## 4 Methodology Application
### Proposed Health Indicators: Application to the Case-Study  
NPSD and HI can be interpreted by visualizing their significance on FFT spectra. Figures 16 and 17 report the example of the 0.021 in defect with 3 hp (vibration signal) and 0.021 and \(P_{u}\)/2 (contact pressure signal), but all the analyzed cases retraced this behavior. As long as the pressure signal is nonenveloped (Figure 16), most of the energetic content is concentrated in the low frequency range. The jumps in the cumulative NPSD point out the frequencies that mostly contribute to the signal PSD. Indeed, the very rapid increase detectable in the jumps corresponds to the harmonics in which the signal power is lumped. In particular, this occurred in the rotation frequency and x_BPFI_ harmonics. When the pressure signal is enveloped, NPSD shows peaks corresponding to fault harmonics. This results in higher jumps in the cumulative NPSD. Raw vibration data did not exhibit this trend, since a great part of the signal power is given by resonance contributions. Conversely, it is interesting to notice that, in the enveloped vibration data (Figure 17), the energetic jumps are mostly related to the x_BPFI_ content. This is consistent with the extensive literature supporting the strength of the envelope analysis for damage detectability [1; 22; 23; 35; 37; 70]. NPSD and cumulative NPSD were computed for nonenveloped and enveloped signals considering all the loads and damage level cases.  
The HI proposed in Equation (18) provides a quantitative extent of the jumps, since it represents the fraction of the power contained in these gaps relative to the whole signal power. As anticipated, it was hypothesized that the higher this fraction is, the more accentuated the damage severity, since a greater part of the signal energy is relatable to the presence of the fault. It appeared that this assumption was valid for the pressure signal, in which it was found a linear trend of NPSD and HI with respect to the defect size (Figure 18). As expected, the indicators, though showing a similar trend, exhibited lower values for the nonenveloped signal.  
Figure 19 shows the trend of these features for the enveloped and raw DE and FE signals. It can be observed that the damage is hardly detectable by means of these indicators without demodulation. On the other hand, in the enveloped signals, it is possible to allocate up to 20% of the signal power to the presence of localized faults. Interestingly, these values are comparable with the FE signal, since the adopted indicators are normalized with respect to the properties of each signal. Hence, in FE signals, low power fractions are related to low signal powers, resulting in values comparable with DE ones. Differently from K and CF, which have neutral physical units in the same way, NPSD and HI assume similar values in the vibration and in the pressure signal. Indeed, NPSD and HI refer to the relation  
Figure 15: x_BPFI_ contents for contact pressure, DE and FE enveloped signals.  
between an isolated event (damage) and signal power, whereas K and CF globally measure the effect of the damage on the time domain shape.  
Figure 16: Normalized power spectral density (NPSD) and cumulative NPSD nonenveloped and enveloped signals: pressure signal.  
Figure 17: NPSD and cumulative NPSD nonenveloped and enveloped signals: vibration signal.