Vibration signals always contain noise and irregularities, which makes spectrum analysis difficult to extract high-level features. Recently, graph theory has been applied to spectrum analysis to improve the performance of feature extraction. By converting the raw data into graphs, hidden structural and topological information can be obtained. In this article, a spatial-temporal graph-based feature extraction, called SuperGraph, for rotating machinery fault diagnosis is proposed. Specifically, graph theory-based spectrum analysis is used to construct the spatial-temporal graph. Then, the Laplacian matrix-based feature vector is extracted from the constructed spatial-temporal graph. By this means, the spatial-temporal graph is converted into the one-dimensional (1-D) vector for further constructing SuperGraph, where each node of the SuperGraph represents a spatial-temporal graph and the SuperGraph is composed of many local graphs. In the local graph, only the same type of nodes are connected to form a fully connected graph. Thus, the task of graph classification can be transformed into classifying the nodes in the SuperGraph. After graph convolutional network is established for learning and obtaining deep features, the label of nodes is identified from a $softmax$ model. Experiments are conducted on two benchmarking datasets and a practical experimental platform to verify effectiveness of the proposed fault diagnosis method.

Due to its ability to learn the relationship among nodes from graph data, the graph convolution network (GCN) has received extensive attention. In the machine fault diagnosis field, it needs to construct input graphs reflecting features and relationships of the monitoring signals. Thus, the quality of the input graph affects the diagnostic performance. But it still has two limitations: 1) the constructed input graph usually has redundant edges, consuming excessive computational costs; 2) the constructed input graph cannot reflect the relationship between the noisy signals well. In order to overcome them, a dynamic graph-based feature learning with few edges considering noisy samples is proposed for rotating machinery fault diagnosis in this article. Noisy vibration signals are converted into one spectrum feature-based static graph, where redundant edges are simplified by the distance metric function. Edge connections of the input static graph are updated according to the relationship among high-level features extracted by the GCN. Based on this, dynamic input graphs are reconstructed as new graph representations for noisy samples. To verify the effectiveness of the proposed method, validation experiments were conducted on practical platforms, and results show that the dynamic input graph with few edges can effectively improve the diagnostic performance under different SNRs.

Graph data-driven machine fault diagnosis methods make success using sufficient data recently. However, in the actual industry, there are rare failure data in historical data, leading to insufficient graph representation ability and reducing diagnosis performance. In this article, a generalized graph contrastive learning (GCL) framework for few-shot machine fault diagnosis is proposed. First, spectrum features of vibration data-based samples are used to calculate Euclidean distance matrix for constructing K-nearest neighborhood graph (KNNG), where K adjacent neighbors of each sample are connected. Avoiding excess calculation cost for graph construction, positive and negative KNNGs are constructed by changing parameter K . To make full use of few-shot samples, an unsupervised GCL subtask is set for pretraining graph deep learning model. Further, the unsupervised pretrained model is semisupervised trained using original KNNGs for outputting unlabeled nodes’ labels. The proposed method achieves 99.83%, 99.56% in bearing and gearbox dataset, respectively, and the proposed GCL framework works for different graph neural networks.

By learning effective information from unlabeled nodes, node-level graph data-driven diagnosis methods perform better than graph-level methods. However, features of unlabeled nodes, indirectly involved in graph feature learning, are not fully utilized. To overcome aforementioned limitations, a semisupervised machine fault diagnosis fusing unsupervised graph contrastive learning (GCL) is proposed. A new GCL framework, where positive and negative graphs are generated by calculating Pearson correlation coefficient, is fused into the graph transformer network (GTN). Furthermore, a new combined loss, including a supervised cross-entropy loss and a new unsupervised GCL loss, is designed for GTN training. Contrastive learning of positive and negative graphs is guided by the unsupervised GCL loss. While the semisupervised graph feature learning for original graphs is mainly driven by the supervised cross-entropy loss, where the GTN for graph feature learning shares parameters. Experimental results on public and real datasets show the proposed method achieves a competitive performance.