• Journal of Advanced Marine Engineering and Technology
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• v.24 no.1
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• pp.18-24
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• 2000

As ship's propulsion shafting system has been complicated, many linear methods that have been used until now are not sufficient enough to produce proper solutions and these solutions are ofter unreasonable. So we need to solve nonlinear systems, and many methods for solving nonlinear vibration system have been developed. In this study, the propulsion shafting system was modeled with Duffing's nonlinear vibration system and multi-degree-of-freedom, and analyzed by using Quasi-Newton method. And for the purpose of confirming the reliability of the calculating results for nonlinear forced torsional vibration of the propulsion shafting system, the nonlinear calculated results were compared with the linear calculated ones for ship's propulsion shafting system. In the result, for analysis of the forced torsional vibration of the propulsion systems with nonlinear elements, the modified Newton's method is confirmed reasonable.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.91-107
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• 2002

This paper presents two new self-scaling variable-metric algorithms. The first is based on a known two-parameter family of rank-two updating formulae, the second employs an initial scaling of the estimated inverse Hessian which modifies the first self-scaling algorithm. The algorithms are compared with similar published algorithms, notably those due to Oren, Shanno and Phua, Biggs and with BFGS (the best known quasi-Newton method). The best of these new and published algorithms are also modified to employ inexact line searches with marginal effect. The new algorithms are superior, especially as the problem dimension increases.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.219-225
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• 1998

The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.702-705
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• 2001

This paper deals with a method to predict the flying state of the head slider in a optical disk drive(ODD). The Dual Solver based on the Quasi-Newton method and the Newton method has been developed to simulate the steady-state flying conditions. The numerical results show the effectiveness and reliability of this new solver.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.319-328
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• 1993

The actual convergence rate of Newton-Raphson iteration method at each step is studied under the regularity conditions for the limiting distribution: The convergence rate of it is accelerated with good starting values. Hence we can decide a number of iterations according to our purposes.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.675-691
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• 2002

The focus of this work is on the development of large-scale numerical optimization methods for optimal control of steady incompressible Navier-Stokes flows. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. We develop reduced Hessian sequential quadratic programming. Both quasi-Newton and Newton variants are developed and compared to the approach of eliminating the flow equations and variables, which is effectively the generalized reduced gradient method. Optimal control problems we solved for two-dimensional flow around a cylinder. The examples demonstrate at least an order-of-magnitude reduction in time taken, allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.325-331
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• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.127-134
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• 1989

This paper proposes a deformation method for solving practical nonlinear programming problems. Utilizing the nonlinear parametric programming technique with Quasi-Newton method [6,7], the method solves the problem by imbedding it into a suitable one-parameter family of problems. The approach discussed in this paper was originally developed with the aim of solving a system of structural optimization problems with frequently appears in various kind of engineering design. It is assumed that we have to solve more than one structural problem of the same type. It an optimal solution of one of these problems is available, then the optimal solutions of thel other problems can be easily obtained by using this known problem and its optimal solution as the initial problem of our parametric method. The method of nonlinear programming does not generally converge to the optimal solution from an arbitrary starting point if the initial estimate is not sufficiently close to the solution. On the other hand, the deformation method described in this paper is advantageous in that it is likely to obtain the optimal solution every if the initial point is not necessarily in a small neighborhood of the solution. the Jacobian matrix of the iteration formula has the special structural features [2, 3]. Sectioon 2 describes nonlinear parametric programming problem imbeded into a one-parameter family of problems. In Section 3 the iteration formulas for one-parameter are developed. Section 4 discusses parametric approach for Quasi-Newton method and gives algorithm for finding the optimal solution.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.8-12
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• 1984

Algorithms for solving a set of nonlinear simultaneous equations, which is frequently required in problems of controlling nonlinear processes, are proposed. Here the equation variables are first parameterized and a recursive identification technique is utilized. The forms and characteristics of the resultant algorithms are vary similar to the Broyden's quasi-Newton method, but their derivations and final recursion equations are different. Our methods possess almost all the merits of the Broyden's and numerical comparisons show our methods to be more efficient and reliable for some difficult problems.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.7-14
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• 2000

Nowadays, the viscous damper using high viscosity oil was much to be used for engine shafting system to reduce the excessive additional stress by torsional vibration. In general, it was assumed that the viscous damper could be modelled having only damping coefficient, that is to say, whose stiffness be ignored. But it is found that there exists a jump phenomenon, as a kind of non-linear vibration, in the actual engine shafting system with a damper of high viscosity. Therefore the damper ring and the casing are modelled as two mass elastic system with a complex viscosity. Also, to analyze a non-linear phenomenon, it is assumed that the viscous damper has a linear stiffness coefficient in proportion to the angular amplitude and a non-linear stiffness coefficient in proportion to cube of the angular amplitude. For the analysis, Quasi-Newton method with BFGS(Broyden-Fletcher-Goldfarb-Shanno) formula is used. Both calculated and measured values are provided in this paper which confirm the possibility of applying non-linear theory to engine shafting system with viscous damper.