Skip to main content
SpringerLink
Log in

Variable-Fidelity Aerodynamic Shape Optimization

  • Chapter
Computational Optimization, Methods and Algorithms

Part of the book series: Studies in Computational Intelligence ((SCI,volume 356))

Abstract

Aerodynamic shape optimization (ASO) plays an important role in the design of aircraft, turbomachinery and other fluid machinery. Simulation-driven ASO involves the coupling of computational fluid dynamics (CFD) solvers with numerical optimization methods. Although being relatively mature and widely used, ASO is still being improved and numerous challenges remain. This chapter provides an overview of simulation-driven ASO methods, with an emphasis on surrogate-based optimization (SBO) techniques. In SBO, a computationally cheap surrogate model is used in lieu of an accurate high-fidelity CFD simulation in the optimization process. Here, a particular focus is given to SBO exploiting surrogate models constructed from corrected physics-based low-fidelity models, often referred to as variable- or multi-fidelity optimization.

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

Access this chapter

Log in via an institution
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
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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. Hicks, R.M., Henne, P.A.: Wing Design by Numerical Optimization. Journal of Aircraft 15(7), 407–412 (1978)

    Article  Google Scholar 

  2. Braembussche, R.A.: Numerical Optimization for Advanced Turbomachinery Design. In: Thevenin, D., Janiga, G. (eds.) Optimization and Computational Fluid Dynamics, pp. 147–189. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Percival, S., Hendrix, D., Noblesse, F.: Hydrodynamic Optimization of Ship Hull Forms. Applied Ocean Research 23(6), 337–355 (2001)

    Article  Google Scholar 

  4. Leoviriyakit, K., Kim, S., Jameson, A.: Viscous Aerodynamic Shape Optimization of Wings including Planform Variables. In: 21st Applied Aerodynamics Conference, Orlando, Florida, June 23-26 (2003)

    Google Scholar 

  5. van Dam, C.P.: The aerodynamic design of multi-element high-lift systems for transport airplanes. Progress in Aerospace Sciences 8(2), 101–144 (2002)

    MathSciNet  Google Scholar 

  6. Lian, Y., Shyy, W., Viieru, D., Zhang, B.: Membrane Wing Aerodynamics for Micro Air Vehicles. Progress in Aerospace Sciences 39(6), 425–465 (2003)

    Article  Google Scholar 

  7. Secanell, M., Suleman, A., Gamboa, P.: Design of a Morphing Airfoil Using Aerodynamic Shape Optimization. AIAA Journal 44(7), 1550–1562 (2006)

    Article  Google Scholar 

  8. Antoine, N.E., Kroo, I.A.: Optimizing Aircraft and Operations for Minimum Noise. In: AIAA Paper 2002-5868, AIAA‘s Aircraft Technology, Integration, and Operations (ATIO) Technical Forum, Los Angeles, California, October 1-3 (2002)

    Google Scholar 

  9. Hosder, S., Schetz, J.A., Grossman, B., Mason, W.H.: Airframe Noise Modeling Appropriate for Multidisciplinary Design and Optimization. In: 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Paper 2004-0698, January 5-8 (2004)

    Google Scholar 

  10. Giannakoglou, K.C., Papadimitriou, D.I.: Adjoint Methods for Shape Optimization. In: Thevenin, D., Janiga, G. (eds.) Optimization and Computational Fluid Dynamics, pp. 79–108. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Celik, F., Guner, M.: Energy Saving Device of Stator for Marine Propellers. Ocean Engineering 34(5-6), 850–855 (2007)

    Article  Google Scholar 

  12. Jameson, A.: Aerodynamic Design via Control Theory. Journal of Scientific Computing 3, 233–260 (1988)

    Article  MATH  Google Scholar 

  13. Reuther, J., Jameson, A.: Control Theory Based Airfoil Design for Potential Flow and a Finitie Volume Discretization. In: AIAA Paper 94-0499, AIAA 32nd Aerospace Sciences Meeting and Exhibit, Reno, Nevada (January 1994)

    Google Scholar 

  14. Jameson, A., Reuther, J.: Control Theory Based Airfoil Design using Euler Equations. In: Proceedings of AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analsysis and Optimization, Panama City Beach, pp. 206–222 (September 1994)

