• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1557-1560
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• 2003

This paper presents the effect of varying boundary conditions such as ground subsidence on failure prediction of buried pipelines. The first order Taylor series expansion of the limit state function is used in order to estimate the probability of failure associated with three cases of ground subsidence. We estimate the distribution of stresses imposed on the buried pipelines by varying boundary conditions and calculate the probability of pipelines with von-Mises failure criterion. The effects of random variables such as pipe diameter, internal pressure, temperature, settlement width, load for unit length of pipelines, material yield stress and thickness of pipeline on the failure probability of the buried pipelines are also systematically studied by using a failure probability model for the pipeline crossing a ground subsidence region.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.1097-1100
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• 1999

Due to the significant computation of full search in motion estimation, extensive research in fast motion estimation algorithms has been carried out. However, most of the algorithms have the degradation in predicted images compared with the full search algorithm. To reduce an amount of significant computation while keeping the same prediction quality of the full search, we propose a fast block-matching algorithm based on gradient magnitude of reference block without any degradation of predicted image. By using Taylor series expansion, we show that the block matching errors between reference block and candidate block are proportional to the gradient magnitude of matching block. With the derived result, we propose fast full search algorithm with adaptively determined scan direction in the block matching. Experimentally, our proposed algorithm is very efficient in terms of computational speedup and has the smallest computation among all the conventional full search algorithms. Therefore, our algorithm is useful in VLSI implementation of video encoder requiring real-time application.

• Journal of Ship and Ocean Technology
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• v.11 no.4
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• pp.21-28
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• 2007

Recently the importance of the utilization of engineering data is gradually increasing. Engineering data contains the experiences and know-how of experts. Data mining technique is useful to extract knowledge or information from the accumulated existing data. This paper deals with generating optimal polynomials using genetic programming (GP) as the module of Data Mining system. Low order Taylor series are used to approximate the polynomial easily as a nonlinear function to fit the accumulated data. The overfitting problem is unavoidable because in real applications, the size of learning samples is minimal. This problem can be handled with the extended data set and function node stabilization method. The Data Mining system for the ship design based on polynomial genetic programming is presented.

• ETRI Journal
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• v.34 no.5
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• pp.684-689
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• 2012

A mode-singular-value-decomposition (SVD) maximum likelihood (ML) estimation procedure is proposed for the source localization problem under an additive measurement error model. In a practical situation, the noise variance is usually unknown. In this paper, we propose an algorithm that does not require the noise covariance matrix as a priori knowledge. In the proposed method, the weight is derived by the inverse of the noise magnitude square in the ML criterion. The performance of the proposed method outperforms that of the existing methods and approximates the Taylor-series ML and Cram$\acute{e}$r-Rao lower bound.

• Journal of Power System Engineering
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• v.19 no.3
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• pp.42-47
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• 2015

This paper studies on the design of a servo controller for an antilock brake system(ABS) based on the car tire model. First, a nonlinear differential equation of the car tire is constructed and its linearization model is obtained by Taylor's series. Second, a servo controller based on the mathematical model is analytically designed to obtain the maximum brake force, where the tire velocity and the slip ratio of car tire are respectively controlled to the given command values. Third, it is theoretically shown that the proposed control algorithm has good usefulness in ABS.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.645-655
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• 2011

Chandrasekar et al. (2004) introduced a generalized Type-II hybrid censoring. In this paper, we propose generalized doubly Type-II hybrid censoring. In addition, this paper presents the statistical inference on the scale parameter for the half logistic distribution when samples are generalized doubly Type-II hybrid censoring. The approximate maximum likelihood(AMLE) method is developed to estimate the unknown parameter. The scale parameter is estimated by the AMLE method using two di erent Taylor series expansion types. We compar the AMLEs in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20; 30; 40 and various censored samples. The $AMLE_I$ is better than $AMLE_{II}$ in the sense of the MSE.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.427-432
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• 2003

An analytical method to predict the flexural behavior of composite girder is presented in which the early-age properties of concrete are specified including maturing of elastic modulus, creep and shrinkage. The time dependent constitutive relation accounting for the early-age concrete properties is derived in an incremental format by expanding the total form of stress-strain relation by the first order Taylor series with respect to the reference time. The sectional analysis calculates the axial and curvature strains based on the force and moment equilibriums. The deflection curve of the box girder approximated by the quadratic polynomial function is calculated by applying to the proper boundary conditions in the consecutive segments. Numerical applications are made for the 3-span double composite steel box girders which is a composite bridge girder filled with concrete at the bottom of the steel box in the negative moment region. The one dimensional finite element analysis results are compared with those of the three dimensional finite element analysis and the analytical method based on the sectional analysis. Close agreement is observed among the three methods.