Generalized stepwise demodulation transform and synchrosqueezing for time–frequency analysis and bearing fault diagnosis

Abstract

The energy concentration level is an important indicator for time–frequency analysis (TFA). Weak energy concentration would result in time–frequency representation (TFR) diffusion and thus leading to ambiguous results or even misleading signal analysis results, particularly for nonstationary multicomponent signals. To improve the energy concentration level, this paper proposes a generalized stepwise demodulation transform (GSDT). The rationale of the proposed method is that (1) the generalized demodulation (GD) can map the original signal into an analytic signal with constant instantaneous frequency (IF) and improve the energy concentration level on time–frequency plane, and (2) focusing on a short window around the time instant of interest, a backward demodulation operation can recover the original frequency at the time instant without affecting the improved energy concentration level. By repeating the backward demodulation at every time instant of interest, the TFR of the entire signal can be attained with enhanced energy concentration level. With the GSDT, an iterative GSDT (IGSDT) is developed to analyze multicomponent signal that is subjected to different modulating sources for their constituent components. The IGSDT iteratively demodulates each constituent component to attain its TFR and the TFR of the whole signal is derived from superposing all the resulting TFRs of constituent components. The cross-term free and more energy concentrated TFR of the signal is, therefore, obtained, and the diffusion in the TFR can be reduced. The GSDT-based synchrosqueezing transform is also elaborated to further enhance the GSDT(IGSDT) yielded TFR. The effectiveness of the proposed method in TFA is tested using both simulated monocomponent and multicomponent signals. The application of the proposed method to bearing fault detection is explored. Bearing condition and fault pattern can be revealed by the proposed method resulting TFR. The main advantages of the proposed method for bearing condition monitoring under variable speed conditions include: (a) it can simultaneously improve energy concentration level of signals of interest and remove interferences in the TFR, (b) it is resampling-free and hence can avoid the resampling related errors, and (c) it yields instantaneous frequencies for fault and shaft rotation and thus can carry out both fault detection and diagnosis tasks.