Improved VMD-FRFT based on initial center frequency for early fault diagnosis of rolling element bearing

Abstract The extraction of weak fault signatures with periodic impulse characteristics is a crucial aspect of detecting an early fault of bearing. In order to suppress the interference of background noise to the weak fault signatures extraction by variational mode decomposition (VMD), some scholars recently proposed to use fractional Fourier transform (FRFT) to make the weak fault signatures concentrate more energy in the narrowband, which is called VMD-FRFT. Nevertheless, VMD-FRFT is more sensitive to the initial center frequency (ICF) than VMD according to our study, which will make it derive undesirable mode components due to unreasonable ICFs. Inspired by the resonant demodulation method to find the appropriate frequency band for demodulation, an improved VMD-FRFT with the guidance of ICF is proposed, which is to take the center frequencies corresponding to K selected frequency bands as the initial values of VMD-FRFT. Hence, the modal components hidden in multiple resonant frequency bands can be obtained in terms of performing iterative optimization. In this paper, a novel indicator named reciprocal of spectral autocorrelation smoothness index being sensitive to the periodic impulses is introduced to detect resonance frequency bands. Both simulated and experimental examples are used to verify the proposed method. The results show that the proposed method can effectively identify weak faults and detect bearing faults at an earlier time than other methods such as Infogram, reciprocal of spectral smoothness index and improved VMD.