## 5 Results and Discussion
### Compared with Other Methods  
To demonstrate the efficacy and superiority of our proposed diagnostic approach, it is essential to compare it with other intelligent fault diagnosis methods. Accordingly, we benchmarked our GIN-ST algorithm against ARGCN [25], DCA-BiGRU [24], GCN [26], GAT [27], GIN [28], and other similar algorithms. Moreover, we compared our proposed method against the traditional five-layer CNN [23]. During our experimental process, the labeled samples were utilized before constructing the weighted graph as the input of CNN, while the weighted graph was used as the input of GCN. All models underwent training using 100 epochs with an initial learning rate of 0.001, and the learning rate during the model training process was adjusted through a multi-step strategy, which was divided into four stages: 0-10, 10-30, 30-60, and 60-100 training epochs, each using a different learning rate. The specific setting strategy is shown in Figure 13 and the optimizer was set to Adam. To mitigate potential impacts of random events on our findings and to underscore the robustness and dependability of our proposed methodology, five experiments were performed. The assessment of classification efficacy centered on the overall classification accuracy, encompassing metrics such as maximum accuracy (max-acc), minimum accuracy (max-acc), and minimum accuracy (max-acc). The results are shown in Figure 14.  
Figure 12: Feature representations visualized by t-SNE. (**a**) time domain input; (**b**) frequency domain input. Figure 13: Learning rate multi-step setting strategy. racy (min-acc), average accuracy (avg-acc) across five trials, and training duration. The classification outcomes of various methods are delineated in Table 6.  
The failure diagnosis model presented in this study learns the process of graph feature in each layer, as demonstrated in Figure 14. The graph depicts scattered points in the distribution of features of the raw input. However, certain features in the RDFB category ( ) tend to cluster; meanwhile, the majority of features representing other category faults continue to display almost uniform distribution, even after being processed by GConv1. Further information extraction by GConv2 enables the classification and clustering of distinct faults features. Eventually, feature clustering is established in the same type through the learning of FC, and clear classes are distinguishable at this stage. By utilizing the frequency domain input of the pressure signals, GIN-AM successfully accomplishes fault classification of the axial piston pump. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **Max-acc (\%)** & **Min-acc (\%)** & **Avg-acc (\%)** & **Time (s)** \\ \hline CNN & 93.83 & 90.94 & 92.81 \(\pm\) 1.19 & 119 \\ ARGCN & 91.36 & 86.88 & 89.35 \(\pm\)1.38 & 101.8 \\ DCA-BiGRU & 94.82 & 92.64 & 93.94 \(\pm\) 0.87 & 182.6 \\ GCN & 90.61 & 86.92 & 89.27 \(\pm\) 1.41 & **93.4** \\ GAT & 94.06 & 91.86 & 93.09 \(\pm\) 0.84 & 94.1 \\ GIN & 96.72 & 93.69 & 95.2 \(\pm\) 1.24 & 98.5 \\
**GIN-ST** & 98.8 & 96.06 & **97.31\(\pm\)0.40** & 105.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Failure diagnosis results of axial piston pumps using different methods. Figure 14: Feature learning process for each layer. Figure 15 illustrates the confusion matrices of various intelligent failure diagnosis methods, excluding the proposed approach, under a similar frequency domain input. The classification results indicate substantial inconsistencies in sensitivity to strong noise among different diagnosis model input features. Moreover, it is commonly observed that graph convolutional neural networks with an attention mechanism (GAT) and GIN show significant superiority over other methods. Therefore, this paper provides an idea for designing a spatio-temporal attention mechanism module based on the traditional GIN model. Figure 15: Confusion matrices of different failure diagnosis methods. (**a**) MLP; (**b**) CNN; (**c**) DCA-BiGRU; (**d**) GCN; (**e**) GAT; and (**f**) GIN.