Universal Matrix Perturbation Method for Structural Dynamic Reanalysis of General Damped Gyroscopic Systems

2004 ◽  
Vol 10 (4) ◽  
pp. 525-541 ◽  
Author(s):  
J. K. Liu ◽  
H. C. Chan
Keyword(s):  
Perturbation Method ◽  
Eigenvalue Problems ◽  
Matrix Perturbation ◽  
Structural Dynamic ◽  
Decomposition Procedure ◽  
Complex Eigenvalues ◽  
Left And Right ◽  
Value Decomposition ◽  
Dynamic Reanalysis ◽  
Gyroscopic Systems

We investigate an effective matrix perturbation method for structural dynamic reanalysis of general damped gyroscopic systems. By using the complex eigensubspace condensation and the or thogonal decomposition procedures, two greatly reduced generalized eigenvalue equations are obtained. The lower-order perturbations of eigensolutions (i.e. complex eigenvalues and the corresponding left and right eigenvectors) are then determined by solving the two reduced eigenvalue problems. The higher-order perturbations of eigensolutions are obtained by executing a singular value decomposition procedure for a complex matrix. The proposed method is a universal perturbation method, for it is universally applicable to the reanalysis of general damped gyroscopic systems with all three cases of complex eigenvalues: distinct, repeated, and closely spaced eigenvalues. Numerical examples corresponding to the three different cases of eigenvalues are presented. The perturbed eigensolutions are computed using the present method and compared with the exact solutions.

scholarly journals Bearing Damage Detection of a Bridge under the Uncertain Conditions Based on the Bayesian Framework and Matrix Perturbation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Baojun Li ◽  
Yongzhi Lei ◽  
Dongming Zhou ◽  
Zhiheng Deng ◽  
Yuhou Yang ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Damage Detection ◽  
Damage Identification ◽  
Impact Load ◽  
Service Condition ◽  
Single Type ◽  
Matrix Perturbation ◽  
Repeated Impact ◽  
Structural Dynamic ◽  
Bearing Damage

The bearing of a bridge, as a critical component, is important in the force transformation of the superstructure; however, due to the service condition and repeated impact load, the bearing is prone to be damaged but difficult to detect the damage; the present research has few studies that focused on the damage detection of the structural bearing. Meanwhile, practical engineering is always surrounded by variational environmental conditions, and sometimes, the element and bearing damage both exist in the structure. Thus, these uncertain conditions all cause inaccurate damage identification results using the vibration-based damage detection method. In order to detect the damage of the structural bearing and improve the precision, firstly, the structural dynamic characteristic equation considering uncertain conditions has been deduced; then, a damage detection framework constructed by the Bayesian theory and perturbation method has been developed in this article; a numerical example of an 8-span concrete continuous beam and a practical example of I-40 steel-concrete composite bridge are utilized to validate the feasibility of the proposed method, and single type and two types of damage cases are studied. The outcomes demonstrate that the damage of structural elements and bearings can be detected with high accuracy. The proposed method is of great applicability and good potential.

A Perturbation Method Based on Singular Value Decomposition and Feature Selection for Privacy Preserving Data Mining

2014 ◽  
Vol 10 (1) ◽  
pp. 55-76 ◽  
Author(s):  
Mohammad Reza Keyvanpour ◽  
Somayyeh Seifi Moradi
Keyword(s):  
Data Mining ◽  
Feature Selection ◽  
Singular Value Decomposition ◽  
Perturbation Method ◽  
Privacy Preserving ◽  
Singular Value ◽  
Privacy Preserving Data Mining ◽  
Selection For ◽  
Value Decomposition ◽  
Different Levels

In this study, a new model is provided for customized privacy in privacy preserving data mining in which the data owners define different levels for privacy for different features. Additionally, in order to improve perturbation methods, a method combined of singular value decomposition (SVD) and feature selection methods is defined so as to benefit from the advantages of both domains. Also, to assess the amount of distortion created by the proposed perturbation method, new distortion criteria are defined in which the amount of created distortion in the process of feature selection is considered based on the value of privacy in each feature. Different tests and results analysis show that offered method based on this model compared to previous approaches, caused the improved privacy, accuracy of mining results and efficiency of privacy preserving data mining systems.

