• 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.

• 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.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2012년도 춘계학술대회 논문집
• /
• pp.423-424
• /
• 2012

• 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.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2004년도 추계학술대회 논문집
• /
• pp.672-676
• /
• 2004

In this paper, measuring system of 5 DOF motion errors are proposed using two capacitive type sensor, a straight edge and a laser interfoerometer. Yawing error and pitching error are measured using the laser interferometer, and rolling error is measured by the reversal method using a capacitive type sensor. Linear motion errors of horizontal and vertical direction are measured using the sequential two point method. In this case, influence of angular motion errors is compensated using the previously measured angular motion errors. In the horizontal direction, measuring accuracy is within 0.05 $\mu$m and 0.27 arcsec, and in the vertical direction, it is within 0.15 $\mu$m and 0.5 arcsec. From these results, it is confirmed that the proposed measureing system is very effective to the measurement of 5 DOF motion errors in the ultra precision feed tables.

• 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.

• 한국정밀공학회지
• /
• 제24권3호
• /
• pp.117-123
• /
• 2007

This paper describes a three-probe system that can be used to measure the parallelism and straightness of a pair of rails simultaneously. The parallelism is measured using a modified reversal method, while the straightness is measured using a sequential two-point method. The measurement algorithms were analyzed numerically using a pair of functionally defined rails to validate the three-probe system. Tests were also performed on a pair of straightedge rails with a length of 250 mm and a maximum straightness deviation of $0.05{\mu}m$, as certified by the supplier. The experimental results demonstrated that the parallelism-measurement algorithm had a cancellation effect on the probe stage motion error. They also confirmed that the proposed system could measure the slope of a pair of rails about $0.06{\mu}rad$. Therefore, by combining this technique with a sequential differential method to measure the straightness of the rails simultaneously, the surface profiles could be determined accurately and eliminate the stage error. The measured straightness deviation of each straight edge was less than $0.05{\mu}m$, consistent with the certified value.

• 한국정밀공학회지
• /
• 제22권11호
• /
• pp.135-141
• /
• 2005

Measurement of five DOF motion errors in a ultra precision feed table was attempted in this study. Yaw and pitch error were measured by using a laser interferometer and roll error was measured by using the reversal method. Linear motion errors in the vertical and horizontal directions were measured by using the sequential two point method. In this case, influence of angular motion errors was compensated by using the previously measured ones by the laser interferometer and the reversal method. The capacitive type sensors and an optical straight edge were used in the reversal method and the sequential two point method. Influence of thermal deformation on sensor jig was investgated and minimized by the periodic measurement according to the variation of room temperature. Deviation of gain between sensors was also compensated using the step response data. 5 DOF motion errors of a hydrostatic table driven by the linear motor werer tested using the measurement method. In the horizontal direction, measuring accuracies for the linear and angular motion were within ${\pm}0.02\;{\mu}m$ and ${\pm}0.04$ arcsec, respectively. In the vertical direction, they were within ${\pm}0.02{\mu}m$ and ${\pm}0.05$ arcsec. From these results, it was found that the introduced measurement method was very effective to measure 5 DOF motion errors of the ultra precision feed tables.

• 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.

• Nuclear Engineering and Technology
• /
• 제4권1호
• /
• pp.11-22
• /
• 1972

최대치(또는 최소치) 원리의 기본개념을 써서 제어함수 u(t)를 찾는데는 2점간 경계치 문제의 해결이 요구된다. 그런데 최근에는 2점간 문제를 푸는 방법으로 초기 costate vector를 찾아 문제를 해결하는 여러가지 편법이 개발되고 있다. 여기에서는 최적제어 함수를 찾는 새로운 방법의 하나로써 고안된 Newton's sequential방법을 써서 여러가지 공학적 문제를 풀어 봄으로써 이 방법이 매우 유효하다는 것을 알아냈다.