Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansionReport as inadecuate




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1 ICA - Institut Clément Ader 2 EDF - R&D Department MMC and MAI 3 ICAM - Institut Catholique d-Arts et Métiers

Abstract : Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol- indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate variance-based sensitivity indices. Indeed, their computation is analytically derived from the expansion coefficients but without error estimators of the meta-model approximation. In order to evaluate the reliability of these indices, we propose to build confidence intervals by bootstrap re-sampling on the experimental design used to estimate the polynomial chaos approximation. Since the evaluation of the sensitivity indices is obtained with confidence intervals, it is possible to find a design of experiments allowing the computation of sensitivity indices with a given accuracy.

Keywords : Sensitivity analysis Polynomial chaos expansion Bootstrap re-sampling





Author: Sylvain Dubreuil - Marc Berveiller - Frank Petitjean - Michel Salaün -

Source: https://hal.archives-ouvertes.fr/



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