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Algorithmes hiérarchiques et stratégies de jeux pour l'optimisation multidisciplinaire Application à l'optimisation de la voilure d'un avion d'affaires

Badr Abou El Majd 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : This thesis aims at the development of innovating methods for optimum design in aerodynamics and more generally for multicriterion or multidisciplinary optimization problems in the aeronautical context. The first part is devoted to the improvement of efficiency of shape-optimization algorithms in terms of convergence. In a first section, multilevel optimization algorithms inspired from multigrid methods, well-known to be particularly efficient in iterative convergence, have been developed on the basis of a hierarchy of nested parameterizations. In a second section, self-adaptive parameterization procedures by regularization have been proposed. By means of three-dimensional flow simulations about geometries of aircraft wings, we have been able to solve problems of drag reduction in a transonic regime, and noise-criterion reduction in a supersonic regime, and to demonstrate that self-adaptive multilevel algorithms permitted to reduce the cost of an optimization by about one order of magnitude. The second part is devoted to the treatment of a problem of concurrent optimization in which the aerodynamicist interacts with the structural designer, in a parallel way in a symmetric Nash game, or hierarchically in a Stackelberg game. Algorithms for the calculation of the equilibrium point have been proposed and successfully tested for this coupled aero-structural shape optimization in a situation where the aerodynamical criterion is preponderant.
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Badr Abou El Majd. Algorithmes hiérarchiques et stratégies de jeux pour l'optimisation multidisciplinaire Application à l'optimisation de la voilure d'un avion d'affaires. Mathématiques [math]. Université Nice Sophia Antipolis, 2007. Français. ⟨tel-00529309⟩

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