Approche novatrice pour la conception et l'exploitation d'avions écologiques

The objective of this PhD work is to pose, investigate, and solve the highly multidisciplinary and multiobjective problem of environmentally efficient aircraft design and operation. In this purpose, the main three drivers for optimizing the environmental performance of an aircraft are the airframe, the engine, and the mission profiles. The figures of merit, which will be considered for optimization, are fuel burn, local emissions, global emissions, and climate impact (noise excluded). The study will be focused on finding efficient compromise strategies and identifying the most powerful design architectures and design driver combinations for improvement of environmental performances. The modeling uncertainty will be considered thanks to rigorously selected methods. A hybrid aircraft configuration is proposed to reach the climatic impact reduction objective.L’objectif de ce travail de thèse est de poser, d’analyser et de résoudre le problème multidisciplinaire et multi-objectif de la conception d’avions plus écologiques et plus économiques. Dans ce but, les principaux drivers de l’optimisation des performances d’un avion seront: la géométrie de l’avion, son moteur ainsi que son profil de mission, autrement dit sa trajectoire. Les objectifs à minimiser considérés sont la consommation de carburant, l’impact climatique et le coût d’opération de l’avion. L’étude sera axée sur la stratégie de recherche de compromis entre ces objectifs, afin d’identifier les configurations d’avions optimales selon le critère sélectionné et de proposer une analyse de ces résultats. L’incertitude présente au niveau des modèles utilisés sera prise en compte par des méthodes rigoureusement sélectionnées. Une configuration d’avion hybride est proposée pouratteindre l’objectif de réduction d’impact climatique

Optimizations for Tensorial Bernstein-Based Solvers by Using Polyhedral Bounds

International audienceThe tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a quadratic number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a change to the tensorial Bernstein basis for domain reduction. The performance is similar for n = 2 variables but only the solver using linear programming on the Bernstein polytope can cope with a large number of variables.We demonstrate this difference with two formulations of the forward kinematics problem of a Gough-Stewart parallel robot: a direct Cartesian formulation and a coordinate-free formulation using Cayley-Menger determinants, followed by a computation of Cartesian coordinates