Symplectic geometry similarity transformationFor roller bearing condition monitoring, the collected signals have complex internal structure, which can be naturally represented as matrices. Support matrix machine (SMM), as a new classifier with matrices as inputs, makes full use of the correlation between...
The key idea of this method is to solve the eigenvalues of the Hamiltonian matrix by using symplectic geometric similarity transformation, and remain the essential characteristics of the original signal unchanged. Through the analysis of the simulated debris signal, the SGMD CRediT authorship ...
yields a similarity transformation on a and takes c to a congruent matrix. The first step of the proof is to make a symplectic transformation so that [Math Processing Error]c=0. The Frobenius decomposition of the skew matrix c says there exists [Math Processing Error]U∈GL(g,Z) such that...
2.2Symplectic structure of the phase space In Sect.2.1, we saw that the Fourier transform preserves the Poisson brackets of the phase-space variables. Another example of a transformation that preserves the Poisson brackets is provided by the Hamiltonian evolution itself. Indeed, the equation of moti...
Therefore, this paper presents a Symplectic transformation based Variational Bayesian Learning (ST-VBL) de-noising method. In this method, the initial de-noising matrix is constructed by using symplectic geometry similarity transformation and the contribution rate method, and most of the noise is ...
Symplectic geometry similarity transformationFor roller bearing condition monitoring, the collected signals have complex internal structure, which can be naturally represented as matrices. Support matrix machine (SMM), as a new classifier with matrices as inputs, makes full use of the correlation between...
First, this method uses the symplectic geometry similarity transformation for the constructed trajectory matrix to obtain the characteristics and eigenvectors of useful components and noise. Linear estimation is then used to approximate the pure signal, and a Lagrange multiplier is used to enhance the ...
Symplectic geometry matrix machineSymplectic geometry similarity transformationRoller bearingFault diagnosisIn many classification problems such as roller bearing fault diagnosis, it is often met that input samples are two-dimensional matrices constructed by vibration signals, and the rows or columns in the ...
Symplectic geometry matrix machineSymplectic geometry similarity transformationRoller bearingFault diagnosisIn many classification problems such as roller bearing fault diagnosis, it is often met that input samples are two-dimensional matrices constructed by vibration signals, and the rows or columns in the ...
GEOMETRYMATHEMATICAL invariantsEUCLIDEAN geometryISOTROPIC propertiesA linear transformation with an invariant being a nondegenerate quadratic form is symplectic. The geometric properties of such transformations are discussed. A complete set of quadratic invariants which are pairwise in involution is explicitly ...