## 5 Results
### Feature Importance Analysis  
The next factor considered during the analysis was the verification of attribute importance for the obtained model. The quality of the attributes was assessed using the permutation method applied to both test datasets. As discussed in the previous section, the correlation between all attributes was measured first. The results obtained are presented in Table 9. In the experiment, we compared all three datasets, and in all cases, the correlations between the attributes were almost identical. The table contains the average correlation for all three datasets. The values obtained indicate a very strong dependency between the output temperature (\(T_{out}\)) and the suction line temperature (\(T_{suct. }\)), with a correlation level of 0.99. Similarly, there is a high correlation between the output temperature (\(T_{out}\)) and the leak line temperature (\(T_{leak}\)), with a correlation level of 0.91. As described above, a typical approach to overcome the problems of correlated features when performing permutation-based feature importance assessment is based on the PCA analysis, so the three attributes with a correlation coefficient above 0.9 were separated from the remaining attributes, and the PCA analysis on those tree attributes was performed. From the PCA, the first principal component was used to replace the three temperature attributes. Therefore, the results presented in Figure 8 represent only six attributes (with a single temperature attribute) instead of eight. The coefficients obtained that describe the importance of the individual attributes are presented in Figure 8 separately for both datasets. In the figures, the \(X\)-axis represents the decrease in accuracy and the \(y\)-axis represents the name of the feature. The whiskers represent statistics of the data collected for 10 random permutations of the values for each attribute. Figure 7: Confusion matrix obtained for the Failure 2 and Failure 3 datasets. Class 0 indicates normal operation conditions and class 1 indicates failure state conditions; **(a)** Failure 2; **(b)** Failure 3. \begin{table}
\begin{tabular}{r r r r r r r r} \hline  & \(P_{leak}\) & \(T_{leak}\) & \(P_{out}\) & \(T_{suct.}\) & \(T_{out}\) & \(F_{leak}\) & \(F_{out}\) & \(T_{diff}\) \\ \hline \(P_{leak}\) & \(1.00\) & \(-0.35\) & \(0.57\) & \(-0.52\) & \(-0.44\) & \(0.36\) & \(0.03\) & \(0.46\) [t] \\ \(T_{leak}\) & \(-0.35\) & \(1.00\) & \(0.33\) & \(0.88\) & \(\mathbf{0.91}\) & \(0.43\) & \(0.37\) & \(-0.07\) \\ \(P_{out}\) & \(0.57\) & \(0.33\) & \(1.00\) & \(0.05\) & \(0.17\) & \(0.79\) & \(0.26\) & \(0.47\) \\ \(T_{suct.}\) & \(-0.52\) & \(0.88\) & \(0.05\) & \(1.00\) & \(\mathbf{0.99}\) & \(0.23\) & \(0.27\) & \(-0.54\) \\ \(T_{out}\) & \(-0.44\) & \(\mathbf{0.91}\) & \(0.17\) & \(\mathbf{0.99}\) & \(1.00\) & \(0.32\) & \(0.30\) & \(-0.47\) \\ \(F_{leak}\) & \(0.36\) & \(0.43\) & \(0.79\) & \(0.23\) & \(0.32\) & \(1.00\) & \(0.12\) & \(0.29\) \\ \(F_{out}\) & \(0.03\) & \(0.37\) & \(0.26\) & \(0.27\) & \(0.30\) & \(0.12\) & \(1.00\) & \(0.10\) \\ \(T_{diff}\) & \(0.46\) & \(-0.07\) & \(0.47\) & \(-0.54\) & \(-0.47\) & \(0.29\) & \(0.10\) & \(1.00\) [b] \\ \hline \end{tabular}
\end{table} 
Table 9: Correlation between attributes in Failure 1 dataset. The obtained results indicate that the most important parameters in both cases were 'Flow--leak line', and 'Pressure--output'. The next in the order is temperature \(T\) for Failure 2 and \(P_{leak}\) for Failure 3, but their importance is much lower than the initial two attributes. The fourth position is equal to the third position but swapped between the datasets. \(F_{out}\) on both datasets is the least important but still valuable feature. The \(T_{diff}\) has importance 0 which means it can be removed from the dataset.