Spectral structure inducing efficient variational model for enhancing bearing fault feature.

• The convergence property of VME model is first revealed and proved theoretically. • A central frequency identification strategy is presented to detect TCFs of latent modes. • A bandwidth estimation strategy is built to determine the balance parameter efficiently. • Our SSEVM can correctly extract the fault-related mode from the mechanical signal. • The proposed method is validated by one numerical case and two experimental cases. Variational mode extraction (VME) has attracted increasingly attentions due to its characteristic of extracting a specific mode from the complicated signal. Nevertheless, its performance depends on the initial center frequency (ICF) and the balance parameter. To address the issue of setting ICF, a convergence property of VME is first explored by feeding different ICFs into the variational model. During this exploration, a convergence tendency phenomenon of center frequency (CF) is found from the optimization procedure of VME and a mathematical proof is successfully conducted on this phenomenon. As a result, a CF identification strategy is designed to determine the ICFs for the expected modes automatically, where a calibration operation is synchronously built to improve the identification accuracy of ICFs. In addition, to determine the balance parameter efficiently, a bandwidth estimation strategy with a solid theoretical basis is constructed motivated by the filtering structure of VME model. Finally, a spectral structure inducing efficient variational model is proposed to adaptively extract the faulty modes from the complicated signal by combining the CF identification strategy and the bandwidth estimation strategy. The effectiveness of the proposed method for bearings fault diagnosis is verified by a simulated and two experimental cases and its superiority is also confirmed by comparing with some classical and advanced methods. [ABSTRACT FROM AUTHOR]