%0 Unpublished work %T Set inversion under functional uncertainties with Gaussian ProcessRegression defined in the joint space of control and uncertain %+ IFP Energies nouvelles (IFPEN) %+ Probabilités, statistique, physique mathématique (PSPM) %+ Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA) %A El Amri, Reda %A Helbert, Céline %A Munoz Zuniga, Miguel %A Prieur, Clémentine %A Sinoquet, Delphine %8 2021 %D 2021 %K Functional uncertainties %K Data reduction %K Gaussian Process models %K Set inversion %Z Mathematics [math]/Statistics [math.ST] %Z Mathematics [math] %Z Mathematics [math]/Optimization and Control [math.OC]Preprints, Working Papers, ... %X 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. %G English %2 https://ifp.hal.science/hal-02986558v2/document %2 https://ifp.hal.science/hal-02986558v2/file/DreamTeam_jointInversion_soumis.pdf %L hal-02986558 %U https://ifp.hal.science/hal-02986558