Skip to main content
Log in

Coupled Aerostructural Design Optimization Using the Kriging Model and Integrated Multiobjective Optimization Algorithm

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The paper develops and implements a highly applicable framework for the computation of coupled aerostructural design optimization. The multidisciplinary aerostructural design optimization is carried out and validated for a tested wing and can be easily extended to complex and practical design problems. To make the framework practical, the study utilizes a high-fidelity fluid/structure interface and robust optimization algorithms for an accurate determination of the design with the best performance. The aerodynamic and structural performance measures, including the lift coefficient, the drag coefficient, Von-Mises stress and the weight of wing, are precisely computed through the static aeroelastic analyses of various candidate wings. Based on these calculated performance, the design system can be approximated by using a Kriging interpolative model. To improve the design evenly for aerodynamic and structure performance, an automatic design method that determines appropriate weighting factors is developed. Multidisciplinary aerostructural design is, therefore, desirable and practical.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sobieski, J.S., Haftka, R.T.: Multidisciplinary aerospace design optimization: survey of recent developments. AIAA J., AIAA-96-0711 (1996)

  2. Wakayama, S.R.: Lifting surface design using multidisciplinary optimization. Ph.D. Thesis, Stanford University (1997)

  3. Walsh, J.L., Townsend, J.C., Salas, A.O., Samareh, J.A., Mukhopadhyay, V., Barthelemy, J.-F.: Multidisciplinary high-fidelity analysis and optimization of aerospace vehicles. AIAA J., AIAA-2000-0418 (2000)

  4. Martins, R.R.A.: A coupled-adjoint method for high-fidelity aero-structural optimization. Ph.D. Thesis, Stanford University (2002)

  5. Venkataraman, S., Haftka, R.T.: Structural optimization complexity: what has Moore’s law done for us. J. Struct. Multidiscip. Optim. 28, 375–387 (2004)

    Article  Google Scholar 

  6. Kim, Y., Kim, J., Jeon, Y., Bang, J., Lee, D.-H., Kim, Y., Park, C.W.: Multidisciplinary aerodynamic-structural design optimization of supersonic fighter wing using response surface methodology. AIAA J., AIAA-2002-0322 (2002)

  7. Giunta, A.A.: Aircraft multidisciplinary design optimization using design of experiments theory and response surface modeling methods. Ph.D. Thesis, University of Virginia (1997)

  8. Giunta, A.A., Balabanov, V., Haim, D., Grossman, B., Mason, W.H., Watson, L.T., Haftka, R.T.: Wing design for a high-speed civil transport using a design of experiments methodology. AIAA J., AIAA-96-4001 (1996)

  9. Joaquim, R.R., Alonso, J.J., Reuther, J.: Aero-Structural Wing Design Optimization using high-fidelity sensitivity analysis. In: Proceeding to CEAS Conference on Multidisciplinary Aircraft Design Optimization, Germany. Confederation of European Societies (2001)

  10. Chittick, I.R., Martins, J.R.R.A.: Aero-structural optimization using adjoint coupled post-optimality sensitivities. J. Struct. Multidiscip. Optim. DOI 10.1007/s00158-007-0200-9 (2007)

    Google Scholar 

  11. Gumbert, C.R., Newman, P.A.: High-fidelity computational optimization for 3-D flexible wings. J. Optim. Eng. 6, 117–156 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kumano, T., Jeong, S., Obayashi, S., Ito, Y., Hatanaka, K., Morino, H.: Multidisciplinary design optimization of wing shape with nacelle and pylon. In: European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006, TU Delft, The Netherlands (2006)

  13. Weck, O.D., Agte, J., Sobieski, J.S., Arendsen, P., Morris, A., Spieck, M.: State-of-the-art and future trends in multidisciplinary design optimization. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Hawaii, USA. AIAA-2007-1905 (2007)

  14. Martins, J.R.R.A., Marriage, C.: An objective-oriented framework for multidisciplinary design optimization. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Hawaii, USA. AIAA-2007-1906 (2007)

  15. Kamakoti, R., Shyy, W.: Fluid-structure interaction for aeroelastic applications. Prog. Aerospace Sci. 40, 535–558 (2005)

    Article  Google Scholar 

  16. Guruswamy, G.P.: A review of numerical fluids/structures interface methods for computations using high-fidelity equations. J. Comput. Struct. 80, 31–41 (2001)

    Article  Google Scholar 

  17. Hounjet, M.H.L., Meijer, J.J.: Evaluation of elastomechanical and aerodynamic data transfer methods for non-planar configurations in computational aeroelastic analysis. National Aerospace Laboratory NRL, NLR-TP-95690 U (1995)

