## 4 Results
### TCM Data Analysis  
In order to test the effectiveness of vibration sensors for diagnostics, TCM data for the beginning of 2020 were selected to be compared with data for the beginning of 2021. In fact, given that at the end of 2020 T.Tar underwent an extraordinary maintenance intervention, the incipient damage could be visible in such data. T.Ref turbine data were added to validate the method and increase the statistical confidence of the analysis. A total of four acquisitions at nominal conditions were chosen (i.e., rpm, MW, see Table 3), each of them involving seven uniaxial accelerometers MnBrgRr, MnBrgFr, NaXdir, NaXdir, GbxHssRr, GbxHssFr, GbxIss sampled at 25.6 kHz for about 10 s. This dataset was processed according to [40; 41; 42]. In particular, each signal was divided into 100 chunks of 0.1 s each, and 5 time feature was extracted (i.e., RMS, skewness, kurtosis, crest factor, peak value). Every acquisition was then turned into a matrix of 100 rows by 35 columns (7 channels, 5 time-features). First, the data were pre-processed by removing univariate outliers using a Hampel filter of a size of 10 samples. Then, a second univariate pre-processing followed. Each feature of the outlier-free dataset was standardized by removing the mean value and dividing by the standard deviation, and computed on the training set alone. The previously proposed multivariate Novelty Detection algorithm was finally implemented on the pre-processed dataset to quantify the novelty in the acquisitions, i.e., the distance of a sample from the reference healthy distribution. Given the stationarity of the acquisitions (i.e., nominal speed and power, see Table 3) novelty can be easily related to the presence of damage [39]. In this framework then, a simple yet effective Novelty Metric based on PCA was used. The principal Principal Component Analysis was carried out on the whole pre-processed dataset. The result of the corresponding dimensional reduction is shown in Figure 9. In this 2D representation only the first two principal directions are considered; nevertheless, these, respectively, explain 68% and 22% of the total variability in the dataset. As is clearly visible, along PC1 most of the variability is related to a shift of the turbine T.Tar cloud to higher values, further away with respect to the Training and Healthy Validation clouds. Hence, the PC1 information can be used as a good Novelty Indicator. This NI is shown in Figure 10 where the training and the validation sets are reported. The rationale for showing this Figure is a qualitative assessment of the fact that the NI is in general higher in the faulty validation data set, despite the measurements having been recorded almost 7 months before the failure: from this Figure, one can argue that the TCM vibration data can clearly highlight the presence of Novelty related to an anomalous health condition. In order to complete the analysis, a quantitative result is helpful regarding the damage detection ability of such an NI indicator for the incipient damage on T.Tar: therefore, a Receiver Operating Characteristic (ROC) curve is reported in Figure 11, in terms of true positive rate vs. false positive rate. The area under such a curve corresponds to 94% of the total, indicating a nearly optimal performance. In particular, if a false positive rate of 5% is accepted (i.e., the threshold set at NI = 158), more than 70% of the points coming from T.Tar in the faulty condition are correctly identified as damaged. \begin{table}
\begin{tabular}{c c c c c} \hline
**Id. Turbine** & **Period** & **Rot. Speed [RPM]** & **Power [kW]** & **Dataset** \\ \hline T.Tar & 2021/05 & 28 & 1999 & Training (Healthy) \\ T.Ref & 2021/02 & 28.1 & 2003.8 & Training (Healthy) \\ T.Tar & 2020/02 & 27.9 & 2005.9 & Validation (Faulty) \\ T.Ref & 2020/04 & 27.8 & 1887.9 & Validation (Healthy) \\ \hline \end{tabular}
\end{table} 
Table 3: Vibrational events considered for the analysis.