This study proposes a novel resonance demodulation frequency band selection method named the initial center frequency-guided filter (ICFGF) to diagnose the bearing fault. The proposed technology has a better performance on resisting the interference from the random impulses. More explicitly, the ICFGF can be summarized as two steps. In the first step, a variance statistic index is applied to evaluate the energy spectrum distribution, which can adaptively determine the center frequency of the fault impulse and suppress the interference from random impulse effectively. In the second step, a modified mayfly optimization algorithm (MMA) is applied to search the optimal resonance demodulation frequency band based on the center frequency from the first step, which has faster convergence. Finally, the filtered signal is processed by the squared envelope spectrum technology. Results of the proposed method for signals from an outer fault bearing and a ball fault bearing indicate that the ICFGF works well to extract bearing fault feature. Furthermore, compared with some other methods, including fast kurtogram, ensemble empirical mode decomposition, and conditional variance-based selector technology, the ICFGF can extract the fault characteristic more accurately.

A novel method named residual-variational mode decomposition (RVMD) is proposed in this study to extract bearing fault features accurately. RVMD can determine the number of modes and the balance parameter adaptively, and it has two stages. In the first stage, the signal is decomposed into a series of modes until the correlation coefficient between the raw signal and the decomposition results reaches the threshold. A redefined kurtosis, which can resist the interferences from aperiodic impulse efficiency, is applied to rebuild the ensemble kurtosis index. The mode that has the largest rebuild-ensemble kurtosis, and its neighbors, are kept. By putting the residual signal into the second stage, an iteration process is applied to determine the optimal parameters for variational mode decomposition (VMD). VMD is re-run with the optimal parameters, and the sub-mode filtered with the larger rebuild-ensemble kurtosis is examined by the envelope analysis technology to observe the fault feature. The effectiveness of RVMD is verified by the simulation signal and three experiment signals. Its superiority is shown by comparing it with some existing methods.

The short-time linear canonical transform (STLCT) is a novel time-frequency analysis tool, which has attracted some attention recently. However, its applications in signal processing are limited because the time-frequency properties of the STLCT are still little known. Most existing studies focus on mathematical properties rather than time-frequency properties in signal processing. To handle this problem, first, we investigate some basic time-frequency properties such as 2-D resolution of the time-frequency plane, the STLCT domain support, computation of the STLCT, etc by generalizing the short-time Fourier transform to the STLCT. Then, based on these derived properties, we find that the Gaussian window is optimal window of the STLCT. Signal separation verified the results.