• 전기의세계
• /
• 제30권6호
• /
• pp.375-385
• /
• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• 대한기계학회논문집
• /
• 제18권1호
• /
• pp.12-23
• /
• 1994

This paper proposes an optimal design software for the open-chain dynamic systems whose governing equations are expressed as differential equation. In this software, an input module and an automatic creation module of the equation of motion are developed to contrive the user's convenience. To analyze the equation of motion of the dynamic systems, variable-order and variable-stepsize Adams-Bashforth-Moulton predictor-corrector method is used to improve the efficiency. For the optimization and the design sensitivity analysis, ALM(augmented lagrange multiplier)method and adjoint variable method are adopted respectively. An output module with which the user can compare and investigate the analysis and the optimization results through tables and graphs is also provided. The developed software is applied to three typical dynamic response optimization problems, and the results compare very well with those available in the literature, demonstrating its effectiveness.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1996년도 추계학술대회 논문집 학회본부
• /
• pp.133-136
• /
• 1996

In the paper, an artificial neural network (ANN) approach based on Lagrange multiplier method (Lagrangian ANN) is used to solve an economic load dispatch (ELD) problem. Traditionally ELD problem has one convex cost function as its objective function and nonlinear constraints such as power balance and maximum-minimum limits of real power. In this study, modification is given to the Lagrangian ANN proposed by Gong et all[5] to guarantee the convergence to the optimal solution. Simulation results demonstrate the effectiveness of the proposed method applied to the ELD problem.

• 한국컴퓨터정보학회논문지
• /
• 제22권10호
• /
• pp.145-150
• /
• 2017

This study aims to analyze panel data using OECD Health data of 34 years to examine how significant the inequality of income is to the inequality of health. The data was from OECD's pooled Health data of 32 countries from 1980 to 2013. The process of determining analysis model was as follows; First, through the descriptive statistics, we examined averages and standard deviation of variables. Second, Lagrange multiplier test has done. Third, through the F-test, we compared Least squares method and Fixed effect model. Lastly, by Hausman test, we determined proper model and examined effective factor using the model. As a result, rather than Pooled OLS Model, Fixed Effect Model was shown as effective in order to consider the characteristics of individual in the panel. The results are as follows: First, as relative poverty rate(${\beta}=-19.264$, p<.01) grows, people's life expectancy decreases. Second, as the rate of smoking(${\beta}=-.125$, p<.05) and the rate of unemployment (${\beta}=-.081$, p<.01) grows, people's life expectancy decreases. Third, as health expenditure(${\beta}=.414$, p<.01) shares more amount of GDP and as the number of hospital beds(${\beta}=-.190$, p<.05) grows, people's life expectancy increases.

• 한국전산구조공학회논문집
• /
• 제35권5호
• /
• pp.249-257
• /
• 2022

본 논문은 직접해법 기반 FETI 알고리즘의 개선 방안을 제시하였다. 개선 대상은 FETI-local로, 해당 알고리즘은 국부 Lagrange 승수를 통해 부영역 간 경계 문제를 정의한다. 부영역 경계 강성 및 하중 계산 단계의 경우, 전체 역행렬 계산 등 과도한 비용을 요구했던 기존 알고리즘을 Boolean 행렬 특성을 활용한 선택적 역행렬 성분 계산으로 개선하였다. 전역 경계 행렬식 계산 단계의 경우, 기존 단일 프로세서 연산을 다중 프론탈 기법 기반 병렬 연산으로 대체하였다. 제시된 FETI-local 알고리즘의 성능 개선은 64만 자유도 수치 예제를 통해 검증되었으며, 기존 대비 최대 97.8%의 계산 시간 감소가 달성되었다. 또한, 기존 대비 안정적이고 개선된 확장성이 가속 지표를 통해 확인되었다. 추가로, 432만 자유도의 대용량 계산 성능 비교가 제시된 알고리즘과 상용 프로그램인 ANSYS 간에 수행되었다. 그 결과, 계산 시간 측면에선 ANSYS가 우수하였으나, 프로세서 수에 따른 가속 성능 증가율 측면에선 제시된 알고리즘이 우수한 것이 확인되었다.

• 한국자동차공학회논문집
• /
• 제1권3호
• /
• pp.74-82
• /
• 1993

Optimal designs of a 3-point and a 4-point engine mount system are presented for reducing the idle shake of a Front Wheel Drive(FWD) vehicle. Design variables used in this study are the locations, the angles and the stiffness of an engine mount system. The goal of the optimization is minimizing the transmitted force without violating the constraints such as static weight sag, resonant frequency and side limits of design variables. The Augmented Lagrange Multiplier(ALM) Method is used for solving the nonlinear constrained optimization. The generalized Jacobi and the impedence method are employed for a free vibration analysis and a forced response analysis. The trend of analysis results well meet that of the experimental results. The optimization results reveal that the 4-point system transmits less torque than the 3-point system. It is also found from the design sensitivity analysis that the vibration characteristics of the 4-point system is less sensitive than those of the 3-point system.

• Journal of Mechanical Science and Technology
• /
• 제16권8호
• /
• pp.1072-1078
• /
• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• 한국공작기계학회논문집
• /
• 제12권2호
• /
• pp.71-78
• /
• 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 all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, 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 variables, 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 variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables 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 variables variations.

• Industrial Engineering and Management Systems
• /
• 제4권2호
• /
• pp.145-157
• /
• 2005

There are a lot of raw materials, work-in-processes and finished goods in manufacturing industry. Here, the less stock of materials and work-in-processes manufacturing industry has, the worse the rate of the production is. Inversely, the more manufacturing industry has, the more expensive the cost to support them is. Thus, it is important for us to balance them efficiently. In general, inventory problems are to decide appropriate times to produce goods and to determine appropriate quantities of goods. Therefore, inventory problems require as more useful information as possible. For example, there are demand, lead time, ordering point and so on. In this paper, we deal with an optimal ordering policy on both way substitutable two-commodity inventory control system. That is, there is a problem of how to allocate the produced two kinds of goods in a factory to m areas so as to minimize the total expected inventory cost. The demand of each area is probabilistic, and we adopt the exponential distribution as a probability density function of demand. Moreover, we provide numerical examples of the problem.

• 한국항공우주학회지
• /
• 제38권2호
• /
• pp.141-149
• /
• 2010

위성 편대 비행 시 주위성과 부위성 간의 연료 소비 균형을 고려한 임펄스 기동에 관한 연구를 수행하였다. 위성 간 사용가능한 연료량을 비교하여 가중치(weight)를 두고 가격함수(cost function)를 설계하여 라그랑지 승수법을 통해 필요한 임펄스를 획득하였다. 상대궤도 발산 방지를 위해 에너지 매칭 기법을 사용하였고, 임펄스 기동 후 상대 거리 구속이 이루어짐을 시뮬레이션을 통해 확인하였다. 시뮬레이션은 지구 중력 외의 외란이 없는 경우와 대기 항력이 외란으로 존재하는 상황으로 시나리오를 나누어 수행하였다. 본 논문 결과는 이후 실제로 위성을 편대로 사용한 위성 군집 비행 시, 상대 궤도 구속 요건을 만족하고 각 위성의 연료량을 비교한 임펄스 기동이 요구될 때 사용가능할 것으로 기대된다.