    Google Scholar 

  15. Reuther, J., Jameson, A., Alonso, J.J., Rimlinger, M.J., Sauders, D.: Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computing. In: 35th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA Paper 97-0103, Januvary 6-9 (1997)

    Google Scholar 

  16. Kim, S., Alonso, J.J., Jameson, A.: Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method. In: AIAA paper 2002-0844, AIAA 40th Aerospace Sciences Meeting & Exhibit, Reno, NV (January 2002)

    Google Scholar 

  17. Eyi, S., Lee, K.D., Rogers, S.E., Kwak, D.: High-lift design optimization using Navier-Stokes equations. Journal of Aircraft 33(3), 499–504 (1996)

    Article  Google Scholar 

  18. Nemec, M., Zingg, D.W.: Optimization of high-lift configurations using a Newton-Krylov algorithm. In: 16th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, June 23-26 (2003)

    Google Scholar 

  19. Nemec, M., Zingg, D.W., Pulliam, T.H.: Multi-Point and Multi-Objective Aerodynamic Shape Optimization. In: AIAA Paper 2002-5548, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Altanta, Georgia, September 4-6 (2002)

    Google Scholar 

  20. Giannakoglou, K.C.: Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Sciences 38(2), 43–76 (2002)

    Article  Google Scholar 

  21. Hicks, R.M., Murman, E.M., Vanderplaats, G.: An Assessment of Airfoil Design by Numerical Optimization. NASA TM 3092 (July 1974)

    Google Scholar 

  22. FLUENT, ver. 6.3.26, ANSYS Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317 (2006)

    Google Scholar 

  23. GAMBIT. ver. 2.4.6, ANSYS Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317 (2006)

    Google Scholar 

  24. Tannehill, J.C., Anderson, D.A., Pletcher, R.H.: Computational Fluid Mechanics and Heat Transfer, 2nd edn. Taylor & Francis, Abington (1997)

    Google Scholar 

  25. Hirsch, C.: Numerical Computation of Internal and External Flows – Fundamentals of Computational Fluid Dynamics, 2nd ed., Butterworth-Heinemann (2007)

    Google Scholar 

  26. Leifsson, L., Koziel, S.: Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction. Journal of Computational Science 1(2), 98–106 (2010)

    Article  Google Scholar 

  27. Lepine, J., Guibault, F., Trepanier, J.-Y., Pepin, F.: Optimized Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings. AIAA Journal 39(11), 2033–2041 (2001)

    Article  Google Scholar 

  28. Li, W., Huyse, L., Padula, S.: Robust Airfoil Optimization to Achieve Consistent Drag Reductin Over a Mach Range. In: NASA/CR-2001-211042 (August 2001)

    Google Scholar 

  29. Giunta, A.A., Dudley, J.M., Narducci, R., Grossman, B., Haftka, R.T., Mason, W.H., Watson, L.T.: Noisy Aerodynamic Response and Smooth Approximations in HSCT Design. In: 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City, FL (Septemper 1994)

    Google Scholar 

  30. Burman, J., Gebart, B.R.: Influence from numerical noise in the objective function for flow design optimisation. International Journal of Numerical Methods for Heat & Fluid Flow 11(1), 6–19 (2001)

    Article  MATH  Google Scholar 

  31. Dudley, J.M., Huang, X., MacMillin, P.E., Grossman, B., Haftka, R.T., Mason, W.H.: Multidisciplinary Design Optimization of a High Speed Civil Transport. In: First Industry/University Symposium on High Speed Transport Vehicles, December 4-6. NC A&T University, Greensboro (1994)

    Google Scholar 

  32. Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Tucker, P.K.: Surrogate-Based Analysis and Optimization. Progress in Aerospace Sciences 41(1), 1–28 (2005)

    Article  Google Scholar 

  33. 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 

  34. Alexandrov, N.M., Lewis, R.M.: An overview of first-order model management for engineering optimization. Optimization and Engineering 2(4), 413–430 (2001)

    Article  MATH  Google Scholar 

  35. Alexandrov, N.M., Nielsen, E.J., Lewis, R.M., Anderson, W.K.: First-Order Model Management with Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization. In: 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Design and Optimization, AIAA Paper 2000-4886, Long Beach, CA (September 2000)

