Bearing-Weak-Fault Signal Enhancement and Diagnosis Based on Multivariate Statistical Hilbert Differential TEO

The enhancement of weak-fault signal characteristics in rolling bearings under strong background noise interference has always been a challenging problem in rotating machinery fault diagnosis. Research indicates that multivariate statistical indicators such as skewness and kurtosis can characterize the fault features of vibration signals. However, when the fault features in the signal are weak and severely affected by noise, the characterization capability of these indicators diminishes, significantly compromising diagnostic accuracy. To address this issue, this paper proposes a novel multivariate statistical filtering (MSF) method for multi-band filtering, which can effectively screen the target fault information bands in vibration signals during bearing faults. The core idea involves constructing a multivariate matrix of fused-fault multidimensional features by integrating fault and healthy signals, and then utilizing eigenvalue distance metrics to significantly characterize the spectral differences between fault and healthy signals. This enables the selection of frequency bands containing the most informative fault features from the segmented frequency spectrum. To address the inherent in-band residual noise in the MSF-processed signals, this paper further proposes the Hilbert differential Teager energy operator (HDTEO) based on MSF to suppress the filtered in-band noise, thereby enhancing transient fault impulses more effectively. The proposed method has been validated using both public datasets and laboratory datasets. Results demonstrate its effectiveness in accurately identifying fault characteristic frequencies, even under challenging conditions such as incipient bearing faults or severely weak vibration signatures caused by strong background noise. Finally, comparative experiments confirm the superior performance of the proposed approach.