Metamodel-based importance sampling for the simulation of rare events

TL;DR

This paper introduces a novel reliability analysis method combining kriging meta-models with importance sampling to efficiently estimate rare event probabilities in structural engineering, reducing computational costs while maintaining accuracy.

Contribution

It develops an innovative estimator that integrates kriging meta-models with importance sampling, addressing the challenge of quantifying errors in surrogate-based reliability methods.

Findings

Effective in finite element structural reliability analysis

Reduces computational effort compared to traditional Monte Carlo methods

Provides accurate probability estimates for rare events

Abstract

In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In order to reduce the number of computer experiments, many other approaches known as reliability methods have been proposed. A certain approach consists in replacing the original experiment by a surrogate which is much faster to evaluate. Nevertheless, it is often difficult (or even impossible) to quantify the error made by this substitution. In this paper an alternative approach is developed. It takes advantage of the kriging meta-modeling and importance sampling techniques. The proposed alternative estimator is finally applied to a finite element based structural reliability analysis.