Set inversion under functional uncertainties with joint meta-models

Reda El Amri (1) , Céline Helbert (2) , Miguel Munoz Zuniga (1) , Clémentine Prieur (3) , Delphine Sinoquet (1)

1 IFPEN - IFP Energies nouvelles
2 ECL - École Centrale de Lyon
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows

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.

Mots clés: Set inversion; Gaussian Process models; Data reduction; Functional uncertainties

Domaines: Statistiques [math.ST]; Mathématiques [math]; Optimisation et contrôle [math.OC]

Reda El Amri, Céline Helbert, Miguel Munoz Zuniga, Clémentine Prieur, Delphine Sinoquet. Set inversion under functional uncertainties with joint meta-models. 2020. ⟨hal-02986558v1⟩