Advertisement

Aerodynamic Shape Design by Evolutionary Optimization and Support Vector Machines

  • Esther Andrés-Pérez
  • Leopoldo Carro-Calvo
  • Sancho Salcedo-Sanz
  • Mario J. Martin-Burgos
Part of the Springer Tracts in Mechanical Engineering book series (SPTME)

Abstract

This paper proposes a computational methodology for the aerodynamic shape design of aeronautical configurations, aiming a broad and efficient exploration of the design space. A novel adaptive sampling technique focused on the global optimization problem, the Intelligent Estimation Search with Sequential Learning (IES-SL), is presented. This approach is based on the use of Support Vector Machines (SVMs) as the surrogate model for estimating the objective function, in combination with an evolutionary algorithm (EA) to enable the discovery of global optima. The proposed methodology is applied to improve the aerodynamic performance of a two-dimensional airfoil and a three-dimensional wing and results on surrogate model validation and optimization-focused sampling criteria are discussed.

Keywords

Aerodynamic shape optimization Evolutionary algorithms Support vector machines Surrogate-based global optimization 

Notes

Acknowledgements

The research described in this paper made by INTA, UAH and UPM researchers has been supported under the INTA activity “Termofluidodinámica” (IGB99001). This work is also partially supported by Spanish Ministry of Science and Innovation, under a project number ECO2010-22065-C03-02.

The experiments performed in this paper are also part of a GARTEUR action group (www.garteur.org) that has been established to explore these SBGO approaches. The main objective of the action group is, by means of a European collaborative research, to make a deep evaluation and assessment of SBGO methods for aerodynamic shape design, dealing with the main challenges as the curse of dimensionality, reduction of the design space and error metrics for validation, amongst others.

