Varying-Parameter Time-Frequency Manifold Signal Reconstruction for Gearbox Fault Diagnosis

Noise reduction of vibration signals has always been an important issue in gearbox fault diagnosis. Time-frequency manifold (TFM) is effective in suppressing the noise in the signal time-frequency distribution (TFD). However, the amplitude information of the TFM features is largely deviated from that of the fault component. This paper proposes a new varying-parameter time-frequency manifold signal reconstruction method to restore the amplitude information of the fault component for gearbox fault diagnosis. First, variational mode decomposition (VMD) is employed to extract the fault component in the resonance band. Second, varying-parameter short-time Fourier transform (STFT) is conducted to construct a high-dimensional TFD, followed by down-sampling to reduce the data size. Third, local tangent space alignment (LTSA) is performed to learn the TFM features, and a threshold is set to greatly remove the in-band noise. Fourth, the TFM features are weighted summed to reconstruct the TFD of the fault component, where the weights are obtained based on Euclidean distance. Fifth, with a series of inverse transformations, the time-domain signal of the fault component is reconstructed, which restores the fault amplitude information. Finally, the gearbox fault characteristic frequency can be easily identified in the envelope spectrum of the reconstructed signal. The application in a gearbox fault diagnosis validates the advantages of the proposed method in noise removal, fault impulse enhancement, and amplitude recovery.