Rare event estimation using stochastic spectral embedding

TL;DR

This paper introduces a stochastic spectral embedding-based reliability method that efficiently estimates rare failure probabilities in complex systems by partitioning the input space and refining local surrogate models.

Contribution

It adapts stochastic spectral embedding for rare event probability estimation, improving local approximation and computational efficiency in complex non-linear systems.

Findings

Effective on benchmark problems of various complexities

Reduces computational cost compared to traditional methods

Accurately estimates rare failure probabilities

Abstract

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 \rev{conditional} 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.