Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure

TL;DR

This paper introduces Bayesian Subset Simulation, a novel algorithm combining subset simulation with kriging-based Bayesian methods to efficiently estimate small failure probabilities in computationally expensive models.

Contribution

The paper presents a new kriging-based Bayesian subset simulation algorithm that improves efficiency in estimating small failure probabilities compared to traditional methods.

Findings

Promising results on a literature test case

Significant reduction in the number of simulations needed

Numerical study confirms estimator's statistical properties

Abstract

The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method to solve it. Subset simulation has been shown to provide significant savings in the number of simulations to achieve a given accuracy of estimation, with respect to many other Monte Carlo approaches. The number of simulations remains still quite high however, and this method can be impractical for applications where an expensive-to-evaluate computer model is involved. We propose a new algorithm, called Bayesian Subset Simulation, that takes the best from the Subset Simulation algorithm and from sequential Bayesian methods based on kriging (also known as Gaussian process modeling). The performance of this new algorithm is illustrated using a test case from the literature. We are able to report promising results. In addition, we provide a numerical study of the statistical properties of the estimator.