Skip to main content

Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique

Abstract

The aim of this work is to illustrate how a space mapping technique using surrogate models together with response surfaces can be used for structural optimization of crashworthiness problems. To determine the response surfaces, several functional evaluations must be performed and each evaluation can be computationally demanding. The space mapping technique uses surrogate models, i.e. less costly models, to determine these surfaces and their associated gradients. The full model is used to correct the gradients from the surrogate model for the next iteration. Thus, the space mapping technique makes it possible to reduce the total computing time needed to find the optimal solution. First, two analytical functions and one analytical structural optimization problem are presented to exemplify the idea of space mapping and to compare the efficiency of space mapping to traditional response surface optimization. Secondly, a sub-model of a complete vehicle finite element (FE) model is used to study different objective functions in vehicle crashworthiness optimization. Finally, the space mapping technique is applied to a structural optimization problem of a large industrial FE vehicle model, consisting of 350.000 shell elements and a computing time of 100 h. In this problem the intrusion in the passenger compartment area was reduced by 32% without compromising other crashworthiness parameters.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Bakr, M.H.; Bandler, J.W.; Biernacki, R.M.; Chen, S.H.; Madsen, K. 1998: A Trust Region Aggressive Space Mapping Algorithm for EM Optimization. IEEE Trans Microw Theory Tech46, 2412–2425

    Google Scholar 

  2. 2.

    Bakr, M.H.; Bandler, J.W.; Madsen, K.; Rayas-Sánchez, J.E.; Sondergaard, J. 2000: Space Mapping Optimization of Microwave Circuits Exploiting Surrogate Models. IEEE Trans Microw Theory Tech48

  3. 3.

    Bakr, M.H.; Bandler, J.W.; Madsen, K.; Sondergaard, J. 2002: An introduction to the Space Mapping Technique. Optim Eng2, 369–384

  4. 4.

    Bandler, J.W.; Biernacki, R.M.; Chen, S.H.; Grobelny, R.H.; Hemmers, R.H. 1994: Space Mapping Technique for Elecromagnetic Optimization. IEEE Trans Microw Theory Tech42, 2536–2544

    Google Scholar 

  5. 5.

    Bandler, J.W.; Biernacki, R.M.; Chen, S.H.; Hemmers, R.H.; Madsen, K. 1995: Electromagnetic Optimization Exploition Aggrasive Space Mapping. IEEE Trans Microw Theory Tech43, 2874–2882

    Google Scholar 

  6. 6.

    Craig, K.J.; Stander, N.; Dooge, D.A.; Varadappa, S. 2002: Multidiciplinary design optimization of automotive crashwothiness and nvh using response surface methods. AIAA-2002-5507, Mistree, F. (ed.), 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optim., Atlanta, GA, USA

  7. 7.

    Etman, L.F.P.; Adriaens J.M.T.A.; van Slagmaat, M.T.P.; Schoofs, A.J.G. 1997: Crashworthiness design using Multipoint sequential linerar programming. Struct. Optim.12, 222–8

    Google Scholar 

  8. 8.

    Etman, L.F.P. 1997: Optimization of multibody system using approximation concepts. Ph.D. thesis, Technical University Eindhoven, The Netherlands

  9. 9.

    Forsberg, J. 2002: Simulation based crashwothiness design – Accuracy aspects of structural optimization using response surfaces. LIU-TEK-LIC-2002:27, Linköpings university, Linköping

  10. 10.

    Hallquist, J.O. 1998: LS-DYNA Theoretical Manual. Livermore Software Technology Corp., Livermore

  11. 11.

    Ignatovich, C.L.; Diaz, A.R. 2002: Physical surrogates in design optimization for enhanced crashworthiness, AIAA-2002-5537, Mistree, F. (ed.), 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optim. Atlanta, GA, USA

  12. 12.

    Leary, S.; Bhasker, A.; Keane, A. 2000: A Constraint Mapping Approach to the Structural Optimization of an Expensive Model using Surrogates. Conference on Surrogate Modelling and Space Mapping for Eng. Optim., Madsen, K. (ed.), Lyngby

  13. 13.

