66 G. Colford et al. Fig. 6.5 (a) Process flow diagram for feature selection in classification procedure. (b) Process flow diagram for application phase of classification procedure In Fig. 6.7, box-plots for local, healthy and motor off measurements are shown for each location. Within these boxes, the 25th and 75th percentiles are represented by the lower and upper boundaries of the boxes, the line inside of the boxes represents the median and the length of the whiskers on both ends of the box are the outlier thresholds. The motor off data is plotted alongside the healthy and faulty data to ensure that the information contained in the signals is independent of the noise floor. Taking this into consideration, it is evident that the combination of measurement, processing and analysis techniques that were used in this study was able to capture information at 0 m and 7 m, but not at 16 m. This is because the motor off features for 0 m and 7 m both behave as expected based on Table 6.1 and don’t resemble the calculated noise distribution. In Figs. 6.6 and 6.7, it is evident that at 16 m, the healthy and faulty signals are strongly correlated to the noise distribution. Kurtosis is a useful feature for identifying bearing faults because it successfully quantifies power impulses that are caused by cyclic impacts. These impulses appear in the frequency domain as sharp peaks occurring at the respective impulse frequency. Here, the ball pass frequency for the inner race is identified within the range of 278–282 Hz and it is shown in Fig. 6.7 that calculating the kurtosis over this range for the z-axis signals is successful in separating healthy versus faulty operating conditions at 0 m and 7 m. It is important to note that kurtosis is dependent on the shape of a distribution, and doesn’t necessarily represent the magnitude of a detected fault. Hence, the increase in magnitude in the healthy and faulty distributions going from 0 m to 7 m is representative of the wave propagation path from the point of initiation to the sensor, not the fault observability at each location. The fault observability can be recognized by the separation of distributions in Fig. 6.7 or by the Bhattacharyya distance in Fig. 6.8. The classification threshold shown in Fig. 6.8 represents the fault observability limit, with p-values less than and greater than 0.05 indicating that the fault is and is not observable, respectively. For p-values less than 0.05, the Bhattacharyya distance acts as a metric for relative observability. On this basis, the expected decrease in observability with sensing distance
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