Stratégie de modélisation multi-fidélité via une approche système incluant des métamodèles basés sur les entités NURBS

The more complex the problem, the greater the amount of computational resources needed to simulate it. On the other hand, the need for accuracy in the results of a system will not be the same depending on its design phase and the domain studied. The goal of this thesis is to propose a fast, low-cost multi-fidelity modeling strategy. To meet this need, a hybrid modeling approach is developed that combines Model-Based System Engineering (MBSE) and a metamodel based on Non-Uniform Rational Basis-Spline (NURBS) hypersurfaces. More specifically, the scientific challenge of this work is to develop a metamodel based on NURBS entities to simulate the behavior of highly nonlinear systems that require high fidelity modeling but are capable of providing results in real time to be compatible with the MBSE approach. In this context, the NURBS entity-based metamodel is obtained as a solution to an optimization problem solved with a gradient algorithm. In addition, a smoothing term is included in the problem formulation, not only to reduce the influence of any spurious nonlinearities in the training database, but also to limit the phenomenon of overfitting. The technical and scientific challenge of this work is to couple the general MBSE approach with the NURBS-based metamodel.Plus un problème est complexe, plus la quantité de ressources informatiques nécessaires pour le simuler est importante. D’autre part, le besoin de précision dans les résultats d’un système ne sera pas le même selon sa phase de conception et le domaine étudié. L'objectif de cette thèse est de proposer une stratégie de modélisation multi-fidélité rapide et peu couteuse en ressources de calcul. Pour répondre à ce besoin, une modélisation hybride est développée, couplant approche Model-Based System Engineering (MBSE) et métamodèle basé sur les hypersurfaces Non-Uniform Rational Basis-Spline (NURBS). Plus précisément, l’enjeu scientifique de ce travail est le développement du métamodèle basé sur les entités NURBS pour simuler le comportement de systèmes fortement non-linéaires nécessitant une modélisation haute-fidélité mais capable de fournir les résultats en temps réel pour être compatible avec l’approche MBSE. Dans ce contexte, le métamodèle basé sur les entités NURBS est obtenu comme solution d’un problème d’optimisation résolu avec un algorithme au gradient. En outre, un terme de lissage est intégré dans la formulation du problème pour non seulement réduire l’influence d’éventuelles non-linéarités parasites de la base de données d’entraînement mais également pour limiter le phénomène d’overfitting. L’enjeu technicoscientifique de ce travail est de parvenir à coupler l’approche générale MBSE avec le métamodèle à base de NURBS

A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

The model-based system engineering approach consists of assembling subsystems together to model a complete system. In this context, some functional blocks can have a considerable influence on the overall behaviour of the system. A preliminary identification of the influence of the subsystems on the output responses can help reducing the complexity of the overall system, with a negligible impact on the overall accuracy. Therefore, pertinent indicators must be introduced to achieve this goal. To this purpose, in this work, some well-established methods and algorithms for global sensitivity analysis (GSA) of linear and non-linear systems with independent input variables, i.e., approaches based on Sobol’s indices (different algorithms are considered), and Shapley’s effect, are compared on both benchmark functions and real-world engineering problems.Specifically, in this paper, real-world engineering problems dealing with linear and non-linear systems are modelled through commercial finite element software and/or dedicated programming languages for solving complex non-linear dynamics models, like Modelica. Regarding Modelica models, an efficient strategy based on functional mock-up units is presented to speed up the simulation of highly non-linear dynamic systems. All numerical models are interfaced with the algorithms used for GSA through ad-hoc routines coded in Python environment. For each problem, a systematic comparison between the results provided by the different algorithms making use of Sobol’s indices and Shapley’s indices is performed, in terms of reliability, accuracy and computational costs