Skip to main content

Response Surface Methods for Efficient Aerodynamic Surrogate Models

  • Chapter
Computational Flight Testing

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 123))

Abstract

Response surface methods for the approximation of outputs of computer experiments such as the Kriging method often suffer from a lack of accuracy or efficiency. Many computationally expensive samples are needed for the globally correct reproduction of an unknown response. We investigate adaptive sampling strategies, which can automatically identify critical regions of an input-parameter domain and require less samples than traditional one-stage approaches like Latin hypercube designs. Furthermore, we propose a new method which makes use of the assumption that the aerodynamic responses are not of arbitrary structure, but rather related to other instances of a mutual problem class. Both approaches are validated with numerical test cases, showing that they produce more accurate surrogate models using less samples than traditional approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bui-Thanh, T., Damodaran, M., Willcox, K.: Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA Journal 42(8), 1505–1516 (2004)

    Article  Google Scholar 

  2. Busby, D., Farmer, C.L., Iske, A.: Hierarchical nonlinear approximation for experimental design and statistical data fitting. SIAM Journal on Scientific Computing 29(1), 49–69 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chang, K.J., Haftka, R.T., Giles, G.L., Kao, P.-J.: Sensitivity-based scaling for approximating structural response. Journal of Aircraft 30, 283–288 (1993)

    Article  Google Scholar 

  4. Chung, H.-S., Alonso, J.J.: Using gradients to construct cokriging approximation models for high-dimensional design optimization problems. In: 40th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2002–2317 (2002)

    Google Scholar 

  5. Crombecq, K., De Tommasi, L., Gorissen, D., Dhaene, T.: A novel sequential design strategy for global surrogate modeling. In: Proceedings of the 2009 Winter Simulation Conference (WSC), pp. 731–742 (2009)

    Google Scholar 

  6. Davies, R.H., Twining, C.J., Taylor, C.J.: Statistical Models of Shape—Optimisation and Evaluation. Springer (2008)

    Google Scholar 

  7. Dwight, R., Han, Z.-H.: Efficient uncertainty quantification using gradient-enhanced Kriging. In: Proceedings of 11th AIAA Conference on Non-Deterministic Approaches, Palm Springs CA. AIAA-2009-2276. AIAA (2009)

    Google Scholar 

  8. Everson, R., Sirovich, L.: Karhunen–Loève procedure for gappy data. Journal of the Optical Society of America A 12(8), 1657–1664 (1995)

    Article  Google Scholar 

  9. Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimization. Progress in Aerospace Sciences 45(1-3), 50–79 (2009)

    Article  Google Scholar 

  10. Forrester, A.I.J., Sóbester, A., Keane, A.J.: Multi-fidelity optimization via surrogate modelling. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 463(2088), 3251–3269 (2007)

    Article  MATH  Google Scholar 

  11. Forrester, A.I.J., Sóbester, A., Keane, A.J.: Engineering Design via Surrogate Modelling—A Practical Guide. Wiley (2008)

    Google Scholar 

  12. Gramacy, R.B., Lee, H.K.H.: Adaptive design and analysis of supercomputer experiments. Technometrics 51(2), 130–145 (2009)

    Article  MathSciNet  Google Scholar 

  13. Han, Z.-H., Görtz, S.: Hierarchical kriging model for variable-fidelity surrogate modeling. AIAA Journal 50(9), 1885–1896 (2012)

    Article  Google Scholar 

  14. Han, Z.-H., Görtz, S., Hain, R.: A variable-fidelity modeling method for aero-loads prediction. In: Dillmann, A., Heller, G., Klaas, M., Kreplin, H.-P., Nitsche, W., Schröder, W. (eds.) New Results in Numerical and Experimental Fluid Mechanics VII. NNFM, vol. 112, pp. 17–25. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Han, Z.-H., Zimmermann, R., Görtz, S.: A new cokriging method for variable-fidelity surrogate modeling of aerodynamic data. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, pp. 4–7 (January 2010)

    Google Scholar 

  16. Jin, R., Chen, W., Sudjianto, A.: On sequential sampling for global metamodeling in engineering design. In: Proceedings of DETC 2002 ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, Canada (2002)

    Google Scholar 

  17. Koehler, J., Owen, A.: Computer experiments. In: Ghosh, S., Rao, C. (eds.) Handbook of Statistics, 13: Design and Analysis of Experiments, pp. 261–308. North-Holland (1996)

    Google Scholar 

  18. Krige, D.G.: A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Chemical, Metallurgical and Mining Society of South Africa 52(6), 119–139 (1951)

