Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes

TL;DR

This paper introduces a sensitivity analysis method for Gaussian process-based reliability assessment, quantifying uncertainties from surrogate modeling and sampling, to improve and control failure probability estimation accuracy.

Contribution

It proposes a novel methodology to analyze and control the combined uncertainty sources in Gaussian process-based reliability analysis, enhancing active learning and rare event probability estimation.

Findings

Effective uncertainty quantification for failure probability estimates

Improved active learning stopping criteria based on sensitivity analysis

Enhanced accuracy in rare event probability estimation

Abstract

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. The learning phase of these methods consists in building a Gaussian process surrogate model of the performance function and using the uncertainty structure of the Gaussian process to enrich iteratively this surrogate model. For that purpose a learning criterion has to be defined. Then, the estimation of the probability of failure is typically obtained by a classification of a population evaluated on the final surrogate model. Hence, the estimator of the probability of failure holds two different uncertainty sources related to the surrogate model approximation and to the sampling based integration technique. In this paper, we propose a methodology to quantify the sensitivity of the probability of failure estimator to both uncertainty sources. This analysis also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.