Rolling bearing faults are mainly divided into four categories: normal state, inner race fault, outer race fault, and rolling element fault. Different damage sizes correspond to various fault severity levels [10]. Bearing vibration signals are non-stationary impact time-series signals, and fault impacts manifest as amplitude fluctuations in the time domain and resonance peak shifts in the frequency domain [11]. Figure 1 presents the time-frequency domain analysis of vibration signals collected from bearings with ball faults. The characteristics of these signals serve as the basis for the time-frequency fusion features extracted by the model, and also provide physical support for subsequent fault diagnosis based on spatio-temporal graph convolution. Therefore, combining time-domain statistical features and frequency-domain spectral features can fully characterize fault information.

Figure 1.Time-domain and frequency-domain analysis of typical fault signals.

As a dominant graph neural network for non-Euclidean graph-structured data, GCN is capable of capturing node attributes and topological correlations, which remedies the drawback of conventional CNNs limited to regular data [12][13].

A graph G is formally defined as G = ( V , E ) , where V . represents the set of nodes and E denotes the set of edges. The core idea of graph convolution is to aggregate neighborhood features and perform nonlinear transformations, so as to fuse each node’s own features and its topological neighborhood features, and finally generate node representations containing both attribute and structural information.

As a typical approach to constructing graphs from unstructured data, KNN graph building screens neighbors based on node feature similarity and creates topological connections [14]-[17]. It converts raw feature data into graph data and is extensively used in topology-free deep learning tasks.

Firstly, we compute the feature similarity across all nodes using Euclidean or cosine distance. Next, each node picks its top-K most similar neighbors [10]. Eventually, undirected edges are created to build the entire graph topology. The calculation formula for Euclidean distance is as follows:

In the formula, x i and x j denote the feature vectors of node i and node j respectively, and C stands for the feature dimension. A smaller distance value indicates higher similarity between node features.

Compared to random and fully-connected graph construction methods, traditional KNN graphing is structurally simple and computationally efficient, and can establish semantically meaningful topologies by capturing feature-level relationships [18]-[21]. However, it relies solely on original feature similarity while ignoring global data distribution and implicit connections. The resulting locally optimal topology will impair the learning performance of graph convolution.

Figure 2. Structure of the proposed model.

The overall architecture of the proposed model is illustrated in Figure 2, which consists of five parts: data input layer, spatial-temporal dual-branch graph convolution layer (STDBGCN Layer), residual attention layer (RA Layer), feature fusion layer (FF Layer), and fault classification output layer (FCO Layer).

The raw one-dimensional vibration time-series signals of rolling bearings are fed into the model. The original data are divided into samples via sliding window segmentation, and fused time-domain and frequency-domain features are extracted as node features of the graph. A dynamic weighted K-NN algorithm combining temporal distance and cosine similarity is adopted to generate the adaptive adjacency matrix. The spatial-temporal dual-branch network learns spatial and temporal features in parallel, and residual connections together with the node attention module are used to optimize feature representation. Finally, global pooling and fully connected layers in the fault classification output layer realize the classification of bearing fault patterns.

The original vibration acceleration signals are segmented via non-overlapping sliding windows. The length of each sample is set to L , and each window segment is regarded as an individual node of the graph network.

We extract time-domain features for each signal segment, including mean value, standard deviation, peak value, kurtosis, waveform indicator, and impulse indicator. Meanwhile, frequency-domain features such as spectral centroid, mean square frequency, and variance frequency are also computed. The concatenation of time-domain and frequency-domain features yields a high-dimensional node feature vector x i ∈ ℝ d , which realizes the mapping from raw non-sequential signals to graph node features.

The feature cosine similarity between node i and node j is defined as:

The temporal position distance between node i and node j is defined as:

Here, ε is a small constant preventing a zero denominator. t i and t j are sample temporal indices. Linear normalization is performed on node feature similarity and temporal position distance, respectively, to scale them into the range of [0, 1].

where S i m ˜ i j and D i s ˜ t , i j denote the normalized feature similarity and temporal distance, respectively. The adjacency weights are obtained after weighted fusion. The overall weighted fusion distance is given by:

Here, λ denotes the weight balancing coefficient. To satisfy the requirements of graph convolution operations for the adjacency matrix, S i j is normalized via the Softmax function. Here, k represents the indices of all neighboring nodes of node i, which means the summation is conducted over all j corresponding to node i.

Traditional methods adopt a globally fixed K. In this work, the number of neighbors is adaptively adjusted according to the density of sample features.

Here, K b a s e stands for the base neighbor count, η is the regulation coefficient, and N is the total node number. Higher feature similarity corresponds to more adaptive neighbors, forming a dynamic topology.

The spatial branch adopts a multi-head graph attention network to explore fault topological correlations among nodes. It performs spatial aggregation on the features of dynamic graph nodes and learns the common and distinctive characteristics of samples.

Vibration signals exhibit continuous temporal evolution characteristics. In this paper, gated temporal convolution is introduced to model node sequences in the time dimension, so as to capture the time-varying dependencies of fault impacts and compensate for the lack of temporal information in pure spatial graph networks.

Here, x t ∈ ℝ L × d S . L is the temporal length, d S is the output feature dimension of the spatial branch. W f and W g are one-dimensional convolution kernels for the feature branch and gating branch, and σ ( ⋅ ) is the Sigmoid activation function.

