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Optimization and Engineering

, Volume 6, Issue 1, pp 33–62 | Cite as

A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design

  • Joaquim R.R.A. Martins
  • Juan J. Alonso
  • James J. Reuther
Article

Abstract

This paper presents an adjoint method for sensitivity analysis that is used in an aero-structural aircraft design framework. The aero-structural analysis uses high-fidelity models of both the aerodynamics and the structures. Aero-structural sensitivities are computed using a coupled-adjoint approach that is based on previously developed single discipline sensitivity analysis. Alternative strategies for coupled sensitivity analysis are also discussed. The aircraft geometry and a structure of fixed topology are parameterized using a large number of design variables. The aero-structural sensitivities of aerodynamic and structural functions with respect to these design variables are computed and compared with results given by the complex-step derivative approximation. The coupled-adjoint procedure is shown to yield very accurate sensitivities and to be computationally efficient, making high-fidelity aero-structural design feasible for problems with thousands of design variables.

sensitivity analysis adjoint method aero-structural design complex-step method 

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References

  1. H. M. Adelman and R. T. Haftka, "Sensitivity analysis of discrete structural systems,"AIAA Journal vol. 24, no. 5, pp. 823–832, 1986.Google Scholar
  2. M. A. Akg¨ un, R. T. Haftka, K. C. Wu, and J. L. Walsh, "Sensitivity of lumped constraints using the adjoint method,"AIAA Paper99–1314, 1999.Google Scholar
  3. N. M. Alexandrov and J. E. Dennis, Jr., "Multilevel algorithms for nonlinear optimization," inOptimal Design and Control,J.Borggaard, J. Burkardt, M. Gunzburger, and J. Peterson (eds.), Birkhauser, 1994, pp. 1–22.Google Scholar
  4. N. M. Alexandrov and R. M. Lewis, "Comparative properties of collaborative optimization and other approaches to MDO," inProceedings of the First ASMO UK/ISSMO Conference on Engineering Design Optimization, 1999.Google Scholar
  5. C. Bischof, A. Carle, G. Corliss, A. Grienwank, and P. Hoveland, 'ADIFOR: Generating derivative codes from fortran programs,"Scientific Programming vol. 1, no. 1, pp. 11–29, 1992.Google Scholar
  6. R. Braun and I. Kroo, "Development and application of the collaborative optimization architecture in a multidis-ciplinary design environment," inMultidisciplinary Design Optimization: State of the Art,N.M.Alexandrov and M. Y. Hussaini (eds.), SIAM, 1997, pp. 98–116.Google Scholar
  7. S. A. Brown, "Displacement extrapolation for CFD +CSM aeroelastic analysis,"AIAA Paper97–1090, 1997.Google Scholar
  8. J. Cebral and R. L¨ ohner, "Conservative load projection and tracking for fluid-structure problems,"AIAA Journal vol. 35, no. 4, pp. 687–692, 1997a. Also: AIAA-96–0797 (1996).Google Scholar
  9. J. Cebral and R. L¨ ohner, "Fluid-structure coupling: Extensions and improvements,"AIAA Paper97–0858, 1997b.Google Scholar
  10. E. J. Cramer, J. E. Dennis, P. D. Frank, R. M. Lewis, and G. R. Shubin, "Problem formulation for multidisciplinary optimization,"SIAM Journal on Optimization vol. 4, pp. 754–776, 1994.Google Scholar
  11. A. DeMiguel and W. Murray, "An analysis of collaborative optimization methods,"AIAA Paper2000–4720, 2000.Google Scholar
  12. A. Griewank,Evaluating Derivatives, SIAM: Philadelphia, 2000.Google Scholar
  13. M. E. Holden, "Aeroelastic optimization using the collocation method," Ph.D. thesis, Stanford University, Stanford, CA, 1999.Google Scholar
  14. A. Jameson, "Aerodynamic design via control theory,"Journal of Scientific Computing vol. 3, no. 3, pp. 233–260, 1989Google Scholar
  15. A. Jameson, L. Martinelli, and N. A. Pierce, "Optimum aerodynamic design using the Navier-Stokes equations,"Theoretical and Computational Fluid Dynamics vol. 10, pp. 213–237, 1998.Google Scholar
  16. S. Kodiyalam and J. Sobieszczanski-Sobieski, "Bilevel integrated system synthesis with response surfaces,"AIAA Journal vol. 38, no. 8, pp. 1479–1485, 2002.Google Scholar
