Surrogate-based aerodynamic shape optimization with the active subspace method
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Surrogate-based optimization is criticized in high-dimensional cases because it cannot scale well with the input dimension. In order to overcome this issue, we adopt a snapshot active subspace method to reduce the input dimension. A smoothing operation of samples is used to reduce the demand for snapshots in the construction of active subspaces. This operation significantly reduces the computational cost on the one hand, and on the other hand, it leads to more feasible subspaces. We use a 90∼95% energy coverage criterion to define the dimension of the subspace. With this criterion, the surrogate-based airfoil optimization in the active subspace is both efficient and effective. We also validate this optimization approach in an ONERA M6 wing optimization case with 220 shape variables. Compared with original surrogate-based optimization, the new approach reduces the computational time by 70% and obtains a more practical design with a smaller drag.
KeywordsActive subspace method Surrogate-based optimization High-dimensional optimization
The first author would like to thank the MDO Lab at the University of Michigan for the valuable inspirations and suggestions in this work. The authors are thankful for the constructive feedback and suggestions provided by the reviewers.
This work was supported by the 111 Project of China (B17037).
- Bons N, He X, Mader CA, Martins JRRA (2017) Multimodality in aerodynamic wing design optimization. In: 35th AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-3753
- Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE. https://doi.org/10.1109/mhs.1995.494215
- Han ZH, Zhang KS (2012) Surrogate-based optimization. In: Real-World Applications of Genetic Algorithms. https://doi.org/10.5772/36125. InTech
- Han ZH, Abu-Zurayk M, Görtz S, Ilic C (2018) Surrogate-based aerodynamic shape optimization of a wing-body transport aircraft configuration. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer International Publishing, pp 257–282. https://doi.org/10.1007/978-3-319-72020-3_16
- Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J Chem Metallurgical Mining Soc 52:119–139Google Scholar
- Li J, Bouhlel MA, Martins JRRA (2018a) Data-based approach for fast airfoil analysis and optimization. AIAA Journal (In press)Google Scholar
- Li J, Cai J, Qu K (2018b) Adjoint-based two-step optimization method using proper orthogonal decomposition and domain decomposition. AIAA J:1–13. https://doi.org/10.2514/1.j055773
- Lukaczyk TW, Constantine P, Palacios F, Alonso JJ (2014) Active subspaces for shape optimization. In: 10th AIAA Multidisciplinary Design Optimization Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2014-1171
- Lyu Z, Kenway GK, Paige C, Martins JRRA (2013) Automatic differentiation adjoint of the Reynolds-averaged Navier-Stokes equations with a turbulence model. In: 21st AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2013-2581
- Othmer C, Lukaczyk TW, Constantine P, Alonso JJ (2016) On active subspaces in car aerodynamics. In: 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2016-4294
- Poole DJ, Allen CB, Rendall T (2017) Global optimization of multimodal aerodynamic optimization benchmark case. In: 35th AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-4365
- Streuber GM, Zingg DW (2017) Investigation of multimodality in aerodynamic shape optimization based on the Reynolds averaged Navier-Stokes equations. In: 35th AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-3752