Generalized reassigning transform: Algorithm and applications

Time-frequency analysis (TFA) has attracted the attention of many scholars and engineers for analyzing nonstationary signals in the field of condition monitoring of rotating machinery. For complex mechanical equipment, measured signals always contain both harmonic and impulsive components, which presents a challenge for current TFA methods. To concurrently characterize harmonic and impulsive components, a novel TFA algorithm, called generalized reassigning transform (GRT) is developed in this paper. First, the time-frequency fusion extraction criterion (TFFEC), which includes time-frequency data fusion (TFDF) and time-frequency data extraction (TFDE), is designed to calculate time-frequency representation (TFR) from short-time Fourier transform (STFT) results under different window sizes, which improves time-frequency resolution and eliminates noise influence. Furthermore, the chirp rate (CR)-based postprocessing strategy is constructed to characterize nonstationary signals with both harmonic-like and impulsive-like components. Specifically, the CR discrimination criterion is introduced to classify the TFFEC result into two distinct types: harmonic-like component and impulsive-like component, and then, the TFR with high energy concentration and strong readability is obtained by advanced postprocessing TFA including the synchro-reassigning transform (SRT) and horizontal reassigning transform (HRT). The effectiveness of the GRT in condition monitoring and fault diagnosis is validated through numerical and experiment verification.