The Extraction of Time-Varying Fault Characteristics of Rolling Bearings based on Adaptive Multi-Synchrosqueezing Transform

Purpose The multi-synchrosqueezing transform (MSST) is based on synchrosqueezing transform (SST) and uses an iterative reassignment to concentrate the time-frequency energy step by step. It can study the time-varying features of the non-stationary signal. But the iteration number needs to be completed by experimental trial and error method or relying on the experience of the experimenter, which can’t be selected according to the characteristics of the signal. Therefore, to ensure high time-frequency energy aggregation without increasing the time cost, the adaptive multi-synchrosqueezing transform (AMSST) algorithm is proposed. Methods Firstly, the concept of Rényi entropy difference spectrum is proposed, which is used as the index of iteration termination, and the theoretical derivation and calculation steps of the AMSST are given. Secondly, the main advantages of the AMSST method are verified by the implementation of non-linear frequency modulation simulation signal. Lastly, the AMSST method is used to the actual bearing signal with outer ring fault under complex speed. Results In simulation signal analysis, with the increase of the signal to noise ratio(SNR), the Rényi entropy of the AMSST algorithm is smaller than that of the short-time Fourier transform(STFT), SST and the second-order synchrosqueezing transform(SST2) method. Moreover, the Rényi entropy of the AMSST algorithm changes less than that of the STFT, SST and SST2 algorithm with the increase of SNR. In vibration signal analysis of rolling bearings, compared with SST, SST2 and the MSST with sixth iteration number (SST6), the Rényi entropy of the AMSST decreases by 1.97981, 1.3741 and 0.0053 respectively. Conclusions The experimental results indicate that the AMSST method has adaptivity, the high time-frequency aggregation and noise robustness. So this research can be beneficial for the extraction of time-varying fault characteristics of rolling bearings.