TY - JOUR

T1 - Bayesian active learning line sampling with log-normal process for rare-event probability estimation

AU - Dang, Chao

AU - Valdebenito, Marcos A.

AU - Wei, Pengfei

AU - Song, Jingwen

AU - Beer, Michael

N1 - 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 .

PY - 2024/6

Y1 - 2024/6

N2 - 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.

AB - 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.

KW - Bayesian active learning

KW - Gaussian process

KW - Line sampling

KW - Log-normal process

KW - Numerical uncertainty

KW - Structural reliability analysis

UR - http://www.scopus.com/inward/record.url?scp=85186758921&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2024.110053

DO - 10.1016/j.ress.2024.110053

M3 - Article

AN - SCOPUS:85186758921

VL - 246

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 110053

ER -