Wing Aerodynamic Shape Optimization by Space Mapping

  • Leifur Leifsson
  • Slawomir Koziel
  • Eirikur Jonsson
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 256)


This chapter describes an efficient aerodynamic design optimization methodology for wings in transonic flow. The approach replaces a computationally expensive high-fidelity computational fluid dynamic model (CFD) in an iterative optimization process with a corrected polynomial approximation model constructed by a cheap low-fidelity CFD model. The output space mapping technique is used to correct the approximation model to yield an accurate predictor of the high-fidelity one. The algorithm is applied to two transonic wing design problems.


Transonic Wing Design CFD Surrogate-based Optimization Variable-resolution Modeling Space Mapping 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Raymer, D.: Aircraft design: a conceptual approach. American Institute of Aeronautics and Astronautics (2006)Google Scholar
  2. 2.
    Queipo, N., Haftka, R., Shyy, W., Goel, T., Vaidyanathan, R., Kevin Tucker, P.: Surrogate-based analysis and optimization. Progress in Aerospace Sciences 41, 1–28 (2005)CrossRefGoogle Scholar
  3. 3.
    Forrester, A., Keane, A.: Recent advances in surrogate-based optimization. Progress in Aerospace Sciences 45, 50–79 (2009)CrossRefGoogle Scholar
  4. 4.
    Wild, S., Regis, R., Shoemaker, C.: Orbit: Optimization by radial basis function interpolation in trust-regions. SIAM Journal on Scientific Computing 30, 3197–3219 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Koziel, S., Ciaurri, D.E., Leifsson, L.: Surrogate-based methods. In: Koziel, S., Yang, X.-S. (eds.) COMA. SCI, vol. 356, pp. 33–59. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Simpson, T., Poplinski, J., Koch, P., Allen, J.: Metamodels for computer-based engineering design: survey and recommendations. Engineering with Computers 17, 129–150 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Journel, A., Huijbregts, C.: Mining geostatistics. Academic Press, Number London [ua] (1978)Google Scholar
  8. 8.
    O’Hagan, A., Kingman, J.: Curve fitting and optimal design for prediction. Journal of the Royal Statistical Society. Series B (Methodological), 1–42 (1978)Google Scholar
  9. 9.
    Haikin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall (1998)Google Scholar
  10. 10.
    Minsky, M., Papert, S.: Perceptrons: An introduction to computational geometry. The MIT Press, Cambridge (1969)zbMATHGoogle Scholar
  11. 11.
    Smola, A., Schölkopf, B.: A tutorial on support vector regression. Statistics and Computing 14, 199–222 (2004)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Søndergaard, J.: Optimization using surrogate models by the space mapping technique. PhD thesis, PhD. Thesis, Technical University of Denmark, Informatics and mathematical modelling (2003)Google Scholar
  13. 13.
    Leifsson, L., Koziel, S.: Variable-fidelity aerodynamic shape optimization. In: Koziel, S., Yang, X.-S. (eds.) COMA. SCI, vol. 356, pp. 179–210. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Alexandrov, N., Lewis, R.: An overview of first-order model management for engineering optimization. Optimization and Engineering 2, 413–430 (2001)CrossRefzbMATHGoogle Scholar
  15. 15.
    Bandler, J., Cheng, Q., Dakroury, S., Mohamed, A., Bakr, M., Madsen, K., Sondergaard, J.: Space mapping: the state of the art. IEEE Transactions on Microwave Theory and Techniques 52, 337–361 (2004)CrossRefGoogle Scholar
  16. 16.
    Koziel, S., Cheng, Q., Bandler, J.: Space mapping. IEEE Microwave Magazine 9, 105–122 (2008)CrossRefGoogle Scholar
  17. 17.
    Echeverria, D., Hemker, P.: Space mapping and defect correction. Computational Methods in Applied Mathematics 5, 107–136 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Koziel, S., Leifsson, L.: Airfoil shape optimization using variable-fidelity modeling and shape-preserving response prediction. In: Yang, X.-S., Koziel, S. (eds.) Computational Optimization and Applications. SCI, vol. 359, pp. 99–124. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Robinson, T., Willcox, K., Eldred, M., Haimes, R.: Multifidelity optimization for variablecomplexity design. In: Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA (2006)Google Scholar
  20. 20.
    Jonsson, E., Leifsson, L., Koziel, S.: Transonic wing optimization by variable-resolution modeling and space mapping. In: 2nd Int. Conf. on Simulation and Modeling Methodologies, Technologies, and Applications (SIMULTECH), Rome, Italy, July 28-31 (2012)Google Scholar
  21. 21.
    Jonsson, E., Leifsson, L., Koziel, S.: Aerodynamic optimization of wings by space mapping. In: 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, January 7-10 (2013)Google Scholar
  22. 22.
    Tannehill, J., Anderson, D., Pletcher, R.: Computational fluid mechanics and heat transfer. Taylor & Francis Group (1997)Google Scholar
  23. 23.
    ANSYS: ANSYS FLUENT Theory Guide. ANSYS, Southpointe 275 Thecnology Drive Canonburg PA 15317. Release 13.0 edn. (2010)Google Scholar
  24. 24.
    NASA: Onera-m6-wing validation case (2008),
  25. 25.
    Schmitt, V., Charpin, F.: Pressure distributions on the onera-m6-wing at transonic mach numbers. In: Experimental Data Base for Computer Program Assessment Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138 (May 1979)Google Scholar
  26. 26.
    Zhu, J., Bandler, J., Nikolova, N., Koziel, S.: Antenna optimization through space mapping. IEEE Transactions on Antennas and Propagation 55, 651–658 (2007)CrossRefGoogle Scholar
  27. 27.
    Koziel, S.: Multi-fidelity multi-grid design optimization of planar microwave structures with sonnet. International Review of Progress in Applied Computational Electromagnetics, 719–724 (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Leifur Leifsson
    • 1
  • Slawomir Koziel
    • 1
  • Eirikur Jonsson
    • 1
  1. 1.Engineering Optimization & Modeling Center, School of Science and EngineeringReykjavik UniversityReykjavikIceland

Personalised recommendations