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

The Korean Society of Mechanical Engineers (대한기계학회)
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Design Optimization Using Two-Point Diagonal Quadratic Approximation

이점 대각 이차 근사화 기법을 적용한 최적설계

  • 최동훈 (한양대학교 최적설계신기술연구센터(iDOT)) ;
  • 김민수 (한양대학교 최적설계신기술연구센터(iDOT) 연구) ;
  • 김종립 (한양대학교 대학원 기계설계학과) ;
  • 전재영
  • Published : 2001.09.01
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Abstract

Based on the exponential intervening variable, a new two-point approximation method is presented. This introduces the shifting level into each exponential intervening variable to avoid the lack of def inition 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 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-determined quadratic term to match the value of approximate 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.

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References

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