References

  1. 1.
    Jameson A, Martinelli L, Vassberg J (2002) Using computational fluid dynamics for aerodynamics—a critical assessment. ICAS paper 2002-1.10.1, TorontoGoogle Scholar
  2. 2.
    Leifsson L, Koziel S, Tesfahunegn Y (2014) Aerodynamic design optimization: physics-based surrogate approaches for airfoil and wing design. In: AIAA SciTech. AIAA 2014-0572Google Scholar
  3. 3.
    Li C, Brezillon J, Görtz S (2011) A framework for surrogate-based aerodynamic optimization. In: ONERA-DLR aerospace symposium, ODAS 2011Google Scholar
  4. 4.
    Koziel S, Leifsson L (2013) Multi-level surrogate-based airfoil shape optimization. In: 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Grapevine (Dallas/Ft. Worth Region), 7–10 January 2013. AIAA2013-0778Google Scholar
  5. 5.
    Lukaczyk T, Palacios F, Alonso JJ (2014) Active subspaces for shape optimization. In: AIAA SciTech 2014Google Scholar
  6. 6.
    Iuliano E, Quagliarella D (2013) Proper orthogonal decomposition, surrogate modelling and evolutionary optimization in aerodynamic design. Comput Fluids 84(2013):327–350MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Iuliano E, Quagliarella D (2013) Aerodynamic shape optimization via non-intrusive POD-based surrogate modelling. In: 2013 IEEE congress on evolutionary computation, Cancún, 20–23 June 2013Google Scholar
  8. 8.
    Jahangirian A, Shahrokhi A (2011) Aerodynamic shape optimization using efficient evolutionary algorithms and unstructured CFD solver. Comput Fluids 46:270–276MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Zhong-Hua H, Zimmermann R, Görtz S (2010) A new cokriging method for variable-fidelity surrogate modeling of aerodynamic data. In: American Institute of Aeronautics and Astronautics ConferenceGoogle Scholar
  10. 10.
    Weerdt E, Chu QP, Mulder JA (2005) Neural Network aerodynamic model identification for aerospace reconfiguration. In: AIAA 2005Google Scholar
  11. 11.
    Marinus BG, Rogery M, Braembusschez R (2010) Aeroacoustic and aerodynamic optimization of aircraft propeller blades. In: AIAA 2010Google Scholar
  12. 12.
    Praveen C, Duvigneau R (2007) Radial basis functions and Kriging Metamodels for aerodynamic optimization. INRIA Technical ReportGoogle Scholar
  13. 13.
    Andres E, Salcedo-Sanz S, Monge F, Perez-Bellido AM (2012) Efficient aerodynamic design through evolutionary programming and support vector regression algorithms. Expert Syst Appl 39(2012):10700–10708CrossRefGoogle Scholar
  14. 14.
    Clarke SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. Trans ASME J Mech Des 127(6):1077–1087CrossRefGoogle Scholar
  15. 15.
    Smith C, Doherty J, Jin Y (2013) Recurrent neural network ensembles for convergence prediction in surrogate-assisted evolutionary optimisation. In: IEEE symposium series on computational intelligence, Singapore, 16–19 April 2013Google Scholar
  16. 16.
    Cheng CS, Chen PW, Huang KK (2011) Estimating the shift size in the process mean with support vector regression and neural networks. Expert Syst Appl 38:10624–10630CrossRefGoogle Scholar
  17. 17.
    Salcedo-Sanz S, Ortiz-Garcia E, Perez-Bellido A, Portilla A (2011) Short term wind speed prediction based on evolutionary support vector regression algorithms. Expert Syst Appl 38:4052–4057CrossRefGoogle Scholar
  18. 18.
    Zhou Z, Ong YS, Lim M, Lee B (2007) Memetic algorithms using multi-surrogates for computationally expensive optimisation problems. J Soft Comput 11(10):957–971CrossRefGoogle Scholar
  19. 19.
    Kontoleontos EA, Asouti VG, Giannakoglou KC (2011) An asynchronous metamodel-assisted memetic algorithm for CFD-based shape optimisation. In: Engineering optimisationGoogle Scholar
  20. 20.
    GARTEUR AD/AG52 Members (2013) Partial report on surrogate-based global optimization methods in aerodynamic design, 2013–2015Google Scholar
  21. 21.
    Lepine J, Trepanier J (2000) Wing aerodynamic design using an optimized NURBS geometrical representation. In: 38th Aerospace science meeting and exibit, Reno, 10–13 January 2000Google Scholar
  22. 22.
    Bentamy A, Guibault F, Trepanier J (2005) Aerodynamic optimization of a realistic aircraft wing. AIAA 2005-332Google Scholar
  23. 23.
    Painchaud-Ouellet S, Tribes C, Trepanier JY, Pelletier D (2004) Airfoil shape optimization using NURBS representation under thickness constraint. In: 42nd AIAA aerospace sciences meeting and exhibit, AIAA 2004-1095Google Scholar
  24. 24.
    Mousavi A, Castonguay P, Nadarajah S (2007) Survey of shape parameterization techniques and its effect on three-dimensional aerodynamic shape optimization. In: 18th AIAA computational fluid dynamics, Miami, 25–28 June 2007Google Scholar
  25. 25.
    Piegl L, Tiller W (1997) The NURBS book. Springer, Berlin. ISBN 3-540-61545-8CrossRefGoogle Scholar
  26. 26.
    Technical Documentation of the DLR TAU-Code (1994) Tech. rep., Institut of Aerodynamics and Flow TechnologyGoogle Scholar
  27. 27.
    Gerhold T, Galle M, Friedrichs O, Evans J (1997) Calculation of complex three-dimensional configurations employing the DLR TAU-Code. AIAA-97-0167. AIAAGoogle Scholar
  28. 28.
    Smola A, Schölkopf B, Müller KR (1998) The connection between regularization operators and support vector kernels. Neural Netw 11(4):637–649CrossRefGoogle Scholar
  29. 29.
    Quiancheng W, Shunong Z, Rui K (2011) Research of small samples avionics prognosis based on support vector machines. In: Prognosis & system health management conference (PHM2011 Shenzhen)Google Scholar
  30. 30.
    Ortiz-García EG, Salcedo Sanz S, Pérez-Bellido ÁM, Portilla-Figueras JA (2009) Improving the training time of support vector regression algorithms through novel hyper-parameters search space reductions. Neurocomputing 72:3683–3691CrossRefGoogle Scholar
  31. 31.
    Smith J (2007) On replacement strategies in steady state evolutionary algorithms. Evol Comput 15(1):29–59CrossRefGoogle Scholar
  32. 32.
    Cook PH, McDonald MA et al (1979) Aerofoil RAE 2822—pressure distributions, and boundary layer and wake measurements, experimental data base for computer program assessment. AGARD Report AR 138Google Scholar
  33. 33.
    Vassberg J, Tinoco EN, Mani M et al (2007) Summary of the third AIAA CFD drag prediction workshop. AIAA Paper 2007-0260Google Scholar
  34. 34.
    Martin MJ, Andres E, Valero E, Lozano C (2013) Gradients calculation for arbitrary parameterizations via volumetric NURBS: the control box approach. In: EUCASS conferenceGoogle Scholar
  35. 35.
    Martin MJ, Andres E, Valero E, Lozano C (2014) Volumetric B-Splines shape parameterization for aerodynamic shape design. Int J Aerosp Sci Technol 2014:26–36. doi: 10.1016/j.ast.2014.05.003 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Esther Andrés-Pérez
    • 1
  • Leopoldo Carro-Calvo
    • 2
  • Sancho Salcedo-Sanz
    • 2
  • Mario J. Martin-Burgos
    • 3
  1. 1.Fluid Dynamics Branch, Spanish National Institute for Aerospace Technology (ISDEFE/INTA)Torrejón de ArdozSpain
  2. 2.Department of Signal Theory and CommunicationsUniversidad de Alcalá (UAH)Alcalá de HenaresSpain
  3. 3.School of AeronauticsUniversidad Politécnica de Madrid (UPM)MadridSpain

Personalised recommendations