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Best Practices for Surrogate Based Uncertainty Quantification in Aerodynamics and Application to Robust Shape Optimization

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Optimization Under Uncertainty with Applications to Aerospace Engineering
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Abstract

This chapter introduces the use of aerodynamic shape optimization applied to industrial problems, motivates the use of a robust approach over the classical deterministic optimization, and presents different alternatives for the robust-based and reliability-based problems. The use of surrogates for the Uncertainty Quantification of operational and geometrical uncertainties is a cost-effective solution for high dimensional models if the gradient information is introduced by means of the adjoint method. Finally, the proposed methodology is applied through the reliability-based optimization of an airfoil under operational uncertainties.

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References

  1. S.N. Skinner, H. Zare-Behtash, State-of-the-art in aerodynamic shape optimisation methods. Appl. Soft Comput. 62, 933–962 (2018)

    Article  Google Scholar 

  2. D. Maruyama, S. Goertz, D. Liu, Robust design measures for airfoil shape optimization, in Uncertainty Management for Robust Industrial Design in Aeronautics (Springer, Berlin, 2018), pp. 513–527

    Google Scholar 

  3. L. Huyse, Free-form airfoil shape optimization under uncertainty using maximum expected value and second-order second-moment strategies. Techreport 2001-211020, NASA, 2001s

    Google Scholar 

  4. R. Duvigneau, Aerodynamic shape optimization with uncertain operating conditions using metamodels. Resreport RR-6143, INRIA, 2007

    Google Scholar 

  5. J. Von Neumann, O. Morgenstern, H.W. Kuhn, J. Von Neumann, A. Rubinstein, Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition (Princeton University Press, Princeton, 2009)

    Google Scholar 

  6. D. Quagliarella, G. Petrone, G. Iaccarino, Optimization under uncertainty using the generalized inverse distribution function, In Computational Methods in Applied Sciences (Springer Netherlands, 2014), pp. 171–190

    Google Scholar 

  7. D. Maruyama, D. Liu, S. Goertz, An efficient aerodynamic shape optimization framework for robust design of airfoils using surrogate models, in Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016) (Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016)

    Google Scholar 

  8. R.M. Dudley, Uniform Central Limit Theorems (Cambridge University Press, Cambridge, 1999)

    Book  Google Scholar 

  9. A.T. Beck, W.J.S. Gomes, Rafael .H. Lopez, L.F.F. Miguel, A comparison between robust and risk-based optimization under uncertainty. Struct. Multidiscip. Optim. 52(3), 479–492 (2015)

    Google Scholar 

  10. R. Dwight, Z.-H. Han, Efficient uncertainty quantification using gradient-enhanced kriging, In 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (American Institute of Aeronautics and Astronautics, Reston, 2009)

    Google Scholar 

  11. A.I.J. Forrester, A. Sabester, A.J. Keane, Engineering Design via Surrogate Modelling (Wiley, London, 2008)

    Book  Google Scholar 

  12. M.D. McKay, R.J. Beckman, W.J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)

    MathSciNet  MATH  Google Scholar 

  13. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods. Acta Numer. 7, 1 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  14. S. Kucherenko, D. Albrecht, A. Saltelli, Exploring multi-dimensional spaces: a comparison of Latin hypercube and quasi Monte Carlo sampling techniques (2015). ArXiv e-prints

    Google Scholar 

  15. I.M Sobol, On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7(4), 86–112 (1967)

    Google Scholar 

  16. D. Maruyama, S. Goertz, D. Liu, General introduction to surrogate model-based approaches to UQ, in Uncertainty Management for Robust Industrial Design in Aeronautics (Springer, Berlin, 2018), pp. 203–211

    Google Scholar 

  17. V. Schulz, C. Schillings, Optimal aerodynamic design under uncertainty, in Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, Berlin, 2013), pp. 297–338

    Google Scholar 

  18. D.R. Jones, M. Schonlau, W.J. Welch, Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455–492 (1998)

    Article  MathSciNet  Google Scholar 

  19. A.I.J. Forrester, A.J. Keane, Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1–3), 50–79 (2009)

    Article  Google Scholar 

  20. D. Maruyama, D. Liu, S. Goertz, Comparing surrogates for estimating aerodynamic uncertainties of airfoils, in Uncertainty Management for Robust Industrial Design in Aeronautics (Springer, Berlin, 2018), pp. 213–228

    Google Scholar 

  21. K. Shimoyama, S. Kawai, J.J. Alonso, Dynamic adaptive sampling based on kriging surrogate models for efficient uncertainty quantification, in 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (American Institute of Aeronautics and Astronautics, Reston, 2013)

    Google Scholar 

  22. Z.-H. Han, M. Abu-Zurayk, S. Goertz, C. Ilic, Surrogate-based aerodynamic shape optimization of a wing-body transport aircraft configuration, in Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, Berlin, 2018), pp. 257–282

    Google Scholar 

  23. A. Merle, A. Stueck, A. Rempke, An adjoint-based aerodynamic shape optimization strategy for trimmed aircraft with active engines, in 35th AIAA Applied Aerodynamics Conference (American Institute of Aeronautics and Astronautics, Reston, 2017)

    Google Scholar 

  24. T. Gerhold, Overview of the hybrid RANS code TAU, in MEGAFLOW—Numerical Flow Simulation for Aircraft Design (Springer, Berlin, 2015), pp. 81–92

    Google Scholar 

  25. T. Gerhold, J. Neumann, The parallel mesh deformation of the DLR TAU-code, in Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) (Springer, Berlin, 2006), pp. 162–169

    Google Scholar 

  26. M. Meinel, G. Einarsson, The FlowSimulator framework for massively parallel CFD applications, in PARA 2010—State of the Art in Scientific and Parallel Computing—Extended Abstract no. 44 (University of Iceland, Reykjavik, 2010)

    Google Scholar 

  27. R. M. Hicks, P.A. Henne, Wing design by numerical optimization. J. Aircr. 15(7), 407–412 (1978)

    Article  Google Scholar 

  28. T.H. Rowan, Functional Stability Analysis of Numerical Algorithms. Ph.D. thesis, University of Texas Austin, Austin, 1990. UMI Order No. GAX90-31702

    Google Scholar 

  29. J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)

    Article  MathSciNet  Google Scholar 

  30. Z.-H. Han, S. Goertz, R. Zimmermann, Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function. Aerosp. Sci. Technol. 25(1), 177–189 (2013)

    Article  Google Scholar 

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Acknowledgements

This work is funded by the European Commission’s H2020 programme, through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant Agreement number 722734.

The author also would like to thank Dr. Daigo Maruyama and Dr. Stefan Goertz for their insight into optimization under uncertainty and surrogate modelling applied to aerodynamic design.

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Correspondence to Christian Sabater .

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Sabater, C. (2021). Best Practices for Surrogate Based Uncertainty Quantification in Aerodynamics and Application to Robust Shape Optimization. In: Vasile, M. (eds) Optimization Under Uncertainty with Applications to Aerospace Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-60166-9_14

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