Sequential active learning of low-dimensional model representations for reliability analysis

TL;DR

This paper introduces an active learning method combining dimensionality reduction and surrogate modeling to efficiently perform reliability analysis on high-dimensional, computationally expensive models, improving accuracy and error control.

Contribution

It extends previous surrogate modeling approaches with an adaptive, gradient-free active learning procedure for better error management in high-dimensional reliability problems.

Findings

Effective in low to high dimensions, up to 869 variables.

Handles nonlinear limit-state functions and multiple failure regions.

Reduces computational cost while maintaining accuracy.

Abstract

To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modelling termed partial least squares-driven polynomial chaos expansion (PLS-PCE) to render such problems feasible. Standalone surrogate models typically perform poorly for reliability analysis. Therefore, in a previous work, we have used PLS-PCEs to reconstruct the intermediate densities of a sequential importance sampling approach to reliability analysis. Here, we extend this approach with an active learning procedure that allows for improved error control at each importance sampling level. To this end, we formulate an estimate of the combined estimation error for both the subspace identified in the dimension reduction step and surrogate model constructed therein. With this, it is possible to adapt the design of experiments so as to optimally learn the subspace representation and the surrogate model constructed therein. The approach is gradient-free and thus can be directly applied to black box-type models. We demonstrate the performance of this approach with a series of low- (2 dimensions) to high- (869 dimensions) dimensional example problems featuring a number of well-known caveats for reliability methods besides high dimensions and expensive computational models: strongly nonlinear limit-state functions, multiple relevant failure regions and small probabilities of failure.