## 4 Results and Discussion
### Study A: Forward Stroke Analysis through Segmentation Technique  
Study A consisted in applying the segmentation technique to the three health state datasets and evaluating the change in their features for the forward stroke motion. Figure 8 illustrates the RMS feature that when the segmentation technique is applied to the baseline dataset, limits at 10% (green line) and 20% (red line) above the feature's magnitude were placed to visualize suspect and faulty segments, respectively. The number of divisions used was \(n=3\), thus generating \(n_{s}=8\) segments as per Equation (1). This was selected since the misalignment was introduced past the halfway mark of the stroke, approximately 350 mm from the starting position, and the position where the misalignment was above 0.25 mm was approximately 570 mm from the starting position, as shown in Figure 5.  
As previously shown in Figure 7, the difference of the evaluated features (RMS and standard deviation) is below 10%, and can lead to the system being operated at a misaligned state. Comparatively, other features, such as kurtosis and peak-to-peak, demonstrated a percentage error of approximately 20% when compared to the baseline state at the full stroke analysis, as depicted in Figure 9.  
Figure 8: Segmented baseline dataset for RMS feature. Figure 7: Full stroke healthy vs. faulty comparison of time domain features. (**a**) RMS, (**b**) Standard Deviation. This result leads to a deeper investigation of the former features. When the segmentation technique is applied to the faulty dataset of vibration signals and the same features are calculated, a change can rapidly be observed. As illustrated in Figure 10, the signal's RMS exceeds the 10% limit at the half stroke analysis. Upon further segmentation, at the quarter stroke, it can be observed that the last quarter segment exceeds the 20% limit focusing the analysis in that area. When segmenting once more at the eighth-stroke level, the signal's RMS in the last section of the stroke has a percentage error of 42%. Comparatively, the standard deviation of the vibration signal also exhibits similar results to that of the RMS feature. These results are significant, since they demonstrated that, by utilizing the segmentation technique, the usability of the RMS and standard deviation features increased by going from a 6% error at the full stroke level to a 42% error when compared to the baseline state. Figure 10: Forward stroke faulty dataset signal segmentation analysis. (**a**) RMS, (**b**) Standard Deviation. Figure 9: Full forward stroke healthy vs. faulty comparison of time domain features. (**a**) Peak-to-Peak, (**b**) Kurtosis. Finally, the analysis is taken a step further by relating each evaluated segment to the position of the linear axis. As per the methodology described in Section 3.1, the full stroke is equivalent to a travelled distance of 700 mm. Therefore, when segmenting the vibration signal, each segment consists of an equivalent travelled distance based on the number of segments. Table 3 outlines each segment and their respective distance travelled. As previously stated, the misalignment was introduced at the back end of the testbed, as shown in Figure 5, approximately at the 350 mm mark. Due to the nature of the misalignment introduced, the measured deviation progressively increased up to 0.5 mm at the end of the stroke. Through the segmentation technique, the results demonstrated that, as the linear axis moved in the forward direction, the vibration exceeded the proposed limits at the last 175 mm (4 th quarter stroke) of the stroke where the misalignment ranged between 0.25-0.5 mm. The other evaluated statistical features, such as peak-to-peak and kurtosis, demonstrated approximately a 20% error at the full stroke analysis when compared to the baseline dataset. However, when the segmentation technique was applied, as shown in Figure 11, the following results occurred:  
* The peak-to-peak demonstrated a remarkable result when the segmentation technique was applied.