• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.4
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.3
• /
• pp.259-266
• /
• 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 Korea Concrete Institute Conference
• /
• 2010.05a
• /
• pp.3-4
• /
• 2010

Strength of PC walls with diagonal reinforcements can be obtained by using the section analysis. Deformation of the diagonal reinforcements is related to that of flexural reinforcement and makes the another tensile strength on the PC wall. Another tensile strength due to diagonal reinforcements is assumed to be 1/3 point of the distance between the flexural reinforcements.

• Journal of Mechanical Science and Technology
• /
• v.15 no.9
• /
• 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.

• Proceedings of the KSME Conference
• /
• 2001.06c
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.9
• /
• 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.

• Journal of Ocean Engineering and Technology
• /
• v.21 no.6
• /
• pp.7-15
• /
• 2007

A mechanical model was developed to predict the behavior of point-loaded RC slender beams (a/d > 2.5) without stirrups. It is commonly accepted by most researchers that a diagonal tension crack plays a predominant role in the failure mode of these beams, but the failure mechanism of these members is still debatable. In this paper, it was assumed that diagonal tension failure was triggered by the concrete cover splitting due to the dowel action at the initial location of diagonal tension cracks, which propagate from flexural cracks. When concrete cover splitting occurred, the shape of a diagonal tension crack was simultaneously developed, which can be determined from the principal tensile stress trajectory. This fictitious crack rotates onto the crack tip with load increase. During the rotation, all forces acting on the crack (i.e, dowel force of longitudinal bars, vertical component of concrete tensile force, shear force by aggregate interlock, shear force in compression zone) were calculated by considering the kinematical conditions such as crack width or sliding. These forces except for the shear force in the compression zone were uncoupled with respect to crack width and sliding by the proposed constitutive relations for friction along the crack. Uncoupling the shear forces along the crack was aimed at distinguishing each force from the total shear force and clarifying the failure mechanism of RC slender beams without stirrups. In addition, a proposed method deriving the dowel force of longitudinal bars made it possible to predict the secondary shear failure. The proposed model can be used to predict not only the entire behavior of point-loaded RC slender shear beams, but also the ultimate shear strength. The experiments used to validate the proposed model are reported in a companion paper.

• Journal of the Korean Society for Precision Engineering
• /
• v.25 no.2
• /
• pp.43-48
• /
• 2008

This paper proposes a new method for measuring the power of spherical and cylindrical lens with 6 points light source, which is composed of a LED and six holes, and magnification ellipse fitting algorithm. Each measured diagonal length of 6 points light source is determined by the target lens power. After finding the center position of each light point with threshold method, 3 axis-diagonal lengths were calculated. The long axis and short axis power of cylindrical lens can be calculated by using magnification ellipse fitting algorithm with the magnification relationships between the initial diagonal lengths and the measured diagonal lengths changed by lens power.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.17 no.7
• /
• pp.1841-1857
• /
• 2023

CenterNet, a novel object detection algorithm without anchor based on key points, regards the object as a single center point for prediction and directly regresses the object's height and width. However, because the objects have different sizes, directly regressing their height and width will make the model difficult to converge and lose the intrinsic relationship between object's width and height, thereby reducing the stability of the model and the consistency of prediction accuracy. For this problem, we proposed an algorithm based on the regression of the diagonal half-length and the center angle, which significantly compresses the solution space of the regression components and enhances the intrinsic relationship between the decoded components. First, encode the object's width and height into the diagonal half-length and the center angle, where the center angle is the angle between the diagonal and the vertical centreline. Secondly, the predicted diagonal half-length and center angle are decoded into two length components. Finally, the position of the object bounding box can be accurately obtained by combining the corresponding center point coordinates. Experiments show that, when using CenterNet as the improved baseline and resnet50 as the Backbone, the improved model achieved 81.6% and 79.7% mAP on the VOC 2007 and 2012 test sets, respectively. When using Hourglass-104 as the Backbone, the improved model achieved 43.3% mAP on the COCO 2017 test sets. Compared with CenterNet, the improved model has a faster convergence rate and significantly improved the stability and prediction accuracy.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• 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.