Empirical variational mode extraction and its application in bearing fault diagnosis

Bearing fault signals typically contain rich interference components such as random pulses, harmonics, and environmental noise, posing significant challenges for bearing fault feature identification. Derived from variational mode decomposition (VMD), variational mode extraction (VME) stands out due to its specialized narrowband filtering capabilities, enabling effective extraction of targeted components from complex signals. However, VME's capability notably depends on two key parameters: the penalty factor, which controls the bandwidth of extracted mode, and the central frequency, determining the frequency band's center for extraction. An empirical variational mode extraction (EVME) method, inspired by the structure of empirical wavelet transform (EWT), is introduced to guide optimal filtering and demodulation analysis of fault components. Firstly, the effects of central frequency and penalty factor on the filtering characteristics of VME are thoroughly investigated and the mathematical relationship between bandwidth and penalty parameter is established through mathematical simulations. Secondly, a spectrum background scale-space division (SBSSD) method which incorporates adaptive clutter separation (ACS) and scale-space division is proposed to implement an optimal spectrum division, guiding the parameter determination of VME. Finally, each component is recursively extracted by VME from low to high frequencies following the segmentation outcomes of frequency bands. Simulated and experimental validations confirm the capability of EVME for extracting bearing fault features. Furthermore, comparisons with VMD and EWT underscore its superiority.