Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis. (1st January 2019) - Pan, Haiyang; Yang, Yu; Li, Xin; Zheng, Jinde; Cheng, Junsheng
Highlights: SGMD has good decomposition performance in dealing with complex signals. SGMD, using symplectic geometry similarity transformation, can keep the essential character of the original signals unchanged. The SGMD method is applied to the noisy signal to verify its robustness. The SGMD performs better on the diagnosis of rotating machinery compound fault. Abstract: 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.