• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• Journal of Ocean Engineering and Technology
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• v.19 no.1 s.62
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• pp.64-70
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• 2005

Target Strength(TS) is an important factor for the detection of the target in an active sonar system: thus the numerical model for the prediction of TS is widely being developed. For the frequency range of several kHz, the most important scattering mechanism is known to be specular reflection, which is largely affected by the geometrical shape of the target. In this paper, a numerical algorithm to predict TS is developed based on the Kirchhoff approximation which is computationally efficient. The developed algorithm is applied to the canonical targets of simple shapes, for which the analytical solutions exist. The numerical results show good agreement with the analytical solutions. Also, the algorithm is applied to more complex scatterers, and is compared with the experimental data obtained in the water tank experiment for the purpose of verifying the developed numerical model. Discussions on the effect of spatial sampling and other aspects of numerical m odeling are presented.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.2
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• pp.77-87
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• 2000

The water entry forces acting on an air-dropped torpedo are of the restrictions on launch speed and launch altitude, because it could cause the structural damage to components of torpedo. Therefore, it is necessary to estimate the water entry forces with confidence according to launch conditions. In this study, an approximation method for water entry forces is presented, and the results using this approximation are compared with those of other numerical methods. The magnitude and duration of impact forces estimated by the present approximation agree with those of impact by the analysis of ideal or viscous flow. This method can give useful tools to select the launch in initial design stage.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.347-357
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• 2011

In this paper, we propose an approximation to the overshoot in M/$E_n$/1 queues. Overshoot means the size of excess over the threshold when the workload process of an M/$E_n$/1 queue exceeds a prespecified threshold. The distribution, $1^{st}$ and $2^{nd}$ moments of overshoot have an important role in solving some kind of optimization problems. For the approximation to the overshoot, we propose a formula that is a convex sum of the service time distribution and an exponential distribution. We also do a numerical study to check how exactly the proposed formula approximates the overshoot.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.1
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• pp.33-41
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• 2002

In this paper, we present a frequency weighted model reduction using LMIs for minimizing the H$\infty$ weighted model error compared with the methods of frequency weighted balanced truncation and frequency weighted Hankel norm approximation. The proposed algorithm, its form is equal to the sufficient condition of performance preserving controller approximation, is based on an iterative two-step LMI scheme induced from bound real lemma. So, it can be applied to the problem of the performance preserving controller approximation. The controller reduction is useful in a practical control design and ensures its easy implementation and high reliability The validity of the proposed algorithm is shown through numerical examples. Additionaly, we extend the proposed algorithm to performance preserving controller approximation by applying to the HIMAT(highly maneuverable aircraft technology) system.

• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.876-888
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• 2001

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables is η, the proposed method requires only 2η+1 design points for one approximation, which are a center point and tow additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1423-1431
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• 2001

Based on the exponential intervening variable, a new two-point approximation method is presented. This introduces the shifting level into each exponential intervening variable to avoid the lack of def inition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Journal of electromagnetic engineering and science
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• v.10 no.4
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• pp.296-302
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• 2010

This paper proposes an approximate equation for broad bandwidth conditions in an antenna feeding probe design with a cylindrical magneto material structure (CMMS). The bandwidth calculation has been conducted according to the relation between the distance ($r_m$) between the magneto material and feeding probe, and the magneto material thickness ($t_m$) for a given ${\mu}_r$. The bandwidth of a proposed antenna with CMM feeding structure is improved about 182 %, when ${\mu}_r=20+j0.001$, in comparison with the bandwidth of an antenna without CMMS. The maximum error extent between the bandwidth calculated by the approximation equation and by the numerical calculation of the proposed antenna is about $\pm$3.2 % for ${\mu}_r=10+j0.001$. The approximation equation proposed in this study can solve the conventional problem of the complex process and the long time required for reiterative calculation, and allow simple and precise design with prediction. The accuracy of an approximated equation is compared with the results calculated by a commercial tool and verified by reasonable agreement between them.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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• pp.490-495
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• 2007

This research aims to examine accuracy and efficiency of the first four moments corresponding to mean, standard deviation, skewness, and kurtosis, which are estimated by a function approximation moment method (FAMM). In FAMM, the moments are estimated from an approximating quadratic function of a system response function. The function approximation is performed on a specially selected experimental region for accuracy, and the number of function evaluations is taken equal to that of the unknown coefficients for efficiency. For this purpose, three error-minimizing conditions are utilized and corresponding canonical experimental regions constructed accordingly. An interpolation function is then obtained using a D-optimal design and then the first four moments of it are obtained as the estimates for the system response function. In order to verify accuracy and efficiency of FAMM, several non-linear examples are considered including a polynomial of order 4, an exponential function, and a rational function. The moments calculated from various coefficients of variation show very good accuracy and efficiency in comparison with those from analytic integration or the Monte Carlo simulation and the experimental design technique proposed by Taguchi and updated by D'Errico and Zaino.