# Application of Machine Learning Tools for Long-Term Diagnostic Feature Data Segmentation
## 6 Real Data Analysis
### Real Data with Almost Gaussian Noise  
The FEMTO data set [74] was acquired by Franche-Comte Electronics Mechanics Thermal Science and Optics-Sciences and Technologies institute from a PRONOSTIA platform. The test rig is presented in Figure 21. The data set was shared during the prognosis challenge at the conference IEEE PHM 2012. The data set contains 17 historical long-term feature sets describing the degradation of bearing. Two accelerometers and a temperature sensor were used to acquire acceleration and temperature. The speed of the shaft was kept stable during the test. It is assumed that the failure of the bearing occurs when the amplitude of the vibration signal has arrived above 20 g. This data set was used in many publication for segmentation [75; 76; 77; 78; 79], construction of the health index [80; 81; 82; 83; 84; 85; 86; 87] and predicting RUL [88; 89; 90; 91; 92; 93]. As one can see, this data set perfectly follows the idea of three regimes: for time 0 to c.a. 12,000, it is nearly flat, then up to t = 27,000 it shows linear increase and then rapid growth Figure 22. Some noise, especially in the middle regime, is also seen; additionally, some small outliers can be noticed. Thus, we consider it as a trend with nearly Gaussian noise. In Figure 23 features extracted using the proposed methodology are plotted. As one can see, RMS and mean value are very similar, and STD reacts significantly only for the third regime. Unfortunately, kurtosis and skewness seem to be not related to degradation. Three features are used for further analysis: STD, RMS and mean value. Figure 21: Overview of PRONOSTIA FEMTO data set [74]. Figure 22: _Cont._  
In Figure 24, the selected features are plotted together as a 3D plot. As one can expect, data corresponding to the third regime are pretty different compared to regimes 1 and 2, so it can be a bit challenging to recognize regimes 1 and 2. Next, the PCA is applied. As presented in Figure 25, PC1 contains over 95% of information. In Figure 26, the results of the PCA analysis are presented. Three original features are plotted together with three principal components. It is clear that the PC1 is following the original features, while PC2 and especially PC3 do not contain too much information. As PC1 is the most informative, one can use the probability density function (PDF) to set up thresholds for regime change point detection. As mentioned above, as original features  
Figure 24: Features space FEMTO data set. Figure 23: Features extracted according to proposed methodology for FEMTO data set. Figure 22: Health index (RMS) from FEMTO data set: (**a**) representation of Health index with points cloud, (**b**) representation of Health index with line. are highly correlated and the PC1 contains most of the information, the clustering can be done. In Figure 27, one can see the trajectory of PC1 (left) and its PDF. One can easily notice three modes related to three stages: the first one with amplitude less than 0 is related to the healthy (good condition) stage, the second one with amplitude more than 0 and less 0.2 (degradation stage, i.e., warning), and samples with amplitude higher than 0.2 could be considered as critical stages (Alarm). Figure 26: Results of PCA applied to FEMTO data set. Figure 25: PCA scores for FEMTO data set. In Figure 28, the results of the selected clustering techniques are presented. The data with high dispersion correspond to regime no. 3 (red color). Cluster in green color corresponds to the healthy stage. The last one is medium degradation regime (yellow). In general, the EM algorithm provides the most effective result; however, it is not perfect. BIRCH and K-means provide similar results. In Figure 29, the final result of segmentation is presented. Original data divided into three regimes are plotted with different colors associated to a given regime. As shown in Figure 29, the BIRCH and K-means discovered the second change point much later than what really exists.