Empirical Fourier-Bessel heuristic denoising and its application to gear fault diagnosis

Traditional methods based on Fourier spectrum segmentation have been successfully applied to gear fault diagnosis. However, conventional spectrum segmentation approaches, which typically use the minimum point or the midpoint between adjacent local maxima as segmentation boundaries, often result in inaccurate division of frequency bands containing important gear fault information. In addition, the Fourier spectrum suffers from low frequency resolution and is not well-suited for characterizing non-stationary signals. To address the above issue, this paper proposes empirical Fourier-Bessel heuristic denoising method (EFBHD), Fourier-Bessel series expansion is used to characterize the signal, which can better represent non-stationary signals and provides higher frequency resolution. The new concept of envelope local mutation point is defined, and heuristic search-based spectrum segmentation is employed to realize the segmentation of Fourier-Bessel series spectrum. The EFBHD method effectively captures local variations in the frequency band through the use of envelope local mutation points. Moreover, its heuristic segmentation strategy enables the extraction of local narrow bands rich in fault information, while filtering out interference components. Simulation and experimental results demonstrate that EFBHD exhibits strong gear fault feature extraction capabilities.