Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure

TL;DR

This paper introduces a Bayesian method using Gaussian processes to estimate the probability of failure in multi-fidelity simulators, explicitly accounting for hyper-parameter uncertainties to improve reliability assessments.

Contribution

It presents a novel fully Bayesian approach that integrates hyper-parameter uncertainties into multi-fidelity probabilistic failure estimation.

Findings

Effective incorporation of hyper-parameter uncertainties.

Accurate estimation of failure probabilities.

Method demonstrated on academic example.

Abstract

A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a multi-fidelity stochastic simulator. We propose a fully Bayesian approach based on Gaussian processes to compute the posterior probability distribution of this probability. We pay special attention to the hyper-parameters of the model. Our methodology is illustrated on an academic example.