## 4 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target** & \(\mathbf{NMAE}\) **(\%)** & \(\mathbf{NRMSE}\) **(\%)** & \(\mathbf{MAPE}\) **(\%)** \\ \hline Power \(P\) & 2.0 \(\pm\) 0.1 & 3.1 \(\pm\) 0.1 & 5.5 \(\pm\) 1.2 \\ Voltage \(V\) & 0.63 \(\pm\) 0.01 & 0.80 \(\pm\) 0.01 & 0.04 \(\pm\) 0.02 \\ Current \(I\) & 1.9 \(\pm\) 0.1 & 2.9 \(\pm\) 0.2 & 6.3 \(\pm\) 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average error metrics and standard deviations for the 10-fold cross validation on the \(D_{test}\) data set PCA model. Figure 3: Comparison of the simulation of the current for the healthy Ref wind turbine, with and without PCA. In Figure 6, the same kind of plot as in Figure 4 is reported for a sample data set after the replacement of the Tar generator. From Figure 6, it arises that the reference and the target are hardly distinguishable, which is different to what happened in proximity of the fault. The situation depicted in Figures 4 and 5 can be interpreted quantitatively by computing the Pearson correlation coefficients \(r_{xy}\) between the measurements of the targets and of the input variables in the data set \(D_{after}\) for the target wind turbine. The results are reported in Table 4, from which it arises that the correlation coefficients change drastically with respect to the \(D_{train}\) data set (Table 1). In this sense, it is confirmed that the onset of generator damage can also be individuated as a change in the correlation between relevant operation variables (as suggested in [19]). In Table 5, the Pearson correlation coefficients \(r_{xy}\) are reported for the data set \(D_{after}\) and, compatibly, it results that the obtained values return to being of the order of those reported in Table 1 for the target wind turbine in healthy conditions. Figure 4: Measured and simulated power for the reference (Ref) and the target (Tar) wind turbines, for several examples of time windows approaching the fault (\(D_{fault}\)). Figure 5: Measured and simulated current for the reference (Ref) and the target (Tar) wind turbines: data set \(D_{fault}\). In Figure 7, the behavior of Figure 4 is elaborated through the indication of meaningful historical thresholds for the detection of the incoming fault. In Figure 7, the difference in NMAE between the Tar and the Ref wind turbines is plotted for the \(D_{fault}\) data set. The statistical indicators for the quantity of Figure 7 have been computed using the \(D_{test}\) data set: these are the average (blue line) and the standard deviation (yellow line). Therefore, for each measurement of Figure 7 in the \(D_{fault}\) data set, it is possible to estimate by how many standard deviations the difference in NMAE between the Tar and the Ref deviates from the historical normal trend. This allows observation of the evolution of the incoming fault and two reasonable thresholds can be defined: a pre-alert one (two standard deviations) and an alert one (three standard deviations). From Figure 7, it arises that two relevant peaks above the alert thresholds have occurred before the stopping of the wind turbine. It was crosschecked against the alarm log book for the wind turbines that both peaks are concomitant with the onset of alarms individuating current anomalies reaching the converter: in light of the present work, this phenomenon can be explained as being due to anomalous electrical behavior of the generator, eventually resulting in converter current anomalies. It should be pointed out that the present method is more informative with respect to the analysis of the alarm log book: alarms are impulsive events, while the approach of this study can be employed for online continuous monitoring. Defining appropriately, as is done in this work, a set of thresholds, it is possible to individuate possible faults with more advance with respect to the mere elaboration of the alarm logs.