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Analyse d’incertitudes et de robustesse pour les modèles à entrées et sorties fonctionnelles.

Mohamed Reda El Amri 1, 2, 3
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
UGA [2016-2019] - Université Grenoble Alpes [2016-2019], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK - Laboratoire Jean Kuntzmann , Inria Grenoble - Rhône-Alpes
Abstract : This thesis deals with the inversion problem under uncertainty of expensive-to-evaluate functions in the context of the tuning of the control unit of a vehicule depollution system. The effect of these uncertainties is taken into account through the expectation of the quantity of interest. The problem lies in the fact that the uncertainty is partly due to a functional variable only known through a given sample. We propose two approaches to solve the inversion problem, both methods are based on Gaussian Process modelling for expensive-to-evaluate functions and a dimension reduction of the functional variable by the Karhunen-Loève expansion. The first methodology consists in applying a Stepwise Uncertainty Reduction (SUR) method on the expectation of the quantity of interest. At each evaluation point in the control space, the expectation is estimated by a greedy functional quantification method that provides a discrete representation of the functional variable and an effective sequential estimate from the given sample. The second approach consists in applying the SUR method directly to the quantity of interest in the joint space. Devoted to inversion under functional uncertainties, a strategy for enriching the experimental design exploiting the properties of Gaussian processes is proposed. These two approaches are compared on toy analytical examples and are applied to an industrial application for an exhaust gas post-treatment system of a vehicle. The objective is to identify the set of control parameters that leads to meet the pollutant emission norms under uncertainties on the driving cycle.
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Mohamed Reda El Amri. Analyse d’incertitudes et de robustesse pour les modèles à entrées et sorties fonctionnelles.. Mathématiques [math]. Université Grenoble Alpes, 2019. Français. ⟨tel-02433324⟩

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