## 3 Results
However, k-NN has low scalability, as it computes the distance between a point and all other points at each iteration, making the process time-consuming for large datasets. Similar performances are also provided by the SVM, which has high scalability. In addition,  
Figure 6: Pearson correlation matrix of the whole set of features (**a**) and Pearson correlation matrix of the selected features (**b**) in scenario 1. Pearson correlation matrix of the whole set of features (**c**) and Pearson correlation matrix of the selected features (**d**) in scenario 2.  
its execution time is equal to 0.02 s. However, the basic SVM does not provide the class estimation probability. As one of the main goals of the present study is to provide an industrial solution that is easy to implement, and as both precision and recall of DT are slightly worse than those of the SVM, the DT has been chosen for the online fault diagnosis. In scenario 2, all models have the 100% of precision and recall. The last output of the training phase is the model selection for real-time anomaly detection. The three models introduced in Section 2.1.4 are evaluated in terms of the metrics defined by Equations (3) and (4). In addition, they are also compared in terms of execution time as they have to process streaming data and provide real-time feedback. The application of mini-batch k-means, one-class SVM, and kitNET led to the results summarized in Tables 5-7, respectively. In addition, the parameters set by the user for each model are also present. In both scenarios, kitNET is the best model from all perspectives. It is fast, has the highest recall and the lowest false positive rate. On the contrary, the mini batch k-means has low values of recall, and the value of the false positive rate is lower than the FPR of the OCSVM in the first scenario. In the second scenario, the FPR of OCSVM cannot be computed, as both false positives and true negatives are equal to zero. As a result, the kitNET has been chosen for the online monitoring. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**9** & \multicolumn{6}{c}{**Scenario 1**} & \multicolumn{6}{c}{**Scenario 2**} \\ \hline
**Parameter** & **Value** & \
\begin{tabular}{c} **Execution** \\ **Time (sec)** \\ \end{tabular} & **Recall** & **FPR** &
\begin{tabular}{c} **Value** \\ **Time (sec)** \\ \end{tabular} & **Recall** & **FPR** \\ \hline Initialization time & 100 cycles & & & & & & \\ Amplitude of the sliding window & 10 & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters and results of OC-SVM of scenario 1 (S1) and scenario 2 (S2). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Scenario 1**} & \multicolumn{3}{c}{**Scenario 2**} \\ \hline
**Model** & \begin{tabular}{c} **Hyperparameters** \\ **(Hyp.)** \\ \end{tabular} & \begin{tabular}{c} **Optimal** \\ **Hyp.** \\ \end{tabular} & **Precision** & **Recall** & \
\begin{tabular}{c} **Optimal** \\ **Hyp.** \\ \end{tabular} & **Precision** & **Recall** &
\begin{tabular}{c} **Velocity and** \\ **Scalability** \\ \end{tabular} \\ \hline DT & Maximum depth & 9 & 92.3\% & 92.5\% & 5 & 100\% & 100\% & High \\ SVM & C & 1000 & 95.0\% & 93.6\% & 1 & 100\% & 100\% & High \\ kernel & RBF & 95.0\% & 93.6\% & Linear & 100\% & 100\% & High \\ k-NN & K & 3 & 95.1\% & 93.7\% & 1 & 100\% & 100\% & Low \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fault diagnosis performance of scenario 1 (S1) and scenario 2 (S2).