• Title/Summary/Keyword: Block Diagonal Matrix

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Numerical Heat Transfer and Fluid Flow of Brake Disk-lining for Rolling Stock (철도차량용 제동 디스크-라이닝의 열유동 해석)

  • 남성원;조장형
    • Proceedings of the KSR Conference
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    • 1999.11a
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    • pp.93-98
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    • 1999
  • Numerical simulation is conducted to clarify the heat transfer and fluid flow characteristics of brake disk-lining for rolling stock. Multiple rotational reference frame, k-epsilon turbulent model and SIMPLE algorithm based on finite volume method are used to solve the physical disk-lining model. The governing equations are solved by TDMA(TriDiagonal Matrix Algorithm) with line-by-line method and block correction, From the results of simulation, the characteristics of cooling pattern is strongly affected by the grooves in lining. The face lift of lining affects on the temperature distribution of rear surface of lining as well as the front surface of that. Due to the grooves in lining, it will be expected to extend the maintenance life circle of lining.

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Methods of Weighting Matrices Determination of Moving Double Poles with Jordan Block to Real Poles By LQ Control (LQ 제어로 조단블록이 있는 중근을 실근으로 이동시키는 가중행렬 결정 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.6
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    • pp.634-639
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    • 2020
  • In general, the stability and response characteristics of the system can be improved by changing the pole position because a nonlinear system can be linearized by the product of a 1st and 2nd order system. Therefore, a controller that moves the pole can be designed in various ways. Among the other methods, LQ control ensures the stability of the system. On the other hand, it is difficult to specify the location of the pole arbitrarily because the desired response characteristic is obtained by selecting the weighting matrix by trial and error. This paper evaluated a method of selecting a weighting matrix of LQ control that moves multiple double poles with Jordan blocks to real poles. The relational equation between the double poles and weighting matrices were derived from the characteristic equation of the Hamiltonian system with a diagonal control weighting matrix and a state weighting matrix represented by two variables (ρd, ϕd). The Moving-Range was obtained under the condition that the state-weighting matrix becomes a positive semi-definite matrix. This paper proposes a method of selecting poles in this range and calculating the weighting matrices by the relational equation. Numerical examples are presented to show the usefulness of the proposed method.

An Alternative Model for Determining the Optimal Fertilizer Level (수도(水稻) 적정시비량(適正施肥量) 결정(決定)에 대한 대체모형(代替模型))

  • Chang, Suk-Hwan
    • Korean Journal of Soil Science and Fertilizer
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    • v.13 no.1
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    • pp.21-32
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    • 1980
  • Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

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Rapid Speaker Adaptation Based on MAPLR with Adaptive Hybrid Priors Estimated from Reference Speakers (참조화자로부터 추정된 적응적 혼성 사전분포를 이용한 MAPLR 고속 화자적응)

  • Song, Young-Rok;Kim, Hyung-Soon
    • The Journal of the Acoustical Society of Korea
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    • v.30 no.6
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    • pp.315-323
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    • 2011
  • This paper proposes two methods of estimating prior distribution to improve the performance of rapid speaker adaptation based on maximum a posteriori linear regression (MAPLR). In general, prior distribution of the transformation matrix used in MAPLR adaptation is estimated from all of the training speakers who are employed to construct the speaker-independent model, and it is applied identically to all new speakers. In this paper, we propose a method in which prior distribution is estimated from a group of reference speakers, selected using adaptation data, so that the acoustic characteristics of the selected reference speakers may be similar to that of the new speaker. Additionally, in MAPLR adaptation with block-diagonal transformation matrix, we propose a method in which the mean matrix and covariance matrix of prior distribution are estimated from two groups of transformation matrices obtained from the same training speakers, respectively. To evaluate the performance of the proposed methods, we examine word accuracy according to the number of adaptation words in the isolated word recognition task. Experimental results show that, for very limited adaptation data, statistically significant performance improvement is obtained in comparison with the conventional MAPLR adaptation.

Time- and Frequency-Domain Block LMS Adaptive Digital Filters: Part Ⅱ - Performance Analysis (시간영역 및 주파수영역 블럭적응 여파기에 관한 연구 : 제 2 부- 성능분석)

  • Lee, Jae-Chon;Un, Chong-Kwan
    • The Journal of the Acoustical Society of Korea
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    • v.7 no.4
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    • pp.54-76
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    • 1988
  • In Part Ⅰ of the paper, we have developed various block least mean-square (BLMS) adaptive digital filters (ADF's) based on a unified matrix treatment. In Part Ⅱ we analyze the convergence behaviors of the self-orthogonalizing frequency-domain BLMS (FBLMS) ADF and the unconstrained FBLMS (UFBLMS) ADF both for the overlap-save and overlap-add sectioning methods. We first show that, unlike the FBLMS ADF with a constant convergence factor, the convergence behavior of the self-orthogonalizing FBLMS ADF is governed by the same autocorrelation matrix as that of the UFBLMS ADF. We then show that the optimum solution of the UFBLMS ADF is the same as that of the constrained FBLMS ADF when the filter length is sufficiently long. The mean of the weight vector of the UFBLMS ADF is also shown to converge to the optimum Wiener weight vector under a proper condition. However, the steady-state mean-squared error(MSE) of the UFBLMS ADF turns out to be slightly worse than that of the constrained algorithm if the same convergence constant is used in both cases. On the other hand, when the filter length is not sufficiently long, while the constrained FBLMS ADF yields poor performance, the performance of the UFBLMS ADF can be improved to some extent by utilizing its extended filter-length capability. As for the self-orthogonalizing FBLMS ADF, we study how we can approximate the autocorrelation matrix by a diagonal matrix in the frequency domain. We also analyze the steady-state MSE's of the self-orthogonalizing FBLMS ADF's with and without the constant. Finally, we present various simulation results to verify our analytical results.

