Details
| Original language | English |
|---|---|
| Article number | 103613 |
| Number of pages | 12 |
| Journal | Probabilistic Engineering Mechanics |
| Volume | 76 |
| Early online date | 26 Mar 2024 |
| Publication status | Published - 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.
Keywords
- Bayesian active learning, Learning function, Parallel computing, Small failure probability, Stopping criterion, Structural reliability analysis
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Engineering(all)
- Civil and Structural Engineering
- Energy(all)
- Nuclear Energy and Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
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In: Probabilistic Engineering Mechanics, Vol. 76, 103613, 04.2024.
Research output: Contribution to journal › Article › Research › peer review
}
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
N2 - 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.
AB - 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.
KW - Bayesian active learning
KW - Learning function
KW - Parallel computing
KW - Small failure probability
KW - Stopping criterion
KW - Structural reliability analysis
UR - http://www.scopus.com/inward/record.url?scp=85189557601&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2024.103613
DO - 10.1016/j.probengmech.2024.103613
M3 - Article
AN - SCOPUS:85189557601
VL - 76
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
M1 - 103613
ER -