Parallel Bayesian probabilistic integration for structural reliability analysis with small failure probabilities

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Changsha University of Science and Technology
  • The University of Liverpool
  • Tsinghua University
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Details

OriginalspracheEnglisch
Aufsatznummer102409
Seitenumfang13
FachzeitschriftStructural safety
Jahrgang106
Frühes Online-Datum17 Nov. 2023
PublikationsstatusVeröffentlicht - Jan. 2024

Abstract

Bayesian active learning methods have emerged for structural reliability analysis and shown more attractive features than existing active learning methods. However, it remains a challenge to actively learn the failure probability by fully exploiting its posterior statistics. In this study, a novel Bayesian active learning method termed ‘Parallel Bayesian Probabilistic Integration’ (PBPI) is proposed for structural reliability analysis, especially when involving small failure probabilities. A pseudo posterior variance of the failure probability is first heuristically proposed for providing a pragmatic uncertainty measure over the failure probability. The variance amplified importance sampling is modified in a sequential manner to allow the estimations of posterior mean and pseudo posterior variance with a large sample population. A learning function derived from the pseudo posterior variance and a stopping criterion associated with the pseudo posterior coefficient of variance of the failure probability are then presented to enable active learning. In addition, a new adaptive multi-point selection method is developed to identify multiple sample points at each iteration without the need to predefine the number, thereby allowing parallel computing. The effectiveness of the proposed PBPI method is verified by investigating four numerical examples, including a turbine blade structural model and a transmission tower structure. Results indicate that the proposed method is capable of estimating small failure probabilities with superior accuracy and efficiency over several other existing active learning reliability methods.

ASJC Scopus Sachgebiete

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Parallel Bayesian probabilistic integration for structural reliability analysis with small failure probabilities. / Hu, Zhuo; Dang, Chao; Wang, Lei et al.
in: Structural safety, Jahrgang 106, 102409, 01.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Hu Z, Dang C, Wang L, Beer M. Parallel Bayesian probabilistic integration for structural reliability analysis with small failure probabilities. Structural safety. 2024 Jan;106:102409. Epub 2023 Nov 17. doi: 10.1016/j.strusafe.2023.102409
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abstract = "Bayesian active learning methods have emerged for structural reliability analysis and shown more attractive features than existing active learning methods. However, it remains a challenge to actively learn the failure probability by fully exploiting its posterior statistics. In this study, a novel Bayesian active learning method termed {\textquoteleft}Parallel Bayesian Probabilistic Integration{\textquoteright} (PBPI) is proposed for structural reliability analysis, especially when involving small failure probabilities. A pseudo posterior variance of the failure probability is first heuristically proposed for providing a pragmatic uncertainty measure over the failure probability. The variance amplified importance sampling is modified in a sequential manner to allow the estimations of posterior mean and pseudo posterior variance with a large sample population. A learning function derived from the pseudo posterior variance and a stopping criterion associated with the pseudo posterior coefficient of variance of the failure probability are then presented to enable active learning. In addition, a new adaptive multi-point selection method is developed to identify multiple sample points at each iteration without the need to predefine the number, thereby allowing parallel computing. The effectiveness of the proposed PBPI method is verified by investigating four numerical examples, including a turbine blade structural model and a transmission tower structure. Results indicate that the proposed method is capable of estimating small failure probabilities with superior accuracy and efficiency over several other existing active learning reliability methods.",
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AU - Hu, Zhuo

AU - Dang, Chao

AU - Wang, Lei

AU - Beer, Michael

N1 - Funding Information: This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFB2600900 ), and China Scholarship Council.

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KW - Bayesian probabilistic integration

KW - Gaussian process

KW - Importance sampling

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