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 -