• Transactions of the Korean Society of Machine Tool Engineers
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• 제12권2호
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• pp.9-16
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• 2003

A strategy of the optimal shape design with FEA(Finite Element Analysis) for 2-D structure is proposed by comparing subproblem approximation method with first order approximation method. A cantilever beam with two different loading conditions, a concentrated load and an evenly distribute load, and truss structure with a concentrated loading condition are implemented to optimize the shape. It gives a good design strategy on the optimal truss structure as well as the optimal cantilever beam shape. It is found that the convergence is quickly finished with the iteration number below ten. Optimized shapes of cantilever beam and truss structure are shown with stress contour plot by the results of the subproblem approximation method and the first order approximation methd.

• Korean Journal of Computational Design and Engineering
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• 제11권1호
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제13권1호
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• pp.39-46
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• 1993

The need to develop method which can improve the shape design efficiency using high quality approximation is being brought up. In this study, to perform shape optimal design of three-dimensional continuum structures an efficient approximation method for stress constraints is proposed, based on expanding the nodal forces in Taylor series with respect to shape variables. Numerical examples are performed using the 3-D cantilever beam and fixed-fixed beam and compared with other method to demonstrate the efficiency and convergence rate of the Force Approximation method. It is shown that by taking advantage of this high quality approximation, the total number of finite element analysis required for shape optimization of 3-D continuum structures can be reduced significantly, resulting to the same level of efficiency achieved previously in sizing optimization problems. Also, shape representation by super curve technique applied to obtain optimal shape finds useful method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 한국공작기계학회 2004년도 춘계학술대회 논문집
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• pp.166-171
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• 2004

In this study, shape optimization of micro-static mixer with a cantilever beam was accomplished for mixing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Journal of Biomedical Engineering Research
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• 제28권5호
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• pp.665-675
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• 2007

The morphological change of ECG is the important diagnostic parameter to finding the malfunction of a heart. Generally ST segment deviation is concerned with myocardial abnormality. The aim of this study is to detect the change of ST in shape using a polynomial approximation method and the reference ST type. The developed algorithm consists of feature point detection, ST level detection and ST shape classification. The detection of QRS complex is accomplished using it's the morphological characteristics such as the steep slope and high amplitude. The developed algorithm detects the ST level change, and then classifies the ST shape type using the polynomial approximation. The algorithm finds the least squares curve for the data between S wave and T wave in ECG. This curve is used for the classification of the ST shapes. ST type is classified by comparing the slopes of the specified points between the reference ST set and the least square curve. Through the result from the developed algorithm, we can know when the ST level change occurs and what the ST shape type is.

• Structural Engineering and Mechanics
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• 제76권6호
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• pp.799-821
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• 2020

The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

• Journal of the Korean Society of Manufacturing Process Engineers
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• 제10권5호
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• pp.117-124
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• 2011

Tire's performance plays important roles in improving vehicle's performances. Tire makers carry out a lot of research to improve tire's performance. They are making effort to meet multi purposes using various optimization methods. Recently, the tire makers perform the shape optimization using approximation models, which are surrogate models obtained by statistical method. Generally, the reason why we increase sampling points during optimization process, is to get more reliable approximation models, but the more we adopt sampling points, the more we need time to test. So it is important to select approximation model and proper number of sampling points to balance between reliability and time consuming. In this research, we studied to compare two kind cases for a approximation construction. First, we compare RSM and Kriging which are Curve Fitting Method and Interpolation Method, respectively. Second, we construct approximation models using three different number of sampling points. And then, we recommend proper approximation model and orthogonal array adopt tire's design optimization.

• Journal of the Institute of Electronics Engineers of Korea SP
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• 제41권3호
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• pp.121-127
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• 2004

This paper presents a new vertex selection scheme for shape approximation. In the proposed method, final vertex points are determined by "two-step procedure". In the first step, initial vertices are simply selected on the contour, which constitute a subset of the original contour, using conventional methods such as an iterated refinement method (IRM) or a progressive vertex selection (PVS) method In the second step, a vertex adjustment Process is incorporated to generate final vertices which are no more confined to the contour and optimal in the view of the given distortion measure. For the optimality of the final vertices, the dynamic programming (DP)-based solution for the adjustment of vertices is proposed. There are two main contributions of this work First, we show that DP can be successfully applied to vertex adjustment. Second, by using DP, the global optimality in the vertex selection can be achieved without iterative processes. Experimental results are presented to show the superiority of our method over the traditional methods.

• Journal of the Korean Society for Precision Engineering
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• 제16권5호통권98호
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제10권3호
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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.