Abstract
The use of robust design in aerodynamic shape optimization is increasing in popularity in order to come up with configurations less sensitive to operational conditions. However, the addition of uncertainties increases the computational cost as both design and stochastic spaces must be explored. The objective of this work is the development of an efficient framework for gradient-based robust design by using an adjoint formulation and a non-intrusive surrogate-based uncertainty quantification method. At each optimization iteration, the statistic of both the quantity of interest and its gradients are efficiently obtained through Gaussian Processes models. The framework is applied to the aerodynamic shape optimization of a 2D airfoil. With the presented approach it is possible to reduce both the mean and standard deviation of the drag compared to the deterministic optimum configuration. The robust solution is obtained at a reduced run time that is independent of the number of design parameters.
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References
Duvigneau R (2007) Aerodynamic shape optimization with uncertain operating conditions using metamodels. resreport RR-6143, INRIA
Schulz V, Schillings C (2013) Optimal aerodynamic design under uncertainty. In: Notes on numerical fluid mechanics and multidisciplinary design. Springer, Heidelberg, pp 297–338
Maruyama D, Liu D, Görtz S (2016) An efficient aerodynamic shape optimization framework for robust design of airfoils using surrogate models. In: Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016). NTUA, Greece
Kumar D, Raisee M, Lacor C (2018) Combination of polynomial chaos with adjoint formulations for optimization under uncertainties. In: Uncertainty management for robust industrial design in aeronautics. Springer International Publishing, pp 567–582
Shan S, Wang GG (2009) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multi Optim 41:219–241
Giles MB, Pierce NA (2000) An introduction to the adjoint approach to design. Flow, Turbul Combust 65:393–415
Maruyama D, Görtz S, Liu D (2018) General introduction to surrogate model-based approaches to UQ. In: Uncertainty management for robust industrial design in aeronautics. Springer International Publishing, pp 203–211
Hicks RM, Henne PA (1978) Wing design by numerical optimization. J Aircr 15:407–412
Gerhold T (2015) Overview of the hybrid RANS code TAU. In: MEGAFLOW—numerical flow simulation for aircraft design. Springer Berlin Heidelberg, pp 81–92
Sabater C, Görtz S (2019) An efficient bi-level surrogate approach for optimizing shock control bumps under uncertainty. In: AIAA Scitech 2019 forum. American Institute of Aeronautics and Astronautics
Gerhold T, Neumann J (2006) The parallel mesh deformation of the DLR TAU-code. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM). Springer Berlin Heidelberg, pp 162–169
Brezillon J, Dwight RP (2011) Applications of a discrete viscous adjoint method for aerodynamic shape optimisation of 3d configurations. CEAS Aeronaut J 3:25–34
Dwight R (2006) Efficiency improvements of rans-based analysis and optimization using implicit and adjoint methods on unstructured grids. In: DLR Deutsches Zentrum fur Luft- und Raumfahrt e.V. - Forschungsberichte
Reuther J, Jameson A, Farmer J, Martinelli L, Saunders D (1996) Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation. In: 34th aerospace sciences meeting and exhibit. American Institute of Aeronautics and Astronautics
Forrester AI, Keane AJ (2009) Recent advances in surrogate-based optimization. Progress Aerosp Sci 45:50–79
Maruyama D, Liu D, Görtz S (2018) Surrogate model-based approaches to UQ and their range of applicability. In Uncertainty management for robust industrial design in aeronautics. Springer International Publishing, pp 703–714
Sobol I (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput Math Math Phys 7:86–112
Han Z-H, Görtz S, Zimmermann R (2013) Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function. Aerosp Sci Technol 25:177–189
Dwight R, Han Z-H (2009) Efficient uncertainty quantification using gradient-enhanced kriging. In 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. American Institute of Aeronautics and Astronautics
Acknowledgments
This work is funded by the European Commission’s H2020 programme, through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant Agreement number 722734.
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Sabater, C., Görtz, S. (2021). Gradient-Based Aerodynamic Robust Optimization Using the Adjoint Method and Gaussian Processes. In: Gaspar-Cunha, A., Periaux, J., Giannakoglou, K.C., Gauger, N.R., Quagliarella, D., Greiner, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-030-57422-2_14
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