• Title/Summary/Keyword: Eigenvector Method

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Improved Algebraic Method for Computing Eigenpair Sensitivities of Damped Systems (감쇠 시스템의 고유진동수와 모드의 민감도를 계산하기 위한 대수적 방법의 개선)

  • 조홍기;박선규;이인원
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2000.04b
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    • pp.277-285
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    • 2000
  • This paper presents a very simple procedure for determining the sensitivities of the eigenpairs of damped vibratory system with distinct eigenvalues. The eigenpairs derivatives can be obtained by solving algebraic equation with a symmetric coefficient matrix whose order is (n+1)×(n+1), where n is the number of degree of freedom the method is an improvement of recent work by I. W. Lee, D. O. Kim and G. H. Junng; the key idea is that the eigenvalue derivatives and the eigenvector derivatives are obtained at once via only one algebraic equation, instead of using two equations separately as like in Lee and Jung's method Of course, the method preserves the advantages of Lee and Jung's method.

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Structural Topology Optimization for the Natural Frequency of a Designated Mode

  • Lim, O-Kaung;Lee, Jin-Sik
    • Journal of Mechanical Science and Technology
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    • v.14 no.3
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    • pp.306-313
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    • 2000
  • The homogenization method and the density function method are common approaches to evaluate the equivalent material properties for design cells composed of matter and void. In this research, using a new topology optimization method based on the homogenized material with a penalty factor and the chessboard prevention strategy, we obtain the optimal layout of a structure for the natural frequency of a designated mode. The volume fraction of nodes of each finite element is chosen as the design variable and a total material usage constraint is imposed. In this paper, the subspace method is used to evaluate the eigenvalue and its corresponding eigenvector of the structure for the designated mode and the recursive quadratic programming algorithm, PLBA algorithm, is used to solve the topology optimization problem.

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Calculation of Degenerated Eigenmodes with Modified Power Method

  • Zhang, Peng;Lee, Hyunsuk;Lee, Deokjung
    • Nuclear Engineering and Technology
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    • v.49 no.1
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    • pp.17-28
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    • 2017
  • The modified power method has been studied by many researchers to calculate the higher eigenmodes and accelerate the convergence of the fundamental mode. Its application to multidimensional problems may be unstable due to degenerated or near-degenerated eigenmodes. Complex eigenmode solutions are occasionally encountered in such cases, and the shapes of the corresponding eigenvectors may change during the simulation. These issues must be addressed for the successful implementation of the modified power method. Complex components are examined and an approximation method to eliminate the usage of the complex numbers is provided. A technique to fix the eigenvector shapes is also provided. The performance of the methods for dealing with those aforementioned problems is demonstrated with two dimensional one group and three dimensional one group homogeneous diffusion problems.

Convergence Decision Method Using Eigenvectors of QR Iteration (QR 반복법의 고유벡터를 이용한 수렴 판단 방법)

  • Kim, Daehyun;Lee, Jingu;Jeong, Seonghee;Lee, Jaeeun;Kim, Younglok
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.41 no.8
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    • pp.868-876
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    • 2016
  • MUSIC (multiple signal classification) algorithm is a representative algorithm estimating the angle of arrival using the eigenvalues and eigenvectors. Generally, the eigenvalues and eigenvectors are obtained through the eigen-analysis, but this analysis requires high computational complexity and late convergence time. For this reason, it is almost impossible to construct the real-time system with low-cost using this approach. Even though QR iteration is considered as the eigen-analysis approach to improve these problems, this is inappropriate to apply to the MUSIC algorithm. In this paper, we analyze the problems of conventional method based on the eigenvalues for convergence decision and propose the improved decision algorithm using the eigenvectors.

Image quality enhancement using signal subspace method (신호 부공간 기법을 이용한 영상화질 향상)

  • Lee, Ki-Seung;Doh, Won;Youn, Dae-Hee
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.33B no.11
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    • pp.72-82
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    • 1996
  • In this paper, newly developed algorithm for enhancing images corrupted by white gaussian noise is proposed. In the method proposed here, image is subdivided into a number of subblocks, and each block is separated into cimponents corresponding to signal and noise subspaces, respectively through the signal subspace method. A clean signal is then estimated form the signal subspace by the adaptive wiener filtering. The decomposition of noisy signal into noise and signal subspaces in is implemented by eigendecomposition of covariance matrix for noisy image, and by performing blockwise KLT (karhunen loeve transformation) using eigenvector. To reduce the perceptual noise level and distortion, wiener filtering is implementd by adaptively adjusting noise level according to activity characteristics of given block. Simulation results show the effectiveness of proposed method. In particular, edge bluring effects are reduced compared to the previous methods.

