Total variation on horizontal visibility graph and its application to rolling bearing fault diagnosis

Abstract

The total variation on graph (TVG) is a powerful vertex domain index for measuring the smoothness of graph signals, but its performance is closely related to the underlying graph. Since the horizontal visibility graph can better reflect the dynamics characteristics of bearing vibration signals than the path graph, the underlying graph of TVG is designated as horizontal visibility graph. The vertex domain index TVG defined on horizontal visibility graph is called simply as TVHVG in this paper. For better distinguishing the different states of rolling bearings, the bearing vibration signal is converted into the graph signal indexed by its horizontal visibility graph, and the vertex domain index TVHVG is extracted as the single fault feature. Based on TVHVG feature extraction and Mahalanobis distance classification, a novel fault diagnosis method for rolling bearings is proposed. The proposed method is applied to analyze two sets of experimental data containing normal and faulty rolling bearings. The results indicate that the proposed method can diagnose the bearing faults with different types and degrees effectively, and the vertex domain index TVHVG is superior to some classical time domain indexes in distinguishing the different states of rolling bearings.