## 4 Experimental Results  
### Fault Diagnosis Accuracy for Single Bearing Faults  
We conducted the experiments to evaluate the prediction accuracy for single bearing faults in our proposed method under variable motor speed conditions. These experiments were performed with datasets 1, 2, 3, and 4. The experimental results in Table 4 show that the proposed method provides a high level of predictability compared to the existing high accuracy method, which uses the bi-spectrum to represent vibration signals and a shallow CNN model under the same conditions [8]. To obtain stable results, all of the experiments in this paper were repeated multiple times. Specifically, we repeated each of the experiments more than ten times and we found that the achieved results are consistent. Sensitivity is the diagnosis ability to classify an individual fault correctly, which is one of the most important indicators to evaluate a diagnosis method and to compare its efficiency with other diagnostic methods. Therefore, most previous researches related to fault diagnosis have used the sensitivity value to evaluate performance. For this reason, we use the sensitivity value as the major \begin{table}
\begin{tabular}{l l} \hline \hline \multirow{2}{*}{**NEXUS conditioning amplifier (type 2692-C)**} & (1) Frequency range: 0.1 Hz–100 kHz \\  & (2) Sensitivity: 10 mV/ms\(-2\) \\ \hline \multirow{2}{*}{**Piezoelectric charge accelerometer (type 4371)**} & (1) Frequency range: 0.1 Hz–12.6 kHz \\  & (2) Sensitivity: 9.8 pC/g \\ \hline \multicolumn{2}{l}{**Portable data acquisition device (PULSE type 3560-C)**} & Maximum sampling frequency: 25.6 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specification of the data acquisition system. \begin{table}
\begin{tabular}{l l c c c c} \hline \hline  & \multicolumn{2}{c}{**Rotational Speed**} & \multicolumn{4}{c}{**Crack Size**} \\ \cline{3-6}  & & **(RPM)** & **Length (mm)** & **Width (mm)** & **Depth (mm)** \\ \hline \multirow{2}{*}{Dataset 5} & Training dataset & 300, 400, 500 & \multirow{2}{*}{3} & \multirow{2}{*}{0.60} & \multirow{2}{*}{0.30} \\  & Test dataset & 250, 350, 450 & & & \\ \hline \multirow{2}{*}{Dataset 6} & Training dataset & 300, 400, 500 & \multirow{2}{*}{6} & \multirow{2}{*}{0.60} & \multirow{2}{*}{0.50} \\  & Test dataset & 250, 350, 450 & & & \\ \hline \multirow{2}{*}{Dataset 7} & Training dataset & 300, 400, 500 & \multirow{2}{*}{12} & \multirow{2}{*}{0.60} & \multirow{2}{*}{0.50} \\  & Test dataset & 250, 350, 450 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dataset for compound bearing faults. Figure 6: Single and combined bearing faults: (**a**) outer raceway crack (BCO), (**b**) inner raceway crack (BCI), (**c**) roller crack (BCR), (**d**) inner and outer raceway cracks (BCIO), (**e**) outer and roller cracks (BCOR), (**f**) inner and roller cracks (BCIR), and (**g**) inner-outer-roller cracks (BCIOR). index to evaluate and compare our method with previous methods. Sensitivity is calculated by the following Equation (3):  
\[\textit{Sensitivity}=\frac{N_{\textit{True\_Positive}}}{N_{\textit{True\_Positive}}+N_{ \textit{False\_Negative}}}\times 100(\%) \tag{3}\]  
where \(N_{\textit{True\_Positive}}\) is the number of samples from a particular class which are correctly classified and \(N_{\textit{False\_Negative}}\) is the number of samples from a particular class that are incorrectly classified. The average classification accuracy (ACA) is measured by Equation (4) to show the average classification performance for each dataset:  
\[ACA=\frac{\sum\textit{Sensitivity}}{\sum N_{\textit{Classes}}} \tag{4}\]  
where \(\sum\textit{Sensitivity}\) is the sum of class-wise accuracy for a specific dataset. As shown in Table 4, for 4 bearing fault types (inner race bearing fault, outer race bearing fault, roller fault, and normal condition), our proposed method provides the average prediction accuracy 98.8, 99.4, 98.9, and 99.3% whereas the existing method provides the average accuracies 81.2, 81.4, 80.4, and 78.6% for datasets 1, 2, 3, and 4, respectively.