Metamodel-based importance sampling for structural reliability analysis

TL;DR

This paper introduces a metamodel-based importance sampling method using kriging surrogates to efficiently estimate failure probabilities in complex structural systems, reducing computational costs while maintaining accuracy.

Contribution

It proposes a novel importance sampling approach that leverages kriging surrogates to improve reliability analysis accuracy and efficiency, especially for high-dimensional problems.

Findings

Effective for problems with up to 100 random variables

Reduces computational cost compared to traditional methods

Provides unbiased failure probability estimates

Abstract

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate computational model (e.g. a finite element model). In this respect simulation methods, which may require $10^{3-6}$ runs cannot be used directly. Surrogate models such as quadratic response surfaces, polynomial chaos expansions or kriging (which are built from a limited number of runs of the original model) are then introduced as a substitute of the original model to cope with the computational cost. In practice it is almost impossible to quantify the error made by this substitution though. In this paper we propose to use a kriging surrogate of the performance function as a means to build a quasi-optimal importance sampling density. The probability of failure is eventually obtained as the product of an augmented probability computed by substituting the meta-model for the original performance function and a correction term which ensures that there is no bias in the estimation even if the meta-model is not fully accurate. The approach is applied to analytical and finite element reliability problems and proves efficient up to 100 random variables.