## 5 Methodology Validation  
In order to investigate the feature sensitivity to the damage severity, the indicators were analyzed by considering multiple powers or applied loads as different realizations of a given damage level. The boxplots of Figure 20 indicate the attitudes of the different features for the three damage levels: L1, L2 and L3, which correspond, respectively, to 0.007, 0.014 and 0.021 in. It appears that, for all the feature distributions, it is slightly identifiable as a clear distinction between damage levels, except for NPSD and HI, which emphasize an evident discrimination. This reinforces the original assumption taken for the construction of NPSD and HI and confirms that, actually, the power fraction merely imputable to the presence of the defect is very sensitive to damage severity. However, boxplots are employed to give a graphical representation of the data, but their significance must be consolidated by a larger amount of realizations for each damage level. Figure 19: NPSD and HI for the enveloped and nonenveloped vibration signals. (**a**) DE and (**b**) FE. Figure 18: NPSD and health indicator (HI) for the enveloped and nonenveloped pressure signal. Detectability is studied by adopting the same approach even for the baseline and fault analysis performed on the vibration data, validating the capabilities of the proposed Indicators. As shown in Figures 21 and 22, all the features are able to discern faulty bearings, with the exception of the central frequency of the maximum SK band. Evidently, this feature is related to the research of nonstationarity, and no linear trend is expected between this parameter and damage severity. A clear separation between indicators for different damage levels is not identifiable for all the features. However, kurtosis (K) showed an increasing trend with well-separable distributions related to different damage levels. Figure 21: Boxplots for the features extracted from the vibration signal: peak value, RMS, CF and K.  
Figure 20: Boxplots for the features extracted from the pressure signal: (**a**) peak value, root mean square (RMS), crest factor (CF) and kurtosis (K) and (**b**) central frequency of the maximum spectral kurtosis (SK) band, 1x_BPFI_ content in the NFSD and HI in the 1x_BPFI_. Interestingly, the NPSD and HI were revealed to be promising features, since they fulfilled three main criteria. First, they can classify faulty bearings with respect to healthy ones. Secondly, they assume an increasing trend with respect to the damage level. Finally, their boxplots do not suffer excessive superimposition. Nevertheless, only a larger amount of data will confirm this attitude. One of the extremely attractive features of NPSD and HI is their values in the pressure signal and in the experimental signal of the damaged-bearing range in similar intervals for each fault size. Given the fact that NPSD and HI are endowed with neutral physical units, the diagnostic correlation between contact pressure and vibration was investigated (Figure 23). Figure 23 shows the results of the correlation study carried out by means of Equation (19) described in Section 3. The mean value of the damage-related power HI and of NPSD are computed for each fault level. These values constitute the _FP_ and _FV_ of Equation (19). The noteworthy correlation  
Figure 23: Correlation between the pressure and vibration signals by means of HI and NPSD. Figure 22: Boxplots for the features extracted from the vibration signal: central frequency of the maximum SK band, 1x_BPFI_ content in the NPSD and HI in the 1x_BPFI_. coefficients (Table 5) confirm these indicators to provide an evaluable key to link two different quantities from a diagnostic content perspective. This evidence reinforces the initial idea that one of the sources generating the dynamic response is actually related to this latter in a diagnostic sense. Moreover, it is found that, by taking into account diagnostic quantities, the possible correlation lies in the signal power.