WOA-based Parameter Adaptive VMD Combined with Wavelet Thresholding for Bearing Fault Feature Extraction

Variational Mode Decomposition (VMD) is widely used in fault feature extraction for rotating machinery to identify anomalies and fault characteristics. However, in most studies, VMD parameters are typically pre-set, which introduces a degree of randomness in the signal decomposition process, making it difficult to obtain reliable fault diagnosis results. Consequently, this study proposes a whale optimization algorithm (WOA)-based parameter-adaptive VMD method integrated with wavelet threshold denoising (WTD), termed the WOA-VMD-WTD approach, for analyzing bearing fault signals. This method can adaptively determine the optimal parameter combination for the number of modes and the quadratic penalty term. First, an index based on the kurtosis and the maximum mutual information coefficient is developed, named the maximum kurtosis mutual information coefficient. Next, the index serves as the optimization goal, and WOA is employed to fine-tune the VMD parameters. And meanwhile, this index is utilized for screening reconstruction of signal decomposition modes. Finally, the reconstructed signal undergoes secondary denoising using the WTD method to obtain a more accurate Hilbert envelope spectrum, which enhances the feature representation of bearing faults. Three case studies demonstrate the effectiveness and feasibility of the proposed method, and comparisons with other two methods taking the same function highlight its superiority in feature extraction and fault identification.