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Set inversion under functional uncertainties with Gaussian Process Regression defined in the joint space of control and uncertain

Reda El Amri 1 Céline Helbert 2 Miguel Munoz Zuniga 1 Clémentine Prieur 3 Delphine Sinoquet 1
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : In this paper we propose an efficient sampling strategy to solve an inversion problem subjected to functional uncertainties. More precisely, we aim at characterizing a control variable region defined by exceedance above a prescribed threshold of specific Quantities of Interest (QoT). This study is motivated by an automotive industrial application consisting in the identification of the set of values of control variables of a gas after-treatment device, in line with pollutant emission standards of a vehicle under driving profile uncertainties. In that context, driving profile uncertainties are modelled by a functional random variable and the constrained response in the inversion problem is formulated as the expectation over this functional random variable only known through a set of realizations. As often in industrial applications, this problem involves time-consuming computational models. We thus propose an approach that uses Gaussian Process meta-models built on the joint space of control and uncertain input variables. Specifically, we define a learning criterion based on uncertainty in the excursion of the Gaussian Process and derive tractable expressions for variance reduction in such a framework. Applications to analytical examples, followed by the automotive industrial test case show the accuracy and the efficiency brought by the procedure we propose.
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https://hal-ifp.archives-ouvertes.fr/hal-02986558
Contributor : Delphine Sinoquet Connect in order to contact the contributor
Submitted on : Thursday, September 30, 2021 - 4:16:46 PM
Last modification on : Tuesday, October 19, 2021 - 11:25:56 AM

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Reda El Amri, Céline Helbert, Miguel Munoz Zuniga, Clémentine Prieur, Delphine Sinoquet. Set inversion under functional uncertainties with Gaussian Process Regression defined in the joint space of control and uncertain. 2021. ⟨hal-02986558v2⟩

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