Graph shift regularization is a new and effective graph-based semi-supervised classification method, but its performance is closely related to the representation graphs. Since directed graphs can convey more information about the relationship between vertices than undirected graphs, an intelligent method called graph shift regularization with directed graphs (GSR-D) is presented for fault diagnosis of rolling bearings. For greatly improving the diagnosis performance of GSR-D, a directed and weighted k-nearest neighbor graph is first constructed by treating each sample (i.e., each vibration signal segment) as a vertex, in which the similarity between samples is measured by cosine distance instead of the commonly used Euclidean distance, and the edge weights are also defined by cosine distance instead of the commonly used heat kernel. Then, the labels of samples are considered as the graph signals indexed by the vertices of the representation graph. Finally, the states of unlabeled samples are predicted by finding a graph signal that has minimal total variation and satisfies the constraint given by labeled samples as much as possible. Experimental results indicate that GSR-D is better and more stable than the standard convolutional neural network and support vector machine in rolling bearing fault diagnosis, and GSR-D only has two tuning parameters with certain robustness.

图移位正则化是一种基于图的新型有效半监督分类方法，但其性能与表示图密切相关。由于有向图比无向图可以传达更多关于顶点之间关系的信息，因此提出了一种称为有向图的图偏移正则化（GSR-D）的智能方法，用于滚动轴承的故障诊断。为了大大提高GSR-D的诊断性能，有针对性的加权k-最近邻图是通过将每个样本（即每个振动信号段）作为一个顶点来构造的，其中样本之间的相似性是通过余弦距离而不是常用的欧几里德距离来测量的，并且边缘权重也由余弦距离，而不是常用的热核。然后，将样本的标签视为由表示图的顶点索引的图信号。最后，通过找到具有最小总变化并尽可能满足标记样本给定约束的图形信号来预测未标记样本的状态。实验结果表明，在滚动轴承故障诊断中，GSR-D比标准卷积神经网络和支持向量机更好，更稳定，