Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T12:20:49.613Z Has data issue: false hasContentIssue false
  • English
  • Français

Gradient-based multifidelity optimisation for aircraft design using Bayesian model calibration

Published online by Cambridge University Press:  27 January 2016

A. March ,
K. Willcox  and
Q. Wang
A. March*
Affiliation:
Massachusetts Institute of Technology, Massachusetts, USA
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Optimisation of complex systems frequently requires evaluating a computationally expensive high-fidelity function to estimate a system metric of interest. Although design sensitivities may be available through either direct or adjoint methods, the use of formal optimisation methods may remain too costly. Incorporating low-fidelity performance estimates can substantially reduce the cost of the high-fidelity optimisation. In this paper we present a provably convergent multifidelity optimisation method that uses Cokriging Bayesian model calibration and first-order consistent trust regions. The technique is compared with a single-fidelity sequential quadratic programming method and a conventional first-order trust-region method on both a two-dimensional structural optimisation and an aerofoil design problem. In both problems adjoint formulations are used to provide inexpensive sensitivity information.

Type
Research Article
Information
The Aeronautical Journal , Volume 115 , Issue 1174 , December 2011 , pp. 729 - 738
Copyright
Copyright © Royal Aeronautical Society 2011 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Nx Nastran, Numerical Methods User’s Guide. Siemens Product Lifecycle Management Software, 2008.Google Scholar
2. Alexandrov, N., Dennis, J., Lewis, R. and Torczon, V. A trust region framework for managing the use of approximation models in optimization. Tech. Rep. CR-201745, NASA, October 1997.Google Scholar
3. Alexandrov, N., Lewis, R., Gumbert, C., Green, L. and Newman, P. Optimization with variable-fidelity models applied to wing design. Tech. Rep. CR-209826, NASA, December 1999.Google Scholar
4. Alexandrov, N., Lewis, R., Gumbert, C., Green, L. and Newman, P. Approximation and model management in aerodynamic optimization with variable-fidelity models, AIAA J, November-December, 2001, 38, (6), pp 1093–1101.Google Scholar
5. Antoulas, A. Approximation of Large-Scale Dynamical Systems. SIAM, 2005.Google Scholar
6. Booker, A.J., Dennis, J.E., Frank, P.D., Serafini, D.B., Torczon, V. and Trosset, M.W. A rigorous framework for optimization of expensive functions by surrogates, Structural Optimization, February 1999, 17, (1), pp 1–13.Google Scholar
7. Castro, J., Gray, G., Giunta, A. and Hough, P. Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multi-fidelity model interactions. Tech. Rep SAND2005-7498, Sandia, November 2005.Google Scholar
8. Conn, A., Gould, N. and Toint, P. Trust-Region Methods. MPS/SIAM Series on Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000.Google Scholar
9. Eldred, M. and Dunlavy, D. Formulations for surrogate-based optimization with data-fit, multifidelity and reduced-order models. 11thAIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, USA, 2006. AIAA 2006-7117.Google Scholar
10. Eldred, M., Giunta, A. and Collis, S. Second-order corrections for surrogate-based optimization with model hierarchies. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004. AIAA 2004-4457.Google Scholar
11. Forrester, A., Sobester, A. and Keane, A. Multi-fidelity optimization via surrogate modelling, J Royal Statistical Society, September 2007, 463, (2), pp 3251–3269.Google Scholar
12. Gano, S.E., Renaud, J.E. and Sanders, B. Hybrid variable fidelity optimization by using a Kriging-based scaling function, AIAA J, November 2005, 43, (11), 2422–2430.Google Scholar
