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Set inversion under functional uncertainties with joint meta-models

Reda 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 inversion problem under functional uncertainty. This approach aims to characterize region of a control space defined by exceedance above prescribed threshold. This study is motivated by an application on identifying the set of control parameters leading to meet the pollutant emission standards of a vehicle under driving profile uncertainties. In that context, the constrained response in the inversion problem is here formulated as the expectation over the functional random variable only known through a set of realizations and the unknown set is thus associated with the control variables. As often in industrial applications, this problem involves high-fidelity and time-consuming computational models. We thus proposed an approach that makes use of Gaussian Process meta-models built on the joint space of control and uncertain input variables. Specifically, we define a design criterion based on uncertainty in the excursion of the Gaussian Process and derive tractable expressions for the 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 proposed procedure.
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Submitted on : Tuesday, November 3, 2020 - 10:00:00 AM
Last modification on : Tuesday, November 24, 2020 - 4:00:09 PM

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Reda Amri, Céline Helbert, Miguel Munoz Zuniga, Clémentine Prieur, Delphine Sinoquet. Set inversion under functional uncertainties with joint meta-models. 2020. ⟨hal-02986558⟩

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