## 3 Experimental Technology Validation for Bearing Race Defect
#### Technology Validation on Inner Race Fault  
Bearing vibration signals were resampled into the angular domain using a tachometer signal. The SK is calculated individually for each short vibration segment to identify the excited resonant frequency bands, and the optimal denoising Wiener filter parameters are also adapted individually for each vibration segment. Figure 4 shows the SK vs. frequency for fault free (a) and damaged (b) cases for 340 short segments. In the fault-free case, the SK remained below 1.5 for all segments and frequency bands (Figure 4a), which suggests the dominant presence of stationary noise of a fault-free bearing. The SK of a damaged bearing shows multiple resonant frequency bands, excited by a fault exceeding amplitude of 12. Figure 4b shows three main resonant frequency bands at central frequencies 5 kHz, 12 kHz and 16 kHz. As can be seem from Figure 4b, the SK has the highest peak amplitude at 12 kHz, which indicates that the structural resonances are dominant within 12 kHz band. The bands at 5 kHz and 16 kHz have slightly lower but comparable amplitude indicating additional resonant behaviour within those bands as well. Given that different realisations excite resonant bands with varying amplitude, this phenomenon could be attributed to the variation in location of the damaged area (the inner race damage is not static; but, rotates with a shaft), which is causing partial smearing of the frequency bands due to two effects: (a) varying fault induced excitations with higher amplitudes, when the damaged area is within the load zone, and with lower amplitude outside; and (b) varying transfer function between the source of the excitation and the sensor with rotating damaged area (unknown transmission path). The varying nature of bearing inner race faults and consequent excitation requires observation of multiple consequent segments over time to capture multiple responses of the bearing, where each response is shown with a different colour in Figure 5. As can be seen in Figure 5, resonances at frequency bands 5 kHz and 12 kHz are excited for three realisatons, while resonances at 16 kHz band were only excited twice out of three times. The amplitude of SK peaks also varies between 12-21, which gives further evidence to varying nature of bearing damage signals. \begin{table}
\begin{tabular}{c c} \hline Frequency response & 1 Hz–5 kHz \\ \hline Axial sensitivity & 5.21 pC/ms\({}^{2}\) \\ \hline Resonance frequency & 25 kHz \\ \hline Max acceleration & 80 g \\ \hline Mass & 28 g \\ \hline Piezo material & PZT-5 \\ \hline Isolation resistance & \(10\times 109\) Ohm \\ \hline Capacitance & 1200 pF \\ \hline Temperature range & \(-40\) to 150 degC \\ \hline Shock limit & 800 g \\ \hline Temperature sensitivity & 4 mg/degC \\ \hline Structural strain sensitivity & 0.2 mg/micro strain \\ \hline Magnetic field sensitivity & 2 g/T \\ \hline \end{tabular}
\end{table} 
Table 2: KCF AG107M accelerometer specification. Figure 4: Spectral kurtosis for consequent bearing vibration segments. Figure 5: SK for three randomly selected short segments from bearing signal. Three segments are shown with three colors (segment 1 - green, segment 2 - red, segment 3 - blue). According to Equation (4), the SK is used to design the optimal denoising (Wiener) filter upon being compared to the statistical significance threshold s. The presented results are achieved using 1% statistical significance. The filtering is achieved using Equation (7) in frequency domain, and resulted in removal of the stationary noise, thus, retaining the non-stationary fault-related component--the SK-filtered signal. The diagnostic features for all 340 segments are shown in Figure 6 for fault-free (a) and damaged (b) cases. The feature maps show mainly low amplitude (<10) apart from the high amplitude features in damaged case (b) due to extracted impulsive components. The diagnostic features have high amplitudes at the moment of the impact and low amplitudes between  
Figure 6: The diagnostic features—squared envelope of the SK-filtered signal.