Generalized demodulation with tunable E-Factor for rolling bearing diagnosis under time-varying rotational speed

Generalized demodulation (GD) is one of the most effective approaches to demodulating the time-varying frequency component. However, it is sensitive to the initial frequency value. Theoretically, the slower the rotational speed is, the lower frequency estimation precision based on the time-frequency representation (TFR) will be. Therefore, for the vibration signal whose phase function is estimated by the instantaneous frequency extracted from the TFR under lower initial speed, the demodulation error is significant. As such, the concept of energy factor (E-Factor) is defined. E-Factor represents the frequency coordinate value of the target instantaneous frequency on the demodulated time-frequency plane, i.e., the energy of the instantaneous frequency can be converted to a changeable parameter E-Factor, rather than the fixed initial value. Based on it, we propose the generalized demodulation with tunable E-Factor (GDTEF), which can map the trajectory of time-varying frequency to a line parallel to time axis with the frequency coordinate E-Factor in the time-frequency domain, and further exploit its merit to bearing fault detection. First, extract the instantaneous fault characteristic frequency (IFCF) from the TFR of the envelope obtained by the joint application of Hilbert transform and short-time Fourier transform (STFT). Second, configure E-Factor adaptively according to the IFCF fitting function, and then reconstruct the original signal according to the E-Factor. Then, finalize the phase function of the reconstructed signal based on the fitting function. Finally, identify the fault pattern via the demodulation spectrum. It is validated that the novel method can enhance the demodulation precision by processing the simulated and measured signals. What's more, the proposed method possesses stronger noise immunity in processing the time-varying frequency vibration signal.