The spatial and temporal feature vectors are concatenated along the channel dimension to construct the global spatio-temporal feature representation. The fused feature is defined as:

To address the over-smoothing problem of deep graph convolution, we design residual skip connections and a node attention weighting module.

Shallow original features are directly delivered to deep networks via skip connections to avoid feature homogenization after multi-layer aggregation. The node attention mechanism amplifies important fault features by weighting, suppresses noisy and redundant information, and enhances the representation of weak faults.

The fused spatio-temporal features are processed by global average pooling and then fed into the fully connected neural network. The Softmax activation function outputs the probability of each fault category to implement fault classification.

We use the CWRU rolling bearing dataset from Case Western Reserve University. The CWRU dataset consists of vibration time series of various rolling bearing conditions collected from the test rig, as shown in Figure 3. The test bearing is the 6205-2RS deep groove ball bearing with a sampling frequency of 12 kHz. Four load conditions are set, namely 0 hp, 1 hp, 2 hp, and 3 hp. The fault types include normal condition (NC), inner race fault (IR), outer race fault (OR), and ball fault (B). Fault defect sizes are 0.1778 mm, 0.3556 mm, and 0.5334 mm. The ten fault modes are shown in Table 1. To strictly meet the generalization requirements for industrial applications, the training, validation, and test sets are divided according to experimental working conditions and acquisition batches. Specifically, the data collected under 1 hp and 2 hp loads are used as the training and validation sets, while the data from the independent 3 hp working condition is adopted as the test set. All sample windows segmented from the original vibration signals are assigned to a single dataset only, without distribution across the training and test sets. The dataset is split into a training set (70%), a validation set (20%), and a test set (10%).

Figure 3. Test rig for rolling bearings.

Table 1. Classification information of rolling bearings.

Sliding window segmentation is applied to the original vibration signals to construct training samples. The sliding window length is set to 1024 sampling points with a sliding step of 512 sampling points, corresponding to an overlap rate of 50%, which fully preserves the temporal characteristics of fault impulses. Variational Mode Decomposition (VMD) is used for signal denoising and reconstruction. Afterwards, each sample window is standardized to zero mean and unit variance to eliminate dimensional and amplitude interference .

Four mainstream methods are selected for comparative experiments:

1) SVM: A classic traditional machine learning algorithm. It constructs an optimal hyperplane to achieve sample classification, and performs well on small-scale datasets. It is widely used in traditional bearing fault diagnosis as a benchmark method.

2) LSTM: A typical recurrent neural network. It is designed to capture long-range temporal dependencies of time-series signals and is widely applied to vibration signal analysis and time-series fault classification tasks.

3) KNN-GCN: It first constructs a graph structure based on K-nearest neighbor relationships of samples, then leverages graph convolution to aggregate node features. This method combines traditional distance metric learning with graph neural networks.

4) GAT: It introduces the attention mechanism into graph learning, adaptively assigns different weights to neighboring nodes during feature aggregation, and effectively highlights important associative relationships between nodes.

All baseline models adopt the same dataset partition. The Adam optimizer is used in the experiments with a learning rate of 0.001 and a batch size of 32. The total training epochs are set to 100. CrossEntropyLoss is selected as the loss function, and the basic adjacency number K b a s e is set to 8.

Multi-class fault diagnosis experiments are conducted on the bearing fault dataset. We comprehensively evaluate the overall performance of the proposed AdaDKNN-STGCN model from multiple perspectives, including model convergence, classification accuracy, confusion matrix , and feature visualization. Meanwhile, comparative analysis is carried out against mainstream algorithms such as SVM, LSTM, KNN-GCN, and GAT.

As shown in Table 2, the proposed AdaDKNN-STGCN model achieves an accuracy of 99.78% in the 10-class fault diagnosis task, which is remarkably higher than that of the comparative models including SVM, LSTM, KNN-GCN, and GAT. The standard deviation is merely 0.08, indicating the optimal stability of the model. According to the paired t-test for significance, the p-values between all comparative models and the proposed model are less than 0.05. At the 95% confidence level, the performance difference is statistically significant. It is statistically verified that the diagnostic performance of the proposed model is remarkably superior to existing mainstream algorithms. This verifies the effectiveness and superiority of the proposed method for fault diagnosis.

Table 2.Table comparison of fault diagnosis accuracy of different models.

The training and validation accuracy curves of different models are presented in Figure 4. It can be observed that AdaDKNN-STGCN converges faster. In addition, the training and validation accuracy curves of the model closely overlap, indicating its outstanding generalization ability and effective suppression of overfitting. Figure 5 illustrates the loss curve of AdaDKNN-STGCN, which further demonstrates stable training performance. The classification details are analyzed via the confusion matrix in Figure 6. The results reveal that the proposed model can accurately identify samples under normal conditions as well as bearing samples with different damage severities and fault locations.

To explore the feature learning capability of the model, t-SNE is adopted to reduce the dimensionality of high-dimensional features from the output layer for 2D visualization, as shown in Figure 7. The feature distribution shows that samples of the same fault category are highly clustered in the feature space. This proves that AdaDKNN-STGCN can fully extract deep features from vibration signals and effectively distinguish different fault types and damage degrees. The excellent feature representation capability lays a solid foundation for the high diagnosis accuracy of the model.

Figure 4. Comparison curves of training and validation accuracy of models.

Figure 5. Training and validation curve for loss.

Figure 6. Confusion matrix for each category.

Figure 7.Visualization based on t-SNE algorithm.