Partially Bayesian active learning cubature for structural reliability analysis with extremely small failure probabilities

verfasst von: Chao Dang, Matthias G.R. Faes, Marcos A. Valdebenito, Pengfei Wei, Michael Beer
Abstract: The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by taking advantage of the BFPI framework. In this work, three Bayesian active learning methods are proposed under the name ‘partially Bayesian active learning cubature’ (PBALC), based on a cleaver use of the BFPI framework for structural reliability analysis, especially when small failure probabilities are involved. Since the posterior variance of the failure probability is computationally expensive to evaluate, the underlying idea is to exploit only the posterior mean of the failure probability to design two critical components for Bayesian active learning, i.e., the stopping criterion and the learning function. On this basis, three sets of stopping criteria and learning functions are proposed, resulting in the three proposed methods PBALC1, PBALC2 and PBALC3. Furthermore, the analytically intractable integrals involved in the stopping criteria are properly addressed from a numerical point of view. Five numerical examples are studied to demonstrate the performance of the three proposed methods. It is found empirically that the proposed methods can assess very small failure probabilities and significantly outperform several existing methods in terms of 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
Typ: Artikel
Journal: Computer Methods in Applied Mechanics and Engineering
Band: 422
Anzahl der Seiten: 17
ISSN: 0045-7825
Publikationsdatum: 15.03.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
Elektronische Version(en): https://doi.org/10.1016/j.cma.2024.116828 (Zugang: Offen)

BibTeX

@article{195cc27df34c4caa9019e08088c78fec,
title = "Partially Bayesian active learning cubature for structural reliability analysis with extremely small failure probabilities",
abstract = "The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by taking advantage of the BFPI framework. In this work, three Bayesian active learning methods are proposed under the name {\textquoteleft}partially Bayesian active learning cubature{\textquoteright} (PBALC), based on a cleaver use of the BFPI framework for structural reliability analysis, especially when small failure probabilities are involved. Since the posterior variance of the failure probability is computationally expensive to evaluate, the underlying idea is to exploit only the posterior mean of the failure probability to design two critical components for Bayesian active learning, i.e., the stopping criterion and the learning function. On this basis, three sets of stopping criteria and learning functions are proposed, resulting in the three proposed methods PBALC1, PBALC2 and PBALC3. Furthermore, the analytically intractable integrals involved in the stopping criteria are properly addressed from a numerical point of view. Five numerical examples are studied to demonstrate the performance of the three proposed methods. It is found empirically that the proposed methods can assess very small failure probabilities and significantly outperform several existing methods in terms of accuracy and efficiency.",
keywords = "Bayesian active learning, Bayesian failure probability inference, Learning function, Small failure probability, Stopping criterion, Structural reliability analysis",
author = "Chao Dang and Faes, {Matthias G.R.} and Valdebenito, {Marcos A.} and Pengfei Wei and Michael Beer",
note = "Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC) . Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ). ",
year = "2024",
month = mar,
day = "15",
doi = "10.1016/j.cma.2024.116828",
language = "English",
volume = "422",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}