基于变分模态分解和互相关分析的旋转机械信号降噪研究

辛几何模态分解（SGMD）方法利用周期相似性进行信号分量重组，且需要人为设置终止条件，这导致分解结果具有不确定性。针对这一不足，提出一种聚类辛几何模态分解（CSGMD）方法。首先将时间序列的信号转化成轨迹矩阵；其次，对轨迹矩阵进行矩阵变换，获得由多组初始单分量重构矩阵组成的重构矩阵；然后利用对角平均化方法将每一个重构矩阵转化成相应的一维时间序列初始分量；最后使用K-means聚类算法对初始分量进行重组，得到最终的辛几何分量。相比SGMD和变分模态分解（VMD）方法，该方法提取的有效分量失真程度和频率混淆程度更低，干扰分量更少，故障冲击特性提升更为明显。该方法能够有效提取出转子故障特征，提高转子故障诊断的准确性。

A review on empirical mode decomposition in fault diagnosis of rotating machinery

Symplectic geometric mode decomposition (SGMD) uses periodic similarity to reconstruct signal components, and requires manual setting of termination conditions, which leads to uncertain decomposition results. To solve this problem, a clustered symplectic geometric modal decomposition (CSGMD) method is proposed in this work. First, the time series signal is transformed to a trajectory matrix, and secondly, the trajectory matrix is transformed to a reconstruction matrix consisting of several groups of initial single component reconstruction matrices. Then, the diagonal averaging method is applied to convert each reconstruction matrix into the corresponding initial components of the one-dimensional time series. Finally, K-means clustering algorithm is used to recombine the initial components to obtain the final symplectic geometric components. Compared with SGMD and variational mode decomposition (VMD), the effective components extracted by CSGMD method has lower distortion degree and frequency confusion degree, less interference components and more obvious improvement of fault impact characteristics. This method can effectively extract rotor fault features and improve the accuracy of rotor fault diagnosis.