Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carlo method for this problem. In SS, the small failure probability is evaluated as a product of larger conditional probabilities by iteratively sampling a sequence of nested sub-domains of the parameter space, encompassing the target failure domain of interest, using Markov chain Monte Carlo methods. For failure domains with multiple modes, the Markov chain samples used to explore the intermediate levels of SS can be trapped in a confined region of the input parameter space, leading to inaccurate failure probability estimates. In this contribution, we propose the directional subset simulation (dSS) method for this problem, which uses concepts from directional sampling to informedly propagate samples towards failure. This is accomplished through a novel selection of the intermediate failure domains, which preserves samples in several directions in the parameter space in each intermediate level. The merits of the dSS method are illustrated through a selection of numerical examples.

翻译：估计稀有失效事件的概率是物理系统可靠性分析中的关键挑战。子集模拟（SS）是一种非常流行的自适应蒙特卡罗方法，用于解决此问题。在SS中，小失效概率被评估为一系列较大条件概率的乘积，通过使用马尔可夫链蒙特卡罗方法迭代采样参数空间中包含目标失效域的一系列嵌套子域。对于具有多模态的失效域，用于探索SS中间层次的马尔可夫链样本可能被困在输入参数空间的有限区域内，导致失效概率估计不准确。本文针对此问题提出了方向性子集模拟（dSS）方法，该方法利用方向性抽样的概念，以信息导向的方式将样本向失效域传播。这一目标通过新颖的中间失效域选择实现，在每个中间层次中保留参数空间多个方向上的样本。通过一系列数值示例展示了dSS方法的优势。