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Improved Algebraic Method for Computing Eigenpair Sensitivities of Damped System (감쇠 시스템의 고유진동수와 모드의 미분을 구하기 위한 대수적 방법의 개선)

  • Jo, Hong-Ki;Ko, Man-Gi;Lee, In-Won
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.501-507
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    • 2000
  • This paper presents a very simple procedure for determining the sensitivities of the eigenpairs of damped vibratory system with distinct eigenvalues. The eigenpairs derivatives can be obtained by solving algebraic equation with a symmetric coefficient matrix whose order is (n+1) ${\times}$ (n+1), where n is the number of degree of freedom the mothod is an improvement of recent work by I. W. Lee, D. O. Kim and G. H. Jung; the key idea is that the eigenvalue derivatives and the eigenvector derivatives are obtained at once via only one algebraic equation, instead of using two equations separately as like in Lee and Jung's method. Of course, the method preserves the advantages of Lee and Jung's method.

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Beamforming for Downlink Multiuser MIMO Time-Varying Channels Based on Generalized Eigenvector Perturbation

  • Yu, Heejung;Lee, Sok-Kyu
    • ETRI Journal
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    • v.34 no.6
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    • pp.869-878
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    • 2012
  • A beam design method based on signal-to-leakage-plus-noise ratio (SLNR) has been recently proposed as an effective scheme for multiuser multiple-input multiple-output downlink channels. It is shown that its solution, which maximizes the SLNR at a transmitter, can be simply obtained by the generalized eigenvectors corresponding to the dominant generalized eigenvalues of a pair of covariance matrices of a desired signal and interference leakage plus noise. Under time-varying channels, however, generalized eigendecomposition is required at each time step to design the optimal beam, and its level of complexity is too high to implement in practical systems. To overcome this problem, a predictive beam design method updating the beams according to channel variation is proposed. To this end, the perturbed generalized eigenvectors, which can be obtained by a perturbation theory without any iteration, are used. The performance of the method in terms of SLNR is analyzed and verified using numerical results.

Analysis of Eigenderivative for the Non-Proportional Damped Structure Using the Iterative Method of the Sensitivity Coefficient (감도계수 반복법을 이용한 비비례감쇠계의 고유치 및 고유벡터 변화량 해석)

  • Lee Jung-Youn
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.7 s.250
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    • pp.750-756
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    • 2006
  • This study predicts the modified eigenvectors and eigenvalues of the non-proportional damped structure due to the change in the mass, damping and stiffness of structure by iterative method of the sensitivity coefficient using the original dynamic characteristic. The method is applied to the non-proportional damped 3 degree of freedom system by modifying the mass, damping and stiffness. The predicted dynamic characteristics are showed a good agreement with these from the structural reanalysis using the modified mass, damping and stiffness.

A Study for Obtaining Weights in Pairwise Comparison Matrix in AHP

  • Jeong, Hyeong-Chul;Lee, Jong-Chan;Jhun, Myoung-Shic
    • The Korean Journal of Applied Statistics
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    • v.25 no.3
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    • pp.531-541
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    • 2012
  • In this study, we consider various methods to estimate the weights of a pairwise comparison matrix in the Analytic Hierarchy Process widely applied in various decision-making fields. This paper uses a data dependent simulation to evaluate the statistical accuracy, minimum violation and minimum norm of the obtaining weight methods from a reciprocal symmetric matrix. No method dominates others in all criteria. Least squares methods perform best in point of mean squared errors; however, the eigenvectors method has an advantage in the minimum norm.

A REFINED SEMI-ANALYTIC DESIGN SENSITIVITIES BASED ON MODE DECOMPOSITION AND NEUMANN SERIES IN REDUCED SYSTEM (축소모델에서 강체모드 분리와 급수전개를 통한 준해석적 민감도 계산 방법)

  • Kim, Hyun-Gi;Cho, Maeng-Hyo
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.491-496
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    • 2003
  • In sensitivity analysis, semi-analytical method(SAM) reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Recently such errors of SAM resulted by the finite difference scheme have been improved by the separation of rigid body mode. But the eigenvalue should be obtained first before the sensitivity analysis is performed and it takes much time in the case that large system is considered. In the present study, by constructing a reduced one from the original system, iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The sensitivity analysis is performed by the eigenvector acquired from the reduced system. The error of SAM caused by difference scheme is alleviated by Von Neumann series approximation.

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