GLOBAL SENSITIVITY ANALYSIS MEASURES BASED ON STATISTICAL DISTANCES

Global sensitivity analysis aims at quantifying and ranking the relative contribution of all the uncertain inputs of a mathematical model that impact the uncertainty in the output of that model, for any input-output mapping. Motivated by the limitations of the well-established Sobol' indices which are variance-based, there has been an interest in the development of non-moment-based global sensitivity metrics. This paper presents two complementary classes of metrics (one of which is a generalization of an already existing metric in the literature) which are based on the statistical distances between probability distributions rather than statistical moments. To alleviate the large computational cost associated with Monte Carlo sampling of the input-output model to estimate probability distributions, polynomial chaos surrogate models are proposed to be used. The surrogate models in conjunction with sparse quadrature-based rules, such as conjugate unscented transforms, permit efficient calculation of the proposed global sensitivity measures. Three benchmark sensitivity analysis examples are used to illustrate the proposed approach.