## 3 Results
### Machine Learning-Based Classification  
The metric used to assess the different algorithms under the various cases is accuracy, defined as the proportion of correctly classified examples divided by the total number of  
Figure 4: Greyscale images of drive-end REB signals. Faults located in the rolling elements (**a**,**b**), inner race (**c**) and outer race orthogonal to the load zone (**d**). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Kernel**} & \multicolumn{2}{c}{**Stride**} & \multicolumn{3}{c}{**Fadding**} \\ \cline{2-10}  & **Height** & **Width** & **Vertical Step Size** & **Horizontal Step Size** & **Top** & **Bottom** & **Left** & **Right** \\ \hline
**Convolutional Layers** & 5 & 5 & 1 & 1 & aut. & aut. & aut. & aut. \\ \hline
**Pooling layers** & 2 & 2 & 2 & 2 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyper-parameters of the proposed CNN. examples within the dataset. As mentioned in the previous section, to learn which features work better for every ML algorithm under each case, the procedure will be to compute each algorithm with a features vector of dimension 1, increasing its dimensionality until it reaches its maximum for every case, following the order of importance established by each statistical test. Prior to ranking any feature, let us observe various scatter plots of both datasets. The aim is to find significant differences between the features' distributions for each group. Figures 5 and 6 depict 3D scatter plots from the time- and frequency-domain datasets. As drawn from these figures, the frequency-domain features seem to be the ones that take the most segregated values for each group, especially the logarithmic ratios between the maximum amplitudes of the envelope spectrum around the pulses spaced at the faults' characteristic frequency. The time-domain features seem to take less segregated values between the groups. Therefore, lower accuracy is expected to be obtained from these features. Moreover, data belonging to the faulty balls class (2) are more spread than the other groups' data in the cases where a significant difference between the latter can be observed. Considering all of the above, two case studies will be defined. 1. Case (A) Classification using the whole dataset. 2. Case (B) Classification removing the second class from the dataset. The features' ranking results are shown in Figure 7 and collected in Tables 4-7. Figure 5: Scatter plots of time\(-\)domain features. (**a**) Mean, Standard deviation & Impulse factor. (**b**) Standard deviation, Peak value & Clearance factor. (**c**) RMS, Crest factor & Shape factor. (**d**) Skewness, Clearance factor & Kurtosis. \begin{table}
\begin{tabular}{l c} \hline \hline
**Features** & **F** \\ \hline LOG\_BPFI\_Amplitude\_BPFO\_Amplitude & 258.3292 \\ LOG\_BSF\_Amplitude\_BPFO\_Amplitude & 122.8081 \\ LOG\_BPFI\_Amplitude\_BSF\_Amplitude & 116.2330 \\ BPFI\_Amplitude & 92.2322 \\ BPFO\_Amplitude & 77.7082 \\ BSF\_Amplitude & 9.5288 \\ Crest factor & 6.0064 \\ Shape factor & 5.8229 \\ Impulse factor & 3.4917 \\ Clearance factor & 2.7894 \\ Kurtosis & 1.9256 \\ Mean & 1.4055 \\ Peak value & 1.3931 \\ Standard deviation & 0.9941 \\ RMS & 0.9637 \\ Skewness & 0.6254 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Features sorted by importance according to one-way ANOVA. Case A.  
Figure 6: Scatter plots of frequency—domain features. **(a)** BPFO Amplitude, BPFI Amplitude & BSF Amplitude. **(b)** Log(BPFI Amplitude/BPFO Amplitude), Log(BPFI Amplitude/BSF Amplitude) & BPFI Amplitude. **(c)** Log(BPFI Amplitude/BSF Amplitude), Log(BPFI Amplitude/BPFO Amplitude) & Log