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A STUDY ON NUMERICAL SIMULATION OF TOWED LOW-TENSION CABLE WITH NONUNIFORM CHARACTERISTICS (불균일 단면을 갖는 저장력 예인케이블에 관한 수치해석적 연구)

  • Jung, Dong-Ho;Park, Han-Il
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.05a
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    • pp.161-166
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    • 2002
  • Low-tension cables have been increasingly used in recent years due to deep-sea developments and the advent of synthetic cables. In the case of low-tension cables, large displacements may happen due to relatively small restoring forces of tension and thus the effects of fluid and geometric non-linearities become predominant. In this study, three-dimensional (3-D) dynamic behavior of a towed low-tension cable with non-uniform characteristics is numerically analyzed by considering fluid and geometric non-linearities and bending stiffness. A Fortran program is developed by employing a finite difference method. In the algorithm, an implicit time integration and Newton-Raphson iteration are adopted. For the calculation of huge size of matrices, block tri-diagonal matrix method is applied, which is much faster than the well-known Gauss-Jordan method in two point boundary value problems. Some case studies are carried out and the results of numerical simulations are compared with a in-house program of WHOI Cable with good agreements.

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Blind Color Image Watermarking Based on DWT and LU Decomposition

  • Wang, Dongyan;Yang, Fanfan;Zhang, Heng
    • Journal of Information Processing Systems
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    • v.12 no.4
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    • pp.765-778
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    • 2016
  • In watermarking schemes, the discrete wavelet transform (DWT) is broadly used because its frequency component separation is very useful. Moreover, LU decomposition has little influence on the visual quality of the watermark. Hence, in this paper, a novel blind watermark algorithm is presented based on LU transform and DWT for the copyright protection of digital images. In this algorithm, the color host image is first performed with DWT. Then, the horizontal and vertical diagonal high frequency components are extracted from the wavelet domain, and the sub-images are divided into $4{\times}4$ non-overlapping image blocks. Next, each sub-block is performed with LU decomposition. Finally, the color image watermark is transformed by Arnold permutation, and then it is inserted into the upper triangular matrix. The experimental results imply that this algorithm has good features of invisibility and it is robust against different attacks to a certain degree, such as contrast adjustment, JPEG compression, salt and pepper noise, cropping, and Gaussian noise.

Analysis of Large-Scale Network using a new Network Tearing Method (새로운 분할법에 의한 회로망해석)

  • 김준현;송현선
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.12 no.3
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    • pp.267-275
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    • 1987
  • This paper concerns a study on the theory of tearing which analyzes a large scale network by partitioning it into a number of small subnetworks by cutting through some of the existing nodes and branches in the network. By considering of the relationship its voltage and current of node cutting before and after, the consititutive equations of tearing method is equvalent to renumbering the nodes of untorn network equations. Therefore the analysis of network is conveniently applied as same algorithm that is used in untorn network. Also the proposed nodal admittnace matrix is put in block diagonal form, therefore this method permit parallel processing analysis of subnetworks. 30 nodes network was tested and the effectiveness of the proposed algorithm was proved.

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A Heuristic Approach to Machine-Part Grouping Cellular Manufacturing (셀 생산방식에서 기계-부품 그룹을 형성하는 발견적 해법)

  • Kim Jin-Seock;Lee Jong-Sub;Kang Maing-Kyu
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.28 no.1
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    • pp.121-128
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    • 2005
  • This paper proposes the heuristic approach for the generalized GT(Group Technology) problem to consider the restrictions which are given the number of cell, maximum number of machines and minimum number of machines. This approach is classified into two stages. In the first stage, we use the similarity coefficient method which is proposed and calculate the similarity values about each pair of all machines and align these values in descending order. If two machines which is selected is possible to link the each other on the edge of machine cell and they don't have zero similarity value, then we assign the machines to the machine cell. In the second stage, it is the course to form part families using proposed grouping efficacy. Finally, machine-part incidence matrix is realigned to block diagonal structure. The results of using the proposed approach are compared to the Modified p-median model.

A Numerical and Experimental Study on Dynamics of A Towed Low-Tension Cable

  • Jung, D.H.;Park, H.I.;Koterayama, W.
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.191-196
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    • 2002
  • The paper presents a numerical and experimental investigation on dynamic behaviors of a towed low tension cable. In the numerical study, an implicit finite difference algorithm is employed for three-dimensional cable equations. Fluid and geometric non-linearity and bending stiffness are considered and solved by Newton-Raphson iteration. Block tri-diagonal matrix method is applied for the fast calculation of the huge size of matrices. In order to verify the numerical results and to see real physical phenomena, an experiment is carried out for a 6m cable in a deep and long towing tank. The cable is towed in two different ways; one is towed at a constant speed and the other is towed at a constant speed with top end horizontal oscillations. Cable tension and shear forces are measured at the top end. Numerical and experimental results are compared with good agreements in most cases but with some differences in a few cases. The differences are due to drag coefficients caused by vortex shedding. In the numerical modeling, non-uniform element length needs to be employed to cope with the sharp variation of tension and shear forces at near top end.

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