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MODÈLES DE SUBSTITUTION POUR L'OPTIMISATION GLOBALE DE FORME EN AÉRODYNAMIQUE ET MÉTHODE LOCALE SANS PARAMÉTRISATION

Abstract : Optimum-shape design in aerodynamics has been an an active research area in recent years, with high-technology industrial applications to aeronautics. With the development of the adjoint method, an efficient computation of the derivatives of the functions of interest with respect to shape parameters is now available. The cost of this calculation is independent of the number of shape parameters. This study concerns the use of the gradient calculated by the adjoint method to improve local and global algorithms for shape optimization. In a first part, these derivatives are used to build surrogate models, then used to reduce the cost of global optimization methods. Several types of models are presented and combined with an algorithm called " differential evolution " using the procedure EGO (Efficient Global Optimization). This method is applied to the optimization of mathematical functions, and to aerodynamic optimization of airfoils. The results are interesting : the surrogate models allow to reduce the number of evaluations of the physical model, and the use of derivatives in the surrogate models further reduces this number. In the second part of this work, the adjoint method is used to calculate the derivatives of the function of interest with respect to node coordinates of the airfoil surface. A local optimization algorithm, using these points as shape parameters and the field of the smoothed gradient as descent direction, is then applied. The study should be pursued, but early results are encouraging yet.
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https://tel.archives-ouvertes.fr/tel-00771799
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Submitted on : Wednesday, January 9, 2013 - 1:55:14 PM
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  • HAL Id : tel-00771799, version 1

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Manuel Bompard. MODÈLES DE SUBSTITUTION POUR L'OPTIMISATION GLOBALE DE FORME EN AÉRODYNAMIQUE ET MÉTHODE LOCALE SANS PARAMÉTRISATION. Analyse numérique [math.NA]. Université Nice Sophia Antipolis, 2011. Français. ⟨tel-00771799⟩

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