Improvement of VMD and Compensation Distance for Rolling Bearing Fault Detection Methods

To address the problem of varying detection performance and the lack of universal standards for early fault detection in rolling bearings, a method for early fault detection in rolling bearings based on an improved variational modal decomposition (IVMD) and compensation distance (CD) is proposed from the perspective of constructing performance degradation curves. Firstly, the number of modes K for variational mode decomposition (VMD) is adaptively determined using the estimated signal-to-noise ratio (eSNR) method. Secondly, the probability density function (PDF) distribution of the intrinsic mode function (IMF) obtained from the decomposition is calculated, and the compensation distance (CD) degradation evaluation index is constructed by integrating the inter-class and intra-class distances. Then, a sliding window is used to repair the false fluctuations in the CD degradation index based on linear regression equations and the $3 \sigma$ principle, resulting in a sensitive degradation index that accurately characterizes the rolling bearing degradation process Improved Compensation Distance (ICD). Finally, the Chebyshev inequality is used to establish the relationship between the healthy threshold and the ICD index, enabling early fault detection in rolling bearings. Comparative analysis of one set of experiments shows that the proposed method can accurately characterize the degradation process of rolling bearings and effectively detect early faults, providing a new solution for early fault diagnosis of bearings.