Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Augmented D-Optimal Design for Effective Response Surface Modeling and Optimization

  • Kim, Min-Soo (Research Professor, Center of Innovative Design Optimization Technology, Hanyang University) ;
  • Hong, Kyung-Jin (Graduate Research Assistant, Center of Innovative Design Optimization Technology, Hanyang University) ;
  • Park, Dong-Hoon (Director, Center of Innovative Design Optimization Technology, Hanyang University)
  • Published : 2002.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

For effective response surface modeling during sequential approximate optimization (SAO), the normalized and the augmented D-optimality criteria are presented. The normalized D-optimality criterion uses the normalized Fisher information matrix by its diagonal terms in order to obtain a balance among the linear-order and higher-order terms. Then, it is augmented to directly include other experimental designs or the pre-sampled designs. This augmentation enables the trust region managed sequential approximate optimization to directly use the pre-sampled designs in the overlapped trust regions in constructing the new response surface models. In order to show the effectiveness of the normalized and the augmented D-optimality criteria, following two comparisons are performed. First, the information surface of the normalized D-optimal design is compared with those of the original D-optimal design. Second, a trust-region managed sequential approximate optimizer having three D-optimal designs is developed and three design problems are solved. These comparisons show that the normalized D-optimal design gives more rotatable designs than the original D-optimal design, and the augmented D-optimal design can reduce the number of analyses by 30% - 40% than the original D-optimal design.

Keywords

References

  1. Alexandrov, N.,1996, 'Robustness Properties of a Trust Region Frame Work for Managing Approximations in Engineering Optimization,' Proceedings of the 6th AIAA/NASA/USAF multidisciplinary Analysis & Optimization Symposium, AIAA 96-4102-CP, Bellevue, Washington, September 7-9, pp. 1056-1059
  2. Azam, S. and Li, W.C., 1989, 'Multi-Level Design Optimization Using Global Monotonicity Analysis,Journal of Mechanisms,' Transmissions, and Automation in Design, Vol. 111, pp. 259-263
  3. Barthelemy,J.F. and Haftka,R.T., 1993, 'Approximation Concepts for Optimum Structural Design-a Review,' Struct.Optim., 5, pp. 129-144 https://doi.org/10.1007/BF01743349
  4. Box, G.P and Wilson, K.B., 1951, 'On the Experimental Attainment of Optimum Conditions,' Journal of the Royal Statistical Society Series B, Vol. 13, pp. 1-45
  5. Box, G.P. and Draper, N.R., 1987, Empirical Model-Building and Response Surfaces, John Wiley & Sons, New York, pp. 481-489
  6. Box, M.J.and Draper, N.R., 1971, 'Fractional Designs, the |XX| Criterion and Some Related Matters,' Technometrics, Vol. 13, No. 4, pp. 731-742 https://doi.org/10.2307/1266950
  7. Carpenter, W.C., 1993, Effect of Design Selection on Response Surface Performance, NASA Contract Report 4520
  8. Dennis, J.E. and Torczon, T., 1996, 'Approximation Model Management for Opimization,' Proceedings of the 6th AIAA/NASA/USAF Multidisciplinary Analysis & Optimization Symposium, AIAA 96-4046, pp. 1044-1046
  9. Fletcher, R., 1987, Practical Method of Optimization, John Wiley & Sons; Chichester, pp.296-304
  10. Haftka, R.T., Scott ,E.P. and Cruz, J.R., 1998, 'Optimization and Experiments:A Survey,' ASME Appl. Mech., Vol. 51, No. 7, pp. 435-448 https://doi.org/10.1115/1.3099014
  11. Haug, E.J. and Arora, J.S., 1979, Applied Optimal Design, Wiley-Interscience, New York
  12. Hong, K.J., Kim, M.S. and Choi, D.H., 2001, 'Efficient Approximation Method for Constructing Quadratic Response Surface Model,' KSME International Journal, Vol. 15, No. 7, pp. 876-888
  13. John, P.W.M., 1998, Statistical Design and Analysis of Experiments(Classics In Applied Mathematics 22), SIAM: Philadelpia, pp. 123-216
  14. Kim, M.S. and Choi, D.H., 1998, 'Dynamic Response Optimization of Mechanical Systems Using Approximate Augmented Lagrangian,' International Journal for Numerical Methods in Engineering, Vol. 43, pp. 549-564 https://doi.org/10.1002/(SICI)1097-0207(19981015)43:3<549::AID-NME446>3.0.CO;2-V
  15. Kim, M.S. and Park, H.W., 2001, Fast and Global Convergence Genetic program with Adaptive Fitness Target, iDOT Technical Report OPT-01-01
  16. Miller, A.J. and Nguyen, N.K., 1993, An Algorithm for generating experimental designs which are close to being D-optimal designs using Fedorov's exchange algorithm. http://lib.stat.cmu.edu/design/dopt.
  17. Rodriguez, J.F., Renaud, J.E. and Watson, L.T., 1998, 'Trust Region Augmented Lagrangian methods for Sequential Response Surface Approximation and Optimization,' Journal of Mechanical Design, Vol. 120, pp. 58-66
  18. Roux, W.J., 1998, 'Response Surface Approximation for Structural Optimization,' International Journal for Numerical methods in Engineering, Vol. 42, pp. 517-534 https://doi.org/10.1002/(SICI)1097-0207(19980615)42:3<517::AID-NME370>3.0.CO;2-L
  19. Unal, R., Lepsch, R.A. and McMilin, M.L., 1998, 'Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Disigns,' Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 405-411
  20. Sobieski, J.S., Kodiyalam, S. and Yang, R.J., 2000, 'Optimization of Car Body under Constraints of Noise,' Proceedings of the 41st AIAA/ASME/ASCE/AHS/ASC, Structures, Structural Dynamics and Materials Conference and Exhibit, April 3-6 AIAA-2000-4521