Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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A Sequential Optimization Algorithm Using Metamodel-Based Multilevel Analysis

메타모델 기반 다단계 해석을 이용한 순차적 최적설계 알고리듬

  • 백석흠 (동아대학교 대학원 기계공학과) ;
  • 김강민 (선우씨에스(주) 연구개발팀) ;
  • 조석수 (강원대학교 삼척캠퍼스 기계자동차공학부) ;
  • 장득열 (강원대학교 삼척캠퍼스 기계자동차공학부) ;
  • 주원식 (동아대학교 기계공학과)
  • Published : 2009.09.01
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Abstract

An efficient sequential optimization approach for metamodel was presented by Choi et al. This paper describes a new approach of the multilevel optimization method studied in Refs. [2] and [20,21]. The basic idea is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. After fitting a metamodel based on an initial space filling design, this model is sequentially refined by the expected improvement criterion. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to understand and use. As a check on effectiveness, the proposed method is applied to an engineering example.

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References

  1. Kwon, O. H., 1998, Nonsmooth Optimization, Korea University Press
  2. Vanderplaats, G. N., 1984, Numerical Optimization Techniques for Engineering Design, McGraw-Hill
  3. Barthelemy, J. F. M. and Haftka, R. T., 1993, 'Approximation Concepts for Optimal Structural Design-A Review,' Struct. Optim., Vol. 5, pp. 129~144 https://doi.org/10.1007/BF01743349
  4. Haftka, R. T., Scott, E. P. and Cruz, J. R., 1998, 'Optimization and Experiments: A Survey,' Appl. Mech. Rev., Vol. 517, pp. 435~448 https://doi.org/10.1115/1.3099014
  5. Koch, P. N., Simpson, T. W., Allen, J. K. and Mistree, F., 1999, 'Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size,' J. Aircr., Vol. 36, No. 1, pp. 275~286 https://doi.org/10.2514/2.2435
  6. Perez, V. M., Renaud, J. E. and Watson, L. T., 2002, 'Adaptive Experimental Design for Construction of Response Surface Approximations,' AIAA J., Vol. 40, No. 12, pp. 2495~2503 https://doi.org/10.2514/2.1593
  7. Roache, P. J., 1998, Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, NM
  8. Meckesheimer, M., Booker, A. J., Barton, R. R. and Simpson, T. W., 2002, 'Computationally Inexpensive Metamodel Assessment Strategies,' AIAA J., Vol. 40, No. 10, pp. 2053~2060 https://doi.org/10.2514/2.1538
  9. Wang, G. G. and Shan, S., 2007, 'Review of Metamodeling Techniques in Support of Engineering Design Optimization,' ASME J. Mech. Des., Vol. 129, No. 4, pp. 370~380 https://doi.org/10.1115/1.2429697
  10. Lee, T. H., Seong, J. Y. and Jung, J. J., 2006, 'Sequential Feasible Domain Sampling of Kriging Metamodel by Using Penalty Function,' Trans. of the KSME(A), Vol. 30, No. 6, pp. 691~697 https://doi.org/10.3795/KSME-A.2006.30.6.691
  11. Kim, S. W., Jung, J. J. and Lee, T. H., 2007, 'Candidate Points and Representative Cross-Validation Approach for Sequential Sampling,' Trans. of the KSME(A), Vol. 31, No. 1, pp. 55~61 https://doi.org/10.3795/KSME-A.2007.31.1.055
  12. Kim, J. R. and Choi, D. H., 2003, 'Design Optimization Using the Two-Point Convex Approximation,' Trans. of the KSME(A), Vol. 27, No. 6, pp. 1041~1049 https://doi.org/10.3795/KSME-A.2003.27.6.1041
  13. Lee, Y. B., Lee, H. J., Kim, M. S. and Choi, D. H., 2005, 'Sequential Approximate Optimization Based on a Pure Quadratic Response Surface Method with Noise Filtering,' Trans. of the KSME(A), Vol. 29, No. 6, pp. 842~851 https://doi.org/10.3795/KSME-A.2005.29.6.842
  14. Shin, Y. S., Lee, Y. B., Ryu, J. S. and Choi, D. H., 2005, 'Sequential Approximate Optimization Using Kriging Metamodels,' Trans. of the KSME(A), Vol. 29, No. 9, pp. 1199-1208 https://doi.org/10.3795/KSME-A.2005.29.9.1199