13. Chung, H. and Alonso, J.J. Design of a low-boom supersonic business jet using cokriging approximation models. In 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, USA, September 2002, AIAA 2002-5598.Google Scholar
14. Chung, H. and Alonso, J.J. Using gradients to construct cokriging approximation models for high-dimensional design optimization problems. In 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, January 2002, AIAA 2002-0317.Google Scholar
15. Haftka, R.T. and Adelman, H.M. Recent developments in structural sensitivity analysis, Structural Optimization, 1, 1989, pp 137-151.Google Scholar
16. Haug, E.J., Choi, K.K. and Komkov, V. Design Sensitivity Analysis of Structural Systems, Academic Press Inc, 1986.Google Scholar
17. Jameson, A. Aerodynamic design via control theory, J Scientific Computing, September 1988, 3, (3), pp 233–260.Google Scholar
18. Jones, D., Schonlau, M. and Welch, W. Efficient global optimization of expensive black-box functions, J Global Optimization, 1998, 13, pp 455–492.Google Scholar
19. Kennedy, M. and O’Hagan, A. Predicting the output from a complex computer code when fast approximations are available, Biometrika, 2000, 87, (1), pp 1–13.Google Scholar
20. Kennedy, M. and O’Hagan, A. Bayesian calibration of computer models, J Royal Statistical Society, 63, (2), (2001), pp 425–464.Google Scholar
21. Laurenceau, J., Meaux, M., Montagnac, M. and Sagaut, P. Comparison of gradient-based and gradient-enhanced response-surface-based optimizers, AIAA J, May 2010, 48, (5), pp 981–994.Google Scholar
22. Leary, S., Bhaskar, A. and Keane, A. A knowledge-based approach to response surface modelling in multifidelity optimization, J Global Optimization, 2003, 26, pp 297–319.Google Scholar
23. Leary, S., Bhaskar, A. and Keane, A. Global approximation and optimization using adjoint computational fluid dynamics codes, AIAA J, March 2004, 42, (3), pp 631–641.Google Scholar
24. Liepmann, H.W. and Roshko, A. Elements of Gasdynamics, Dover Publications, Mineola, NY, USA, 1993.Google Scholar
25. Liu, W. Development of Gradient-Enhanced Kriging Approximations for Multidisciplinary Design Optimization, PhD thesis, University of Notre Dame, USA, July 2003.Google Scholar
26. Martins, J.R.R.A. A Coupled-Adjoint Method for High-Fidelity Aero-Structural Optimization. PhD thesis, Stanford University, USA, October 2002.Google Scholar
27. Matern, B. Spatial Variation. Lecture Notes in Statistics, SpringerVerlag, Berlin, Germany, 1986.Google Scholar
28. Nemec, M. and Aftosmis, M. Aerodynamic shape optimization using a Cartesian adjoint method and cad geometry. In 25th AIAA Applied Aerodynamics Conference, San Francisco, USA, June 2006, AIAA 2006–3456.Google Scholar
29. Poon, N.M.K. and Martins, J.R.R.A. An adaptive approach to constraint aggregation using adjoint sensitivity analysis. Structural and Multidisciplinary Optimization, 2007, 34, pp 61–73.Google Scholar
30. Rasmussen, C. and Williams, C. Gaussian Processes for Machine Learning. The MIT Press, 2006.Google Scholar
31. Robinson, T., Eldred, M., Willcox, K. and Haimes, R. Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping, AIAA J, November 2008, 46, (11), pp 2814–2822.Google Scholar
32. Sacks, J., Welch, W., Mitchell, T. and Wynn, H. Design and analysis of computer experiments, Statistical Science, 1989, 4, (4), pp 409–435.Google Scholar
33. Simpson, T., Peplinski, J., Koch, P. and Allen, J. Metamodels for computer-based engineering design: Survey and recommendations, Engineering with Computers, 2001, 17, pp 129–150.Google Scholar
34. Venter, G., Haftka, R. and Starnes, J. Construction of response surface approximations for design optimization, AIAA J, 1998, 36, (12), 2242–2249.Google Scholar
35. Wang, Q., Duraisamy, K., Alonso, J.J. and Iaccarino, G. Risk assessment of scramjet unstart using adjoint-based sampling methods. In 51stAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Orlando, FL, USA, April 2010. AIAA 2010-2921.Google Scholar