Data-driven time-frequency analysis method based on variational mode decomposition and its application to gear fault diagnosis in variable working conditions

The data-driven time-frequency analysis (DDTFA)-method-based initial phase selection directly influences the convergence and calculation results of the algorithm. The central frequency accuracy of each component by means of variational mode decomposition (VMD) is high, the calculation speed of VMD is fast, and the method shows satisfactory noise resistance, but the decomposed components are sensitive to noise. A VMD method that is complementary to the DDTFA method is introduced in this paper to estimate the initial phase of DDTFA, and the VMD-DDTFA method is proposed for time-varying non-stationary signals. This method first analyzes the time-varying non-stationary signal through VMD and estimates the initial phase of each signal component, then uses DDTFA to sparsely decompose the signal after phase smoothing. To examine the analytical ability of VMD-DDTFA on time-varying non-stationary signals, the five aspects of the VMD-DDTFA method, accuracy, noise resistance, efficiency, applicability and anti-mode-mixing ability, are analyzed. The VMD-DDTFA method compares with the current commonly used signal analysis methods of VMD and ensemble empirical mode decomposition (EEMD) and the comparison results confirm that VMD-DDTFA has a superior decomposition accuracy, satisfactory noise resistance and efficiency. In addition, VMD-DDTFA features strong anti-mode mixing and applicability even under strong noise. The VMD-DDTFA method is applied to the fault diagnosis of measured gear crack and broken tooth in variable working conditions. In addition, the results of the VMD-DDTFA method are compared with those obtained by VMD and EEMD; the results verify the effectiveness and superiority of the method.