  17. I. M. Kroo, "Decomposition and collaborative optimization for large scale aerospace design," inMultidisciplinary Design Optimization: State of the Art, SIAM, 1996.Google Scholar
  18. I. Kroo, R. Tracy, J. Chase, and P. Sturdza, "Natural laminar flow for quiet and efficient supersonic aircraft,"AIAA Paper2002–0146, 2002.Google Scholar
  19. N. Maman and C. Farhat, "Matching fluid and structure meshes for aeroelastic computations: Aparallel approach,"Comput. and Struc. vol. 54, pp. 779–785, 1995.Google Scholar
  20. J. R. R. A. Martins, "Acoupled-adjoint method for high-fidelity aero-structural optimization," Ph.D. thesis, Stanford University, Stanford, California, 2002.Google Scholar
  21. J. R. R. A. Martins, J. J. Alonso, and J. Reuther, "Aero-structural wing design optimization using high-fidelity sen-sitivity analysis," in H. Honlinger (ed.):Proceedings-CEAS Conference on Multidisciplinary Aircraft Design Optimization, Cologne, Germany. Bonn, 2001, pp. 211–226, Lilienthal-Oberth e.V.Google Scholar
  22. J. R. R. A. Martins, J. J. Alonso, and J. J. Reuther, "Complete configuration aero-structural optimization using a coupled sensitivity analysis method,"AIAA Paper2002–5402, 2002.Google Scholar
  23. J. R. R. A. Martins, P. Sturdza, and J. J. Alonso, "The complex-step derivative approximation,"ACM Transactions on Mathematical Software vol. 29, no. 3, pp. 245–262, 2003.Google Scholar
  24. K. Maute, M. Nikbay, and C. Farhat, "Coupled analytical sensitivity analysis and optimization of three-dimensional nonlinear aeroelastic systems,"AIAA Journal vol. 39, no. 11, pp. 2051–2061, 2001.Google Scholar
  25. S. Nadarajah and A. Jameson, "A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization,"AIAA Paper2000–0667, 2000.Google Scholar
  26. S. Obayashi and D. Sasaki, "Self-organizing map of pareto solutions obtained from multi objective supersonic wing design,"AIAA Paper2002–0991, 2002.Google Scholar
  27. J. J. Reuther, "Aerodynamic shape optimization using control theory," Ph.D. thesis, University of California Davis. also NASA-CR-201064, 1996.Google Scholar
  28. J. Reuther, J. J. Alonso, A. Jameson, M. Rimlinger, and D. Saunders, "Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers: Part I,"Journal of Aircraft vol. 36, no. 1, pp. 51–60, 1999a.Google Scholar
  29. J. Reuther, J. J. Alonso, A. Jameson, M. Rimlinger, and D. Saunders, "Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers: Part II,"Journal of Aircraft vol. 36, no. 1, pp. 61–74, 1999b.Google Scholar
  30. J. Reuther, J. J. Alonso, J. R. R. A. Martins, and S. C. Smith, "A coupled aero-structural optimization method for complete aircraft configurations,"AIAA Paper99–0187, 1999c.Google Scholar
  31. J. Reuther, J. J. Alonso, J. C. Vassberg, A. Jameson, and L. Martinelli, "An efficient multiblock method for aerodynamic analysis and design on distributed memory systems,"AIAA Paper97–1893, 1997.Google Scholar
  32. J. Reuther, A. Jameson, J. Farmer, L. Martinelli, and D. Saunders, "Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation,"AIAA Paper96–0094, 34th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 1996.Google Scholar
  33. D. Sasaki, S. Obayashi, and K. Nakahashi, "Navier-stokes optimization of supersonic wings with four design objectives using evolutionary algorithm,"AIAA Paper2001–2531, 2001.Google Scholar
  34. J. Sobieszczanski-Sobieski, "Sensitivity of complex, internally coupled systems,"AIAA Journal vol. 28, no. 1, pp. 153–160, 1990.Google Scholar
  35. J. Sobieszczanski-Sobieski and R. T. Haftka, "Multidisciplinary aerospace design optimization: Survey of recent developments,"AIAA Paper96–0711, 1996.Google Scholar
  36. J. Yao, J. J. Alonso, A. Jameson, and F. Liu, "Development and validation of a massively parallel flow solver for turbomachinery flow,"Journal of Propulsion and Power vol. 17, no. 3, pp. 659–668, 2001.Google Scholar

Copyright information

© Kluwer Academic Publishers 2005

Authors and Affiliations

  • Joaquim R.R.A. Martins
    • 1
  • Juan J. Alonso
    • 2
  • James J. Reuther
    • 3
  1. 1.University of Toronto Institute for Aerospace StudiesTorontoCanada
  2. 2.Stanford UniversityStanfordUSA
  3. 3.NASA Ames Research CenterMoffett FieldUSA

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