    Google Scholar 

  19. Kroll, N., Fassbender, J. (eds.): MEGAFLOW—Numerical Flow Simulation for Aircraft Design. Springer (2005)

    Google Scholar 

  20. Kunisch, K., Volkwein, S.: Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM Journal on Numerical Analysis 40(2), 492–515 (2003)

    Article  MathSciNet  Google Scholar 

  21. Lam, X., Kim, Y., Hoang, A., Park, C.: Coupled aerostructural design optimization using the Kriging model and integrated multiobjective optimization algorithm. Journal of Optimization Theory and Applications 142, 533–556 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Laurenceau, J., Meaux, M.: Comparison of gradient and response surface based optimization frameworks using adjoint method. AIAA Paper, 2008-1889 (2008)

    Google Scholar 

  23. Laurenceau, J., Sagaut, P.: Building efficient response surfaces of aerodynamic functions with kriging and cokriging. AIAA Journal 46(2), 498–507 (2008)

    Article  Google Scholar 

  24. Leifsson, L., Koziel, S.: Variable-fidelity aerodynamic shape optimization. In: Koziel, S., Yang, X.-S. (eds.) Computational Optimization, Methods and Algorithms. SCI, vol. 356, pp. 179–210. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Liu, W.: Development of Gradient-Enhanced Kriging Approximations for Multidisciplinary Design Optimization. PhD thesis, University of Notre Dame (2003)

    Google Scholar 

  26. Lockwood, B., Anitescu, M.: Gradient-enhanced universal kriging for uncertainty propagation. Nuclear Science and Engineering 170(2), 168–195 (2012)

    Google Scholar 

  27. Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE—A MATLAB kriging toolbox. Technical Report IMM-REP-2002-12, Technical University of Denmark, Copenhagen (2002)

    Google Scholar 

  28. Martin, J., Simpson, T.: Use of adaptive metamodeling for design optimization. In: AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. AIAA (September 2002)

    Google Scholar 

  29. Matheron, G.: Principles of geostatistics. Economic geology 58(8), 1246–1266 (1963)

    Article  Google Scholar 

  30. Morris, M.D., Mitchell, T.J., Ylvisaker, D.: Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. Technometrics 35(3), 243–255 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  31. Robinson, T., Eldred, M., Willcox, K., Haimes, R.: Strategies for multifidelity optimization with variable dimensional hierarchical models. In: Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2nd AIAA Multidisciplinary Design Optimization Specialist Conference), Newport, RI (2006)

    Google Scholar 

  32. Rosenbaum, B., Schulz, V.: Comparing sampling strategies for aerodynamic kriging surrogate models. ZAMM - Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik (2012), doi:10.1002/zamm.201100112

    Google Scholar 

  33. Rosenbaum, B., Schulz, V.: Efficient response surface methods based on generic surrogate models. SIAM Journal on Scientific Computing (2012) arXiv:1206.4172 (submitted to)

    Google Scholar 

  34. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical Science 4(4), 409–423 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  35. Santner, T.J., Williams, B.J., Notz, W.: The Design and Analysis of Computer Experiments. Springer (2003)

    Google Scholar 

  36. Schwamborn, D., Gerhold, T., Heinrich, R.: The DLR TAU-code: Recent applications in research and industry. In: European conference on computational fluid dynamics, ECCOMAS CFD (2006)

    Google Scholar 

  37. Shan, S., Wang, G.: Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Structural and Multidisciplinary Optimization 41, 219–241 (2010)

    Article  MathSciNet  Google Scholar 

  38. Tang, C., Gee, K., Lawrence, S.: Generation of aerodynamic data using a design of experiment and data fusion approach. In: 43rd AIAA Aerospace Sciences meeting, Reno, Nevada (2005)

    Google Scholar 

  39. Viana, F.A.C., Venter, G., Balabanov, V.: An algorithm for fast optimal Latin hypercube design of experiments. International Journal for Numerical Methods in Engineering 82(2), 135–156 (2010)

    MathSciNet  MATH  Google Scholar 

  40. Volkwein, S.: Optimal control of a phase-field model using proper orthogonal decomposition. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 81(2), 83–97 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wackernagel, H.: Multivariate Geostatistics: An Introduction with Applications. Springer (2003)

    Google Scholar 

  42. Yamazaki, W., Rumpfkeil, M., Mavriplis, D.: Design optimization utilizing gradient/hessian enhanced surrogate model. AIAA Paper, 2010-4363 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rosenbaum, B., Schulz, V. (2013). Response Surface Methods for Efficient Aerodynamic Surrogate Models. In: Kroll, N., Radespiel, R., Burg, J., Sørensen, K. (eds) Computational Flight Testing. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38877-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38877-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38876-7

  • Online ISBN: 978-3-642-38877-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics