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

Chao Dang

doi:10.1016/j.ress.2024.110053

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

2024-06-01

Chao Dang *

Marcos A. Valdebenito

Pengfei Wei

Jingwen Song

Michael Beer

DOI：10.1016/j.ress.2024.110053

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Abstract

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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.

Keywords:

Structural reliability analysis

Line sampling

Bayesian active learning

Numerical uncertainty

Log-normal process

Gaussian process

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