    Google Scholar 

  36. Alexandrov, N.M., Lewis, R.M., Gumbert, C.R., Green, L.L., Newman, P.A.: Optimization with Variable-Fidelity Models Applied to Wing Design. In: 38th Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA Paper 2000-0841(January 2000)

    Google Scholar 

  37. Robinson, T.D., Eldred, M.S., Willcox, K.E., Haimes, R.: Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping. AIAA Journal 46(11) (November 2008)

    Google Scholar 

  38. Booker, A.J., Dennis Jr., J.E., Frank, P.D., Serafini, D.B., Torczon, V., Trosset, M.W.: A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization 17(1), 1–13 (1999)

    Article  Google Scholar 

  39. Lee, D.S., Gonzalez, L.F., Srinivas, K., Periaux, J.: Multi-objective robust design optimisation using hierarchical asynchronous parallel evolutionary algorithms. In: 45th AIAA Aerospace Science Meeting and Exhibit, AIAA Paper 2007-1169, Reno, Nevada, USA, January 8-11 (2007)

    Google Scholar 

  40. Barrett, T.R., Bressloff, N.W., Keane, A.J.: Airfoil Design and Optimization Using Multi-Fidelity Analysis and Embedded Inverse Design. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, AIAA Paper 2006-1820, Rhode Island, May 1-4 (2006)

    Google Scholar 

  41. Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design, 3rd edn. Vanderplaats Research and Development (1999)

    Google Scholar 

  42. Rai, M.M.: Robust optimal design with differential evolution. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4588, Albany, New York, August 30 - September 1 (2004)

    Google Scholar 

  43. Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows. In: 30th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 6-9 (1992)

    Google Scholar 

  44. Anderson, J.D.: Modern Compressible Flow – With Historical Prespective, 3rd edn. McGraw-Hill, New York (2003)

    Google Scholar 

  45. Katz, J., Plotkin, A.: Low-Speed Aerodynamics, 2nd edn. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  46. Anderson, J.D.: Fundamentals of Aerodynamics, 4th edn. McGraw-Hill, New York (2007)

    Google Scholar 

  47. Gauger, N.R.: Efficient Deterministic Approaches for Aerodynamic Shape Optimization. In: Thevenin, D., Janiga, G. (eds.) Optimization and Computational Fluid Dynamics, pp. 111–145. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  48. Abbott, I.H., Von Doenhoff, A.E.: Theory of Wing Sections. Dover Publications, New York (1959)

    Google Scholar 

  49. Peigin, S., Epstein, B.: Robust Optimization of 2D Airfoils Driven by Full Navier-Stokes Computations. Computers & Fluids 33, 1175–1200 (2004)

    Article  MATH  Google Scholar 

  50. Sobieczky, H.: Parametric Airfoils and Wings. In: Fuji, K., Dulikravich, G.S. (eds.) Notes on Numerical Fluid Mechanics, vol. 68. Wiesbaden, Vieweg (1998)

    Google Scholar 

  51. Derksen, R.W., Rogalsky, T.: Bezier-PARSEC: An Optimized Aerofoil Parameterization for Design. Advances in Engineering Software 41, 923–930 (2010)

    Article  MATH  Google Scholar 

  52. ICEM CFD. ver. 12.1, ANSYS Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317 (2006)

    Google Scholar 

  53. Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Review 45(3), 385–482 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  54. Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)

    MATH  Google Scholar 

  55. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  56. Michalewicz, Z.: Genetic Algorithm + Data Structures = Evolutionary Programs, 3rd edn. Springer, Heidelberg (1996)

    Google Scholar 

  57. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)

    Google Scholar 

  58. Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6(1), 58–73 (2002)

    Article  Google Scholar 

  59. Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  60. Kirkpatrick, S., Gelatt Jr, C., Vecchi, M.: Optimization by simulated annealing. Science 220(4498), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  61. Giunta, A.A., Wojtkiewicz, S.F., Eldred, M.S.: Overview of modern design of experiments methods for computational simulations. In: 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2003-0649, Reno, NV (2003)

    Google Scholar 

  62. Simpson, T.W., Peplinski, J., Koch, P.N., Allen, J.K.: Metamodels for computer-based engineering design: survey and recommendations. Engineering with Computers 17(2), 129–150 (2001)

