Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

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

Externe Organisationen

  • Technische Universität Dortmund
  • Northwestern Polytechnical University
  • The University of Liverpool
  • Tongji University
  • University of Cambridge
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer103613
Seitenumfang12
FachzeitschriftProbabilistic Engineering Mechanics
Jahrgang76
Frühes Online-Datum26 März 2024
PublikationsstatusVeröffentlicht - Apr. 2024

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.

ASJC Scopus Sachgebiete

Zitieren

Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method. / Dang, Chao; Cicirello, Alice; Valdebenito, Marcos A. et al.
in: Probabilistic Engineering Mechanics, Jahrgang 76, 103613, 04.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Dang C, Cicirello A, Valdebenito MA, Faes MGR, Wei P, Beer M. Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method. Probabilistic Engineering Mechanics. 2024 Apr;76:103613. Epub 2024 Mär 26. doi: 10.1016/j.probengmech.2024.103613
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title = "Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method",
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 {\textquoteleft}Quasi-Bayesian Active Learning Cubature{\textquoteright}, 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.",
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TY - JOUR

T1 - Structural reliability analysis with extremely small failure probabilities

T2 - A quasi-Bayesian active learning method

AU - Dang, Chao

AU - Cicirello, Alice

AU - Valdebenito, Marcos A.

AU - Faes, Matthias G.R.

AU - Wei, Pengfei

AU - Beer, Michael

N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC). Alice Cicirello would like to thank the financial support provided by the Alexander von Humboldt Foundation Research Fellowship for experienced researchers. Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194).

PY - 2024/4

Y1 - 2024/4

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KW - Learning function

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KW - Stopping criterion

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