KSME International Journal

, Volume 15, Issue 9, pp 1257–1267 | Cite as

Efficient mechanical system optimization using two-point diagonal quadratic approximation in the nonlinear intervening variable space

  • Min-Soo Kim
  • Jong-Rip Kim
  • Jae-Young Jeon
  • Dong-Hoon Choi
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design

Abstract

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determinded quadratic term to match the value of aproximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

Key Words

Two-Point Approximation Sequential Approximate Optimization 

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References

  1. Arora, J. S., 1989,Introduction to Optimum Design, McGraw-Hill, New York, pp. 489–493.Google Scholar
  2. Fadel, G. M., Riley, M. F. and Barthelemy, J. F. M., 1990, “Two Point Exponential Approximation Method for Structural optimization,”Structural Optimization, Vol. 2, pp. 117–124.CrossRefGoogle Scholar
  3. Haug, E. J. and Arora, J. S., 1979,Applied optimal Design Mechanical and Structural Systems, John Wiley & Sons, New York, pp. 242–245.Google Scholar
  4. Reklaitis, G. V., Ravindran, A. and Ragsdell, K. M., 1983,Engineering Optimization Methods and Applications, John Wiley & Sons, New York, pp. 11–15.Google Scholar
  5. Schmit, L. A. and Farshi, B., 1974, “Some Approximation Concepts for Structural Synthesis,”AIAA Journal, Vol. 12, pp. 692–699.CrossRefGoogle Scholar
  6. Schmit, L. A. and Miura, H., 1976, “A New Structural Analysis/Synthesis Capablity-ACCESS 1,”AIAA Journal, Vol. 14, pp. 661–671.CrossRefGoogle Scholar
  7. Schmit, L. A. and Fleury, C., 1980, “Structural Synthesis by Combining Approximation Concepts and Dual Methods,”AIAA Journal, Vol, 18, pp. 1252–1260.MATHCrossRefMathSciNetGoogle Scholar
  8. Vanderplaats, G. N., 1984,Numerical Optimization Techniques for Engineering with Applications, McGraw-Hill, New York, pp. 195–199.MATHGoogle Scholar
  9. Wang, L. P. and Grandhi, R. V., 1995, “Improved Two-Point Function Approximation for Design Optimization,”AIAA Journal, Vol. 33, No. 9, pp. 1720–1727.MATHCrossRefGoogle Scholar
  10. Wang, L. P. and Grandhi, R. V., 1996a, “Multipoint Approximations: Comparisons Using Structural Size, Configuration and Shape Design,”Structural Optimization, Vol. 12, pp. 177–185.CrossRefGoogle Scholar
  11. Wang, L. P. and Grandhi, R. V., 1996b, “Multivariate Hermite Approximation for Design Optimization,”International Journal for Numerical Methods in Engineering, Vol. 39, pp. 787–803.MATHCrossRefMathSciNetGoogle Scholar
  12. Xu, S. and Grandhi, R. V., 1998, “An Effective Two-Point Function Approximation for Design Optimization,”Proceedings of the AIAA/ASME/ASCE/AHS/ASC 39th Structural, Structural Dynamics, and Materials Conference, Long beach CA, April 20–23, pp. 2181–2191.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2001

Authors and Affiliations

  • Min-Soo Kim
    • 1
  • Jong-Rip Kim
    • 1
  • Jae-Young Jeon
    • 1
  • Dong-Hoon Choi
    • 1
  1. 1.Center of Innovative Design Optimization TechnologyHanyang UniversitySeoulKorea

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