Structural reliability analysis with extremely small failure probabilities

A quasi-Bayesian active learning method

verfasst von

Chao Dang, Alice Cicirello, Marcos A. Valdebenito, Matthias G.R. Faes, Pengfei Wei, Michael Beer

Abstract

The concept of Bayesian active learning has recently been introduced from machine learning to structural reliability analysis. Although several specific methods have been successfully developed, significant efforts are still needed to fully exploit their potential and to address existing challenges. This work proposes a quasi-Bayesian active learning method, called ‘Quasi-Bayesian Active Learning Cubature’, for structural reliability analysis with extremely small failure probabilities. The method is established based on a cleaver use of the Bayesian failure probability inference framework. To reduce the computational burden associated with the exact posterior variance of the failure probability, we propose a quasi posterior variance instead. Then, two critical elements for Bayesian active learning, namely the stopping criterion and the learning function, are developed subsequently. The stopping criterion is defined based on the quasi posterior coefficient of variation of the failure probability, whose numerical solution scheme is also tailored. The learning function is extracted from the quasi posterior variance, with the introduction of an additional parameter that allows multi-point selection and hence parallel distributed processing. By testing on four numerical examples, it is empirically shown that the proposed method can assess extremely small failure probabilities with desired accuracy and efficiency.

Organisationseinheit(en)

Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

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

Typ

Artikel

Journal

Probabilistic Engineering Mechanics

Band

76

Anzahl der Seiten

12

ISSN

0266-8920

Publikationsdatum

04.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistische und nichtlineare Physik, Tief- und Ingenieurbau, Kernenergie und Kernkraftwerkstechnik, Physik der kondensierten Materie, Luft- und Raumfahrttechnik, Meerestechnik, Maschinenbau

Elektronische Version(en)

https://doi.org/10.1016/j.probengmech.2024.103613 (Zugang: Offen)