Path Graph Fourier Transformation and Its Applications to Rolling Bearing Fault Diagnosis

doi:10.3901/JME.2015.23.076

Abstract

Abstract: The graph signal processing (GSP) is a new research field, which is derived from the spectral graph techniques. The foundation of GSP is the graph Fourier transformation (GFT), which is the expansion of a graph signal in terms of the eigenfunctions of graph Laplacian matrix. The GFT on path graph is analyzed. It is found that the eigenvalue spectra obtained by GFT and the frequency spectra obtained by the classical Fourier transformation (FT) have a one to one correlation. Meanwhile, the amplitude of an eigenvalue is correlated with the amplitude of the corresponding eigenvector. The GFT is introduced into the fault diagnosis of rolling bearings and a fault diagnosis method based on the GFT and the K-means clustering is proposed. The path graph signal of the vibration signal of a rolling bearing is transformed by GFT into the eigenvalue spectrum domain. The statistical quantities of eigenvalues are calculated for fault feature extraction. The K-means clustering classifier is used to identify the work condition and fault patterns of the roller bearing. The analysis results of the practical vibration signals of rolling bearings demonstrate that the diagnosis approach based on the GFT and the K-means clustering can be used to identify the fault patterns of roller bearings accurately and effectively.

Key words: fault diagnosis, graph Fourier transformation, K-means clustering, path graph, rolling bearing

OU Lu, YU Dejie. Path Graph Fourier Transformation and Its Applications to Rolling Bearing Fault Diagnosis[J]. Journal of Mechanical Engineering, 2015, 51(23): 76-83.

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