Synchronous fault feature extraction for rolling bearings in a generalized demodulation framework

Generalized demodulation (GD) has the potential to process non-stationary vibration signals since it can demodulate a signal with a curved time–frequency (TF) ridge into a signal, with a TF ridge parallel to a time axis with an improved time-frequency representation (TFR) energy concentration level. However, current GD methods require iteration operations and cannot simultaneously deal with vibrations from multiple components of rolling bearings. This paper proposes a method based on the GD framework, which can simultaneously demodulate multiple components of interest using the Hadamard product between matrices. A synchronous extractor is also constructed to post-process TFRs of generalized demodulated signals to further improve the TF aggregation. Unlike the conventional synchronous extraction transform, the synchronous extractor in this paper can be directly applied to TF ridges parallel to the time axis without the estimation of instantaneous frequencies (IFs). Then, the post-processed TF ridges are backward demodulated to restore the actual IF. The proposed synchronous fault feature extraction method in the GD framework also allows for the signal reconstruction. Both simulated and experimental signals are applied to validate the effectiveness of the proposed method for rolling bearing fault diagnosis.