Variable-Scale Spectral Feature Gram (VSFgram): A Convergence Property-Driven Autonomous Periodic Transients Extraction Approach

Precise localization of the optimal frequency band (OFB) and extraction of periodic transients are crucial for effective bearing fault diagnosis. This article proposes a novel approach called the variable-scale spectral feature gram (VSFgram) for periodic transients extraction. The method begins with the development of a spectral feature detector (SFD) based on the convergence property of the variational mode extraction (VME), enabling the identification of the spectral feature. Building on the SFD, a novel multilevel spectral segmentation framework based on variable-scale spectral feature detection (VSFD) is developed, where boundary frequencies (BFs) are adaptively derived from the vibration signal to effectively isolate the OFB. To refine the process, an improved fault feature metric named autonomous frequency domain signal-to-noise ratio (AFDSNR) is proposed, which guides OFB selection and automatically estimates fault characteristic frequency (FCF) from enhanced envelope spectrum (EES) information. The OFB is then located by maximizing the AFDSNR, enabling the reconstruction of corresponding periodic transients. The superiority of the proposed method is validated through simulations and experimental analyses. Compared to methods such as Fast Kurtogram (FK) and Autogram, the VSFgram demonstrates superior accuracy and robustness in bearing fault diagnosis.