, Reliability and Quality, Industrial and Manufacturing Engineering

Electronic version(s)

https://doi.org/10.1016/j.ress.2024.110053 (Access: Open)