  18. Bhadra, S., Ganguli, R.: Aeroelastic optimization of a helicopter rotor using orthogonal array-based metamodels. AIAA J. 44(9), 1941–1951 (2006)

    Article  Google Scholar 

  19. Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, New York (1996)

    MATH  Google Scholar 

  20. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, New Jersey (1999)

    MATH  Google Scholar 

  21. Hagan, M.T., Demuth, H.B., Beale, M.: Neural Network Design. Massachusetts (1996)

  22. Friedman, J.H.: Multivariate adaptive regression splines, invited paper. Ann. Stat. 19(1), 1–67 (1991)

    Article  MATH  Google Scholar 

  23. Turner, C.J., Crawford, R.H., Campbell, M.I.: Multidimensional sequential sampling for NURBs-based metamodel development. J. Eng. Comput. 23, 155–174 (2007)

    Article  Google Scholar 

  24. Mullur, A.A., Messac, A.: Extended radial basis functions: More flexible and effective metamodeling. AIAA J. 43(6), 1306–1315 (2005)

    Article  Google Scholar 

  25. Mullur, A.A., Messac, A.: Metamodeling using extended radial basis functions: A comparative approach. J. Eng. Comput. 21, 203–217 (2006)

    Article  Google Scholar 

  26. Koehler, J.R., Owen, A.B.: Computer Experiments. Handbook of Statistics 13: Design and Analysis of Experiments. Elsevier, Amsterdam (1996)

    Google Scholar 

  27. Giunta, A.A., Watson, L.T.: A comparison of approximation modeling techniques: Polynomial versus interpolating models. AIAA J., AIAA-98-4758 (1998)

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

    Article  MATH  MathSciNet  Google Scholar 

  29. Jeong, S., Murayama, M., Yamamoto, K.: Efficient optimization design method using Kriging model. AIAA J., AIAA-2004-118 (2004)

  30. Simpson, T.W., Dennis, L., Chen, W.: Sampling strategies for computer experiments: design and analysis. Int. J. Reliab. Appl. 23(2), 209–240 (2001)

    Google Scholar 

  31. Simpson, T.W., Booker, A.J., Ghosh, D., Giunta, A.A., Koch, P.N., Yang, R.-J.: Approximation methods in multidisciplinary analysis and optimization: A panel discussion. J. Struct. Multidiscip. Optim. 27, 302–313 (2004)

    Google Scholar 

  32. Martin, J.D., Simpson, T.W.: Use of Kriging models to approximate deterministic computer models. AIAA J. 43(4), 853–863 (2005)

    Article  Google Scholar 

  33. Clarke, S.M., Griebsch, J.H., Simpson, T.W.: Analysis of support vector regression for approximation of complex engineering analyses. ASME J. 127, 1077–1087 (2005)

    Article  Google Scholar 

  34. Maisuradze, G.G., Thompson, D.L.: Interpolating moving least-squares methods for fitting potential energy surfaces: illustrative approaches and applications. J. Phys. Chem. A 107(37), 7118–7124 (2003)

    Google Scholar 

  35. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley Longman Inc, Cambridge (1989)

    MATH  Google Scholar 

  36. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1996)

    MATH  Google Scholar 

  37. Yang, G., Reinstein, L.E., Pai, S., Xu, Z.: A new genetic algorithm technique in optimization of permanent prostate implants. J. Med. Phys. 25(12), 2308–2315 (1998)

    Article  Google Scholar 

  38. Carroll, D.L.: Chemical laser modeling with genetic algorithms. AIAA J. 34(2), 338–346 (1996)

    Article  Google Scholar 

  39. Arora, J.S.: Introduction to optimum design. Elsevier Academic, San Diego (2004)

    Google Scholar 

  40. Arora, J.S., Elwakeil, O.A., Chahande, A.I., Hsieh, C.C.: Global optimization methods for engineering applications: A review. J. Struct. Optim. 9, 137–159 (1995)

    Article  Google Scholar 

  41. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. J. Sci. 220(4598), 671–680 (1983)

    MathSciNet  Google Scholar 

  42. Goffe, W.L., Ferrier, G.D., Rogers, J.: Global optimization of statistical functions with simulated annealing. J. Econom. 60(1/2), 65–100 (1993)

    Google Scholar 

  43. Corana, A., Marchesi, M., Martini, C., Ridella, S.: Minimizing multimodal functions of continuous variables with the ‘Simulated Annealing’ algorithm. ACM Trans. Math. Softw. 13(3), 262–280 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  44. Yao, X.: Simulated annealing with extended neighbourhood. Int. J. Comput. Math. 40, 169–189 (1991)

