A NEW MATRIX PERTURBATION METHOD FOR ANALYTICAL SOLUTION OF THE COMPLEX MODAL EIGENVALUE PROBLEM OF VISCOUSLY DAMPED LINEAR VIBRATION SYSTEMS

A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.

Image registration based on matrix perturbation analysis using spectral graph

We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.

Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

RELATIVE ASYMPTOTICS FOR ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A PERTURBED MATRIX MEASURE ON THE UNIT CIRCLE

Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.

Capacity analysis of high-rank line-of-sight MIMO channels

Matrix perturbation theory is utilized to investigate high-rank line of sight multiple input multiple output channels in a microwave relay system. The upper and lower bounds of channel capacity are derived based on space time block codes technique and singular values decomposition. A useful constraint for designing LOS MIMO channels is developed by the use of the condition number of the MIMO channel matrix. The theoretical analysis of channel capacity is confirmed by the simulation. The results show that the proposed method is able to give a physical explanation of the high-rank LOS MIMO channel matrix characteristics.

Binary discrete method of topology optimization

The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate, even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements, meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.

A matrix-perturbation-theory-based optimal strategy for small-signal stability analysis of large-scale power grid

In this paper,a sensitivity matrix based approach is proposed to improve the minimum damping ratio.The proposed method also avoids burdensome deviation calculations of damping ratio of large-scale power grids when compared to the Small-Signal-Stability Constrained Optimal Power Flow(SSSC-OPF)approach.This is achieved using the Matrix Perturbation Theory(MPT)to deal with the 2nd order sensitivity matrices,and the establishment of an optimal corrective control model to regulate the output power of generating units to improve the minimum damping ratio of power grids.Finally,simulation results on the IEEE 9-bus,IEEE 39-bus and a China 634-bus systems show that the proposed approach can significantly reduce the burden of deviation calculation,while enhancing power system stability and ensuring calculation accuracy.