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

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Function Approximation Using an Enhanced Two-Point Diagonal Quadratic Approximation

개선된 이점 대각 이차 근사화를 이용한 함수 근사화

  • 김종립 (최적설계신기술연구센터) ;
  • 강우진 (한양대학교 대학원 기계설계학과) ;
  • 최동훈 (최적설계신기술연구센터)
  • Published : 2004.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

Function approximation is one of the most important and active research fields in design optimization. Accurate function approximations can reduce the repetitive computational effort fur system analysis. So this study presents an enhanced two-point diagonal quadratic approximation method. The proposed method is based on the Two-point Diagonal Quadratic Approximation method. But unlike TDQA, the suggested method has two quadratic terms, the diagonal term and the correction term. Therefore this method overcomes the disadvantage of TDQA when the derivatives of two design points are same signed values. And in the proposed method, both the approximate function and derivative values at two design points are equal to the exact counterparts whether the signs of derivatives at two design points are the same or not. Several numerical examples are presented to show the merits of the proposed method compared to the other forms used in the literature.

Keywords

References

  1. Schmit, L.A., Farshi, B., 1974, 'Some Approximation Concepts for Structural Synthesis,' AIAA Journal, Vol. pp. 692-699 https://doi.org/10.2514/3.49321
  2. Schmit, L. A. and Fleury, C., 1980, 'Structural Synthesis by Combining Approximation concepts and Dual Methods,' AIAA Journal, Vol. 18, pp. 1252-1260 https://doi.org/10.2514/3.50877
  3. 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 https://doi.org/10.1007/BF01745459
  4. 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 https://doi.org/10.2514/3.12715
  5. Wang, L.P., Grandhi, R.V., 1996a, 'Multipoint Approximation: Comparisons Using Structural Size, Configuration and Shape Design,' Structural Optimization, Vol. 12, pp. 177-185 https://doi.org/10.1007/BF01196954
  6. 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 https://doi.org/10.1002/(SICI)1097-0207(19960315)39:5<787::AID-NME881>3.0.CO;2-5
  7. 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
  8. Min-Soo Kim,Jong-Rip Kim,Jae-Young Jeon,Dong-Hoon Choi, 2001, 'Efficient Mechanical System Optimization Using Two-Point Diagonal Approximation in the Nonlinear Interening Variable Space,' Journal of KSME, Vol. 15, No. 9, pp.1257-1267 https://doi.org/10.1007/BF03185666