Loïc Brevault

Contributions à l'optimisation multidisciplinaire sous incertitude, application à la conception de lanceurs: La conception de lanceurs est un problème d’optimisation multidisciplinaire dont l’objectif est de trouverl’architecture du lanceur qui garantit une performance optimale tout en assurant un niveau de fiabilité requis.En vue de l’obtention de la solution optimale, les phases d’avant-projet sont cruciales pour le processus deconception et se caractérisent par la présence d’incertitudes dues aux phénomènes physiques impliqués etaux méconnaissances existantes sur les modèles employés. Cette thèse s’intéresse aux méthodes d’analyse et d’optimisation multidisciplinaire en présence d’incertitudes afin d’améliorer le processus de conception de lanceurs. Trois sujets complémentaires sont abordés. Tout d’abord, deux nouvelles formulations du problème de conception ont été proposées afin d’améliorer la prise en compte des interactions disciplinaires. Ensuite, deux nouvelles méthodes d’analyse de fiabilité, permettant de tenir compte d’incertitudes de natures variées, ont été proposées, impliquant des techniques d’échantillonnage préférentiel et des modèles de substitution. Enfin, une nouvelle technique de gestion des contraintes pour l’algorithme d’optimisation ”Covariance Matrix Adaptation - Evolutionary Strategy” a été développée, visant à assurer la faisabilité de la solution optimale. Les approches développées ont été comparées aux techniques proposées dans la littérature sur des cas tests d’analyse et de conception de lanceurs. Les résultats montrent que les approches proposées permettent d’améliorer l’efficacité du processus d’optimisation et la fiabilité de la solution obtenue.

The preliminary design and optimization of aerospace systems often requires to make architectural and technological choices and to perform computationally expensive numerical simulations. In early design phases, the decision makers may be interested in obtaining a set of valuable solutions presenting a diversity of characteristics. This paper proposes two approaches tackling these challenges by formulating and solving a particular optimization problem. The latter is called Conditional Search-Space Problem because architectural and technological choices are represented by design variables, called conditional, which are acting on the structure of the optimization problem (e.g., number of design variables and constraints). To produce a broad diversity of solutions, a Quality-Diversity (QD) algorithm adapted to deal with conditional variables and expensive functions is developed. The proposed methods consist in decomposing the optimization problem in several subproblems that have a non-conditional structure. A Bayesian optimization strategy coupled with a QD algorithm is used to search for potential solutions among the subproblems. The most performing potential solutions are then evaluated with the exact functions. The methodology is tested on two analytical and an aerospace system design problems.

The present article proposes an algorithm for the sensitivity analysis of a multidisciplinary problem, in which the derivative-based global sensitivity indices are computed with multifidelity Gaussian process models. Two levels of fidelity are used to estimate the indices, where the low-fidelity samples are obtained by stopping the multidisciplinary analysis solver before convergence. A dedicated refinement strategy for the multifidelity Gaussian process is proposed to ensure the accuracy of the sensitivity index estimation. This algorithm is tested on three multidisciplinary problems of increasing complexity (one analytical and two representative engineering design problems), and proved to be both reliable in detecting the noninfluential variables and computationally efficient, compared to classical Monte Carlo integration and to three other candidate algorithms.

Uncertainty quantification is widely used in engineering domains to provide confidence measures on complex systems. It often requires to accurately estimate extreme statistics on computationally intensive black-box models. In case of spatially or temporally distributed model outputs, one valuable metric results in the estimation of extreme quantile of the output stochastic field. In this paper, a novel active learning surrogate-based method is proposed to determine the quantile of an unidimensional output stochastic process with a confidence measure. This allows to control the error on the estimation of a extreme quantile measure of a stochastic process. The proposed approach combines dimension reduction techniques, Gaussian process and an adaptive refinement strategy to enrich the surrogate model and control the accuracy of the quantile estimation. The proposed methodology is applied on an analytical test case and a realistic aerospace problem for which the estimation of a flight envelop is of prime importance for launch safety reasons in the space industry.