## 2 Materials and Methods
### Test Rig Description and Data Collection  
This section describes the methodology followed to construct system-level features for system setting recognition and component-level features for prognostics. The system under analysis, which is shown in Figure 1, is a test rig built in the Department of Industrial Engineering of the University of Bologna. It consists of an asynchronous motor, a gearbox made of two pulleys exchanging the rotational motion through a belt, two shafts that share the torques due to a couple of gears, and an electromagnetic brake. The three-phase electric motor is an eight poles motor with 0.23 kW power and possible rotation speeds equal to 710 rpm and 910 rpm. The motion is transmitted to the first shaft through the belt running on the pulleys and put in tension thanks to a screw-system positioned on the motor's support, allowing a regulation of the belt's tension which is essential for accelerated run-to-failure tests. The braking system consists of an electromagnetic dust brake with adjustable braking torque in 0-7.5 Nm and a 90 VDC command control fed by a transformer. The platform's data acquisition device is composed of three accelerometers and a pyrometer. Three Dytran 3093D3 triaxial accelerometers are placed on the bearing's support, next to the second pulley and the two gearboxes. The three sensors have \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Feature Extraction**} & \multicolumn{2}{c}{**Fitness Function**} \\ \cline{3-4}  & & **Features Construction** & **HI Construction** \\ \hline
[30] & - & Fisher ratio & - \\
[31] & Embedded in the function set & k-NN & - \\
[32] & 7 Time-domain features & - & Monotonicity \\  & & & Monotonicity, trendability, failure \\  & & & consistency, scale similarity, \\
[33] & 11 Time-domain features & - & robustness, mutual information \\  & & & Spearman correlation with RUL, \\  & & & F-test \\
[34] & 68 Time- and frequency-domain & - & Monotonicity \\  & features & - & Weighted sum of failure consistency \\
[35] & - & & and the average range \\
[24] & 21 Time, frequency, and & - & Arithmetic mean of monotonicity, \\  & time–frequency domain features & - & trendability, and deviation quantity \\ This paper & 81 Time-domain features & k-NN & Weighted mean of monotonicity, \\  & & Silhouette index & trendability, and prognosability \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similarities and differences between the proposed approach and other works. a sampling frequency of 12.8 kHz per axis and an acceleration range of 500 Gpeak. An OPTRIS CSmicro infrared sensor is placed near the second pulley measuring the pulley or the belt's temperature at a sampling frequency of 1 kHz. The accelerometers are connected to a computer through three-channel NI9230 I/O modules with a maximum sampling rate of 12.8 kS/s for each channel mounted on a four-slot NI 9274 chassis that collects all the data from the acceleration sensors before sending it to the computer through a USB connection. A data acquisition interface is placed in the pyrometer's cable, and temperature measurements are collected using the plug-n-play software CompactConnect supplied by the Optris company. The technical characteristics of all components included in the test rig can be found in Appendix A. The component under analysis for prognostics is the belt. In particular, six run-to-failure tests are conducted, in which the belt is stressed until its failure. The more significant stress is caused by putting the belt at its maximum stretch to accelerate its degradation until it suddenly breaks. A greater tension of the belt usually occurs because of an improper mounting, which causes faster wear of the component and consequently more system downtimes. Tests are conducted in three different operating conditions, named C1, C2, and C3, defined by distinct braking torque values and the motor speed (Table 3). The braking force values have been set to 0.1 and 0.2 Nm because of the low power of the electric motor.