Density modification-based reliability sensitivity analysis

Abstract

Sensitivity analysis (SA) 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 SA method is analysed through three case studies.

Keywords:

• computer experiment
• Kullback–Leibler
• sensitivity analysis
• structural reliability
• uncertainty

Acknowledgements

Part of this work has been backed by French National Research Agency (ANR) through COSINUS program (project COSTA BRAVA noANR-09-COSI-015). We thank Dr Daniel Busby (IFP EN) for several discussions and Emmanuel Remy (EDF R&D) for proofreading. We also thank an anonymous reviewer and the associated editor for their helpful comments. All the statistical parts of this work have been performed within the R environment, including the mistral and sensitivity packages.