Global sensitivity analysis: A flexible and efficient framework with an example from stochastic hydrogeology

Abstract

When investigating, modeling or operating uncertain systems, sensitivity analysis with respect to uncertain model parameters yields valuable information. It helps to quantify the relevance of parameters, to estimate their individual contributions to prediction uncertainty, and to better direct further data acquisition. In this work, we propose a response surface method for global sensitivity analysis (based on the arbitrary polynomial chaos expansion, aPC). The key advantages of our proposed technique are: (1) aPC alleviates the computational burden associated with conventional global sensitivity analysis methods that require many evaluations of a simulation model; (2) the proposed method incorporates arbitrary independent probability densities or weighting functions for the investigated model parameters, thus generalizing several existing methods to reflect the expected relevance of parameters values within their allowable ranges; and (3) our framework allows to incorporate this information while requiring only a finite number of statistical moments for the investigated parameters. We generalize the polynomial-based computation of Sobol indices to arbitrary distributions, and suggest an associated complementary new sensitivity measure based on polynomial representation, which allows both univariate and multivariate global analysis. Compared to Sobol indices, our new weighted measure is absolute rather than relative, and converges faster with increasing order of expansion. We use analytical and hybrid analytical-numerical formulations that further improve computational efficiency. Altogether, we can conduct global sensitivity analysis at computational costs that are almost as low as those of local sensitivity analyses. We illustrate our approach for a 3D groundwater quality and human health risk problem in heterogeneous porous media.