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.

中文翻译：

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极小失效概率的结构可靠性分析：一种准贝叶斯主动学习方法

贝叶斯主动学习的概念最近已从机器学习引入到结构可靠性分析中。尽管已经成功开发了几种具体方法，但仍需要付出巨大努力才能充分发挥其潜力并应对现有挑战。这项工作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Cuature”，用于故障概率极小的结构可靠性分析。该方法是基于贝叶斯失效概率推理框架的切割器使用而建立的。为了减少与故障概率的精确后验方差相关的计算负担，我们提出了准后验方差。然后，随后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。停止准则是基于失效概率的拟后验变异系数定义的，其数值求解方案也是定制的。学习函数是从准后验方差中提取的，并引入了允许多点选择并因此进行并行分布式处理的附加参数。通过对四个数值例子的测试，经验表明该方法可以以期望的精度和效率评估极小的失效概率。