Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. In this work we apply SSE to the LSF, giving rise to a stochastic spectral embedding-based reliability (SSER) method. The resulting partition of the input space decomposes the failure probability into a set of easy-to-compute domain-wise failure probabilities. We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems. These modifications include specialized refinement domain selection, partitioning and enrichment strategies. We showcase the algorithm performance on four benchmark problems of various dimensionality and complexity in the LSF.

翻译：估算稀有故障事件的概率是工程系统可靠性评估的一个必要步骤。计算复杂的非线性系统的这种故障概率具有挑战性,最近还刺激了主动学习可靠性方法的开发。这些方法与使用经过一系列连续浓缩模型评估培训的代用模型的极限状态功能(LSF)相近。最近提出的一种称为随机光谱嵌入(SSE)的方法,目的是通过在输入空间的子域内按顺序嵌入本地剩余扩展,提高全球光谱代谢建模技术的当地近似精确度。在这项工作中,我们将SSE应用到 LSF, 从而产生一种基于光谱嵌入可靠性的光谱嵌入法(SSER)方法。因此,输入空间的分割将失败概率分解成一套容易比较的域性失常概率。我们提出了一套修改方法,使算法适合有效解决稀有事件估计问题。这些修改包括专门改进域选择、分割和浓缩战略。我们展示了LSF中不同维性和复杂性的四个基准问题的算法性表现。