Statistics

White noise

Algorithm

Physics

Singular spectrum analysis

Artificial intelligence

Eigenvalues and eigenvectors

Symplectic geometry

Eigendecomposition of a matrix

Wavelet transform

Programming language

Singular value decomposition

Geometry

Hilbert–Huang transform

SIGNAL (programming language)

Mathematics

Computer science

Discrete wavelet transform

Wavelet

Quantum mechanics

Mechanical Systems and Signal Processing

Various existed time-series decomposition methods, including wavelet transform, ensemble empirical mode decomposition (EEMD), local characteristic-scale decomposition (LCD), singular spectrum analysis (SSA), etc., have some defects for nonlinear system signal analysis. When the signal is more complex, especially noisy signal, the component signal is forced to decompose into several incomplete components by LCD and SSA. In addition, the wavelet transform and EEMD need user-defined parameters, and they are very sensitive to the parameters. Therefore, a new signal decomposition algorithm, symplectic geometry mode decomposition (SGMD), is proposed in this paper to decompose a time series into a set of independent mode components. SGMD uses the symplectic geometry similarity transformation to solve the eigenvalues of the Hamiltonian matrix and reconstruct the single component signals with its corresponding eigenvectors. Meanwhile, SGMD can efficiently reconstruct the existed modes and remove the noise without any user-defined parameters. The essence of this method is that signal decomposition is converted into symplectic geometry transformation problem, and the signal is decomposed into a set of symplectic geometry components (SGCs). The analysis results of simulation signals and experimental signals indicate that the proposed time-series decomposition approach can decompose the analyzed signals accurately and effectively.

Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis