## 7 Results  
Results concerning the multi-fault classification are shown on Table 2. The SD and CCM features are considered as well as the statistical features that are presented for comparison. Both RF classification algorithms are tested for each of the vibrations signals. The statistical set of features and the SD set of features enable perfect classification of multi-fault for this dataset including 13 different fault conditions. The CCM set of features provides slightly lower classification accuracy. However, the ESK algorithm attains averaged classification accuracies higher than 99% for the three vibrations signals collected from the accelerometers A1, A2, A3. An example of the confusion matrix is shown in Figure 21. This confusion matrix is for the EBT algorithm when the multi-fault classification is performed using the set of signals collected from the accelerometer A3. The average accuracy obtained in this case is the lowest of all developed experiments. A detailed quantification of results for this particular case are shown on Table 3, where the sensitivity, specificity, and F1-Score are presented for each of the fault classes. The lowest sensitivity is attained by class P12 taking a value of 79%. However, eleven of the classes have sensitivities higher than 90%. Concerning the specificity, the lowest value of 98% is attained by class P13. The rest of classes have specificities higher than 99%. The F1-score attains the lowest value of 82% for class P13. Classes P2, P3, P10 and P11 are classified with score up to 100% while classes P1, P4, P5, P6, P7 and P9 obtain scores higher than 90%.  
Finally, Table 4 shows the performance of the proposed SD and CCM features over the dataset in [20].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & **Model** & **A1** & **A2** & **A3** \\ \hline Statistical & EBT & 100 & 100 & 100 \\  & ESK & 100 & 100 & 100 \\ \hline SD & EBT & 100 & 100 & 100 \\  & ESK & 100 & 100 & 100 \\ \hline CCM & EBT & 99.4 & 96.8 & 94.2 \\  & ESK & 100 & 100 & 99.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Percent accuracy for each of features types and models calculated for each vibration signal.  
Figure 20: Accuracy according to \(Lag=\tau\) for SD features.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & **Model** & **A1** & **A2** & **A3** & **A4** \\ \hline Statistical & EBT & 73.2 & 83.5 & 73.4 & 74.4 \\  & ESK & 52.6 & 61.7 & 57.2 & 49.0 \\ \hline SD & EBT & 100 & 100 & 100 & 100 \\  & ESK & 100 & 100 & 100 & 100 \\ \hline CCM & EBT & 91.7 & 98.7 & 95.3 & 97.9 \\  & ESK & 97.8 & 99.8 & 97.8 & 99.5 \\ \hline \end{tabular}
\end{table}
Table 4: Percent accuracy for each of features types and models calculated over the dataset of valve faults in [20].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Condition** & **Sensitivity** & **Specificity** & **F1-Score** \\ \hline P1 & 0.92 & 1.00 & 0.96 \\ P2 & 1.00 & 1.00 & 1.00 \\ P3 & 1.00 & 1.00 & 1.00 \\ P4 & 1.00 & 0.99 & 0.96 \\ P5 & 1.00 & 0.99 & 0.96 \\ P6 & 0.92 & 1.00 & 0.96 \\ P7 & 0.92 & 0.99 & 0.92 \\ P8 & 0.85 & 0.99 & 0.88 \\ P9 & 1.00 & 0.99 & 0.96 \\ P10 & 1.00 & 1.00 & 1.00 \\ P11 & 1.00 & 1.00 & 1.00 \\ P12 & 0.79 & 0.99 & 0.85 \\ P13 & 0.90 & 0.98 & 0.82 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results for the EBT model using features extracted from signals recorded with the accelerometer A3.  
Figure 21: Confusion matrix for CCM features and EBT.