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1 LCFR - Laboratoire de Conduite et Fiabilité des Réacteurs 2 GdR MASCOT-NUM - Méthodes d-Analyse Stochastique des Codes et Traitements Numériques 3 UR HHLY - Hydrologie-Hydraulique 4 INRS - Institut National de la Recherche Scientifique Québec

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 applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol 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 meta-modeling 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 SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation.

keyword : functional data Sobol indices joint modeling generalized additive model metamodel

Author: Bertrand Iooss - Mathieu Ribatet -



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