• Nuclear Engineering and Technology
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• 제31권2호
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• pp.172-181
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• 1999

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7.

• 대한수학회보
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• 제36권4호
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권3호
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Wind and Structures
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• 제16권6호
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• pp.561-577
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• 2013

Rational Functions are used to express the self-excited aerodynamic forces acting on a flexible structure for use in time-domain flutter analysis. The Rational Function Approximation (RFA) approach involves obtaining of these Rational Functions from the frequency-dependent flutter derivatives by using an approximation. In the past, an algorithm was developed to directly extract these Rational Functions from wind tunnel section model tests in free vibration. In this paper, an algorithm is presented for direct extraction of these Rational Functions from section model tests in forced vibration. The motivation for using forced-vibration method came from the potential use of these Rational Functions to predict aerodynamic loads and response of flexible structures at high wind speeds and in turbulent wind environment. Numerical tests were performed to verify the robustness and performance of the algorithm under different noise levels that are expected in wind tunnel data. Wind tunnel tests in one degree-of-freedom (vertical/torsional) forced vibration were performed on a streamlined bridge deck section model whose Rational Functions were compared with those obtained by free vibration for the same model.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 춘계학술대회 논문집
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• pp.299-304
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• 1996

This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.

• Wind and Structures
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• 제14권2호
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• pp.133-151
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• 2011

For a detailed investigation of the dynamic behaviour of slender bridges under wind action especially the motion-induced fluid forces should be available not only for harmonic motions but also for more general ones. If linear transfer behaviour is assumed, the force-displacement relation for almost arbitrary motions can be handled in the frequency domain using aerodynamic transfer functions. In aerospace engineering as well as in bridge engineering, these functions are usually approximated by special kinds of complex-valued rational functions which depend on complex frequencies. The quality of this approximation is evaluated for several bridge cross sections in this article. It is shown that rational functions are for some sections scarcely suitable to realistically represent the transfer behaviour of motion-induced aerodynamic forces for arbitrarily complex frequencies.

• 한국정밀공학회지
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• 제16권5호통권98호
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• 한국정밀공학회지
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• 제14권1호
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• pp.194-204
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• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 하계종합학술대회 논문집(3)
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• pp.17-20
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• 2002

This paper proposes a new 75 fuzzy model approximation method which reduces error in nonlinear fuzzy model approximation over the V-type decision rules. Employing rational Bezier curves used in computer graphics to represent curves or surfaces, the proposed method approximates the decision rule by constructing a tractable linear equation in the highly non-linear fuzzy rule interval. This algorithm is applied to the self-adjusting air cushion for spinal cord injury patients to automatically distribute the patient's weight evenly and balanced to prevent decubitus. The simulation results indicate that the performance of the proposed method is bettor than that of the conventional TS Fuzzy model in terms of error and stability.

• Wind and Structures
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• 제10권3호
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• pp.215-232
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• 2007

This paper presents an aeroelastic analysis procedure to highlight the influence of wind velocity on the structural damping and frequency of a long span cable-stayed bridge. Frequency dependent self-excited forces in terms of flutter derivatives are expressed as continuous functions using rational function approximation technique. The aeroelastically modified structural equation of motion is expressed in terms of frequency independent modal state-space parameters. The modal logarithmic dampings and frequencies corresponding to a particular wind speed are then determined from the eigen solution of the state matrix.