## 3 Application
### Data Mining with Feature Extraction  
Feature selection helps to avoid overfitting and improve model performance, and provides efficient and cost-effective process monitoring while acquiring better insights into the underlying processes that generated the data [12]. Various time domain features can be extracted to describe the characteristics of the sensed signal from different aspects, such as RMS, kurtosis, and crest factor etc. For example [13], any spikiness in the vibration signals indicated by the crest factor and kurtosis implies incipient defects, where the high energy level given by the value of RMS indicates sever defects. Therefore, selected feature fusion might result in better data mining for machine learning. As displayed in Figure 7, the raw data converted to synergy position signals were divided into 331 segments after packaging, as in Equation (11). Each segment was labeled as one cell with its own feature vectors, and each feature vector contained nine feature elements, namely, the RMS error, kurtosis, variance, crest factor, standard deviation, skewness, mean, maximum, and minimum of the synergy position signals.  
Figure 6: Synergy-deviated positioning plot of data based on Figure 5b.  
Before feature extraction from the nine features of the feature vector of each of the 331 cells, outliers (extreme values) were removed using the Z-score technique. The criterion for determining outliers though Z-score computation was set at three times the standard deviation. A red dot was treated as an outlier after Z-score computation (Figure 8). Therefore, 16 cells were removed from the original 331 cells. The representative quantitative values were extracted from the remaining 315 cells, and reflected the WHRA degradation behavior from health status to failure mode.  
Using all the extracted features to assess the prognostic-diagnosis health model is unfeasible and inefficient, since some extracted features have a low contribution in classification models. Therefore, the Fisher criterion was used to select among the nine features those that could distinguish between healthy status class (labeled as CV of 1) and call-for-maintenance class (labeled as CV of 0). The Fisher criterion score (Equation (12)) of each feature was calculated to identify the significant features from the feature vectors as follows:  
\[\text{Fisher score}\ =\ \frac{\mu_{1}-\mu_{2}}{{S_{1}}^{2}\ +\ {S_{2}}^{2}} \tag{12}\]  
where \(\mu\) and S indicate the mean and standard deviation, respectively, of each class; subscripts 1 and 2 represent classes 1 and 2, respectively. Figure 9 plots the Fisher scores for all nine features. Four high-score features (RMS error, mean, maximum, and minimum of signals) that could distinguish between the healthy and call-for-maintenance classes were selected. For the 315 cells, 315 \(\times\) 4 arrays  
Figure 8: Z-scores distinguishing outliers (red) from the acquired inlier data (black).  
Figure 7: Flow chart of diagnosis based on feature extraction followed by the GA–GRNN and LR to create a RUL model of a WHRA.  
were constructed. Each cell contained four column features, including the healthy status class, working asset, and call-for-maintenance class to be used for the next CV labeling. The \(315\times 4\) arrays were normalized to a N (\(\mu\), S) distribution within [0,1]. The formula is given in Equation (13) for the new value of each cell feature:  
\[X_{ij}=\frac{x_{ij}\ -\ x_{\min}}{x_{\max}\ -\ x_{\min}},\text{where}\ i\ =\ 1,\ 2,\ \ldots,\ 315\ \text{and}\ j\ =\ 1,\ 2,\ 3,\ 4. \tag{13}\]  
This normalization was preserved as a new \(315\times 4\) array, which was then used in the GA-GRNN and LR models of the RUL.