    Madsen, K.; Sondergaard, J. 2000: Space Mapping From a Mathematical Viewpoint. Conference on Surrogate Modelling and Space Mapping for Eng. Optim., Madsen, K. (ed), Lyngby

  14. 14.

    Marklund, P.-O. 1999: Optimization of a Car Body Component Subjected to Impact. LIU-TEK-LIC-1999:34, Linköpings university, Linköping

  15. 15.

    Marklund, P.-O.; Nilsson, L. 2001: Optimization of a Car Body Component Subjected to Impact. Struct Multidisc Optim21, 383–392

    Google Scholar 

  16. 16.

    Myers, R.H.; Montgomery, D.C. 1995: Response Surface Methodology. New York: Wiley

  17. 17.

    Redhe, M. 2001: Simulation Based Design – Structural optimization at early design stages. LIU-TEK-LIC-2001:51, Linköpings university, Linköping

  18. 18.

    Redhe, M.; Nilsson, L. 2002a: A Method to Determine Structural Sensitivities in Vehicle Crashworthiness Design. Int J Crashworthiness7(2), 179–190

  19. 19.

    Redhe, M.; Forsberg, J.; Jansson, T.; Marklund, P.O.; Nilsson, L. 2002: Using the Response Surface Methodology and the D-Optimality Criterion in Crashworthiness Related Problems – an analysis of the surface approximation error versus the number of function evaluations. Struct Multidisc Optim24(3), 185–194

    Google Scholar 

  20. 20.

    Redhe, M.; Nilsson, L. 2002c: Using Space Mapping and Surrogate Models to Optimize Vehicle Crashworthiness Design, AIAA-2002-5536, Mistree, F. (ed.), 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optim., Atlanta, GA, USA

  21. 21.

    Roux, W.J.; Stander, N.; Haftka, R.T. 1998: Response Surface Approximations for Structural Optimization. Int J Numer Methods Eng42, 517–534

    Google Scholar 

  22. 22.

    Schramm, U.; Thomas, H. 1998: Structural optimization in occupant safety and crash analysis. Des Optim1(4), 374–387

    Google Scholar 

  23. 23.

    Schramm, U.; Thomas, H. 1999: Crashworthiness design using structural optimization. AIAA Pap, 98–4729

  24. 24.

    Schramm, U. 2001: Multi-disciplinary Optimization for NVH and crashworthiness. The First MIT Conference on Computational Fluid and Solid Mechanics (Boston, June 12–15), Bathe, K.J. (ed.), Oxford, Elsevier Science

  25. 25.

    Schramm, U. 2002: Designing with structural optimization – A practical point of view, AIAA Paper 2002-5191. Mistree, F. (ed.), 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optim., Atlanta, GA, USA

  26. 26.

    Sobieszczanski-Sobieski, J.; Kodiyalam, S.; Yang, R.-J. 2000: Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. AIAA Pap, 2000–1521

  27. 27.

    Stander, N.; Craig K.J.; Roux, W. 2002a: LS-OPT User’s Manual v. 2. Livermore Software Technology Corporation, Livermore

  28. 28.

    Yamazaki, K.; Han, J. 1998: Maximization of the Crushing Energy Absorption of Tubes. Struct Optim16, 37–46

    Google Scholar 

  29. 29.

    Yang, R.-J.; Gu, L.; Tho, C.H.; Sobieszczanski-Sobieski, J. 2001: Multidisciplinary design optimization of a full vehicle with high performance computing. AIAA Pap, 2001–1273

  30. 30.

    Yang, R.-J.; Tho, C.H.; Gu, L. 2002: Recent development in Multidisciplinary design optimization of vehicle structures, AIAA-2002-5606. Mistree, F. (ed.), 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optim., Atlanta, GA, USA

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. Redhe.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Redhe, M., Nilsson, L. Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique. Struct Multidisc Optim 27, 411–420 (2004). https://doi.org/10.1007/s00158-004-0396-x

Download citation

Keywords

  • crashworthiness
  • finite element
  • optimization
  • response surface
  • space mapping