Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling

Abstract

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N -sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.

Partitioning the contributions of dependent offshore forcing conditions in the probabilistic assessment of future coastal flooding

“…However, to reach an operative level, two key aspects deserve further investigation: (1) the optimized computational effort with appropriate metamodelling techniques (e.g. Betancourt et al, 2020, for functional inputs andZhu andSudret, 2021, for stochastic simulators) combined with an advanced Monte Carlo sampling scheme (like importance sampling, Demange-Chryst et al, 2022) and (2) the capability to assess the impact of alternative modelling choices (extreme value modelling and numerical modelling, in addition to those described in Sect. 5.1) on the sensitivity analysis, i.e.…”