Gaussian process surrogates for failure detection: a Bayesian experimental design approach

TL;DR

This paper introduces a Bayesian experimental design method using Gaussian process surrogates to efficiently identify failure boundaries and estimate failure probabilities in computationally expensive models, enabling parallel sampling.

Contribution

It proposes a novel limit-state inference approach that determines multiple sampling points simultaneously for failure detection in expensive models.

Findings

Effective in academic and practical examples

Capable of parallel sampling for multiple points

Improves failure probability estimation accuracy

Abstract

An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian {process} surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.