## 2 Digital Twin-Assisted Gearbox Monitoring
### Bearing Faults
#### 2.1.2 Experimental Procedure  
For the experimental procedure to study bearing faults, it is preferable to minimize the transmission components as much as possible. In fact, bearing failures are often implicit in nature and can easily be overshadowed by other faults or poor mechanical designs [54]. At this stage, it is crucial to measure the rotational speed of the shaft attached to the test bearing and then estimate the fault frequencies that could affect the bearing. Based on these frequencies, the required sampling frequency is calculated by following [PERSON]'s theorem, which states that a signal must be sampled at a rate at least twice its maximum frequency in order to be accurately captured [55]. This principle forms a bridge between a continuous signal and its discrete representation. Moreover, a higher sampling frequency increases the fidelity of the discrete signal. However, if the frequency is too high, it can lead to slower processing due to redundant data and storage issues. These two factors are particularly critical in real-time monitoring, making the appropriate choice of sampling frequency essential. In practice, signals are typically sampled at 5 to 10 times the maximum defect frequency to capture transient impacts and account for the roll-off of anti-aliasing filters. These frequency considerations also directly influence sensor selection, as the transducer must have adequate bandwidth and sensitivity over the relevant range to effectively detect faults. Bearings are generally sourced from well-known manufacturers. It is therefore recommended to consult catalogs to extract information about the bearing's geometric characteristics and the material used for its manufacturing. If the material information is unavailable, it can be determined using characterization methods. The geometry and material data can then be used to calculate the weight of each bearing component. As for the stiffness and damping values, a modal analysis is necessary to estimate them [56]. The first example from [22] involves data collected on a laboratory test bench. To validate the response accuracy of a constructed five-DOF dynamic bearing model, the ABLT-1A test bench was used to acquire real vibration signals from a 6205 bearing. The rotational speed was set to 1500 rpm (i.e., 24.88 Hz). The dataset was sampled at a frequency of 12 kHz, with each sample containing 2048 data points. Measurements were taken under four conditions: healthy (HN), ball fault (BF), inner ring fault (IF), and outer ring fault (OF). The corresponding theoretical fault frequencies were 134.73 Hz (IF), 117.51 Hz (BF), and 89.19 Hz (OF). Both the measured and simulated waveforms exhibited periodic impulses with similar trends across the different fault types. The second example from [21] is based on real-world vibration data collected from three 1.5 MW wind turbines located at a wind farm in Wuzhong, Ningxia (China), each with known pitch bearing conditions. The data acquisition system included W610-500 IPEE accelerometers (500 mV/g, 0.1 Hz-10 kHz bandwidth), a data logger, and a host computer connected via Ethernet. The optimal accelerometer placement was identified as the outer race of the pitch bearing. However, due to physical constraints, the accelerometers were instead installed at point 3 on the internal web of the hub, where signal intensity (RMS) and cross-correlation with points 1 and 2 remained high. Vibrational data were recorded over 80-s intervals at a sampling frequency of 2560 Hz. This setup enabled the collection of high-quality signals for fault diagnosis, even in a constrained environment. It is worth noting that both studies yielded high-quality results, although they focus on different aspects: the first on fault diagnosis, and the second on fault detection. Laboratory conditions are stable and controllable, whereas real-world environments are subject to fluctuations.