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

Theory and algorithm

verfasst von

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

Abstract

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.

Organisationseinheit(en)

Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

Technische Universität Dortmund
Northwestern Polytechnical University
The University of Liverpool
Tongji University

Typ

Artikel

Journal

Computer Methods in Applied Mechanics and Engineering

Band

412

ISSN

0045-7825

Publikationsdatum

01.07.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik

Elektronische Version(en)

https://doi.org/10.1016/j.cma.2023.116068 (Zugang: Geschlossen)