## 3 Results
### Fault Detection  
The computation of statistical parameters is of paramount importance to reveal the presence of an incoming fault, accomplishing the first phase of condition monitoring. In the following analyses, parameter calculation is performed on each set of 20,480 (\(f_{\text{s}}\)) samples acquired for each second of testing, so that only one statistical value per second is obtained. If a parameter trend is examined along the time duration of the whole registration (made continuous with the exclusion of the interruptions of acquisition occurring in real time), it can be observed that the Mean, Variance and Standard Deviation of bearings 1 and 2 (Figures 4a and 5a) remain almost constant, with a slight increase just at the very end of the experiment, probably due to the propagation of vibrations produced by other damaged bearings and detected by sensors 1 and 3 because of the physical continuity of the testing, in which all the components are installed on a single shaft. RMS value, Skewness and Kurtosis (Figures 4b-d and 5b-d), albeit oscillating, do not exhibit a global monotonicity too, except for in the last measurements, for the reason just mentioned. On the contrary, the presence of faults on bearings 3 and 4 can be clearly deduced from the RMS value (Figures 6b and 7b) and even more from the Kurtosis (Figures 6d and 7d), which starting from a value around 3, typical of a Gaussian distribution, raises over 70 from the 1831 st second (31 st day of test) for the third bearing and from the 1486 th second (28 th day of test) for the fourth one. Mean, Variance and Standard Deviation (Figures 6a and 7a) remain mostly stable, and Skewness (Figures 6c and 7c) does not show a clear reduction, as expected in the case of a fault. Figure 4: First group of statistical parameters applied to the signal from sensor 1 on bearing 1: (**a**) Mean (red), Variance (green), Standard Deviation (blue); (**b**) RMS value; (**c**) Skewness; (**d**) Kurtosis. Figure 5: First group of statistical parameters applied to the signal from sensor 3 on bearing 2: (**a**) Mean (red), Variance (green), Standard Deviation (blue); (**b**) RMS value; (**c**) Skewness; (**d**) Kurtosis. Similar results can be obtained by considering advanced statistical parameters, i.e., Peak, Crest Factor, Clearance Factor, Shape Factor, Impulse Factor and Peak-to-Peak. On one hand, these parameters do not provide relevant information if applied to the signals from bearings 1 and 2 (Figures 8 and 9). On the other hand, with respect to the vibration signals acquired from bearings 3 and 4, consistent information is provided by Clearance Factor (Figures 10a and 11a) and Impulse Factor (Figures 10b and 11b). Figure 6: First group of statistical parameters applied to the signal from sensor 5 on bearing 3: (**a**) Mean (red), Variance (green), Standard Deviation (blue); (**b**) RMS value; (**c**) Skewness; (**d**) Kurtosis. Figure 7: First group of statistical parameters applied to the signal from sensor 7 on bearing 4: (**a**) Mean (red), Variance (green), Standard Deviation (blue); (**b**) RMS value; (**c**) Skewness; (**d**) Kurtosis. Figure 8: Second group of statistical parameters applied to the signal from sensor 1 on bearing 1: (**a**) Peak (red), Crest Factor (blue), Clearance Factor (green); (**b**) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green). Figure 10: Second group of statistical parameters applied to the signal from sensor 5 on bearing 3: (**a**) Peak (red), Crest Factor (blue), Clearance Factor (green); (**b**) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green). Figure 9: Second group of statistical parameters applied to the signal from sensor 3 on bearing 2: (**a**) Peak (red), Crest Factor (blue), Clearance Factor (green); (**b**) Shape Factor (red), Impulse Factor (blue), Peak-to-Peak (green).