• 제목/요약/키워드: Two-point approximation

검색결과 106건 처리시간 0.021초

개선된 이점 대각 이차 근사화를 이용한 함수 근사화 (Function Approximation Using an Enhanced Two-Point Diagonal Quadratic Approximation)

  • 김종립;강우진;최동훈
    • 대한기계학회논문집A
    • /
    • 제28권4호
    • /
    • pp.475-480
    • /
    • 2004
  • 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.

이점 볼록 근사화 기법을 적용한 최적설계 (Design Optimization Using the Two-Point Convex Approximation)

  • 김종립;최동훈
    • 대한기계학회논문집A
    • /
    • 제27권6호
    • /
    • pp.1041-1049
    • /
    • 2003
  • In this paper, a new local two-point approximation method which is based on the exponential intervening variable is proposed. This new algorithm, called the Two-Point Convex Approximation(TPCA), use the function and design sensitivity information from the current and previous design points of the sequential approximate optimization to generate a sequence of convex, separable subproblems. This paper describes the derivation of the parameters associated with the approximation and the numerical solution procedure. In order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve several typical design problems. These optimization results are compared with those of other optimizers. Numerical results obtained from the test examples demonstrate the effectiveness of the proposed method.

이점 대각 이차 근사화 기법과 통계적 제한조건을 적용한 강건 최적설계 기법 (Robust Optimal Design Method Using Two-Point Diagonal Quadratic Approximation and Statistical Constraints)

  • 권용삼;김민수;김종립;최동훈
    • 대한기계학회논문집A
    • /
    • 제26권12호
    • /
    • pp.2483-2491
    • /
    • 2002
  • This study presents an efficient method for robust optimal design. In order to avoid the excessive evaluations of the exact performance functions, two-point diagonal quadratic approximation method is employed for approximating them during optimization process. This approximation method is one of the two point approximation methods. Therefore, the second order sensitivity information of the approximated performance functions are calculated by an analytical method. As a result, this enables one to avoid the expensive evaluations of the exact $2^{nd}$ derivatives of the performance functions unlike the conventional robust optimal design methods based on the gradient information. Finally, in order to show the numerical performance of the proposed method, one mathematical problem and two mechanical design problems are solved and their results are compared with those of the conventional methods.

Efficient Mechanical System Optimization Using Two-Point Diagonal Quadratic Approximation in the Nonlinear Intervening Variable Space

  • Park, Dong-Hoon;Kim, Min-Soo;Kim, Jong-Rip;Jeon, Jae-Young
    • Journal of Mechanical Science and Technology
    • /
    • 제15권9호
    • /
    • pp.1257-1267
    • /
    • 2001
  • 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-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.

  • PDF

이점 대각 이차 근사화 기법을 쌍대기법에 적용한 순차적 근사 최적설계 (Sequential Approximate Optimization by Dual Method Based on Two-Point Diagonal Quadratic Approximation)

  • 박선호;정상진;정승현;최동훈
    • 대한기계학회논문집A
    • /
    • 제35권3호
    • /
    • pp.259-266
    • /
    • 2011
  • 본 논문에서는 SD-TDQAO (Sequential Dual - Two-point Diagonal Quadratic Approximate Optimization)라는 쌍대기법을 이용한 순차적 최적설계 알고리즘을 제안한다. 이 방법은 비선형 목적함수와 제한조건이 포함되어 있는 공학적인 문제를 효과적으로 풀 수 있도록 하는데 목적이 있다. 기존의 볼록성과 분리성이 만족되지 않는 eTDQA2 방법을 이용하여 쌍대기법에 이용할 수 있도록 이차 근사함수의 헤시언 대각요소에 이를 적용하여 쉽게 볼록성과 분리성을 보장할 수 있도록 하였다. 또한 이를 수학적 예제와 위상 최적설계문제를 통해 기존의 쌍대기법 알고리즘인 MMA 와의 비교로 그 성능을 입증하였다.

신뢰성을 고려한 유연 날개의 다점 최적 설계에 관한 연구 (A STUDY ABOUT MULTI-POINT RELIABILITY BASED DESIGN OPTIMIZATION OF FLEXIBLE WING)

  • 김수환;이재훈;권장혁
    • 한국전산유체공학회:학술대회논문집
    • /
    • 한국전산유체공학회 2005년도 추계 학술대회논문집
    • /
    • pp.99-104
    • /
    • 2005
  • For the efficient reliability analysis, Bi-direction two-point approximation(BTPA) method is developed which solves shortcomings of conventional two-point approximation(TPA) methods that generate an approximate surface with low accuracy or sometimes do an unstable approximate surface. The conventional reliability based design optimization(RBDO) methods require high computational cost compared with the deterministic design optimization(DO) methods. To overcome the computational inefficiency of RBDO, the approximate reliability analysis approaches on the TPA surface are proposed. Using these FORM and SORM analysis strategies, multi-point aerodynamic-structure interacted shape design optimizations with uncertainty are performed very efficiently.

  • PDF

Point Particle Approximation for Single and Two Species Diffusion-Influenced Reactions

  • Kim, Hyojoon
    • Bulletin of the Korean Chemical Society
    • /
    • 제34권5호
    • /
    • pp.1454-1456
    • /
    • 2013
  • The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

Polygonal Approximation of Digital Curves to Preserve Original Shapes

  • Lee, Dae-Ho;Lee, Seung-Gwan
    • ETRI Journal
    • /
    • 제32권4호
    • /
    • pp.630-633
    • /
    • 2010
  • In this letter, we propose a novel polygonal approximation of digital curves that preserve original shapes. The proposed method first detects break points, which have two different consecutive vectors, and sets an initial dominant point set. The approximation is then performed iteratively by deleting a dominant point using a novel distance, which can measure both the distance and the angle acuteness. The experimental results show that the proposed method can preserve original shapes and is appropriate for various shapes, including slab-sided shapes.

이점 대각 이차 근사화(TDQA) 기법을 적용한 최적설계 (Design Optimization Using Two-Point Diagonal Quadratic Approximation(TDQA))

  • 김민수;김종립;최동훈
    • 대한기계학회:학술대회논문집
    • /
    • 대한기계학회 2001년도 춘계학술대회논문집C
    • /
    • pp.386-391
    • /
    • 2001
  • This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. 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 computed in a closed form, which correct 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 original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

  • PDF

이점 대각 이차 근사화 기법을 적용한 최적설계 (Design Optimization Using Two-Point Diagonal Quadratic Approximation)

  • 최동훈;김민수;김종립;전재영
    • 대한기계학회논문집A
    • /
    • 제25권9호
    • /
    • pp.1423-1431
    • /
    • 2001
  • 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.