  15. Wang, G. G., 2003, 'Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points,' ASME J. Mech. Des., Vol. 125, No. 2, pp. 210~220 https://doi.org/10.1115/1.1561044
  16. Jin, R., Chen, W. and Simpson, T. W., 2001, 'Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria,' Struct. Multidisc. Optim., Vol. 23, No. 1, pp. 1~13 https://doi.org/10.1007/s00158-001-0160-4
  17. Simpson, T. W., Mauery, T. M., Korte, J. J. and Mistree, F., 2001, 'Kriging Metamodels for Global Approximation in Simulation-based Multidisciplinary Design Optimization,' AIAA J., Vol. 39, No. 12, pp. 2233~2241 https://doi.org/10.2514/2.1234
  18. Wang, G. G. and Simpson, T. W., 2004, 'Fuzzy Clustering Based Hierarchical Metamodeling for Space Reduction and Design Optimization,' Eng. Optimiz., Vol. 36, No. 3, pp. 313~335 https://doi.org/10.1080/03052150310001639911
  19. Clarke, S. M., Griebsch, J. H. and Simpson, T. W., 2005, 'Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses,' ASME J. Mech. Des., Vol. 127, No. 6, pp. 1077~1087 https://doi.org/10.1115/1.1897403
  20. Kashiwamura, T., Yu, Q. and Shiratori M., 1998， , Optimization of Nonlinear Problem Using Design of Experiment-Statistical Design Support System, Asakura Publishing Co., Ltd., Tokyo, pp. 94~104
  21. Vadde, S., Allen, J. K. and Mistree, F., 1994, 'The Bayesian Compromise Decision Support Problem for Multilevel Design Involving Uncertainty,' ASME J. Mech. Des., Vol. 116, No. 2, pp. 388~395 https://doi.org/10.1115/1.2919391
  22. Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P., 1989, 'Design and Analysis of Computer Experiments,' Stat. Sci., Vol. 4, No. 4, pp. 409~435 https://doi.org/10.1214/ss/1177012413
  23. Lophaven, S. N., Nielsen, H. B. and Sondergaard, J., 2002, DACE-A Matlab Kriging Toolbox-Version 2.0, Informatics and Mathematical Modelling, Technical University of Denmark, Kgs. Lyngby, Denmark, Rep. No. IMMREP-2002-12
  24. Vapnik, V., 1995, The Nature of Statistical Learning Theory, Springer-Verlag, New York
  25. Cristianni, N. and Shawe-Taylor, J., 2000, An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods, Cambridge University Press, Cambridge, UK
  26. Cho, S. S. and Joo, W. S., 2000, 'A Study on Fatigue Crack Growth and Life Modeling using Backpropagation Neural Networks,' Trans. of the KSME(A), Vol. 24, No. 3, pp. 634~644
  27. Gere, J. M., 2003, Mechanics of Materials, 6th Edition, Thomson-Engineering
  28. ANSYS Workbench Release 11.0 Documentations, 2008, ANSYS Inc
  29. Baek, S. H., Hong, S. H., Cho, S. S. and Joo, W. S., 2004, 'Multi-objective Optimization in Discrete Design Space using RSM-Based Approximation Method,' The Third China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems (CJK-OSM3), Japan, pp. 125~130
  30. Baek, S. H., Cho, S. S., Kim, H. S. and Joo, W. S., 2006, 'Tarde-off Analysis in Multi-objective Optimization Using Chebyshev Orthogonal Polynomials,' J. Mech. Sci. Technol., Vol. 20, No. 3, pp. 366~375 https://doi.org/10.1007/BF02917519
  31. Baek, S. H., Hong, S. H., Joo, W. S., Kim, C. K., Jeong, Y. Y. and Shin, S. W., 2008, 'Optimization of Process Parameters for Mill Scale Recycling Using Taguchi Method,' J. KSPE, Vol. 25, No. 2, pp. 88~95
  32. Baek, S. H., Cho, S. S. and Joo, W. S., 2009, 'Response Surface Approximation for Fatigue Life Prediction and Its Application to Multi-Criteria Optimization With a Priori Preference Information,' Trans. of the KSME(A), Vol. 33, No. 2, pp. 114~126 https://doi.org/10.3795/KSME-A.2009.33.2.114

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