• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1041-1049
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• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.3
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• pp.259-266
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• 2011

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.423-424
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• 2012

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1257-1267
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• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.672-676
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• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1423-1431
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• 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.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.3 s.192
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• pp.117-123
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• 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.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.11 s.176
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• pp.135-141
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• 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.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.386-391
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• 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
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• v.4 no.1
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• pp.11-22
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• 1972

Determination of a two-point boundary value problem is the key of finding the control function u(t) with the application of the fundamental idea of Minimum principle. The late development shows the discovery of the initial costate vector for the solution of a two-point value problem. As a new technique of determining the optimal control function, Newton's Sequential method is examined about a number of engineering problems and found available.