An efficient Bayesian updating framework for characterizing the posterior failure probability

被引:0
|
作者
Li, Pei-Pei [1 ]
Zhao, Yan-Gang [2 ]
Dang, Chao [1 ]
Broggi, Matteo [3 ]
Valdebenito, Marcos A. [1 ]
Faes, Matthias G. R. [1 ]
机构
[1] TU Dortmund Univ, Chair Reliabil Engn, Leonhard Euler Str 5, D-44227 Dortmund, Germany
[2] Beijing Univ Technol, Minist Educ, Key Lab Urban Secur & Disaster Engn, Beijing 100124, Peoples R China
[3] Leibniz Univ Hannover, Inst Risk & Reliabil, Callinstr 34, D-30167 Hannover, Germany
基金
中国国家自然科学基金;
关键词
Bayesian updating; Posterior failure probability; Sparse grid numerical integration; Shifted lognormal distribution; STRUCTURAL RELIABILITY; EVOLUTION METHOD; QUANTIFICATION; UNCERTAINTY;
D O I
10.1016/j.ymssp.2024.111768
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Bayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical properties of the posterior failure probability is important, yet challenging task for risk-based decision-making. In this study, an efficient framework is proposed to fully characterize the statistical properties of the posterior failure probability. The framework is based on the concept of Bayesian updating and keeps the effect of aleatory and epistemic uncertainty separated. To improve the efficiency of the proposed framework, a weighted sparse grid numerical integration is suggested to evaluate the first three raw moments of the corresponding posterior reliability index. This enables the reuse of evaluation results stemming from previous analyses. In addition, the proposed framework employs the shifted lognormal distribution to approximate the probability distribution of the posterior reliability index, from which the mean, quantile, and even the distribution of the posterior failure probability can be easily obtained in closed form. Four examples illustrate the efficiency and accuracy of the proposed method, and results generated with Markov Chain Monte Carlo combined with plain Monte Carlo simulation are employed as a reference.
引用
收藏
页数:19
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