Rare event estimation using stochastic spectral embedding
This work addresses reliability assessment for engineering systems, but it is incremental as it modifies an existing method (SSE) for rare event estimation.
The authors tackled the problem of estimating rare failure probabilities in engineering systems by applying stochastic spectral embedding (SSE) to the limit-state function, resulting in the SSER method, which decomposes the failure probability into conditional probabilities and demonstrated performance on four benchmark problems.
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.