• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.55-61
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• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.649-662
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• 2021

Recently the author studied a one-parameter family of divergences and considered the related median minimization problem of finite points over these divergences in general symmetric cones. In this article, to utilize the results practically, we deal with a special symmetric cone called second order cone, which is important in optimization fields. To be more specific, concrete computations of divergences with its gradients and the unique minimizer of the median minimization problem of two points are provided skillfully.

• 한국군사과학기술학회지
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• 제14권4호
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• pp.694-699
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• 2011

A closed-form technique is presented for estimating a single source location from a set of noisy time delay measurements between distributed sensors. The localization formula is derived from nonlinear least squares minimization over the unknowns of target range and bearing in polar coordinates. Computer simulation results are provided for the purpose of performance analysis. Constrained least squares minimization method with prior source location information is also discussed.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표대회 논문집(III)
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• pp.718-723
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• 1998

The program which could determine cross-sectional dimension of the prestressed concrete box girder bridges at the stage of preliminary design was developed using the optimal technique in this study. It could minimize the cost required in the design of box girder bridges and the construction with the full staging method. Objective cost function consisted of six independent variables such as height of cross-section, jacking force and thickness of web and bottom flange. The SUMT(Sequntial Unconstrained minimization Technique) was used to solve the constrained nonlinear minimization optimal problem. Using the program developed in this study, optimum design was performed for existing bridges with one cell cross section of constant depth. The result verify the compatibility of the program.

• Structural Engineering and Mechanics
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• 제48권6호
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• pp.879-914
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• 2013

In part I of the article, formulation and characteristics of the several well-known structural geometrical nonlinear solution techniques were studied. In the present paper, the efficiencies and capabilities of residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control and modified normal flow will be evaluated. To achieve this goal, a comprehensive comparison of these solution methods will be performed. Due to limit page of the article, only the findings of 17 numerical problems, including 2-D and 3-D trusses, 2-D and 3-D frames, and shells, will be presented. Performance of the solution strategies will be considered by doing more than 12500 nonlinear analyses, and conclusions will be drawn based on the outcomes. Most of the mentioned structures have complex nonlinear behavior, including load limit and snap-back points. In this investigation, criteria like number of diverged and complete analyses, the ability of passing load limit and snap-back points, the total number of steps and analysis iterations, the analysis running time and divergence points will be examined. Numerical properties of each problem, like, maximum allowed iteration, divergence tolerance, maximum and minimum size of the load factor, load increment changes and the target point will be selected in such a way that comparison result to be highly reliable. Following this, capabilities and deficiencies of each solution technique will be surveyed in comparison with the other ones, and superior solution schemes will be introduced.

• Structural Engineering and Mechanics
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• 제48권6호
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• pp.849-878
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• 2013

This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

• Journal of Power Electronics
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• 제14권2호
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• pp.351-361
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• 2014

The discrete torque generation mechanism and inherently nonlinear magnetic characterization of switched reluctance motors lead to unacceptable torque ripples and limit the application of these motors. In this study, a phase current profiling technique and torque sharing function are proposed in consideration of magnetic saturation effects and by minimizing power loss in the commutation area between the adjacent phases. Constant torque trajectories are considered in incoming and outgoing phase current planes based on nonlinear T-i-theta curves obtained from experimental measurements. Optimum points on constant torque trajectories are selected by improving drive efficiency and minimizing copper loss in each rotor position. A novel analytic invertible function is introduced to express phase torque based on rotor position and its corresponding phase current. The optimization problem is solved by the proposed torque function, and optimum torque sharing functions are derived. A modification method is also introduced to enhance the torque ripple-free region based on simple logic rules. Compared with conventional torque sharing functions, the resultant reference current from the proposed method has less peak and effective values and exhibits lower copper loss. Experimental and simulation results from a four-phase 4 KW 8/6 SRM validate the effectiveness of the proposed method.

• Journal of Electrical Engineering and Technology
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• 제10권1호
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• pp.118-127
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• 2015

This paper presents an advanced torque ripple minimization method of a switched reluctance motor (SRM) using torque sharing function (TSF). Generally, TSF is applied into the torque control. However, the conventional TSF cannot follow the expected torque well because of the nonlinear characteristics of the SRM. Moreover, the tail current that is generated at a high speed motor drive makes unexpected torque ripples. The proposed method combined TSF with fuzzy logic control (FLC). The advantage of this method is that the torque can be controlled unity at any conditions. In addition, the controller can track the torque under the condition of the wrong TSF. The effectiveness of the proposed algorithm is verified by the simulations and experiments.

• 조명전기설비학회논문지
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• 제28권7호
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• pp.48-54
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• 2014

This paper discusses study of torque ripple minimization employing an improved TDF(torque distribution function)-based instantaneous torque control to reduce acoustic noise and vibration problem of the SRM. As the flux linkage of the SRM is a nonlinear function of phase current and rotor position, design of optimal controller for the SRM is quite complicated. Hence, an accurate mathematical model considering the nonlinearity of the SRM is required. An improved TDF based torque control has been proposed in order to reduce the toque ripple at high speed operation. Dynamic simulation using Matlab/Simulink as well as Finite Element Analysis is presented. A prototype SRM for electric vehicle traction has been manufactured to validate the experimental results comparing the dynamic simulation results.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.