Advertisement

Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 403–419 | Cite as

Surrogate-based aerodynamic shape optimization with the active subspace method

  • Jichao LiEmail author
  • Jinsheng Cai
  • Kun Qu
Research Paper
  • 195 Downloads

Abstract

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.

Keywords

Active subspace method Surrogate-based optimization High-dimensional optimization 

Notes

Acknowledgements

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.

Funding information

This work was supported by the 111 Project of China (B17037).

References

  1. Andrés E, Salcedo-Sanz S, Monge F, Pérez-Bellido A (2012) Efficient aerodynamic design through evolutionary programming and support vector regression algorithms. Expert Syst Appl 39(12):10700–10708.  https://doi.org/10.1016/j.eswa.2012.02.197 CrossRefGoogle Scholar
  2. 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
  3. Chernukhin O, Zingg DW (2013) Multimodality and global optimization in aerodynamic design. AIAA J 51(6):1342–1354.  https://doi.org/10.2514/1.j051835 CrossRefGoogle Scholar
  4. Constantine PG, Dow E, Wang Q (2014) Active subspace methods in theory and practice: applications to Kriging surfaces. SIAM J Sci Comput 36(4):A1500–A1524.  https://doi.org/10.1137/130916138 MathSciNetCrossRefzbMATHGoogle Scholar
  5. Duan Y, Cai J, Li Y (2012) Gappy proper orthogonal decomposition-based two-step optimization for airfoil design. AIAA J 50(4):968–971.  https://doi.org/10.2514/1.j050997 CrossRefGoogle Scholar
  6. 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
  7. Han ZH, Zhang KS (2012) Surrogate-based optimization. In: Real-World Applications of Genetic Algorithms.  https://doi.org/10.5772/36125. InTech
  8. 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
  9. Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3(3):233–260.  https://doi.org/10.1007/bf01061285 CrossRefzbMATHGoogle Scholar
  10. Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13(4):455–492.  https://doi.org/10.1023/A:1008306431147 MathSciNetCrossRefzbMATHGoogle Scholar
  11. Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J Chem Metallurgical Mining Soc 52:119–139Google Scholar
  12. Leifsson L, Koziel S (2010) Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction. J Comput Sci 1(2):98–106.  https://doi.org/10.1016/j.jocs.2010.03.007 CrossRefGoogle Scholar
  13. Li J, Bouhlel MA, Martins JRRA (2018a) Data-based approach for fast airfoil analysis and optimization. AIAA Journal (In press)Google Scholar
  14. 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
  15. Liu J, Song WP, Han ZH, Zhang Y (2016) Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models. Struct Multidiscip Optim 55(3):925–943.  https://doi.org/10.1007/s00158-016-1546-7 CrossRefGoogle Scholar
  16. 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
  17. 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
  18. Mader CA, Martins JRRA, Alonso JJ, van der Weide E (2008) ADJoint: an approach for the rapid development of discrete adjoint solvers. AIAA J 46(4):863–873.  https://doi.org/10.2514/1.29123 CrossRefGoogle Scholar
  19. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239.  https://doi.org/10.2307/1268522 MathSciNetzbMATHGoogle Scholar
  20. Namura N, Shimoyama K, Obayashi S (2017) Kriging surrogate model with coordinate transformation based on likelihood and gradient. J Glob Optim 68(4):827–849.  https://doi.org/10.1007/s10898-017-0516-y MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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
  22. Parr JM, Keane AJ, Forrester AI, Holden CM (2012) Infill sampling criteria for surrogate-based optimization with constraint handling. Eng Optim 44(10):1147–1166.  https://doi.org/10.1080/0305215x.2011.637556 CrossRefzbMATHGoogle Scholar
  23. 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
  24. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1):1–28.  https://doi.org/10.1016/j.paerosci.2005.02.001 CrossRefGoogle Scholar
  25. 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
  26. Wu X, Zhang W, Song S (2017) Robust aerodynamic shape design based on an adaptive stochastic optimization framework. Struct Multidiscip Optim 57(2):639–651.  https://doi.org/10.1007/s00158-017-1766-5 MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Key Laboratory of Aerodynamic Design and Research, School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

Personalised recommendations