    Article  MATH  Google Scholar 

  45. Coello Coello, C.A., Lamont, G.B., Veldhuizen, D.A.V.: Evolutionary Algorithms for Solving Multi-Objective Problems. Springer, New York (2007)

    MATH  Google Scholar 

  46. Deb, K.: Current trends in evolutionary multi-objective optimization. Int. J. Simul. Multidiscip. Des. Optim. 1, 1–8 (2007)

    Article  MATH  Google Scholar 

  47. Marler, R.T.: A study of multi-objective optimization methods for engineering applications. Ph.D. Thesis, University of Iowa (2005)

  48. FLUENT INC: Fluent User’s Manual. Fluent Inc, New Hampshire (2005)

  49. Blom, F.J.: Considerations on the spring analogy. Int. J. Numer. Methods Fluids 32, 647–668 (2000)

    Article  MATH  Google Scholar 

  50. Tsai, H.M., Wong, A.S.F., Cai, J., Zhu, Y., Liu, F.: Unsteady flow calculations with a parallel multiblock moving mesh algorithm. AIAA J. 39(6), 1021–1029 (2000)

    Article  Google Scholar 

  51. Dubuc, L., Cantariti, F., Woodgate, M., Gribben, B., Badcock, K.J., Richards, B.E.: A grid deformation technique for unsteady flow computations. Int. J. Numer. Methods Fluids 32, 285–311 (2000)

    Article  MATH  Google Scholar 

  52. Spekreijse, S.P., Prananta, B.B., Kok, J.C.: A simple, robust and fast algorithm to compute deformations of multi-block structured grids. National Aerospace Laboratory NLR, NLR-TP-2002-105 (2002)

  53. Thompson, J.F., Soni, B.K., Weatherill, N.P.: Handbook of Grid Generation. CRC Press LLC, Boca Raton (1999)

    MATH  Google Scholar 

  54. Sadeghi, M., Liu, F., Lai, K.L., Tsai, H.M.: Application of three-dimensional interfaces for data transfer in aeroelastic computations. AIAA J., AIAA-2004-5376 (2004)

  55. Dowell, E.H., Hall, K.C.: Modeling of fluid-structure interaction. J. Fluid Mech. 33, 445–490 (2001)

    Google Scholar 

  56. Hirsch, C.: Numerical Computation of Internal and External Flows. Butterworth-Heinemann, Oxford (2007)

    Google Scholar 

  57. Blazek, J.: Computational Fluid Dynamics: Principles and Applications. Elsevier Science Ltd, Oxford (2001)

    MATH  Google Scholar 

  58. Chung, T.J.: Computational Fluid Dynamics. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  59. Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics. Springer, Berlin (2002)

    MATH  Google Scholar 

  60. Anderson, J.D.: Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill, Columbus (1995)

    Google Scholar 

  61. Pointwise: Gridgen User’s Manual. Pointwise Inc, Texas, USA (2005)

  62. Zienkiewicz, O.C., Taylor, L.R.: The Finite Element Method, 5th edn. Butterworth-Heinemann, Oxford (2000)

    MATH  Google Scholar 

  63. Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  64. Smith, I.M., Griffiths, D.V.: Programming the Finite Element Method. Wiley, Chichester (2004)

    MATH  Google Scholar 

  65. Reddy, J.N.: An introduction to the Finite Element Method, 3rd edn. McGraw-Hill, New York (2006)

    Google Scholar 

  66. Liu, G.R., Quek, S.S.: The Finite Element Method—A Practical Course. Butterworth-Heinemann, Oxford (2003)

    MATH  Google Scholar 

  67. Ribo, R., Pasenau, M.D.R., Escolano, E., Ronda, J.S.P., Sans, A.C., Gonzalez, L.F.: GiD User’s Manual. CIMNE, Barcelona, Spain (2007)

    Google Scholar 

  68. Mitchell, T.J., Morris, M.D.: Bayesian design and analysis of computer experiments: Two examples. J. Stat. Sinica 2, 359–379 (1992)

    MATH  Google Scholar 

  69. The Mathworks: Matlab User’S Manual. The MathWorks Inc, Massachusetts, USA (2007)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. W. Park.

Additional information

Communicated by K.K. Choi.

The authors acknowledge the support of a Korea Research Foundation Grant funded by the Korean Government and the second stage of Brain Korea 21st project.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lam, X.B., Kim, Y.S., Hoang, A.D. et al. Coupled Aerostructural Design Optimization Using the Kriging Model and Integrated Multiobjective Optimization Algorithm. J Optim Theory Appl 142, 533–556 (2009). https://doi.org/10.1007/s10957-009-9520-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-009-9520-9

Keywords

Navigation