## 3 Results
### Machine Learning-Based Classification
\begin{table}
\begin{tabular}{l r} \hline \hline
**Features** & **H** \\ \hline LOG\_BPFI\_Amplitude\_BPFO\_Amplitude & 217.3216 \\ BPFI\_Amplitude & 167.1512 \\ LOG\_BSF\_Amplitude\_BPFO\_Amplitude & 155.3533 \\ BPFO\_Amplitude & 138.4140 \\ LOG\_BPFI\_Amplitude\_BSF\_Amplitude & 120.2450 \\ BSF\_Amplitude & 43.3603 \\ Standard deviation & 26.0577 \\ RMS & 25.2882 \\ Shape factor & 17.9515 \\ Peak value & 15.7401 \\ Mean & 12.3161 \\ Kurtosis & 11.9904 \\ Clearance factor & 5.3638 \\ Impulse factor & 5.1157 \\ Crest factor & 4.8157 \\ Skewness & 3.0968 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Features sorted by importance according to the Kruskal–Wallis test. Case B. \begin{table}
\begin{tabular}{l r} \hline \hline
**Features** & **H** \\ \hline LOG\_BPFI\_Amplitude\_BPFO\_Amplitude & 152.5596 \\ BPFI\_Amplitude & 145.4471 \\ LOG\_BPFI\_Amplitude\_BSF\_Amplitude & 100.1278 \\ BPFO\_Amplitude & 97.8711 \\ LOG\_BSF\_Amplitude\_BPFO\_Amplitude & 91.5079 \\ BSF\_Amplitude & 24.0144 \\ Standard deviation & 18.0231 \\ RMS & 17.5023 \\ Peak value & 15.3398 \\ Mean & 11.6661 \\ Kurtosis & 10.9086 \\ Shape factor & 10.1311 \\ Clearance factor & 5.9409 \\ Impulse factor & 5.4390 \\ Crest factor & 3.8549 \\ Skewness & 2.7573 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Features sorted by importance according to the Kruskal–Wallis test. Case B. \begin{table}
\begin{tabular}{l r} \hline \hline
**Features** & **F** \\ \hline LOG\_BPFI\_Amplitude\_BPFO\_Amplitude & 289.5471 \\ LOG\_BPFI\_Amplitude\_BSF\_Amplitude & 129.0033 \\ BPFI\_Amplitude & 95.1479 \\ LOG\_BSF\_Amplitude\_BPFO\_Amplitude & 90.1346 \\ BPFO\_Amplitude & 61.6727 \\ BSF\_Amplitude & 6.0888 \\ Shape factor & 4.0389 \\ Clearance factor & 2.9775 \\ Kurtosis & 2.8668 \\ Standard deviation & 2.7570 \\ Translated deviation & 2.6555 \\ RMS & 2.6505 \\ RMS & 2.6403 \\ Peak value & 2.5531 \\ Crest factor & 1.8718 \\ Mean & 1.2457 \\ Skewness & 0.7408 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Features sorted by importance according to the Kruskal–Wallis test. Case B. As shown in Figure 7, for every case, the frequency-domain features are ranked better than the time-domain features, especially with regard to the logarithmic ratios between the maximum amplitudes of the envelope spectrum around the pulses spaced at the faults' characteristic frequencies. This matches the conclusions drawn from the scatter plots in Figures 5 and 6. The hypothesis tests results are summarised in Table A1, Appendix A. Every feature within the dataset violates the normality and equality of continuous distributions requirements. Only one feature (mean) fulfils the homoscedasticity condition. The independence of observations condition is known to be fulfilled for the whole dataset, since the features have been calculated from the raw time signals, which were independently obtained as described in Section 2.1, from different REBs placed in different parts of the setup, in addition to the accelerometers. The classification results are depicted in Figures 8-11 and collected in Tables 8-11. Using the MATLAB(r)-powered _Statistics and Machine Learning Toolbox 11.7_TM, models have been trained by applying five-fold cross-validation, using 80% of the dataset for training and 20% for validation during each iteration. Five-fold cross-validation also protects against overfitting by estimating accuracy on each fold. Figure 7: Bar graphs of cases A & B for both one-way ANOVA and the Kruskal-Wallis test. (**a**) Dataset of case A ranked according to the one-way ANOVA test. (**b**) Dataset of case B ranked according to the one-way ANOVA test. (**c**) Dataset of case A ranked according to the Kruskal-Wallis test. (**c**) Dataset of case B ranked according to the Kruskal-Wallis test.