Structural reliability analysis by line sampling: A Bayesian active learning treatment

doi:10.1016/j.strusafe.2023.102351

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Structural reliability analysis by line sampling: A Bayesian active learning treatment

2023-09-01

Chao Dang *

Marcos A. Valdebenito

DOI：10.1016/j.strusafe.2023.102351

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Abstract

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Line sampling has been demonstrated to be a promising simulation method for structural reliability analysis, especially for assessing small failure probabilities. However, its practical performance can still be significantly improved by taking advantage of, for example, Bayesian active learning. Along this direction, a recently proposed 'partially Bayesian active learning line sampling' (PBAL-LS) method has shown to be successful. This paper aims at offering a more complete Bayesian active learning treatment of line sampling, resulting in a new method called 'Bayesian active learning line sampling' (BAL-LS). Specifically, we derive the exact posterior variance of the failure probability, which can measure our epistemic uncertainty about the failure probability more precisely than the upper bound given in PBAL-LS. Further, two essential components (i.e., learning function and stopping criterion) are proposed to facilitate Bayesian active learning, based on the uncertainty representation of the failure probability. In addition, the important direction can be automatically updated throughout the simulation, as one advantage directly inherited from PBAL-LS. The performance of BAL-LS is illustrated by four numerical examples. It is shown that the proposed method is capable of evaluating extremely small failure probabilities with desired efficiency and accuracy.

Keywords:

Structural reliability analysis

Line sampling

Bayesian active learning

Bayesian inference

Gaussian process

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