• 산업경영시스템학회지
• /
• 제20권41호
• /
• pp.123-134
• /
• 1997

In this paper we consider the CSP requirements determination problem of new equipment system. The CSP we deal with in the paper are restricted to the demand-based spare parts. For the newly procured equipment systems, mathematical analyses are made for the system which is constructed with the repairable items to derive the associated CSP requirement determination model in mathematical expression, respectively. Based on these analyses, a mathematical model is derived for making an optimal CSP requirement determination subject to the constraint of satisfying any given funds limitation. We assume that the failure of a part follows a Poisson process. Firstly, the operational availability concept in CSP is defined and the relation between the general system availability and the operational availability is established. Secondly, the problem is formulated as the operational availability maximization problem that should satisfy the funds limitation, and then, using the generalized Lagrange multipliers method, the optimal solution procedure is derived.

• Journal of Mechanical Science and Technology
• /
• 제17권4호
• /
• pp.538-544
• /
• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• 대한기계학회논문집A
• /
• 제25권12호
• /
• pp.1966-1973
• /
• 2001

The Jacobian matrix of the equations of motion of a system using velocity transformation technique is derived via variation methods to apply the implicit integration algorithm, DASSL. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. DASSL is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, accelerations and Lagrange multipliers are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The derived Jacobian matrix of a system is proved to be valid and accurate both analytically and through solution of numerical examples.

• 품질경영학회지
• /
• 제9권2호
• /
• pp.31-36
• /
• 1981

점증되고 있는 고신뢰성 제품의 설계에 있어 주어진 선형제약조건 내(內)에서 체계의 신뢰성을 최대화하는 방법을 소개하고 이를 해결하는 비선형계획법을 반복단계로 하여 Computer Programming을 하였다. 단, 본 논문에서 다루는 체계는 병렬중복구조를 갖는 직렬다단계 구조이다. 타당성 검토를 위한 예제를 해결하였으며 Computer Programming은 지면관계로 생략하였다.

• 대한기계학회논문집
• /
• 제19권1호
• /
• pp.271-276
• /
• 1995

This paper presents a systematic method for the dynamic analysis of flexible mechanical systems containing closed kinematic loops. Kinematics between pairs of contiguous flexible bodies is described with the joint coordinates and the deformation modal coordinates. The cut-joint constraint equations associated with the closed kinematic loops are derived, simply using the geometric conditions. The equations of motions are initially written in terms of the joint and modal coordinates using the velocity transformation technique. Lagrange multipliers associated with the cut-joint constraints for closed-loop systems are then eliminated systematically using the generalized coordinate partitioning method, resulting to a minimal set of equations of motion.

• Journal of Mechanical Science and Technology
• /
• 제18권11호
• /
• pp.1891-1899
• /
• 2004

The characteristics of dynamic systems subjected to multiple linear constraints are determined by considering the constrained effects. Although there have been many researches to investigate the dynamic characteristics of constrained systems, most of them depend on numerical analysis like Lagrange multipliers method. In 1992, Udwadia and Kalaba presented an explicit form to describe the motion for constrained discrete systems. Starting from the method, this study determines the dynamic characteristics of the systems to have positive semidefinite mass matrix and the continuous systems. And this study presents a closed form to calculate frequency response matrix for constrained systems subjected to harmonic forces. The proposed methods that do not depend on any numerical schemes take more generalized forms than other research results.

• 대한수학회보
• /
• 제51권1호
• /
• pp.287-301
• /
• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• 산업경영시스템학회지
• /
• 제21권48호
• /
• pp.113-122
• /
• 1998

In this paper we consider the CSP requirements determination problem of new equipment(machine) system. For the newly procured equipment systems, mathematical analyses are made for the system which is constructed with the consumable parts to derive the associated CSP requirement determination model in mathematical expression. Based on these analyses, a mathematical model is derived for making an optimal CSP requirement determination subject to tile constraint of satisfying any given operational availability limitation. We assume that the failure of a part follows a Poisson process. Firstly, the operational availability concept in CSP is defined and the relation between the general system availability and the operational availability is established. Secondly, the problem is formulated as the cost minimization problem that should satisfy the operational availability limitation, and then, using the generalized Lagrange multipliers method, the optimal solution procedure is derived.

• Journal of the Korean Data and Information Science Society
• /
• 제14권4호
• /
• pp.965-974
• /
• 2003

In this paper we propose an incremental classification of multi-class data set by LS-SVM. By encoding the output variable in the training data set appropriately, we obtain a new specific output vectors for the training data sets. Then, online LS-SVM is applied on each newly encoded output vectors. Proposed method will enable the computation cost to be reduced and the training to be performed incrementally. With the incremental formulation of an inverse matrix, the current information and new input data are used for building another new inverse matrix for the estimation of the optimal bias and lagrange multipliers. Computational difficulties of large scale matrix inversion can be avoided. Performance of proposed method are shown via numerical studies and compared with artificial neural network.

• Structural Engineering and Mechanics
• /
• 제51권2호
• /
• pp.333-347
• /
• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.