Improved Variational Mode Extraction and Its Application in Rolling Bearing Feature Extraction

Variational mode extraction (VME) introduces a new criterion based on variational mode decomposition (VMD): the residual signal after extracting a specific mode should have minimal or no energy at that mode’s center frequency (CF). This allows VME to effectively extract modes near the CF, reducing the mode aliasing effect seen in VMD. Recursive VME (RVME) successfully applies VME to bearing fault diagnosis. However, VME does not fundamentally improve VMD’s estimation of mode bandwidth, leading to biases in the extracted signals and limiting the full extraction of bearing fault characteristics. To address this issue, this article proposes an improved VME (IVME) method. IVME uses fractional-order derivatives to adjust the L2-norm estimation of mode bandwidth, allowing it to dynamically adapt to signals with varying bandwidths. An empirical formula is provided to relate the penalty factor to the fractional-order derivative. Additionally, IVME adaptively determines the initial CF of the target mode based on the convergence trend of VMD’s CF. This enables adaptive extraction of bearing fault characteristics. The proposed method is tested on both synthetic and experimental bearing fault signals, with its performance compared to other classical fault feature extraction methods. The results show that IVME outperforms VMD, VME, and fast SK in extracting fault features.