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An Adaptive Multipoint Formulation for Robust Parametric Optimization

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Abstract

The performance of a system designed for given functioning conditions often seriously degrades, when operated at other conditions. Therefore, a system operating over a continuous range of conditions should be designed over this range. The aerodynamic shape optimization of an aircraft at multiple altitudes, angles of attack and Mach numbers is a typical case in aerospace. This paper links parametric and multipoint optimizations by the sampling of the operating condition ranges. It is demonstrated that this discrete set of operating conditions, used to formulate a composite objective function, must adequately be chosen. An algorithm is proposed to select these conditions, which ensures a minimal computational cost to the robust optimization. Wing aerodynamic multipoint optimizations using a lifting line model and Reynolds-averaged Navier–Stokes equations, derived with a discrete adjoint formulation, are given as examples.

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Acknowledgments

The authors would like to thank Xavier Pinel for his mathematical feedbacks. Joël Brézillon and the reviewers are greatly acknowledged for their valuable remarks. This work was founded by Airbus and the Association Nationale de la Recherche et de la Technologie.

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Authors and Affiliations

  1. Institute of Technology Antoine de Saint Exupéry, 118 route de Narbonne, CS 44248, 31432, Toulouse Cedex 4, France

    François Gallard

  2. Computational Fluid Dynamics, Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, 42, Avenue Gaspard Coriolis, 31057 , Toulouse Cedex 1, France

    Marc Montagnac

  3. Université de Montpellier, Mathématiques (IMAG), CC51, 34095, Montpellier, France

    Bijan Mohammadi

  4. Airbus Group Innovations, 18 rue Marius TERCE, BP 13050, 31025, Toulouse Cedex 03, France

    Matthieu Meaux

Authors
  1. François Gallard
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  2. Bijan Mohammadi
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  3. Marc Montagnac
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  4. Matthieu Meaux
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Corresponding author

Correspondence to François Gallard.

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Communicated by Emmanuel Trélat.

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Gallard, F., Mohammadi, B., Montagnac, M. et al. An Adaptive Multipoint Formulation for Robust Parametric Optimization. J Optim Theory Appl 167, 693–715 (2015). https://doi.org/10.1007/s10957-014-0595-6

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  • DOI: https://doi.org/10.1007/s10957-014-0595-6

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