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On the influence of robustness measures on shape optimization with stochastic uncertainties

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Abstract

The unavoidable presence of uncertainties poses several difficulties to the numerical treatment of optimization tasks. In this paper, we discuss a general framework attacking the additional computational complexity of the treatment of uncertainties within optimization problems considering the specific application of optimal aerodynamic design. Appropriate measure of robustness and a proper treatment of constraints to reformulate the underlying deterministic problem are investigated. In order to solve the resulting robust optimization problems, we propose an efficient methodology based on a combination of adaptive uncertainty quantification methods and optimization techniques, in particular generalized one-shot ideas. Numerical results investigating the reliability and efficiency of the proposed method as well as the influence of different robustness measures on the resulting optimized shape will be presented.

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Acknowledgements

This research has been partly supported by the German Federal Ministry of Economics and Labour (BMWA) within the collaborative effort MUNA under Contract No. 20A0604K.

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Authors and Affiliations

  1. Universität Trier, Universitätsring 15, 54296, Trier, Germany

    V. Schulz

  2. Seminar for Applied Mathematics, ETH Zentrum, HG G 52.1, Rämistrasse 101, 8092, Zürich, Switzerland

    C. Schillings

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Schillings, C., Schulz, V. On the influence of robustness measures on shape optimization with stochastic uncertainties. Optim Eng 16, 347–386 (2015). https://doi.org/10.1007/s11081-014-9251-0

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