## 5 Results and Discussion
### Parameter Setting and Diagnostic Details  
The experiment was conducted on a NVIDIA GeForce GTX 3080 Ti GPU, The software versions used for data processing in this text are Python version 3.8.6 and MATLAB version R2024b.The GIN-AM model \(f\) is trained using a supervised end-to-end approach with loss \(L=L_{\textit{cross}}+\lambda\mathcal{L}_{\textit{orth}}\), where the cross-entropy loss is \(L_{\textit{cross}}\) and \(\lambda\) is the proportion coefficient of orthogonal regularization. The number of layers \(K=4\) is set, embedding dimension \(D=64\), and regularization coefficient \(\lambda=1.0\times 10^{-5}\). Hyperparameters are adjusted by trial and error, with a batch size of 64, and with specific settings shown in the Table 5.  
Figure 10 illustrates the training and validation process of the suggested fault diagnosis methodology for an axial piston pump on the GIN-ST model. To eliminate any potential random effects, five trails are conducted. The results in Figure 10 demonstrate that the GIN-ST model achieved convergence at epoch 100 with a training and validation loss approaching zero.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Value** \\ \hline batch size & 64 \\ initial learning rate & 0.0001 \\ optimizer & Adam \\ edge weighting & Gaussian kernel \\ momentum & \(1.0\times 10^{-5}\) \\ aggregation hidden size & 128 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental parameters.  
The confusion matrices in Figure 11 illustrate the performance of the proposed diagnostic method under both time domain and frequency domain input conditions. Within the graph, frequency domain input signifies the preprocessing of subsamples through the utilization of fast Fourier transform (FFT), aiding in the mitigation of noise interference inherent in time domain signals. The application of the proposed method to fault classification with two distinct inputs yields results as depicted in Figure 12a,b, respectively. The classification results show that predictions based on frequency domain input are markedly superior to those based on time domain input. This difference in outcome can be attributed to the substantial levels of noise present within the industrial working environment of axial piston pump systems. The application of FFT processing to the data can effectively reduce the disruptive influence of environmental noise on node features of the graph, thus enabling an easier acquisition of more meaningful node and graph representations.  
To examine the outcomes of graph-based feature learning derived from the proposed model, we employed the widely utilized t-distribution stochastic neighbor embedding (t-SNE) method. The horizontal and vertical axes correspond to the two dimensions of the t-SNE embedding space, denoted as Component 1 and Component 2, respectively. As depicted in Figure 12, the t-SNE results reveal that in the time domain (TD), apart from capturing the typical characteristics of the plunger pump, the features associated with other fault categories exhibit incorrect classification. Conversely, in the frequency domain (FD), nearly all fault categories can be accurately classified.  
Figure 11: Confusion matrix of the proposed models. (**a**) time domain input; (**b**) frequency domain input.  
Figure 10: Training and validation process of the GIN-ST model. (**a**) Training and validation accuracy; (**b**) training and validation loss.