辛几何模态分解方法及其分解能力研究

针对经验模态分解(Empirical Mode Decomposition,EMD)、集合经验模态分解(Ensemble Empirical Mode Decomposition,EEMD)、局部特征尺度分解(Local Characteristic scale Decomposition,LCD)等方法的不足,提出了一种新的分析方法——辛几何模态分解(Symplectic Geometry Mode Decomposition,SGMD)方法,该方法采用辛矩阵相似变换求解Hamilton矩阵的特征值,并利用其对应的特征向量重构辛几何分量(Symplectic Geometry Component,SGC),从而对复杂信号去噪的同时进行自适应分解,得到若干个SGC。通过仿真信号模型,研究了SGMD方法的分解性能、噪声鲁棒性,分析了分量信号的频率比、幅值比和初相位差对SGMD方法分解能力的影响。将SGMD方法应用于齿轮故障实验数据分析,结果表明SGMD方法能够有效地对待分解信号完成分解并剔除噪声信号。

Symplectic geometry mode decomposition method and its decomposition ability

Aiming at the shortages of empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD) and local characteristic scale decomposition (LCD), a new analysis method, called Symplectic Geometry Mode Decomposition (SGMD), is proposed in the paper. In SGMD, the symplectic matrix similarity transformation is used to solve the eigenvalues of the Hamiltonian matrix and the Symplectic Geometry Component (SGC) is reconstructed with the corresponding eigenvectors. Therefore, the complicated signal is de-noised and adaptively decomposed into some Symplectic Geometry Components. By using simulation signal model, the decomposition performance and noise robustness of SGMD method is researched. The effect of frequency ratio, amplitude ratio, and initial phase difference with components on decomposition capacity of SGMD are studied. The proposed method is applied to the gear fault test data analysis. The results show that the SGMD method can decompose the decomposed signal effectively with eliminate the noise signal.