## 2 Materials and Methods
### Damage Detection Analysis  
The damage detection analysis was carried out by taking advantage of the well-established concepts presented in the introduction to this work. Namely, different diagnostics features were extracted from both signals. Although the greatest part of these features enabled damage detectability, the fault severity assessment was not straightforward. Furthermore, it was a hardly identifiable correlation between the two signals in a diagnostic sense. For this reason, the authors proposed two health indicators to perform these tasks. Indeed, the dedicated features were constructed in an attempt to investigate direct correlations. Additionally, the conjectured sensitivity to the damage level was endorsed by the experimental validation. Vibration data coming from FE healthy bearing were analyzed as well. Prior to introducing the proposed indicators, the standard features and the methodology for their extraction are presented in the following. * Time features (peak values, root mean square (RMS) and crest factor)
* Frequency features (mean contribution, xN harmonics and x_BPFI_ harmonics)
* Enhancement of the nonstationary part (SK and FK)
* Envelope extraction and signal demodulation (x_BPFI_ harmonics of the demodulated signals)  
Time domain and frequency domain features were investigated considering their variability linked to the damage severity and absorbed power (for the vibration signal) or applied load (for the pressure signal). Root mean square value (RMS), crest factor (CF) and kurtosis (K) are reported in Equations (9)-(11). \[RMS=\sqrt{\frac{1}{T}\int_{-\infty}^{+\infty}x^{2}(t)dt} \tag{9}\]  
Figure 4: Examples of the computed time histories for different load levels and defect sizes. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Damage** & **Damage** & **Load—Fraction** & **Fs—Sampling** & **M—Number** & **T—Time** \\
**Diameter (in)** & **Depth (in)** & **of Pu** & **Frequency (kHz)** & **of Samples** & **Duration (s)** \\ \hline
0.007 (0.18 mm) & 0.011 (0.28 mm) & 1/8-1/4-1/2 & 48 & 63,788 & 1.33 \\
0.014 (0.35 mm) & 0.011 (0.28 mm) & 1/8-1/4-1/2 & 48 & 63,788 & 1.33 \\
0.021 (0.53 mm) & 0.011 (0.28 mm) & 1/8-1/4-1/2 & 48 & 63,788 & 1.33 \\ \hline \end{tabular}
\end{table} 
Table 3: Contact pressure data specifications. \[CF=\frac{x_{peak}}{RMS} \tag{10}\]  
\[K=\frac{E(x-\mu)^{4}}{\sigma^{4}} \tag{11}\]  
where \(T\) is the period, \(x(t)\) is the time signal, \(x_{peak}\) is the peak value of the signal, \(E()\) is the expected value operator, \(\mu\) is the mean value and \(\sigma\) is the standard deviation. Kurtosis thus computed is expected to take the value of three for gaussian signals. Frequency domain features were extracted from FFT raw spectra (Figures 5-7). In particular, the mean contribution, the rotating contribution and the fault contribution, respectively corresponding to the 0-Hz harmonic, 1x\(N\) harmonic and 1x\(BPFI\) harmonic were individually analyzed. Figure 5: Fast Fourier-transform (FFT) raw spectra: vibration signals. DE: drive end. Figure 6: FFT raw spectra: pressure signals. SK and FK were employed for the purpose of enhancing the bearing signal in the vibration data and isolating the impulsive part in the pressure signal. As mentioned earlier, these methods are particularly useful, though many alternatives are available in the literature. Indeed, the potential filtering bands can be underlined by comparing power spectral densities (PSD) of undamaged and damaged bearings [1]. Nevertheless, a major problem with this method is that the machine signature needs always to be known. Besides, wavelet denoising [67; 68; 69] works by taking advantage of wavelet transform and deleting the wavelet contributions that go beyond a defined threshold. However, there are certain drawbacks associated with the use of this methodology, since the result strongly depends on the choice of the mother wavelet and of the thresholding method.