# Out-of-Roundness Wheel Damage Identification in Railway Vehicles Using AutoEncoder Models
## 4 Characterization of the Simulated Data
### Simulated Scenarios  
For the early detection of wheel polygonization stages, a virtual monitoring system was implemented to acquire the dynamic data evaluated in this study. Following the recommendations of [PERSON] et al. (2022) [61; 62], the instrumentation focused on the track, specifically the rail, as sensors placed near the rails are more promising in achieving satisfactory results. Six accelerometers were strategically positioned at the midpoint between sleepers, as shown in Figure 8, to capture vibrations induced by train passages. This configuration enables the precise identification of vibrational signatures characteristic of defective wheels, allowing intervention before more severe damage occurs.  
To evaluate the effectiveness of the proposed method for detecting polygonalized wheels, numerical simulations were conducted under a variety of operating conditions. The simulation dataset included both reference scenarios, characterized by the absence of defects, and scenarios with two distinct stages of wheel wear. This approach enabled the validation of the method's ability to accurately reproduce experimental data obtained under real-world conditions, including cases involving multiple stages of polygonalization. The simulations were performed considering a nominal speed of 80 km/h.  
The analysis of the simulation data focused on three distinct cases: (i) a reference scenario, characterized by the absence of defects in the front right wheel of the first wagon; (ii) a polygonalization scenario in the rear left wheel of the third wagon (Damage 1); and (iii) a polygonalization scenario in the rear right wheel of the fifth wagon (Damage 2). For each case, 10 numerical simulations were performed. The selection of these specific cases was driven by the need to assess the method's ability to detect damage in different positions along the train. Figure 7 provides a graphical visualization of the various wheel positions considered in the simulated scenarios.  
To prepare the simulation data for training the AE model, a preprocessing step was carried out. Each complete simulation, consisting of 39,169 data points, represented the full dynamic signal of the train in a given scenario. However, the high data volume and the limited number of samples per scenario (only 10 simulations) could compromise training effectiveness and increase computational costs. Given this context, each simulation of each of the scenarios was segmented into 10 smaller parts, each containing 3916 points. This strategy significantly expanded the training dataset from 30 simulations to 300 simulations without compromising the representativeness of the original data. Data segmentation is a common practice in Machine Learning, especially when dealing with time series, as it aims to optimize the training process and enhance the model's generalization capability. Table 4 presents a comparison of the number of signals per scenario before and after segmentation, highlighting the substantial increase in the number of samples available for training, validation, and monitoring.  
Figure 8: Virtual wayside monitoring system with accelerometers positioned mid-span between sleepers: (**a**) back view; (**b**) top view. (Adapted from [PERSON] et al. (2024) [3].)The acceleration data, collected in baseline and damaged scenarios, were prepared for numerical simulation through the application of a second-order Chebyshev type II low-pass filter. With a cutoff frequency of 500 Hz, this filter attenuates high-frequency components, isolating the dynamic characteristics of interest. To simulate real operating conditions, random noise with a normal distribution was added to the filtered signals, representing the inherent uncertainties and disturbances in the system. The 10 kHz sampling rate ensures adequate temporal resolution for capturing the system's fast dynamics.