Boundary-constrained empirical Fourier decomposition and its application in gear fault diagnosis

Abstract Feature extraction is crucial for gear fault diagnosis. However, due to the complex vibration interference and strong background noise present in the actual vibration signals, accurately extracting the weak fault features of gear remains a challenging issue. For this reason, this paper proposes a boundary-constrained empirical Fourier decomposition (BCEFD) method. Firstly, BCEFD introduces a Fourier-model fitting method for estimating spectral trend, thereby reducing the complexity of spectrum. Building on this, BCEFD proposes an adaptive spectral trend segmentation technique guided by average envelope harmonic-to-noise ratio (AEHNR) index, which can not only adaptively determine the number and boundaries of segmented frequency bands, but also achieve the accurate division of frequency bands of interest. Additionally, a frequency band selection criterion based on correlation coefficient is designed in the spectral trend segmentation process to remove invalid frequency bands caused by local spectral fluctuations. Finally, the obtained frequency bands are reconstructed by using a zero-phase filter bank and inverse fast Fourier transform to derive a series of signal components. The analysis results of simulation and experimental cases prove that the proposed BCEFD method can effectively extract weak fault features of gear, thereby achieving accurate diagnosis of gear fault.