# Feature Mining and Sensitivity Analysis with Adaptive Sparse Attention for Bearing Fault Diagnosis
## 4 Model Analysis and Comparative Validation
### Visualization of Fault Information  
The fault form of the bearing is closely related to its fault characteristic frequency. The low frequency of the bearing fault characteristic frequency is often used in manual diagnosis. However, due to the modulation of the carrier wave, the fault frequency occasionally appears in the high-frequency region, which brings difficulties to manual diagnosis. Therefore, this paper uses sparse attention to further explore the performance of the fault characteristic frequency when the bearing fails. Figure 10 shows the average value of attention weights learned by the model for each bearing dataset working condition sample, and  
Figure 9: The average attention of each method to the bearing envelope spectrum.  
the visual attention weight of each working condition sample is depicted in Figure 11. The size of the attention weights is indicated by their color, and the red indicates the high level.  
As shown in Figure 10 and Table 8, it is apparent that under the Health condition, the network pays attention to 0-281.25 Hz and 843.75-1031.25 Hz. When the inner ring of the bearing fails, the network mainly pays attention to the 1I and 6I frequencies of the bearing under the case of minor faults. Under medium faults, the network increases the attention of 1-3X, 1I side frequency, and 6I side frequency. Under severe faults, the network focuses emphatically on 1-3X and 1I. When the bearing rolling element fails, the network pays special attention to 2906.245-2999.995 Hz (21B) and the frequency range of 3187.505-3281.255 Hz (23B). In the case of minor faults, the network mainly pays attention to 1-3X, 1B, 2B, 4B of the signal, and it reduces the attention of most frequencies under moderate faults, especially the attention weights of 2B and 4B. The network attention position under serious fault is the same as that of medium fault, but the attention to 1B and 2B is increased. When the bearing outer ring fails, the network focuses on 1O and 2O under the case of minor faults. The network noticed multiple locations under moderate failures, focusing on 1-3X, 1O, 2O, 3O, 8O, 9O, and the high-frequency region (25O, 27O, 28O, 30O) near 3000 Hz. The attention of 1-3X is increased and the attention of 2O is reduced compared with that of minor faults in the case of severe faults.  
In short, except for OF14, which obviously noticed the area around 3000 Hz, and the BF working condition, which slightly noticed the area around 3000 Hz, the attention weight differences of other signals were mainly concentrated in 0-562.5 Hz, 843.75-1031.25 Hz. The attention weights of each signal are summarized and counted in the above frequency domain interval according to the fault type, and the results are depicted in Table 8. Under the Health condition, the network mainly pays attention to 1-3X. Under the IF condition, the network mainly pays attention to 1I, 1I sideband, and 6I, which reduces the attention by 1-3X compared to Health, and also slightly pays attention to the 6I sideband. Under the BF condition, the network mainly pays attention to 1-3X, 1B, 2B, and slightly pays attention to 4B, 6B, 7B. Under the OF condition, the network mainly pays attention to 1O, 2O, and 3O. Compared with Health, the attention is reduced by 1-3X, and the attention is slightly paid to 8O and 9O. The network in [20] focuses on 1I of IF, 1B, and 2B of BF, and 1O, 2O, and 3O of OF, which is consistent with the attention results of the network proposed in this paper to a certain extent. This shows that the test results in this paper conform to the general rule of fault diagnosis knowledge.  
Figure 10: Average attention of each working condition.  
Figure 11: Visualization of attention weights for each working condition.