Sequential design of computer experiments for the estimation of a probability of failure

TL;DR

This paper develops sequential Bayesian strategies using Gaussian process models to efficiently estimate the probability of failure of a system with limited simulation budgets, improving over classical methods.

Contribution

It introduces SUR strategies derived from a Bayesian framework for sequentially reducing uncertainty in failure probability estimation.

Findings

SUR strategies outperform traditional methods in efficiency

Gaussian process models effectively guide simulation evaluations

Sequential design reduces computational costs significantly

Abstract

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.