Density modification based reliability sensitivity analysis

TL;DR

This paper introduces a novel sensitivity analysis method based on modifying input probability densities to assess their influence on failure probabilities, using existing simulation data to minimize computational costs.

Contribution

It proposes a new density modification-based sensitivity index for failure probability analysis, leveraging existing simulation data and Kullback-Leibler divergence for input perturbations.

Findings

Indices can be computed with existing simulation data

Asymptotic properties are derived for Monte Carlo samples

Method validated through three case studies

Abstract

Sensitivity analysis of a numerical model, for instance simulating physical phenomena, is useful to quantify the influence of the inputs on the model responses. This paper proposes a new sensitivity index, based upon the modification of the probability density function (pdf) of the random inputs, when the quantity of interest is a failure probability (probability that a model output exceeds a given threshold). An input is considered influential if the input pdf modification leads to a broad change in the failure probability. These sensitivity indices can be computed using the sole set of simulations that has already been used to estimate the failure probability, thus limiting the number of calls to the numerical model. In the case of a Monte Carlo sample, asymptotical properties of the indices are derived. Based on Kullback-Leibler divergence, several types of input perturbations are introduced. The relevance of this new sensitivity analysis method is analysed through three case studies.