## 3 Proposed Model
### Dynamic Multi-Attention GCNs  
Although a GCN can utilize numerical and structural information, it cannot adaptively assign weight coefficients according to the importance of neighbors, which leads to insufficient attention to key neighbor information. The graph attention network (GAT) solves this problem to a certain extent by adding an attention mechanism to the GCN. The GAT can distinguish the number of connected edges according to the characteristics of the nodes. In addition, it can differentiate the weights of neighbor nodes of the central node. The core of the GAT is the attention coefficient. Figure 3 presents a schematic diagram of the attention layer, which is expressed as follows:  
\[e_{ij}=leakyRelu(\alpha^{T}(wh_{i}||wh_{j})) \tag{19}\]  
where \(e_{ij}\) represents the attention coefficient of the edge connecting \(v_{i}\) and \(v_{j}\), and h is the feature matrix of the node. \(h\in R^{N\times M}\), that is, there are \(N\) nodes in total, and each node has \(M\) features. In addition, w is the trainable weight matrix of the network and plays a role in adjusting the output feature dimension: \(w\in R^{M\times F}\). \(\alpha\) is a trainable calculation function in the network, and its dimension is \(2^{\bullet}\)F. \(||\) is the concatenation operation. To better represent the importance of neighbors, the attention coefficient must be normalized:  
\[a_{ij}=softmax\big{(}e_{ij}\big{)}=\frac{\exp(leakyRelu(\alpha^{T}(wh_{i}||wh _{j})))}{\sum_{k\in N_{i}}\exp(leakyRelu(\alpha^{T}(wh_{i}||wh_{k})))} \tag{20}\]  
where \(a_{ij}\) represents the weight of the edge between \(v_{i}\) and \(v_{j}\), leakyRelu is the activation function, and \(N_{i}\) represents all neighbors of \(v_{i}\). After obtaining the weight of the edge, the node feature matrix of the next layer of the network can be obtained according to Equation (21), and the forward propagation of the GAT node features can be achieved:  
\[{h_{i}}^{\prime}=\sigma\Bigg{(}\sum_{j\in N_{i}}a_{ij}wh_{j}\Bigg{)} \tag{21}\]  
where \({h_{i}}^{\prime}\) represents the feature of \(v_{i}\), and \(\sigma\) represents the activation function.  
Figure 2: Weight function comparison graph.  
However, the attention in the GAT is static attention, that is, there are some nodes whose maximum-weight neighbors are all the same node. Decomposing \(\alpha\) into \(\alpha=[\alpha_{1}||\alpha_{2}]\) allows the weight relationship between nodes to be written as follows:  
\[a_{ij}=leakyRelu\left(\alpha_{1}^{T}wh_{i}+\alpha_{2}^{T}wh_{j}\right) \tag{22}\]  
In all nodes of the graph structure, there must be a node \(j_{max}\) that leads to the largest \(\alpha_{2}^{T}wh_{j}\). Let \(i^{\prime}\) be any neighbor of \(j_{max}\); then, the neighbor with the largest weight for \(i^{\prime}\) is also \(j_{max}\). In the same way, for all neighbor nodes of \(j_{max}\), the neighbor with the largest weight is \(j_{max}\), which is the static attention of the GAT. The expressive ability of static attention is limited, which reduces the expressive ability of the GAT.  
Figure 3: Graph attention layer.  
The acceleration sensors were mounted onto the HVCB beam. Faults are prone to occur during the closing and opening of the HVCB, and when this occurs, it is no longer possible to open and close the circuit breaker normally. Even if the opening and closing function can be achieved occasionally, the contact opening distances and overtravel are unable to return to normal after an action. This experiment included four HVCB working conditions: the normal working condition, closing-spring fatigue failure, opening-spring fatigue failure, and jammed iron core. The total number of samples collected was 400, that is, 100 for each working condition. Figure 6 presents the waveform.  
Figure 5: High-voltage circuit breaker mechanical fault acquisition system.  
Figure 6: _Cont._