## 4 Experimental Results
### Fault Diagnosis Accuracy for Compound Bearing Faults  
We also evaluated the effectiveness of the proposed bearing fault diagnosis method by examining the prediction accuracy for seven types of localized defects (inner raceway crack (BCI), outer raceway crack (BCO), roller crack (BCR), inner and outer raceway cracks (BCIO), inner and roller cracks (BCIR), outer and roller cracks (BCOR), and inner-outer-roller cracks (BCIR)) as recorded under variable operating speeds and fixed crack sizes of 3 mm, 6 mm, and 12 mm (datasets 5, 6, and 7). Figure 8a shows the diagnosis accuracy (sensitivity) of our proposed method for 3 single faults (BCI, BCO, and BCR), 4 combined faults (BCIO, BCIR, BCOR, and BCIOR), and the normal condition (BNC). Experimental results show that the proposed method exhibits high accuracy in the classification of single faults and combined faults independent of the rotational speed. Our method provides average accuracies of 96.3, 98.6, and 100% for datasets 5, 6, and 7, respectively. From these experimental results, we can know that our proposed bearing fault diagnosis method provides very high prediction accuracy for combined bearing faults as well as single bearing faults. In particular, the proposed method produces high and stable results when the bearing has a high level of degradation. For a 12-mm crack size, the proposed method provides an accuracy of up to 100%. The lowest average accuracy is 96.3% when the crack size is 3 mm. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{2}{c}{\multirow{2}{*}{**Fault Diagnosis Method**}} & \multicolumn{4}{c}{**Diagnosis Accuracy (Sensitivity, \%)**} & \multicolumn{2}{c}{**Average Accuracy (\%)**} \\ \cline{3-6}  & **Inner** & **Outer** & **Roller** & **Normal** & \\ \hline \multirow{2}{*}{Dataset 1} & [8] & 81.5 & 81.4 & 79.2 & 82.9 & 81.2 \\  & Proposed method & 98.1 & 99.1 & 98.2 & 100.0 & 98.8 \\ \hline \multirow{2}{*}{Dataset 2} & [8] & 83.9 & 79.1 & 78.6 & 83.9 & 81.4 \\  & Proposed method & 97.6 & 100.0 & 100.0 & 100.0 & 99.4 \\ \hline \multirow{2}{*}{Dataset 3} & [8] & 80.1 & 78.2 & 80.9 & 82.5 & 80.4 \\  & Proposed method & 96.3 & 99.6 & 100.0 & 99.6 & 98.9 \\ \hline \multirow{2}{*}{Dataset 4} & [8] & 78.4 & 77.7 & 77.3 & 80.8 & 78.6 \\  & Proposed method & 98.1 & 100.0 & 100.0 & 99.2 & 99.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Diagnosis accuracy of the proposed method for single faults compared to the method in the paper [8]. Figure 7: Fast convergence ability of the proposed method: (**a**) training loss curves and (**b**) validation loss curves. Figure 9 presents the confusion matrices for the results to show the performance of the classification task corresponding to each class in detail. Each row of a confusion matrix represents the instances in a predicted label, while each column represents the instances in a true label. Confusion matrices are extremely practical to visualize the performance (sensitivity, precision, and accuracy) of the proposed method. Based on the confusion matrices, we additionally provide the precision values of individual classes in Figure 8b to show the performance of our proposed method on the full range of aspects. Precision is calculated by following Equation (5):  
\[Precision=\frac{N_{True\_Positive}}{N_{True\_Positive}+N_{False\_Positive}} \times 100(\%) \tag{5}\]  
where \(N_{True\_Positive}\) is the number of samples from a particular class which are correctly classified and \(N_{False\_Positive}\) is the number of outcomes where the model incorrectly predicts the positive class. The average precisions of our proposed method for datasets 5, 6, and 7 are 96.57, 98.38, and 99.83%, respectively. The evaluated high values both in sensitivity and precision prove that the proposed method performs well in bearing fault diagnosis. Figure 8: Diagnosis sensitivity and precision of the proposed method for compound faults: (**a**) sensitivity and (**b**) precision.