An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis

TL;DR

This paper introduces an active learning method combining sparse polynomial chaos expansions and bootstrap resampling to improve structural reliability analysis, especially in tail regions, by providing local error estimates and iteratively refining the model.

Contribution

It presents a novel bootstrap-based error estimation technique integrated with sparse PCE within an active learning framework for reliability analysis.

Findings

Effective in tail region modeling for reliability problems

Improves experimental design through bootstrap error estimates

Validated on benchmark and real structural problems

Abstract

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the model response and due to the lack of local metamodel error estimates. We propose a new method to provide local metamodel error estimates based on bootstrap resampling and sparse PCE. An initial experimental design is iteratively updated based on the current estimation of the limit-state surface in an active learning algorithm. The greedy algorithm uses the bootstrap-based local error estimates for the polynomial chaos predictor to identify the best candidate set of points to enrich the experimental design. We demonstrate the effectiveness of this approach on a well-known analytical benchmark representing a series system, on a truss structure and on a complex realistic frame structure problem.