## 3 Results  
In this section, the main results of the present study are provided. First, datasets corresponding to all available machinery conditions are considered in the training phase in order to select the best feature subset, the best classification model, and the best anomaly detection model in the hypothesis to know all the machinery behaviors. In this scenario, the online monitoring phase has the only objective of identifying points corresponding to a condition change as anomalies and classifying them in the correct fault class. Note that one dataset for each condition (e.g., dataset D1 for the nominal condition) is considered for the training, except for fault 2, for which the only available dataset is used for both training and online testing. In a second scenario, fault 2 has been removed from the training dataset to evaluate the novelty detection ability of the methodology. The datasets used in both scenarios for the training and the online testing are summarized in Table 3.  
The feature subset represents the first output of the methodology described in previous sections. The ten statistical features extracted in the time domain (see Section 2.1.2) are used to build the Pearson correlation matrices of both scenarios, shown in Figure 6a,c, respectively. It can be seen that, in both cases, some of the extracted features have a high correlation, such as the mean and the mean of the absolute values, which have a correlation coefficient equal to \(-0.98\) (Figure 6a). In this case, the mean absolute on the column is eliminated, while the mean on the raw is kept. This process is repeated until the whole matrix is analyzed. In the end, for scenario 1, only four features, i.e., peak, peak to peak, the mean, and the skewness, are selected, whose correlation coefficients are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Training Datasets** & **Online Testing Datasets** \\ \hline
1 & D1 + D2 + D3 + D5 & D1 + D7 + D8 + D2 + D9 + D4 + D6 + D3 + D5 + D10 \\
2 & D1 + D2 & D1 + D7 + D8 + D2 + D9 + D4 + D6 + D3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Testing Scenarios. shown in Figure 6b. For scenario 2, the peak, peak to peak, and the skewness are selected (Figure 6d). As the described method is affected by the features' order in the correlation matrix, the Pearson correlation analysis is repeated after randomly changing the features' order. In this case, instead of the mean value, the shape factor has been selected. However, the mean correlation index, computed as the arithmetic mean of the absolute values of the Pearson coefficients in the correlation matrix, is similar in both matrix configurations. To further evaluate the goodness of the selected features, the RFE algorithm is applied, which assigns a score equal to 1 to both feature subsets selected through the Pearson correlation analysis. This score confirms that the selected features have a low correlation and positively contribute to the classification accuracy. The fault classification model represents the second output of the methodology. Several considerations lead to choosing a model rather than another. First, the best model should have the highest precision and recall. In addition, as the selected model will be applied to streaming data and provide real-time results, the execution time, i.e., testing time, is also critical. Finally, the model should potentially deal with an infinite amount of data. Hence, it has to be scalable and trained on a large data set quickly. Table 4 summarizes the results in terms of precision, recall, and velocity and scalability, obtained from the application of the grid search algorithm. In addition, the selected hyperparameters for each model are also present in the table. In scenario 1, the model with the best precision and recall is the k-NN that, with \(\mathrm{k}=3\), achieves the 95.1% of precision and the 93.7% of recall.