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

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. In this paper, we propose a methodology to quantify the sensitivity of the failure probability estimator to uncertainties generated by the Gaussian process and the sampling strategy. This quantification 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.

Automated summary

This paper presents a methodology to reduce the computational cost of reliability analysis for engineering problems involving complex numerical models using Gaussian process-based active learning methods. The sensitivity of the failure probability estimator to uncertainties generated by the Gaussian process and sampling strategy is quantified to control the overall error associated with the estimation. The proposed active learning approach aims to improve the estimation of rare event probabilities by reducing the main source of error and stopping when the global variability is sufficiently low, with its performance assessed on several examples.