Recursive Variational Mode Transform for Weak Fault Feature Recognition in Rotor-Bearing Systems

Traditional variational methods face difficulties in extracting fault information from noisy signals. They often struggle to balance minimizing residual energy and suppressing mode aliasing, leading to signal loss and failure to extract the desired mode. To address this, a recursive variational mode transform (RVMT) is proposed for extracting early weak fault features. The core ideas include: 1) minimizing residual energy based on the narrowband hypothesis to solve the variational problem; 2) dynamically updating the parameters of multicomponent signals; and 3) using a spectrum overlap algorithm based on the Hilbert transform for accurate mode decomposition. First, the concept of residual energy is introduced to solve the variational problem and determine the direction of decomposition. Then, adaptive dynamic parameter updating and the spectrum overlap algorithm based on the Hilbert transform are used to reverse-correct mode aliasing components, improving signal resolution accuracy. Finally, by reconstructing the fault information, redundant modes are eliminated. Compared with feature mode decomposition (FMD), empirical Fourier decomposition (EFD), and variational mode estimation (VME), RVMT demonstrates greater effectiveness and robustness in extracting weak fault features under noise interference, as shown by simulations and experimental data of bearing faults. Additionally, quantitative signal-to-noise ratio (SNR) evaluation shows an average increase of 113.07% for the outer race and 107.03% for the inner race.