Fractional iterative variational mode decomposition and its application in fault diagnosis of rotating machinery

Variational mode decomposition (VMD), a recently developed adaptive mode decomposition technique, has attracted much attention in various fields. However, due to the assumption that the obtained intrinsic mode functions should be band-limited and separable in the Fourier domain, VMD has experienced many obstacles when processing wide nonstationary signals. In this paper, a new method named fractional iterative variational mode decomposition (FrIVMD) is proposed for the decomposition of a multicomponent linear frequency modulation signal. By accurately estimating the chirp rate of the linear frequency modulation (LFM) component, the original signal is mapped to the fractional Fourier domain by the fractional Fourier transform (FRFT), where the corresponding LFM component is narrowly banded. Then, the conventional VMD is applied to separate the components. Finally, the signal mode in the time domain is obtained by the inverse FRFT. Numerical and real-world vibration signals arc employed to validate the effectiveness of the FrIVMD technique. The results prove that the proposed method performs well for noisy signals and even signals containing weak components.