## 3 Experimental Technology Validation for Bearing Race Defect
#### Technology Validation on Inner Race Fault
impacts. According to the specially defined length of each segment, the envelope signals cover exactly 8 impacts, produced by 8 balls of the bearing. Dependency of diagnostic features vs. shaft angle reveals inclined line impact patterns (as expected) rather than straight lines. This phenomenon is due to the presence of the random slippage between the rolling elements and bearing races. Although the impacts are clearly visible, to track impacts, produced by the same rolling element, over prolonged periods of time, additional alignment is performed on all segments, using the novel cross-correlation approach. The alignment, using the novel correlation approach, makes the inclined lines of impacts vertically straight (Figure 7). The main purpose of the alignment is to retain impacts, produced by the same ball/roller within a consistent angular band for improved fault localization. To evaluate the separation between the diagnostic features, extracted under damaged and undamaged conditions, the FC is applied. Figure 8 shows essential values of FC in range [2,4] related to a moment of an impact when a rolling element passed through the damaged inner race area. The FC is calculated based on histograms from damaged and undamaged cases and represents a measure of a separation between them. This means, only a single FC graph is obtained from the entire experiment from both feature histograms for damaged and undamaged conditions. In addition, the FC, shown in Figure 8, is a measure of a separation between the diagnostic feature histograms from inner race defect and undamaged cases, and shows the FC values for a complete cycle, including the time of impact (FC peak values) as well as the time between impacts (FC of low values). The FC values suggest a clear separation between diagnostic features, extracted from damaged and undamaged conditions, which is the main requirement for reliable diagnosis. The performance of the SK-based diagnostic features defined within this paper is compared to the wavelet-based features obtained from the same vibration signals acquired under the same experimental conditions [5]. The authors have used wavelet transform for frequency band selection as well as filtering for feature extraction and have obtained the FC values close to 1 for all 8 peaks, summarized in Table 3.  
Figure 7: The aligned diagnostic features—squared envelope of the SK filtered signal. Hence, according to the higher FC values in Table 3, the proposed technology offers much better separation and superior diagnostics compared to the wavelet approach. The diagnostic features, extracted via the proposed technology indicate FC values with a mean of 3.4 (Figure 8). The results indicate effectiveness gain (EG) in range of [1.9, 4.6] in terms of the FC, where EG is the ratio of the FC of the proposed technology to the FC of the wavelet technology \(EG=\frac{FC_{\text{SFL}}}{FC_{\text{LW}}}\). The experimental validation of the proposed technology is also estimated via artificial intelligence decision making, using the k-NN and k-means supervised approaches. Upon creating the clusters, representing undamaged conditions, using the k-means technique and training data from fault-free case, the testing diagnostic features from undamaged and damaged cases were classified. As a result, the decision maps in Figure 9 shows the amount of false detections and missed detections. Figure 8: The FC measures of diagnostic feature separation between inner race defect and undamaged case. \begin{table}
\begin{tabular}{c c c c} \hline
**Rolling Element N** & **Wavelet** & **SK** & **Gain** \\ \hline
1 & 1.2 & 3.6 & 3 \\ \hline
2 & 1.2 & 3.8 & 3.2 \\ \hline
3 & 1.1 & 3.9 & 3.5 \\ \hline
4 & 1.1 & 2.1 & 1.9 \\ \hline
5 & 0.9 & 2.6 & 2.9 \\ \hline
6 & 1.2 & 3.3 & 2.8 \\ \hline
7 & 1 & 3.6 & 3.6 \\ \hline
8 & 0.9 & 4.1 & 4.6 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of FC for the wavelet approach [5] and the proposed approach. In the undamaged case (Figure 9a), the number of false alarms is relatively low, equal to 0.1%.