scholarly journals Internet Photogrammetry for Inspection of Seaports

2017 ◽  
Vol 24 (s1) ◽  
pp. 174-181 ◽  
Author(s):  
Zygmunt Paszotta ◽  
Malgorzata Szumilo ◽  
Jakub Szulwic
Keyword(s):  
Fundamental Matrix ◽  
Laser Scanning ◽  
3D Models ◽  
Digital Cameras ◽  
Correct Orientation ◽  
The Matrix ◽  
Transport Safety ◽  
Left And Right ◽  
Value Decomposition ◽  
The Relationship

Abstract This paper intends to point out the possibility of using Internet photogrammetry to construct 3D models from the images obtained by means of UAVs (Unmanned Aerial Vehicles). The solutions may be useful for the inspection of ports as to the content of cargo, transport safety or the assessment of the technical infrastructure of port and quays. The solution can be a complement to measurements made by using laser scanning and traditional surveying methods. In this paper the authors recommend a solution useful for creating 3D models from images acquired by the UAV using non-metric images from digital cameras. The developed algorithms, created and presented software allows to generate 3D models through the Internet in two modes: anaglyph and display in shutter systems. The problem of 3D image generation in photogrammetry is solved by using epipolar images. The appropriate method was presented by Kreiling in 1976. However, it applies to photogrammetric images for which the internal orientation is known. In the case of digital images obtained with non-metric cameras it is required to use another solution based on the fundamental matrix concept, introduced by Luong in 1992. In order to determine the matrix which defines the relationship between left and right digital image it is required to have at least eight homologous points. To determine the solution it is necessary to use the SVD (singular value decomposition). By using the fundamental matrix the epipolar lines are determined, which makes the correct orientation of images making stereo pairs, possible. The appropriate mathematical bases and illustrations are included in the publication.

A Perturbation Method Based on Singular Value Decomposition and Feature Selection for Privacy Preserving Data Mining

2016 ◽  
pp. 281-304
Author(s):  
Mohammad Reza Keyvanpour ◽  
Somayyeh Seifi Moradi
Keyword(s):  
Data Mining ◽  
Feature Selection ◽  
Singular Value Decomposition ◽  
Perturbation Method ◽  
Privacy Preserving ◽  
Singular Value ◽  
Privacy Preserving Data Mining ◽  
New Model ◽  
Value Decomposition ◽  
Different Levels

In this study, a new model is provided for customized privacy in privacy preserving data mining in which the data owners define different levels for privacy for different features. Additionally, in order to improve perturbation methods, a method combined of singular value decomposition (SVD) and feature selection methods is defined so as to benefit from the advantages of both domains. Also, to assess the amount of distortion created by the proposed perturbation method, new distortion criteria are defined in which the amount of created distortion in the process of feature selection is considered based on the value of privacy in each feature. Different tests and results analysis show that offered method based on this model compared to previous approaches, caused the improved privacy, accuracy of mining results and efficiency of privacy preserving data mining systems.

Analysis of Damped Bloch Waves by the Rayleigh Perturbation Method

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
A. Srikantha Phani ◽  
Mahmoud I. Hussein
Keyword(s):  
Perturbation Method ◽  
State Space ◽  
Phononic Crystal ◽  
Quantitative Agreement ◽  
Unit Cell ◽  
Bloch Waves ◽  
Finite Structures ◽  
Complex Eigenvalues ◽  
Mass Chain ◽  
Computationally Intensive

Bloch waves in viscously damped periodic material and structural systems are analyzed using a perturbation method originally developed by Rayleigh for vibration analysis of finite structures. The extended method, called the Bloch–Rayleigh perturbation method here, utilizes the Bloch waves of an undamped unit cell as basis functions to provide approximate closed-form expressions for the complex eigenvalues and eigenvectors of the damped unit cell. In doing so, we circumvent the solution of a quadratic Bloch eigenvalue problem and subsequent computationally intensive transformation to first order/state-space form. Dispersion curves of a one-dimensional damped spring-mass chain and a two-dimensional phononic crystal with square inclusions are calculated using the state-space method and the proposed method. They are compared and found to be in excellent quantitative agreement for both proportional and nonproportional viscous damping models. The perturbation method is able to capture anomalous dispersion phenomena—branch overtaking, branch cut-on/cut-off, and frequency contour transformation—in parametric ranges where state-space formulations encounter numerical issues. Generalization to other linear nonviscous damping models is permissible.

Sign in / Sign up

Export Citation Format

Share Document