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.

中文翻译：

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水平能见度图的总变差及其在滚动轴承故障诊断中的应用

摘要 图总变异（TVG）是衡量图信号平滑度的一个强大的顶点域指标，但其性能与底层图密切相关。由于水平能见度图比路径图能更好地反映轴承振动信号的动力学特性，因此将TVG的底层图称为水平能见度图。在水平可见性图上定义的顶点域索引TVG在本文中简称为TVHVG。为更好地区分滚动轴承的不同状态，将轴承振动信号转化为其水平可见度图索引的图信号，提取顶点域指标TVHVG作为单一故障特征。基于TVHVG特征提取和马氏距离分类，提出了一种新的滚动轴承故障诊断方法。将所提出的方法应用于分析包含正常和故障滚动轴承的两组实验数据。结果表明，该方法能够有效地诊断出不同类型、不同程度的轴承故障，顶点域指标TVHVG在区分滚动轴承不同状态方面优于一些经典的时域指标。