# Feature Mining and Sensitivity Analysis with Adaptive Sparse Attention for Bearing Fault Diagnosis
## 4 Model Analysis and Comparative Validation
### Model Performance Comparison  
In order to confirm that the proposed adaptive sparse attention network is effective in fault diagnosis, various existing intelligent diagnosis methods and related research are compared and analyzed with the proposed method. Among them, in the BP method, the inputs are manual features and angular domain signals, and each layer has 4-10-7 and 3600-60-7 nodes, respectively. In the CPI method, the network structure described in Section 3.2 is used, the attention module is not included, and the convolution parameters of each sequence are independent. In the global method, the network structure described in Section 3.2 is used, but the structure of attention uses global attention. In the local method, the network described in Section 3.2 is also used, but the structure of attention uses local attention, that is, pays close attention to the target sequence's window area, and the window contains 10 sequences. In the proposed ASAN method, the structure of the network is as shown in Section 3.2. Each method trained the model with angular domain (time domain), spectral, and envelope spectral data containing 10 fault settings under the same 0 hp load condition. As the diagnostic accuracy under the 0 hp load data reached 100%, the cross-working condition diagnosis test was carried out using the data of the 3 hp load, and the average accuracy of 10 cross-working condition diagnoses was calculated, as shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment Method** & **Mean** & **Std** \\ \hline CPS & 100.00\% & 0.00\% \\ CPI & 100.00\% & 0.00\% \\ CPS-cross & 50.80\% & 3.60\% \\ CPI-cross & 87.30\% & 9.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Evaluation of test results for each test.  
Figure 6: Test results of each test. (where cps is the diagnostic accuracy with parameter Convolution parameter sharing, cpi is the diagnostic accuracy with parameter Convolution parameter independence, cps-cross is the diagnostic accuracy with parameter cps and across working conditions, and cpi-cross is the diagnostic accuracy with parameter cpi and across working conditions).  
It can be seen that the CPI method has a faster convergence speed and takes 213.0368 s to converge; Global enhances the model's cross-condition diagnosis performance, but requires more computational cost. The Local method accelerates the model's convergence, but it will lead to a decrease in the diagnostic performance across working conditions. Yet, the ASAN method only takes 196.5402 s of convergence time. Compared with other methods, it has a faster convergence speed and keeps up its excellent performance as global in fault diagnosis and cross-working-condition diagnosis. Taken together, the proposed ASAN method outperforms other algorithms in Table 7 to a certain extent.  
To demonstrate the interpretability of the algorithm, the attention output of each sample is averaged, and Figure 9 shows the visualization results of each method.  
As depicted in Figure 9, the global method mainly pays attention to the frequency around 0-1000 Hz and has second-level attention to the frequency components between 2000-3000 Hz, but the global method also has an attention weight of more than 0.4 for other frequency bands, which the interpretation of the model has a certain adverse effect. Due to the limitation of the window, the Local method can only concentrate on the low-frequency region, especially the 1-times frequency of the working frequency and the fault. After the sparse operation of the network, the ASAN method mainly takes notice of the low-frequency region, around 1000 Hz and 3000 Hz, which has a certain correlation with the attention weights obtained by the global method. However, the ASAN method can greatly suppress the expression of redundant sequences on the premise of ensuring the model's performance, which can aid in our comprehension and diagnosis of fault signals.