Adaptive dynamic mode decomposition and its application in rolling bearing compound fault diagnosis

The decoupling detection of compound faults in rolling bearing is attracting considerable attentions. In recent years, some time-series decomposition methods, such as ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), symplectic geometry mode decomposition (SGMD) etc., are used to extract the fault characteristics of bearing fault vibration signal and achieve the purpose of fault diagnosis. However, the fault characteristics of compound fault vibration signals are unevenly distributed, some fault characteristics are weakly disturbed by noise, which limit these methods application in compound fault diagnosis. In this paper, the Koopman operator is introduced from the perspective of flow field dynamics information extraction, an adaptive dynamic mode decomposition (ADMD) is proposed to decompose the nonlinear time-series data into a set of dynamic mode components (DMCs). In ADMD, a high-degree polynomial is applied to fit the data sequence of flow field, and a low dimensional subspace can be obtained. The dominant dynamics of flow field can be represented by the eigenvalues and eigenvectors of the low-dimensional subspace, which can be transformed into reconstructed time series with different frequency, and obtained the frequency-based DMCs. The simulation and experimental analysis results show that the proposed method can effectively decouple different fault components of compound fault of rolling bearing.