Self-Matched Time-Reassigned Multisynchrosqueezing Wavelet Transform

In mechanical fault diagnosis, the transient signal usually corresponds to the occurrence of faults such as bearing or gear, and how to characterize the transient signal with fast varying group delay (GD) effectively is still a challenging task. This paper proposes an accurate GD estimation and two novel time-frequency (TF) analysis methods, which can characterize fast frequency-varying transient signal accurately. Firstly, self-matched GD estimator is deduced from wavelet transform of frequency-varying Gaussian amplitude linear modulated signal with any wavelet, matching the frequency-varying law of signal. Then, by squeezing the TF coefficients into the estimated GD trajectory along the time direction, a self-matched time-reassigned synchrosqueezing wavelet transform is introduced to improve the energy concentration of TF representation, and its signal reconstruction formula is derived. Furthermore, by applying both self-matched GD estimator and multiple squeeze operations, a self-matched time-reassigned multi-synchrosqueezing wavelet transform is proposed and analyzed theoretically, it can achieve a high-resolution TF representation for fast frequency-varying signal and reconstruct signal. Finally, simulated and real signals are employed to demonstrate the superiority of the proposed methods by comparing with other TF analysis methods on the TF energy concentration, GD estimation and signal reconstruction.