## 4 Experimental Results
### Diagnosis Accuracy for Compound Bearing Faults
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methodologies**} & \multicolumn{6}{c}{**Average Accuracy for Each Fault Type (\%)**} & \multirow{2}{*}{**ACA (\%)**} \\ \cline{2-2} \cline{5-8}  & **BCI** & **BCO** & **BCR** & **BCIO** & **BCIR** & **BCOR** & **BCIOR** & **BNC** \\ \hline \multirow{6}{*}{**Dataset 1**} & Proposed & \multirow{2}{*}{96.00} & \multirow{2}{*}{94.12} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{98.77} \\  & method & & & & & & & & \\ (11) & 100.00 & 98.88 & 98.51 & 97.77 & 95.18 & 100.00 & 100.00 & 99.62 & 98.74 \\  & [10] & 66.60 & 100.00 & 100.00 & 100.00 & 89.10 & 99.20 & 99.20 & 99.60 & 94.20 \\  & [22] & 11.11 & 13.33 & 100.00 & 100.00 & 97.77 & 97.77 & 66.21 & 22.41 & 63.57 \\  & [3] & 19.62 & 47.40 & 75.18 & 47.03 & 59.62 & 30.74 & 49.76 & 58.62 & 48.49 \\ \hline \multirow{6}{*}{**Dataset 2**} & Proposed & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} & \multirow{2}{*}{100.00} \\  & method & & & & & & & & \\ (11) & 100.00 & 100.00 & 98.51 & 95.47 & 99.18 & 100.00 & 98.88 & 99.62 & 98.95 \\  & [10] & 100.00 & 100.00 & 91.80 & 98.10 & 99.20 & 99.20 & 100.00 & 99.20 & 98.40 \\  & [22] & 24.34 & 26.47 & 97.77 & 97.77 & 100.00 & 100.00 & 68.24 & 28.16 & 67.84 \\  & [3] & 7.03 & 70.00 & 66.66 & 79.62 & 5.92 & 44.81 & 74.07 & 62.96 & 51.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Diagnosis accuracy of the proposed method for compound bearing faults compared to the existing methods. that constructs features using the characteristic frequencies of bearing faults was also proposed by [PERSON] et al. in [22]. The compared FD accuracy according to applied bearing FD methods, as listed in Table 3, illustrates that the methods [3,22] that use manual feature calculation based on fault characteristic frequencies fail to adapt well under variable shaft speed. The average accuracies of the method in [22] and method in [3] are 63.57% and 48.49% for Dataset 1, respectively. Even in the case of big crack size (Dataset 2), the two methods achieved similar results. In contrast, the automatic methods that use CNN models to extract the representative feature image that contains bearing fault information under various defect frequencies provide better accuracy. One of those CNN-based existing FD methods [11] provides an average accuracy of up to 98.74% and 98.95% for Dataset 1 and Dataset 2, respectively. Therefore, we can know that the CNN-based FD methods can achieve high accuracy even when the rotational speed varies. Among these compared CNN-based methods, our proposed method achieves the best FD accuracy by adopting a compatible image representation method, a capable and sufficiently deep CNN model, and an SLS optimizer to avoid missing fault features. Especially, when the crack size is 12 mm, the proposed method achieves 100% FD accuracy. The results of the fault classification task can be depicted by using confusion matrices, as shown in Figure 7.  
Moreover, our bearing fault diagnosis method also can provide fast convergence ability (4 to 5 epochs for training). We analyzed the effectiveness of the adopted SLS optimizer by comparing it with the Adamax optimizer [23] in terms of convergence rate and convergence ability. The loss curve shows how well the model is learned from the input data. A higher value trend of the loss curve illustrates that the model's ability is worse at learning from training data. In Figure 8, we observe that the Adamax optimizer has good convergence results on both the training subset and the validation subset, and there is no overfitting phenomenon. That is because the Adamax optimizer is a variant of the Adam algorithm, which uses a momentum and infinity norm suitable for large amounts of data [23].