• Journal of Electrical Engineering and Technology
• /
• 제13권3호
• /
• pp.1099-1109
• /
• 2018

For practical consideration, economic dispatch (ED) problems in power system have non-smooth cost functions with equality and inequality constraints that makes the problems complex constrained nonlinear optimization problems. This paper proposes a new constraint handling method for equality and inequality constraints which is employed to solve ED problems, where the incremental rate is employed to enhance the modification process. In order to prove the applicability of the proposed method, the study cases are tested based on the classical particle swarm optimization (PSO) and differential evolution (DE) algorithm. The proposed method is evaluated for ED problems using six different test systems: 6-, 15-, 20-, 38-, 110- and 140-generators system. Simulation results show that it can always find the satisfactory solutions while satisfying the constraints.

• Journal of Electrical Engineering and Technology
• /
• 제10권4호
• /
• pp.1508-1517
• /
• 2015

Optimal Power dispatch is the short-term decision of the optimal output of a number of power generation facilities, to meet the system demand, with the objective of Power dispatching at the lowest possible cost, subject to transmission lines power loss and operational constraints. The operational constraint includes power balance constraint, generator limit constraint, and emission dispatch constraint and valve point effects. In this paper, Opposition based Differential Evolution Algorithm (ODEA) has been proposed to handle the objective function and the operational constraints simultaneously. Furthermore, the valve point loading effects and transmission lines power loss are also considered for the efficient and effective Power dispatch. The ODEA has unique features such as self tuning of its control parameters, self acceleration and migration for searching. As a result, it requires very minimum executions compared with other searching strategies. The effectiveness of the algorithm has been validated through four standard test cases and compared with previous studies. The proposed method out performs the previous methods.

• Structural Engineering and Mechanics
• /
• 제54권4호
• /
• pp.725-740
• /
• 2015

This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

• 한국전산구조공학회논문집
• /
• 제23권4호
• /
• pp.395-401
• /
• 2010

시간이 지남에 따라 건물의 수직부재가 수축하는 것을 기둥축소라고 한다. 건물의 고층화 및 비정형화 추세 때문에 수직부재들에 작용하는 축하중 크기 간의 차이를 피할 수 없게 되며, 이의 영향으로 인접 수직부재 간의 축방향 축소량이 차이가 나게 된다. 이러한 부등축소량은 수직부재와 수평부재의 접합부에 추가적인 응력을 유발시키거나 슬래브의 기울어짐 또는 간벽이나 창호 등 비구조재의 사용성에 문제를 초래하게 된다. 이러한 부등축소량의 영향을 감소시키기 위하여 시공 중 수직부재의 설치 시 예측된 보정을 하게 된다. 보정의 합리성은 각 부재별 축소량의 정확한 예측과 예측된 축소량을 이용한 각 부재들의 합리적 보정량 산정에 있다. 부등축소량의 예측은 점점 더 정확해지고 있으나 보정 기법에 관한 연구는 거의 없다. 따라서 본 논문에서는 이동 평균법을 사용한 보정 기법과 보정하면서 발생하는 오차에 대한 합리적인 제한조건을 제시하였으며, 제한조건의 변화와 보정 그룹 수의 관계를 살펴봄으로써 제한조건 설정의 객관적인 판단 기준이 되었다. 그리고 이전에 연구되어진 SA 알고리즘을 사용한 최적 보정 기법과 결과를 비교해 봄으로써 이동 평균법 보정 기법의 효과를 검증하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제2권2호
• /
• pp.21-25
• /
• 1998

An algorithm for a solution of ordinary differential equations using a modified corrector in the Adams predictor-corrector method of order four is described. The Lagrange interpolation used in the corrector of the Adams method is replaced partially by the cubic spline interpolation satisfying the first derivative constraints at the two end points. By exhibiting three examples, we show that the proposed method is more effcient when the solution of a differential equation is highly oscillating.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
• /
• pp.376-382
• /
• 1991

In the analysis of constrained holonomic systems, the Lagange multiplier method yields a system of second-order ordinary differential equations of motion and algebraic constraint equations. Conventional holonomic or nonholonomic constraints are defined as geometric constraints in this paper. Previous works concentrate on the geometric constraints. However, if the total energy of a dynamic system can be computed from the initial energy plus the time integral of the energy input rate due to external or internal forces, then the total energy can be artificially treated as a constraint. The violation of the total energy constraint due to numerical errors can be used as information to control these errors. It is a necessary condition for accurate simulation that both geometric and energy constraints be satisfied. When geometric constraint control is combined with energy constraint control, numerical simulation of a constrained dynamic system becomes more accurate. A new convenient and effective method to implement energy constraint control in numerical simulation is developed based on the geometric interpretation of the relation between constraints in the phase space. Several combinations of energy constraint control with either Baumgarte's Constraint Violation Stabilization Method (CVSM) are also addressed.

• 대한기계학회논문집A
• /
• 제27권8호
• /
• pp.1303-1308
• /
• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of ail relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 춘계학술대회
• /
• pp.893-898
• /
• 2004

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• 한국공작기계학회:학술대회논문집
• /
• 한국공작기계학회 2002년도 추계학술대회 논문집
• /
• pp.219-224
• /
• 2002

This paper aims to derive a mathematical model of the dynamics of handling tasks in robot finger which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed. Finally, it is shown that even in the simplest case of dual single D.O.F manipulators there exists a sensory feedback from sensing data of the rotational angle of the object to command inputs to joint actuators and this feedback connection from sensing to action eventually realizes secure grasping of the object, provided that the object is of rectangular shape and motion is confined to a horizontal plane.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2002년도 ICCAS
• /
• pp.108.4-108
• /
• 2002

This paper aims to derive a mathematical model of the dynamics of handling tasks in robot fingers which stably grasps and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for differential-algebraic equations of overall...