## 3 Results
### Analysis Results  
In order to validate the effectiveness of the proposed algorithm, Figure 8a illustrates the training and test processes of MMNet. It is evident from Figure 8a that the proposed method exhibits rapid convergence as the step size increases, reaching a stable curve at approximately 99%. In Figure 8b, the loss function also converges swiftly with increasing step size, stabilizing at ~0.4. These results demonstrate that the proposed algorithm achieves high accuracy in fault diagnosis.  
The output results of the C2 fault input into the morphological network layer at different scales are illustrated in Figure 9, where the ordinate represents the signal amplitude, and the abscissa represents the sampling number. It can be observed from Figure 9 that the morphological filter not only effectively suppresses Gaussian white noise but also extracts impact features. The filtered signal exhibits enhanced smoothness while preserving positive and negative impact characteristics, enriching the fault feature information.  
To comprehend the feature visualization outcomes at different stages of MMNet and achieve low-dimensional visualization of each layer's features, a t-distributed stochastic neighbor embedding algorithm (t-SNE) for feature dimensionality reduction visualization was employed. The visualized outcomes are presented in Figure 10, where x and y denote dimension 1 and dimension 2, respectively. Figure 10a displays the original input data with disorganized data distribution. After undergoing the mathematical morphology layer and channel attention mechanism, the data are shown in Figure 10b with some fault characteristics emerging, indicating that the network learned rolling bearing fault characteristics. As depicted in Figure 10d, when passing through the final network, data features can be precisely clustered with clear boundaries and large spacing between classes. This further validates the superiority of our proposed method.  
Figure 8: Training process: (**a**) Accuracy curve, (**b**) Loss curve.  
Figure 9: _Cont._The test signal was further studied through the convolution pooling layer for feature learning. The feature results learned at the beginning are shown in Figure 11; the horizontal coordinate represents the number of feature points, and the vertical coordinate represents the amplitude. It can be clearly seen from the figure that the impact features of different types of bearing faults were extracted, indicating that the algorithm proposed in this paper is effective in extracting pulse impact features. With the deepening of the network layers, the deep-level processing results of features are shown in Figure 12; the characteristics of the impulse pulse can be clearly seen, and part of the amplitude became 0, indicating that the proposed algorithm can effectively retain the impulse fault and suppress the influence of other irrelevant noises.  
Figure 10: t-SNE visualization results of the method. (**a**) Original input, (**b**) input mathematical morphology layer and channel attention mechanism, (**c**) middle network, (**d**) final network.  
Figure 9: Output results of different morphological scales under the C2 fault of measuring point 1: (**a**) Normal, (**b**) Scale 1, (**c**) Scale 2, (**d**) Scale 3.