## 2 Gearbox Characteristics  
The test bench (test rig system) used for this work is depicted in Figure 1. The system is located at the Polytechnic University of Milan and is composed of 2 shafts, 12 bearings, and 2 gearboxes (service and test) forming 2 gear pairs (Figure 2). Each gear pair has the same center distance and the same gear ratio, and they are connected by two parallel shafts (shafts 1 and 2), obtaining a mechanically closed circuit. Shaft 2 is composed of a rotating servo-hydraulic torque actuator (coupler) that decouples the two semi-shafts (positive shaft 2 and negative shaft 2). The torque is applied to the system by traditional mechanical coupling, which procedure can be similar to the one performed in a FZG (Forschungsstelle fur Zahnrader und Getriebebau) test rig, the technical institute responsible for which develops studies about gears and drive mechanisms. In this study, the system was substituted by a hydraulic actuator of shaft 2. Since this can be used in different operations and varying modes, the applied torque can be changed to test the required system in different modes, which enables a test with variable load. The torque through shaft 1 can be measured by strain gauges, and the vibration signals can be collected through the housing (the location used for the analysis of this paper) by piezoelectric accelerometers. This mechanism, arranged in a closed mechanical loop, applies a rotation to the two semi-shafts to induce equal and opposite torques in the tested gears, and this configuration can be used to test gearing at varying speeds. The test bench is controlled by an inverter, and it is driven by an asynchronous induction motor, which is electric. As a result, the system needs to supply the energy losses, which requires a system equipped with two independent lubrication circuits. The first refers to the hydraulic actuator and the service gearbox, while the second refers to the test gearbox, in which properties such as lubrication and temperature can be adjusted. Therefore, the maximum torque, speed, and lubrication for this test bench are 1000 Nm, 3000 rpm, and 120 C, respectively [47]. The spur gears, components of the test gearbox, were used to investigate cases of damage. In this study, they were used for evaluating the consequences of cracks in the system. The main parameters of the test bench, including information about the test gears, are presented in Table 1.  
Studies of this type of machine can be used for research related to predictive maintenance of industrial rotating machinery. In addition, ML techniques can be used for FD by performing vibration analysis of a system and this approach can prevent the machine from operating in periods in which the components of the system are degrading [48]. Thus, it is important to consider these essential gear train parameters in order to investigate the dynamic behavior of a system and properly implement the ANN architecture to predict different types and levels of damages for each system. Figure 1: Test rig system layout used to perform the real tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Symbol**} & \multicolumn{3}{c}{**Stage 1 (Service Gearbox)**} & \multicolumn{3}{c}{**Stage 2 (Test Gearbox)**} & \multirow{2}{*}{**Units**} \\ \cline{3-3} \cline{5-6}  & & **Helical Gear 1** & & & **Helical Gear 2** & & **Spur Gear 2** \\ \hline Center distance & \(C_{d}\) & & 91.5 & & 91.5 & mm \\ \hline Face width & b & & 80 & & 14 & mm \\ \hline N\({}^{\circ}\) of teeth & \(z\) & 34 & 36 & 17 & 18 & - \\ \hline Normal module & \(m_{n}\) & & 2.5 & & 5.0 & mm \\ \hline Mass & \(m\) & 3.1 & & 3.3 & 3.1 & 3.3 & kg \\ \hline Moment of inertia & \(J\) & 0.0122 & & 0.0146 & 0.0122 & 0.0146 & kg m\({}^{2}\) \\ \hline Pitch circle diameter & \(d_{p}\) & 0.0888 & & 0.0941 & 0.0888 & 0.0941 & m \\ \hline Pressure angle & \(\alpha_{n}\) & & 20 & & 20 & deg \\ \hline Helix angle & \(\beta\) & & 12 & & 0 & deg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test bench parameters.