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

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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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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  • DOI: https://doi.org/10.1007/s11081-014-9251-0

Keywords

  • Optimization under uncertainty
  • Shape optimization
  • Stochastic uncertainties