• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.475-480
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• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.3
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• pp.130-134
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• 1985

In two-dimensional discrete cosine transform(DCT) coding, the measurements of the distributions of the transform coefficients are important because a better approximation yields a smaller mean square distorition. This paper presents the results of distribution tests which indicate that the statistics of the AC coefficients are well approximated to a generalized Gaussian distribution whose shape parameter is 0.6. Furthermore, from a simulation of the DCT coding, it was shown that the above approximation yields a higher experimental SNR and a better agreement between theory and simulation than the Gaussian or Laplacian assumptions.

• Journal of Advanced Navigation Technology
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• v.20 no.1
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• pp.53-58
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• 2016

In this paper, we propose a novel quadratic Kalman filter based object tracking algorithm using moving pictures. Quadratic Kalman filter, which is introduced recently, has not yet been applied to the problem of 3-dimensional (3-D) object tracking. Since the mapping of a position in 2-D moving pictures into a 3-D world involves non-linear transformation, appropriate algorithm must be chosen for object tracking. In this situation, the quadratic Kalman filter can achieve better accuracy than extended Kalman filter. Under the same conditions, we compare extended Kalman filter, unscented Kalman filter and sequential importance resampling particle filter together with the proposed scheme. In conculsion, the proposed scheme decreases the divergence rate by half compared with the scheme based on extended Kalman filter and improves the accuracy by about 1% in comparison with the one based on unscented Kalman filter.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2483-2491
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• 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.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.1
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• pp.56-62
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• 1988

For shape description, a fast sequential method for polygonal approximation of chaincoded plane curves which are object boundaries is proposed. The proposed method performs polygonal approximation by use of the distance error from one point to a line, and its performance is enhanced by the smoothed slopes of lines. Furthermore, accumulated distance error and variable distance error threshold are proposed in order to consider and implement the visual characteristics of the human being.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.113-116
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• 2006

본 논문은 소프트웨어 공정에 대하여 기호코팅을 이용한 유전자 알고리즘 기반 퍼지 다항식 뉴럴 네트워크 (Genetic Algorithms-based Fuzzy Polynomial Neural Networks ; gFPNN)의 모델을 제안한다. 유전자 알고리즘에는 이진코딩, 기호코팅, 실수코딩이 있다. 제안된 모델은 스트링의 길이에 따른 해밍절벽을 기호코딩으로 극복하였다. gFPNN에 전반부 멤버쉽 함수는 삼각형과 가우시안형의 멤버쉽 함수가 사용된다. 그리고 규칙의 후반부는 간략, 선형, 이차식 그리고 변형된 이차식 함수에 의해 설계된다. 실험적 예제를 통하여 제안된 모델의 성능이 근사화 능력과 일반화 능력이 우수함을 보인다.

• 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.

• 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.