# Application of Machine Learning Tools for Long-Term Diagnostic Feature Data Segmentation
## 6 Real Data Analysis
### Real Data with Strong Non-Gaussian Noise  
In this section, we provide an example of real data with strongly non-Gaussian noise. This data set contains diagnostic features based on collected vibrations from wind turbine [94] bearings; see Figure 30.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **1 st Point** & **2 nd Point** \\ \hline EM & 13,170 & 27,120 \\ K-Means & 19,780 & 27,400 \\ BIRCH & 20,200 & 27,800 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Final changing points for the FEMTO data set.  
Figure 30: An experimental setup and picture of damage of bearing inner race [95].  
Figure 29: The segmentation results based on clustering algorithm over whole of FEMTO data set: (**a**) results for EM algorithm, (**b**) results for K-Means algorithm, (**c**) results for Birch algorithm.  
It should be mentioned that this data set has been used for prognosis in several works [94; 96; 97; 98]. In this case, for the construction of the HI, the method proposed in ref. [94] is used. The health index extraction procedure is illustrated on Figure 31. For details of the method, we refer the readers to [94]. The values of inner race energy for a group of measurements for one particular speed (high speed) are demonstrated in Figure 32. In Figure 33, all calculated features are presented. Again, some of them seem not to be useful (does not follow the shape of original data), so they will be ignored for the next step of analysis. In Figure 34, selected features are presented in a 3D plot. Definitely, they are strongly correlated, so the utilization of the PCA is suggested. In Figure 35, the importance of principal components is presented. More than 90 % of the informativeness is included in PC1. In Figure 36, original features and new features (i.e., Principal Components) are presented. One can see that the shape of the PC1 is similar to the original features, while the behavior of PC2 and PC3 is different. Based on PC1 data, the PDF is estimated. It is presented in Figure 37. Threshold values are established experimentally based on PDF of PC1. The right subplot presents segmentation results using colors.  
Figure 34: Wind turbine stochastic features space.  
Figure 35: Wind turbine PCA score.  
Figure 33: Wind turbine stochastic features.  
Based on this fact, the wind turbine data set includes many spikes; it is not easy to select the threshold. However, it can be selected approximately: the first one with an amplitude less than 0 is related to the healthy stage, the second one with an amplitude more than 0 and less than 0.2 (degradation stage), and samples with an amplitude higher than 0.2 could be considered as critical stages. Next, three selected features are subjected to clustering algorithms; see Figure 38. All of the algorithms identified three clusters; however, borders for BIRCH and K-means seem to be more clear than for EM. The final results, i.e., clustering-based segmentation for real non-Gaussian data, are presented in Figure 39. As it was concluded for Figure 38, the EM algorithm detects regime 2 too early. More or less, the second regime is discovered by BIRCH and K-means equally; however, the result for detecting the last regime is different. In Figure 39, the final result for the wind turbine data set is presented. Original data divided into three regimes are plotted with different colors associated to the given regime. As shown in Figure 39, the EM could not detect the third regime (critical stage) properly. The other clustering (BIRCH and K-means) approaches are able to divide data into three regimes in a similar way. For this case, the exact changing points are undefined; see Table 5.  
Figure 37: Wind turbine kernel density based PC1.  
Figure 36: Wind turbine PCA.