    Article  MATH  Google Scholar 

  63. Gunn, S.R.: Support vector machines for classification and regression. Tech. Rep., School of Electronics and Computer Science, University of Southampton (1998)

    Google Scholar 

  64. Forrester, A.I.J., Bressloff, N.W., Keane, A.J.: Optimization Using Surrogate Models and Partially Converged Computationally Fluid Dynamics Simulations. Proceedings of the Royal Society A: Mathematical. Physical and Engineering Sciences 462(2071), 2177–2204 (2006)

    Article  MATH  Google Scholar 

  65. Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Søndergaard, J.: Space mapping: the state of the art. IEEE Trans. Microwave Theory Tech. 52(1), 337–361 (2004)

    Article  Google Scholar 

  66. Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust Region Methods. MPS-SIAM Series on Optimization (2000)

    Google Scholar 

  67. Rao, S.S.: Engineering Optimization: Theory and Practice, 3rd edn. Wiley, Chichester (1996)

    Google Scholar 

  68. Eldred, M.S., Giunta, A.A., Collis, S.S.: Second-Order Corrections for Surrogate-Based Optimizatin with Model Hierarchies. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4457, Albany, NY (2004)

    Google Scholar 

  69. Marsden, A.L., Wang, M., Dennis, J.E., Moin, P.: Optimal aeroacoustic shape design using the surrogate management framework. Optimization and Engineering 5, 235–262 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  70. Robinson, T.D., Eldred, M.S., Willcox, K.E., Haimes, R.: Strategies for Multifidelity Optimization with Variable Dimensional Hierarchical Models. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2006-1819, Newport, Rhode Island, May 1-4 (2006)

    Google Scholar 

  71. Robinson, T.D., Willcox, K.E., Eldren, M.S., Haimes, R.: Multifidelity Optimization for Variable-Complexity Design. In: 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-7114, Portsmouth, VA (September 2006)

    Google Scholar 

  72. Robinson, T.D., Eldred, M.S., Willcox, K.E., Haimes, R.: Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping. AIAA Journal 46(11) (November 2008)

    Google Scholar 

  73. Koziel, S., Bandler, J.W., Madsen, K.: A space mapping framework for engineering optimization: theory and implementation. IEEE Trans. Microwave Theory Tech. 54(10), 3721–3730 (2006)

    Article  Google Scholar 

  74. Koziel, S., Cheng, Q.S., Bandler, J.W.: Space mapping. IEEE Microwave Magazine 9(6), 105–122 (2008)

    Article  Google Scholar 

  75. Redhe, M., Nilsson, L.: Using space mapping and surrogate models to optimize vehicle crashworthiness design. In: 9th AIAA/ISSMO Multidisciplinary Analysis and Optimization Symp., AIAA Paper 2002-5536, Atlanta, GA, pp. 2002–5536 (Septemper 2002)

    Google Scholar 

  76. Echeverria, D., Hemker, P.W.: Space mapping and defect correction. CMAM Int. Mathematical Journal Computational Methods in Applied Mathematics 5(2), 107–136 (2005)

    MATH  MathSciNet  Google Scholar 

  77. Koziel, S.: Efficient Optimization of Microwave Circuits Using Shape-Preserving Response Prediction. In: IEEE MTT-S Int. Microwave Symp. Dig, Boston, MA, pp. 1569–1572 (2009)

    Google Scholar 

  78. Koziel, S., Leifsson, L.: Multi-Fidelity High-Lift Aerodynamic Optimization of Single-Element Airfoils. In: Int. Conf. Engineering Optimization, Lisbon (September 6-9, 2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Optimization & Modeling Center, School of Science and Engineering, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Leifur Leifsson & Slawomir Koziel

Authors
  1. Leifur Leifsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Slawomir Koziel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Science and Engineering Engineering Optimization & Modeling Center, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Slawomir Koziel

  2. Mathematics and Scientific Computing, National Physical Laboratory, TW11 0LW, Teddington, UK

    Xin-She Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Leifsson, L., Koziel, S. (2011). Variable-Fidelity Aerodynamic Shape Optimization. In: Koziel, S., Yang, XS. (eds) Computational Optimization, Methods and Algorithms. Studies in Computational Intelligence, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20859-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20859-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20858-4

  • Online ISBN: 978-3-642-20859-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation