• Title/Summary/Keyword: Eigenvalue and Eigenvector

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Feedback control design for intelligent structures with closely-spaced eigenvalues

  • Cao, Zongjie;Lei, Zhongxiang
    • Structural Engineering and Mechanics
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    • v.52 no.5
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    • pp.903-918
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    • 2014
  • Large space structures may have resonant low eigenvalues and often these appear with closely-spaced natural frequencies. Owing to the coupling among modes with closely-spaced natural frequencies, each eigenvector corresponding to closely-spaced eigenvalues is ill-conditioned that may cause structural instability. The subspace to an invariant subspace corresponding to closely-spaced eigenvalues is well-conditioned, so a method is presented to design the feedback control law of intelligent structures with closely-spaced eigenvalues in this paper. The main steps are as follows: firstly, the system with closely-spaced eigenvalues is transformed into that with repeated eigenvalues by the spectral decomposition method; secondly, the computation for the linear combination of eigenvectors corresponding to repeated eigenvalues is obtained; thirdly, the feedback control law is designed on the basis of the system with repeated eigenvalues; fourthly, the system with closely-spaced eigenvalues is regarded as perturbed system on the basis of the system with repeated eigenvalues; finally, the feedback control law is applied to the original system, the first order perturbations of eigenvalues are discussed when the parameter modifications of the system are introduced. Numerical examples are given to demonstrate the application of the present method.

Adaptable Center Detection of a Laser Line with a Normalization Approach using Hessian-matrix Eigenvalues

  • Xu, Guan;Sun, Lina;Li, Xiaotao;Su, Jian;Hao, Zhaobing;Lu, Xue
    • Journal of the Optical Society of Korea
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    • v.18 no.4
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    • pp.317-329
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    • 2014
  • In vision measurement systems based on structured light, the key point of detection precision is to determine accurately the central position of the projected laser line in the image. The purpose of this research is to extract laser line centers based on a decision function generated to distinguish the real centers from candidate points with a high recognition rate. First, preprocessing of an image adopting a difference image method is conducted to realize image segmentation of the laser line. Second, the feature points in an integral pixel level are selected as the initiating light line centers by the eigenvalues of the Hessian matrix. Third, according to the light intensity distribution of a laser line obeying a Gaussian distribution in transverse section and a constant distribution in longitudinal section, a normalized model of Hessian matrix eigenvalues for the candidate centers of the laser line is presented to balance reasonably the two eigenvalues that indicate the variation tendencies of the second-order partial derivatives of the Gaussian function and constant function, respectively. The proposed model integrates a Gaussian recognition function and a sinusoidal recognition function. The Gaussian recognition function estimates the characteristic that one eigenvalue approaches zero, and enhances the sensitivity of the decision function to that characteristic, which corresponds to the longitudinal direction of the laser line. The sinusoidal recognition function evaluates the feature that the other eigenvalue is negative with a large absolute value, making the decision function more sensitive to that feature, which is related to the transverse direction of the laser line. In the proposed model the decision function is weighted for higher values to the real centers synthetically, considering the properties in the longitudinal and transverse directions of the laser line. Moreover, this method provides a decision value from 0 to 1 for arbitrary candidate centers, which yields a normalized measure for different laser lines in different images. The normalized results of pixels close to 1 are determined to be the real centers by progressive scanning of the image columns. Finally, the zero point of a second-order Taylor expansion in the eigenvector's direction is employed to refine further the extraction results of the central points at the subpixel level. The experimental results show that the method based on this normalization model accurately extracts the coordinates of laser line centers and obtains a higher recognition rate in two group experiments.

Semi-Empirical MO Calculations on ${\pi}$-Nonbonded and ${\sigma}$-Conjugative Interactions (반경험적 분자궤도함수 계산법에 의한 ${\pi}$-비결합 및 ${\sigma}$-컨쥬게이션 상호작용에 관한 연구)

  • Ikchoon Lee;Young Gu Cheun;Kiyull Yang;Wang Ki Kim
    • Journal of the Korean Chemical Society
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    • v.26 no.4
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    • pp.195-204
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    • 1982
  • Semi-empirical MO calculations, EHT, CNDO/2, MINDO/3, and MNDO met hods, were performed on various geometries of n-butane, n-alkyl radical and tetramethylene diracal (triplet) in order to compare eigenvalue and eigenvector properties with those obtained by STO-3G method. All methods predicted the same relative order of stabilities of various geometries for n-butane; geometrical preferences were found to be dominated by one-electron factor, ${\pi}$-orbital energy changes being more impotant in the semi-empirical methods. The hyperconjugative energy changes accompanying structural changes from $(n-{\sigma}{\ast})_{trans}$ to (n-{\sigma}{\ast})cis were underestimated in the EHT, CNDO/2 and MINDO/3, whereas those were overestimated in the MNDO. The net destabilizing effect of $(n-{\sigma}{\ast})_{trans}$ structure was mainly due to the large internuclear energy involved in the structure. Through-space interaction between $n_1$ and $n_2$ orbitals of diradical caused energy gap narrowing of ${\Delta}E_{sp}$ and ${\Delta}{\varepsilon}={\varepsilon}_0$-${\varepsilon}_{av}$; through-space interaction had opposing effect to that of through-bond interaction. Due to the less severe neglect of differential overlaps in the MNDO, this energy gap narrowing effect appeared amplified in the MNDO. In general orbital properties were found to be reproduced satisfactorily, but eigenvalue properties were not, in all the semi-empirical methods especially when ${\sigma}-{\sigma}{\ast}$ and n-$n-{\sigma}{\ast}$interactions were involved.

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A Study on Groundwater Contamination Potential of Pyungtaek-Gun Area, Kyunggi-Do Using GIS (GIS를 이용한 경기도 평택군 지역의 지하수 오염 가능성 평가 연구)

  • 조시범;민경덕;우남칠;이사로
    • Journal of the Korean Society of Groundwater Environment
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    • v.6 no.2
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    • pp.87-94
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    • 1999
  • This study is providing Modified DRASTIC Model to which lineament density and land use are added as additional factors using geographic infomation system(GIS). and then to evaluate groundwater contamination potential of Pyungtek-Gun area in Kyunggi-Do. In this study. the reason for using additional factors is because. in case of lineament density. when we consider that most of aquifer is bedrock aquifer in hydrogeologic environment of the Korea, lineament is very important to flow of groundwater and contamination material. and because land use can reflect indirectly impact of point or non_point source in study area. For statistical analysis. vector coverage per each factor is converted to grid layer and after each correlation coefficient between factors, covariance, variance. eigenvalue and eigenvector by principal component analysis of 3 direction. are calculated. correlation between factors is analyzed. Also after correlation coefficients between general DRASTIC layer and rated lineament density layer and between general DRASTIC layer and rated land use layer are calculated. final modified DRASTIC Model is constructed by using them with each weighting. when modified DRASTIC Model was compared with general DRASTIC Model, comtamination potential in modified DRASTIC Model is fairly detailed and consequently. vulnerable area which has high contamination potential could be presented concretly.

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Robust 3D Model Hashing Scheme Based on Shape Feature Descriptor (형상 특징자 기반 강인성 3D 모델 해싱 기법)

  • Lee, Suk-Hwan;Kwon, Seong-Geun;Kwon, Ki-Ryong
    • Journal of Korea Multimedia Society
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    • v.14 no.6
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    • pp.742-751
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    • 2011
  • This paper presents a robust 3D model hashing dependent on key and parameter by using heat kernel signature (HKS), which is special shape feature descriptor, In the proposed hashing, we calculate HKS coefficients of local and global time scales from eigenvalue and eigenvector of Mesh Laplace operator and cluster pairs of HKS coefficients to 2D square cells and calculate feature coefficients by the distance weights of pairs of HKS coefficients on each cell. Then we generate the binary hash through binarizing the intermediate hash that is the combination of the feature coefficients and the random coefficients. In our experiment, we evaluated the robustness against geometrical and topological attacks and the uniqueness of key and model and also evaluated the model space by estimating the attack intensity that can authenticate 3D model. Experimental results verified that the proposed scheme has more the improved performance than the conventional hashing on the robustness, uniqueness, model space.

Timetabling and Analysis of Train Connection Schedule Using Max-Plus Algebra (Max-Plus 대수를 이용한 환승 스케줄 시간표 작성 및 분석)

  • Park, Bum-Hwan
    • Journal of the Korean Society for Railway
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    • v.12 no.2
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    • pp.267-275
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    • 2009
  • Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.

A study on relationship between the performance of professional baseball players and annual salary (한국 프로야구 선수들의 경기력과 연봉의 관계 분석)

  • Seung, Hee-Bae;Kang, Kee-Hoon
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.2
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    • pp.285-298
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    • 2012
  • This research deals with a relationship between the performance of Korean professional baseball players and their annual salaries. It is based on the sabermetrics, which measures the performance of baseball batters in a refined way. We collect the records of batters of eight professional baseball clubs during the season 2009 and 2010. Then, we calculate every index of the sabermetrics. Principal component analysis is used for examining the relationship between those indexes of sabermetrics and annual salary for the next year. In general, batters who show higher performance get more salary. The result of this research can be useful in order to reach an agreement on salary between a player and his club partner.

Searching for the Hub Module of fMRI Data with the Hypergraph Model (하이퍼그래프 모델을 이용한 fMRI Brain Network 의 허브 모듈 분석)

  • Kim, Joon-Shik;Lim, Byoung-Kwon;Kim, Eun-Sol;Yang, Jin-San;Zhang, Byoung-Tak
    • Proceedings of the Korean Information Science Society Conference
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    • 2010.11a
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    • pp.27-31
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    • 2010
  • 본 논문에서는 하이퍼그래프의 고유벡터를 척도로 하여 fMRI기반 Brain Network를 분석하여 중요한 허브노드를 찾는 방법론을 제시한다. 이 방법을 비디오게임을 수행하면서 촬영한 기능적 자기뇌영상(fMRI) 데이터인 PBAIC 2007 데이터셋에 대하여 그 유용성을 검증하였다. 이 데이터는 각 20분씩 세 세션을 촬영한 것이며 처음 두 세션에는 13가지의 감정 항목의 평가치가 각 스캔마다 주어진다. 한 피험자의 첫번째 세션 데이터로부터 13가지 감정 항목에 대하여 상관관계가 높은 각각의 복셀(voxel)들을 추출하였다. 이 13가지의 복셀들의 집합들을 각각 하이퍼에지로 보고 하이퍼그래프를 구성하였다. 하이퍼그래프로부 터 인접 행렬(adjacency matrix)를 구성한 후 고유치(eigenvalue)와 고유벡터(eigenvector)를 구하였다. 여기서 고유치가 가장 큰 고유벡터의 원소들은 각 복셀들의 중앙성(centrality), 즉 중요성을 나타내며 이로부터 감정과 관련된 중요한 허브 복셀들과 그들의 국소적 집합인 모듈을 찾았다. 모듈들은 감정 및 작업기억(working memory)과 관련된 뇌 영역들의 클러스터(cluster)로 추정된다.

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Self-Calibration for Direction Finding in Multi-Baseline Interferometer System (멀티베이스라인 인터페로미터 시스템에서의 자체 교정 방향 탐지 방법)

  • Kim, Ji-Tae;Kim, Young-Soo;Kang, Jong-Jin;Lee, Duk-Yung;Roh, Ji-Hyun
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.21 no.4
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    • pp.433-442
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    • 2010
  • In this paper, self-calibration algorithm based on covariance matrix is proposed for compensating amplitude/phase mismatch in multi-baseline interferometer direction finding system. The proposed method is a solution to nonlinear constrained minimization problem which dramatically calibrate mismatch error using space sector concept with cost function as defined in this paper. This method, however, has a drawback that requires an estimated initial angle to determine the proper space sector. It is well known that this type of drawback is common in nonlinear optimization problem. Superior calibration capabilities achieved with this approach are illustrated by simulation experiments in comparison with interferometer algorithm for a varitiety of amplitude/phase mismatch error. Furthermore, this approach has been found to provide an exceptional calibration capabilities even in case amplitude and phase mismatch are more than 30 dB and over $5^{\circ}$, respectively, with sector spacing of less than $50^{\circ}$.

Face recognition method using embedded data in Principal Component Analysis (주성분분석 방법에서의 임베디드 데이터를 이용한 얼굴인식 방법)

  • Park Chang-Han;Namkung Jae-Chan
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.42 no.1
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    • pp.17-23
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    • 2005
  • In this paper, we propose face recognition method using embedded data in super states segmentalized that is specification region exist to face region, hair, forehead, eyes, ears, nose, mouth, and chin. Proposed method defines super states that is specification area in normalized size (92×112), and embedded data that is extract internal factor in super states segmentalized achieve face recognition by PCA algorithm. Proposed method can receive specification data that is less in proposed image's size (92×112) because do orignal image to learn embedded data not to do all loaming. And Showed face recognition rate in image of 92×112 size averagely 99.05%, step 1 99.05%, step 2 98.93%, step 3 98.54%, step 4 97.85%. Therefore, method that is proposed through an experiment showed that the processing speed improves as well as reduce existing face image's information.