# Improved Ensemble Learning for Wind Turbine Main Bearing Fault Diagnosis
## 4 Results
### Ensemble vs. Single Models  
The different models that compound the ensemble should provide complementary information, see [17]. Thus, it is important to analyze the correlation between the indicators provided by each of the individual models: the anomaly detection model vs. the normality model. Figure 2 displays the isolation forest indicator vs. the neural network indicator for each WT in the park separately. The Pearson correlation coefficient and \(p\)-value for testing non-correlation are reported as \(r\) and \(p\), respectively. It is shown that, in general, there is no correlation between the individual indicators (low values of the Pearson correlation coefficient are obtained), thus they are complementary in terms of their contained information. Note the particular case of WT05 where the Pearson correlation is about 0.78, which indicates that there is a moderate positive relationship between the variables, as the \(p\)-value in this case is almost zero (which indicates that the correlation coefficient is significant). The explanation of this special behavior is that WT05 suffers the only main bearing fault in the park that is correctly predicted by both indicators, thus in this case the indicators are correlated. Figures 3-5 show the normal behavior model indicator, the anomaly detection indicator, and the ensemble indicator, respectively. In these figures, the blue stars indicate the occurrence of a main bearing fault (as recorded in the work order logs). Note that the normal behavior indicator shows high values in WT01 and WT18, which are healthy over the whole test set, but the anomaly detection indicator shows low values for these WTs. On the contrary, the anomaly indicator shows high values for WT16, which is healthy, but the normality indicator shows low values for this WT. The ensemble indicator adequately combines the information from the single indicators showing low indicator values for WT01, WT16, and WT18 as desired. Figure 4: Main bearing health according to anomaly detection. Faults are marked with a blue star. Figure 3: Main bearing health according to normal behavior model. Faults are marked with a blue star. Figure 2: Scatter plot showing the isolation forest indicator vs. the neural network indicator independently for each WT. The linear regression model fit, that minimizes the squared error of the data, is plot in red. The shaded area represents the 68% confidence interval of the model. Pearson correlation coefficient and \(p\)-value for testing non-correlation are reported as \(r\) and \(p\), respectively. To make a decision to trigger or not an alarm, a decision threshold is needed. Values of the indicator above the threshold will activate an alarm, and values below the threshold will be considered normal. To better visualize the results, a saturation mask is proposed in the following manner: all indicator values below the threshold are saturated to 0, and all indicator values above or equal to the threshold are saturated to 1. Figure 6 shows the ensemble indicator after applying the saturation mask with a decision threshold value of 0.85. It can be observed that the three main bearing faults in the park (highlighted with the blue stars) are warned at least 5 months in advance. On the other hand, there are false alarms at WT01, WT02, and WT09. The value of the decision threshold (DT) has a great impact on the final results. Figure 7 shows the DT value with respect to the different metrics. It is observed that, in general, higher values of the DT lead to better performance metrics, and it is noteworthy that for the same value of the DT the best performance metrics are clearly obtained with the ensemble method (except for low values of the threshold that have no practical relevance as they would lead to an excessive number of false alarms). To further analyze the impact of the DT on the final results, Table 6 shows the confusion matrix information with respect to the DT value for the ensemble method.