Global sensitivity analysis of computer models with functional inputs

Abstract

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are appropriate with computer codes having scalar input variables. This paper aims at illustrating different variance-based sensitivity analysis techniques, based on the so-called Sobol's indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary metamodeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The "mean model" allows to estimate the sensitivity indices of each scalar input variables, while the "dispersion model" allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical sensitivity analysis methodologies on an analytical function.Lastly, the new methodology is applied to an industrial computer code that simulates the nuclear fuel irradiation.

Simplex-based screening designs for estimating metamodels

“…Hence, var(ε)/var(y) is the so-called "total sensitivity index" with respect to the non-important factors, denoted S Tv (Homma et Saltelli [7]). Here, the non-important factors v are considered as noise in the model, and the index S Tv is a measure of this noise over the response y (as in Iooss and Ribatet [8]). A low value confirms that the dropped factors are really non-important.…”

Sensitivity analysis of spatial models using geostatistical simulation

“…Some authors have suggested solutions to handle spatially distributed inputs as well (Volkova et al, 2008 ;Iooss & Ribatet, 2009;Ruffo et al, 2006;Lilburne & Tarantola, 2009). We describe in this section how to estimate sensitivity indices in model M by associating randomly generated realizations of uncertain 2D-field Z(u) to scalar values, according to the approach developed by Lilburne and Tarantola.…”

Surrogate Modeling of Stochastic Functions-Application to Computational Electromagnetic Dosimetry

“…Assum-ing that the model output is a Gaussian field trajectory, recent studies [11,12,13,14] build two independent or joint deterministic metamodels to fit the mean and the covariance of the assumed Gaussian process. Also based on the joint metamodeling approach, [15] simultaneously surrogates the mean and the dispersion using two interlinked Generalized Additive Models. Alternatively, the study carried out in [16] focused on projecting the output density on a basis of chosen probability density functions.…”