## 5 Experimental Results and Discussion
### Experiment 1
#### 5.1.2 Performance Comparison and Discussion  
The effectiveness of the MDI-CNN was validated by comparing the proposed model with other models, including the ordinary CNN (2D-CNN) model and 1D-CNN model. In the comparison process, the input data of the 1D-CNN model was an original one-dimensional signal, which was mapped to the two-dimensional matrix as the input of the ordinary CNN model. In the 2D-CNN, the number of neurons was not changed, the convolution kernel was \(5\times 5\), and the scale of the pool was \(2\times 2\). The 1D-CNN model parameters were the same as of the MDI-CNN. The test results of the methods after twenty iterations are shown in Figure 5, where it can be seen that the training error of the MDI-CNN model was reduced to almost zero when the model reached the convergence condition after a 1000-step training, while the other two models still had the fluctuating training errors after completing 20 iterations. Thus, the MDI-CNN model improved the convergence speed of the CNN model, reducing the training time. The accuracy of the three different models on the test set is shown in Figure 6. The results show that the fault recognition rate of the MDI-CNN model reached 99.96% after training, which proved that the proposed model was feasible and effective, and had high accuracy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter Name** & **C1 Layer** & **P1 Layer** & **C2 Layer** & **P2 Layer** & **Spacing** \\ \hline Parameter value & \(25\times 1\) & \(8\times 1\) & \(20\times 1\) & \(4\times 1\) & 59 \\ Parameter name & numepochs & batchsize & alpha & q1, q2, q3 & Number of neurons \\ Parameter value & 5 & 50 & 0.05 & (1, 1, 1) & (6, 12) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The MDI-CNN parameters; numepochs denotes the number of iterations of the model, batchsize denotes the number of samples processed per batch by the model during the batch training, and alpha denotes the learning rate. Figure 5: The training errors. In order to present more clearly the recognition results of the MDI-CNN in each category of the test set, the confusion matrix was introduced to analyze the experimental results in detail. The results are shown in Figure 7, where the correct classification and error classification for each label are presented. In Figure 7, the horizontal coordinate represents the predicted label, and the vertical coordinate represents the actual label. Only 0.4% of samples of the label 3 in the test set was incorrectly identified as label 2, the rest of the samples were correctly classified, and eventually, the overall accuracy was 99.96%. In order to further verify the learning ability of the MDI-CNN model for different feature categories, the dimension reduction algorithm of the t-SNE was used for feature visualization. The result of feature visualization of the raw samples and fully connected layer samples are presented in Figure 8. In Figure 8, it can be seen that the original signal was so redundant that it was difficult to distinguish between the categories. After the adaptive feature extraction of the MDI-CNN model, ten categories of samples were completely distinguished without intersecting the heterogeneous samples, which was consistent with the classification results of the proposed model. Figure 6: The accuracy of different models. Figure 7: Confusion matrix results with MDI-CNN. Furthermore, the MDI-CNN model was compared with the models presented in the related literature which use the CWRU bearing database. Table 4 shows the classification accuracy of different models. The comparison results show that the recognition rate of the traditional diagnostic model varied significantly, which was because of the need to extract the fault characteristics artificially. Due to the CNN advantages in adaptive extraction of raw signal features, the classification accuracy of the CNN-based intelligent diagnostic model was generally high.