## 4 Results
### Fault Diagnosis Based on Individual Modes  
To clearly highlight the advantages of the MFFD model in the context of single modalities, corresponding time-domain and time-frequency-domain models were developed. Following the signal processing phase, the fault detection methods were validated across different datasets. Specifically, for the Ottawa and Pade datasets, vibration signals were utilized as input for the image modality, while acoustic signals were employed for the time series modality. In the case of the Paderborn dataset, vibration signals were used for the image modality, and current signals were used for the time series modality. All operations were conducted under consistent data preprocessing conditions. The performance of the baseline models for single modalities was compared to that of the multimodal approach in bearing fault diagnosis. The detailed baseline methods and experimental results are provided in Table 4.  
In the fault diagnosis based on image signals, the processed bearing vibration signals were input into the RGCNN model for training. After 20 training epochs, classification prediction results were obtained. The confusion matrix are shown in Figure 5. The network's error gradually decreased with the increase in epochs, and after 20 epochs, the network converged, achieving an accuracy of 95.75% and 96.00%.  
For the fault diagnosis based on time series signals, the processed time series signals were input into the 1 DCNN model for training. After 20 training epochs, classification prediction results were obtained, and the training convergence curve of the network is illustrated in Figure 7. Similar to the previous model, the network's error decreased over the epochs, and after 20 epochs, the network converged, achieving accuracies of 89.25% and 92.25%, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & \multicolumn{3}{c}{**Ottawa**} & \multicolumn{3}{c}{**Pade**} \\ \hline Method & 1 DCNN & RGCNN & MFFD & 1 DCNN & RGCNN & MFFD \\ \hline Accuracy & 89.25 & 95.75 & 98.75 & 92.25 & 96.00 & 99.00 \\ \hline Precision & 0.9012 & 0.9590 & 0.9887 & 0.9255 & 0.9624 & 0.0991 \\ \hline Recall & 0.8998 & 0.9562 & 0.9871 & 0.9240 & 0.9590 & 0.9898 \\ \hline F1 & 0.8992 & 0.9569 & 0.9877 & 0.9231 & 0.9598 & 0.9903 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of comparisons using different methods.  
To demonstrate the effectiveness of the proposed method, 10 repeated experiments were conducted. Additionally, confusion matrix and T-SNE visualizations were performed, as shown in Figures 5 and 6. These visualizations intuitively illustrate the classification performance of the proposed model.  
Figure 5: Confusion matrices for the three methods with the highest accuracy on the Paderborn and Ottawa datasets: (**a**) 1 DCNN-Ottawa; (**b**) RGCNN-Ottawa; (**c**) MFFD-Ottawa; (**d**) 1 DCNN-Pade; (**e**) RGCNN-Pade; (**f**) MFFD-Pade.  
Figure 6: t-SNE feature visualization for the three methods with the highest accuracy on the Paderborn and Ottawa datasets: (**a**) 1 DCNN-Ottawa; (**b**) RGCNN-Ottawa; (**c**) MFFD-Ottawa; (**d**) 1 DCNN-Pade; (**e**) RGCNN-Pade; (**f**) MFFD-Pade.