Synchro-reassigning generalized Chirplet basis transform for analyzing signals with crossover frequencies. (15th July 2023) - Wu, Taihuan; Zhang, Wanyang; Zhang, Baoqiang; Luo, Huageng
Highlights: A non-iterative time–frequency analysis method designed for processing nonstationary signals with crossover frequencies. The generalized Chirplet basis transform and the time–frequency reassignment method are successfully combined, and good results have been achieved. The mode selection time–frequency transform, instead of the enumeration time–frequency transform, reduces computational complexity and improves the computational efficiency. Advantages demonstrated by numerical simulations as well as real examples. Abstract: Analysis of signals with crossover frequencies, existing in rotating machinery, is one of the challenges in time–frequency analysis (TFA). The classical TFA methods can only provide a single base in the step window, whereas the signal with crossover frequencies has at least two nonproportional fundamental frequencies. Therefore, classical methods are not suitable for addressing non-proportional multi-component signals such as those with crossover frequencies. This paper presents a novel TFA method, referred to as the synchro-reassigning generalized Chirplet basis transform (SRGCBT), which is designed for processing the signal with crossover frequencies. In the proposed SRGCBT, the peak ridges search method is utilized to find out all of the Chirplet parameters that match with multiple non-proportional fundamental frequencies in the signal. The precision and computational efficiency are enhanced by eliminating the interference of redundant parameters in the enumeration. Then, the synchro-reassigning operator is formulated and applied to extract the time–frequency (TF) coefficients at the instantaneous frequency (IF) ridges. Subsequently, the TF coefficients are reassembled to obtain a new time–frequency representation (TFR). The advantages of SRGCBT are validated by the simulation signal and the vibration signals gathered in the laboratory. The validation results indicate that the proposed SRGCBT delivers improvements in noise robustness, energy concentration, computational efficiency and accuracy in rendering the final TFR for the signal with crossover frequencies.