matrix perturbation
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2021 ◽  
pp. 1-14
Author(s):  
Huang Meixin ◽  
Liu Caixia

Fractional order grey model is effective in describing the uncertainty of the system. In this paper, we propose a novel variable-order fractional discrete grey model (short for VOFDGM(1,1)) by combining the discrete grey model and variable-order fractional accumulation, which is a more general form of the DGM(1,1). The detailed modeling procedure of the presented model is first systematically studied, in particular, matrix perturbation theory is used to prove the validity in terms of the stability of the model, and then, the model parameters are optimized by the whale optimization algorithm. The accuracy of the proposed model is verified by comparing it with classical models on six data sequences with different forms. Finally, the model is applied to predict the electricity consumption of Beijing and Liaoning Province of China, and the results show that the model has a better prediction performance compared with the other four commonly-used grey models. To the best of our knowledge, this is the first time that the variable-order fractional accumulation is introduced into the discrete grey model, which greatly increases the prediction accuracy of the DGM(1,1) and extends the application range of grey models.


Author(s):  
Animesh Chatterjee

Abstract Turbine blades are critical machine components in power plants and aerospace turbo engines. Failure of these blades in operation leads to catastrophic damages as well as high cost of maintenance and repair. Blades are often assembled in packets with lacing wire or shroud ring interconnections. Natural frequencies of the bladed packets are designed in a specific range to avoid possible resonant stresses. However, frequent damages during operation alter the stiffness of the blade-packet assembly and change the eigen-spectrum. In this work, it is demonstrated that using characteristic eigen-spectrum changes, such damages can be very well identified in severity as well as location. The work employs matrix perturbation theory on the eigen-value problem, formulated from the lumped parameter modeling of the blade packet. Damage is considered as a perturbation in the stiffness matrix with damage severity acting as the perturbation parameter. First a graphical pattern recognition method and then a damage proximity index evaluation method are suggested for damage identification. Further, an estimation algorithm for damage severity is presented with numerically simulated computations, which demonstrates that the methods can exactly identify the damage location and with very little error, can estimate the damage severity.


2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Baojun Li ◽  
Yongzhi Lei ◽  
Dongming Zhou ◽  
Zhiheng Deng ◽  
Yuhou Yang ◽  
...  

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.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giorgio Gnecco ◽  
Andrea Bacigalupo

<p style='text-indent:20px;'>In the present study, matrix perturbation bounds on the eigenvalues and on the invariant subspaces found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems – e.g., those arising in the design of mechanical metamaterial filters – is also discussed, together with possible extensions.</p>


2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Animesh Chatterjee

Abstract Resonant sensors using coupled micro-cantilever array have applications in a wide range of areas including ultrasensitive mass detection of bio-molecules and chemical analytes. A target mass deposited on one of the cantilevers can be detected by measuring shift in eigen-spectrum. Experimental observations indicate that eigenmodes are more sensitive to mass perturbation than resonant frequencies or eigenvalues. However, analytical works, available in literatures, are limited to only two and three cantilever array for eigenvalue sensitivity and only two cantilever array for eigenmode sensitivity. In the present work, an analytical foundation for estimation of eigenmode sensitivities for a general n-array micro-resonator sensor is developed using matrix perturbation theory. The formulation characterizes the modal spectrum and eigenmode sensitivities as a function of elastic interconnection stiffness parameter and unperturbed eigenmodes. Measurement of added mass is demonstrated for different analyte locations using numerically constructed frequency response function (FRF) curves. Error in measurement is also investigated as a function of interconnection stiffness ratio, position of analyte mass, and selection of particular eigenmode to be measured.


2020 ◽  
Vol 153 (16) ◽  
pp. 164105
Author(s):  
Lionel A. Truflandier ◽  
Rivo M. Dianzinga ◽  
David R. Bowler

2020 ◽  
Vol 196 ◽  
pp. 105822
Author(s):  
Bin Yu ◽  
Bing Lu ◽  
Chen Zhang ◽  
Chunyi Li ◽  
Ke Pan

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