Spectral variational mode extraction and its application in fault detection of rolling bearing

The core of fault diagnosis of rolling bearing is to extract the narrowband sub-components containing fault feature information from the bearing fault signal. Variational mode extraction (VME), a novel single sub-component separation algorithm originated from variational mode decomposition (VMD), provides a promising solution to bearing fault detection. However, its performance is closely related to the hyperparameter selection, including the center frequency ω _d and the penalty factor α. This paper proposes a non-recursive and adaptive signal decomposition algorithm termed spectral variational mode extraction (SVME). SVME can be seen as a spectral decomposition technique whose framework is composed of the adaptive spectral boundary division and boundary constrained VME. In the adaptive spectral boundary division, an adaptive iterative spectral envelope method referring to the continuous envelope correlation (CCE) index is developed to integrate with the parameterless scale-space division to adaptively locate the frequency band boundary. The presented adaptive spectral boundary division approach can effectively inhibit the spectral boundary over-division. In the boundary constrained VME, the dominant frequency of each frequency band determined by the optimal spectral division is distinguished as the preset center frequency. Meanwhile, the optimal penalty factor is determined based on the envelope spectral kurtosis (ESK) index and the boundary-constraint principle. The SVME method is utilized in the simulation and experimental case studies to investigate its capability. Furthermore, its superiority is highlighted through the comparison with the variational mode decomposition (VMD) and Autogram methods.