• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2A
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• pp.383-390
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• 2006

In this paper, a stochastic field that is compatible with Monte Carlo simulation is suggested for an expansion-based stochastic analysis scheme of weighted integral method. Through investigation on the way of affection of stochastic field function on the displacement vector in the series expansion scheme, it is noticed that the stochastic field adopted in the weighted integral method is not compatible with that appears in the Monte Carlo simulation. As generally recognized in the field of stochastic mechanics, the response variability is not a linear function of the coefficient of variation of stochastic field but a nonlinear function with increasing variability as the intensity of uncertainty is increased. Employing the stochastic field suggested in this study, the response variability evaluated by means of the weighted integral scheme is reproduced with high precision even for uncertain fields with moderately large coefficient of variation. Besides, despite the fact that only the first-order expansion is employed, an outstanding agreement between the results of expansion-based weighted integral method and Monte Carlo simulation is achieved.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.4B
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• pp.413-419
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• 2008

In this study, we develop analytical solutions for long waves propagating over several types of axis-symmetric topographies where the water depth varies in an arbitrary power of radial distance. The first type is a cylindrical island mounted on a shoal. The second type is a circular island. To get the solution, the methods of separation of variables, Taylor series expansion and Frobenius series are used. Developed analytical solutions are validated by comparing with previously developed analytical solutions. We also investigate various cases with different incident wave periods, radii of the shoal, and the powers of radial distance.

• Journal of Convergence for Information Technology
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• v.11 no.12
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• pp.14-21
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• 2021

In this paper, it is shown how the performance of the monopulse algorithm in the presence of an additive noise can be obtained analytically. In the previous study, analytic performance analysis based on the first-order Taylor series and the second-order Taylor series has been conducted. By adopting the third-order Taylor series, it is shown that the analytic performance based on the third-order Taylor series can be made closer to the performance of the original monopulse algorithm than the analytic performance based on the first-order Taylor series and the second-order Taylor series. The analytic MSE based on the third-order Taylor approximation reduces the analytic MSE error based on the second-order Taylor approximation by 89.5%. It also shows faster results in all cases than the Monte Carlo-based MSE. Through this study, it is possible to explicitly analyze the angle estimation ability of monopulse radar in an environment where noise jamming is applied.

• Journal of the Korea Convergence Society
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• v.13 no.1
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• pp.43-50
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• 2022

In this paper, it is shown how the performance of the monopulse algorithm in additive noise is evaluated. In the previous study, the performance analysis of the amplitude-comparison monopulse algorithm was conducted via the first-order and second-order Taylor expansion of four variables. By defining two new random variables from the four variables, it is shown that computational complexity associated with two random variables is much smaller than that associated with four random variables. Performance in terms of mean square error is analyzed from Monte-Carlo simulation. The scheme proposed in this paper is more efficient than that suggested in the previous study in terms of computational complexity. The expressions derived in this study can be utilized in getting analytic expressions of the mean square errors.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.145-151
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• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.31-39
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• 1985

Using the tensor elastic Green functions an exact integral equation is formulated for two anisotropic precipitates embedded in an infinite anisotropic matrix; the matrix is subjected to an applied strain field or the precipitates undergo a stress-free transformation strain. This equation is reduced to an infinite system of algebraic equations by expanding the strains in Taylor series about the two points within each precipitate, and an approximation of the strain distributions within the two spherical precipitates is obtained by truncating the higher order terms. Since the present method requires no symmetry conditio between the two shperical precipitates, it is possible to obtain the strain distribution within the precipitates when the elastic constants and/or the sizes of the precipitates are different each other. The strains are expanded about arbitrary points, giving more accurate distributions of the strains than those presented elsewhere. The present method can be directly estended to the case of more than two spherical precipitates.

• The Journal of the Acoustical Society of Korea
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• v.33 no.4
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• pp.232-237
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• 2014

A passive sonar of warship is composed of several directional or omni-directional sensors. In order to model the acoustic signal received into a warship sonar, the wave propagation modeling is usually required from arbitrary noise source to all sensors equipped to the sonar. However, the full calculation for all sensors is time-consuming and the performance of sonar simulator deteriorates. In this study, we suggest an asymptotic method to estimate the sonar signal arrived to sensors adjacent to the reference sensor, where it is assumed that all information of eigenrays is known. This method is developed using Taylor series for the time delay of eigenray and similar to Fraunhofer and Fresnel approximation for sonar aperture. To validate the proposed method, some numerical experiments are performed for the passive sonar. The approximation when the second-order term is kept is vastly superior. In addition, the error criterion for each approximation is provided with a practical example.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.6
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• pp.580-598
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• 1987

This paper presents a method to realize the sequential multiple-valued Logic on Galois field. First, We develop so that Taylor series can be corresponded the irreducible polynomial to realize over the finite field, and produce the matrix. This paper object expanded a basic concept of the conbinational Logic circuit so as to apply in the sequential Logic circuit. First of all, We suggest a theory for constructing sequential multiple-valued Logic circuit. Then, We realized the construction with the single input and the multi-output that expanded its function construction. In case of the multi-output, the circuit process by the partition function concept as the mutual independent. This method can be reduced a enormous computer course to need a traditional extention that designed the sequential multi-valued Logic circuit.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.53-60
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• 1995

A multi-leg spread mooring system for floating offshore structures is important, but the multi-leg static analysis is complicated due to the nonlinear behavior of each line and the effect of current which affects each line differently. The pretensioned position of the multi-leg mooring system obtained from the static equilibrium condition changes into a different position due to external loads and current. In this paper, the new position and the static tension at each line are caculated. The relation between the initial static equilibrium position and the new position due to the external loads is expressed in terms of the Taylor's series expansion. The Runge-Kutta $4^{th}$ method is employed in analyzing the 3-dimensional static cable nonlinear equations.

• Journal of Power System Engineering
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• v.6 no.1
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• pp.96-101
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• 2002

In this paper, we address the problem of controlling an end-effector to track and grab a moving target using the visual servoing technique. A visual servo mechanism based on the image-based servoing principle, is proposed by using visual feedback to control an end-effector without calibrated robot and camera models. Firstly, we consider the control problem as a nonlinear least squares optimization and update the joint angles through the Taylor Series Expansion. And to track a moving target in real time, the Jacobian estimation scheme(Dynamic Broyden's Method) is used to estimate the combined robot and image Jacobian. Using this algorithm, we can drive the objective function value to a neighborhood of zero. To show the effectiveness of the proposed algorithm, simulation results for a six degree of freedom robot are presented.