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

verfasst von: 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.
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: Reliability Engineering and System Safety
Band: 246
Anzahl der Seiten: 11
ISSN: 0951-8320
Publikationsdatum: 06.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Sicherheit, Risiko, Zuverlässigkeit und Qualität, Wirtschaftsingenieurwesen und Fertigungstechnik
Elektronische Version(en): https://doi.org/10.1016/j.ress.2024.110053 (Zugang: Offen)

BibTeX

@article{60559be430994c24aa010cbacc72d789,
title = "Bayesian active learning line sampling with log-normal process for rare-event probability estimation",
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 {\textquoteleft}Bayesian active learning line sampling with log-normal process{\textquoteright} (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.",
keywords = "Bayesian active learning, Gaussian process, Line sampling, Log-normal process, Numerical uncertainty, Structural reliability analysis",
author = "Chao Dang and Valdebenito, {Marcos A.} and Pengfei Wei and Jingwen Song 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 ). Jingwen Song acknowledges the financial support from the National Natural Science Foundation of China (grant no. 12202358 and 12220101002 ). Michael Beer would like to thank the support of the National Natural Science Foundation of China under grant number 72271025 . ",
year = "2024",
month = jun,
doi = "10.1016/j.ress.2024.110053",
language = "English",
volume = "246",
journal = "Reliability Engineering and System Safety",
issn = "0951-8320",
publisher = "Elsevier Ltd.",
}