• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• 한국정밀공학회지
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• 제15권4호
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• pp.134-140
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• 1998

The authors have shown that the performance of discrete-time observer-based monitoring systems can be represented by the performance index k$_2$(P) (condition number of the eigensystem P of the observer matrix in terms of L$_2$ norm). The observers with the minimized performance index can be defined as robust observers in the sense that the observer performance can be guaranteed in harsh environments. In this paper, based on the performance index, a design methodology for the robust discrete-time observer is developed. Similar to the continuous-time case, the methodology determines the structure and eigenvalues of the observer matrix simultaneously. A complete design procedure is given for single-output case and is illustrated with a spindle-driver example. The simulation results demonstrate the improved performance compared with a traditional pole-placement observer technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• 대한전기학회논문지
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• 제32권2호
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• pp.43-49
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• 1983

In this study, model simplification problem using singular perturbation technique is considered. The correctness and errors of simplified model which is obtained by the use of this technique, depends upon the order and the time scaling factor of the simplified model But, unfortunately, there is no explicit criteria for selections of these parameters. In this paper, error equations are derived and expanded by using the useful properties of $L_2$-norm. Then, new criteria for selecting the order of the simplified model and time scaling factor with respect to error bound are suggested. Since these criteria, newly proposed in this study, have strong concern about error bound, it can be used to choose the minimum order of the simplified model and time scaling factor with respect to given error bound. Conversely, if the order of the simplified model and time scaling factor are given, the error induced by the simplification can also be computed easily.

• 대한전자공학회논문지SP
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• 제39권1호
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• pp.32-39
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• 2002

영상 압축을 위한 기법인 벡터 양자 부호화는 입력 벡터와 가장 근사한 부호어를 찾기 위해 일반적으로 상당히 많은 계산량을 요구한다. 본 논문은 벡터 양자 부호화 과정을 고속 처리를 위한 새로운 탐색 기법을 제안한다. 먼저, 탐색 과정에서의 불필요한 정합 연산들을 대폭 줄이기 위해 부호책의 효과적인 기하학적 구조에 기반한 강력한 후보 제거 조간을 유도한다. 그런 다음, 그 후보 제거 조건을 이용한 고속 탐색 기법을 제안한다. 모의 실험 결과는 적은 전처리 연산과 메모리만을 사용하는 제안한 기법이 전역 탐색 기법과 동일한 부호화 성능을 유지하면서 부호화 시간을 대폭 줄일 수 있음을 보인다. 또한 기존 탐색 기법들과 비교할 때, 제안한 기법의 성능이 매우 우수함을 알 수 있다.

• 전자공학회논문지SC
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• 제40권2호
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• pp.10-18
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• 2003

본 논문은 시간지연을 갖는 퍼지 시스템에 대한 보장 비용과 H/sub ∞/ 외란감쇄 성능을 갖는 퍼지 필터링 문제를 다룬다. 본 연구는 외란감쇄에 대한 확장 L₂ 노옴 제한조건과 LQ 비용함수의 성능 상한치 제한조건을 만족하는 필터링 설계 방법이다. Lyapunov 함수를 이용하여 필터의 존재성에 대한 충분조건을 유도하고 선형행렬부등식(LMI: linear matrix inequality)으로 나타낸다. 필터 설계는 LMI 해를 구함으로써 바로 구할 수 있다. 제안한 방법의 설계 과정을 설명하기 위한 시뮬레이션 예제를 또한 나타낸다.

• 한국통신학회논문지
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• 제30권12C호
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• pp.1231-1238
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• 2005

본 논문에서는 영상 백터 양자화를 위한 새로운 고속 부호화 기법을 제안하는데, 제안 기법은 다차원의 참조 표로 복수 특징의 부분 거리를 사용한다. 복수 특징을 사용하는 기존 기법은 탐색 순서와 연산 과정을 고려할 때 복수 특징을 단계적으로 처리한다. 반면에 제안 기법은 참조 표를 사용하여 복수 특징들을 동시에 활용한다. 본 논문에서는 가용한 수준의 메모리를 위해 테두리 효과를 고려하는 참조 표의 구성 방법과 참조 표의 부분 거리를 활용하며 현재의 탐색을 중지하는 방법을 상세하게 기술한다. 시뮬레이션 결과는 제안 기법의 효율성을 확인시켜 주는데, 부호책 크기가 256일 때 제안 기법은 OHTPDS 기법이나 $M-L_2NP$ 기법 등과 같이 최근에 제안된 기법들이 요구하는 연산량의 $70\%$ 수준까지 연산량을 감소시킨다. 가용한 수준의 전처리와 메모리를 사용함으로써 제안 기법은 전체탐색 기법과 통일한 화질을 유지하면서 전체 탐색 기법이 요구하는 연산량의 $2.2\%$ 이하로 연산량을 감소시킨다.

• 한국지하수토양환경학회지:지하수토양환경
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• 제18권3호
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• pp.82-92
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• 2013

This study has investigated naturally occurring radioactive materials (N.O.R.M; $^{238}U$, $^{222}Rn$) for 353 drinking groundwater wells in metamorphic rock areas in Korea. Uranium concentrations ranged from N.D (not detected) to 563.56 ${\mu}g/L$ (median value, 0.68 ${\mu}g/L$) and radon concentrations ranged from 108 to 11,612 pCi/L (median value, 1,400 pCi/L). Uranium and radon concentrations in the groundwater generally are similar to USA with similar geological setting. Uranium concentrations in 9 wells (2.6%) exceeded 30 ${\mu}g/L$, which is the maximum contaminant level (MCL) by the US environmental protection agency (EPA), radon concentrations in 46 wells (13%) exceeded 4,000 pCi/L, which is the Alternative MCL (AMCL) by the US.EPA. The log-log correlation coefficient between uranium and radon was 0.32. The correlation coefficient between uranium and pH was 0.12 and the correlation coefficient between radon and temperature was -0.01. The correlation coefficient between uranium and $HCO_3$ was 0.09 and the correlation coefficient between uranium and Ca was 0.11. The median value of uranium was high Chung-Buk (1.78 ${\mu}g/L$), Gyeong-Buk (1.37 ${\mu}g/L$), In-Cheon (1.06 ${\mu}g/L$) for each province. On the other hand, the median value of radon was high In-Cheon (2,962 pCi/L), Chung-Buk (2,339 pCi/L), Jeon-Buk (2,165 pCi/L) for each province. Jeon-Buk for log-log correlation coefficient is the highest (0.63) among provinces.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2001년도 추계학술대회(한국공작기계학회)
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• pp.313-318
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• 2001

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on $L_2-norm$ of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters. In designing Kalman filters for small order systems, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 추계학술대회 논문집 학회본부 B
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• pp.494-496
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for uncertain linear systems with saturating actuators. We consider a general saturating actuator and employ the additive decomposition to deal with it effectively. And the considered uncertainty is the unstructured uncertainty which is only known its norm bound. Based on Linear Matrix Inequality(LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.