故障概率极小的结构可靠性分析:准贝叶斯主动学习法

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-04-01 DOI:10.1016/j.probengmech.2024.103613
Chao Dang , Alice Cicirello , Marcos A. Valdebenito , Matthias G.R. Faes , Pengfei Wei , Michael Beer
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引用次数: 0

摘要

贝叶斯主动学习的概念最近已从机器学习引入结构可靠性分析。虽然已经成功开发了几种具体方法,但仍需付出巨大努力才能充分挖掘其潜力并解决现有挑战。本研究提出了一种准贝叶斯主动学习方法,称为 "准贝叶斯主动学习立方体",用于失效概率极小的结构可靠性分析。该方法的建立基于对贝叶斯失效概率推理框架的巧妙利用。为了减少与失效概率精确后验方差相关的计算负担,我们提出了一种准后验方差。随后,我们开发了贝叶斯主动学习的两个关键要素,即停止准则和学习函数。停止准则是根据故障概率的准后验变异系数定义的,其数值求解方案也是量身定制的。学习函数从准后验方差中提取,并引入了一个额外参数,允许多点选择,从而实现并行分布式处理。通过对四个数值示例的测试,经验表明所提出的方法能够以理想的精度和效率评估极小的故障概率。
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Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method

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.

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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
期刊最新文献
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