# A Hybrid Model for Freight Train Air Brake Condition Monitoring
## 3 Results and Discussion  
### Experimental Model Validation  
In Table 1, the model brake system parameters used for validation are shown. The model is built on a total of 18 parameters, described in detail in Section 2.3 for each air brake component. Tchar, Dmax and Pmax are derived from the UIC 540 Standard, which provides guidelines and specifications for railway braking systems. Tin, R and patm are physical variables assumed to remain constant within the model. The remaining 12 parameters pertain specifically to the brake system modelled: some of them are obtained directly from the T3000e wagon's technical specifications, while others are empirically tuned to reflect the actual operating principles of the air brake system due to the absence of measured data for these parameters. The dataset used for model validation was obtained from a previous field campaign, which was reported in [28]. To validate the model, the overall dataset was divided into two smaller subsets to assess the model's accuracy based on variations in two key input parameters: the braking action, which influences the main brake pipe pressure, and the wagon loading condition, which affects the weighing valve pressure. The model parameters listed in Table 1 were kept constant, as the air brake system used for validation remained unchanged. As shown in Table 2, the first model validation was carried out considering different braking actions in the main brake pipe, maintaining a constant mean pressure in the weighing valve of 2.6 bar (intermediate loading condition) and freight brake mode. In Figure 17a-c, a detailed comparison of the model and the experimental brake cylinder pressure with the input parameters described in Table 2 accounting for different braking actions is shown. As shown from the experimental comparison, the model can correctly replicate the first braking phase, the build-up phase, and the holding and the releasing phase. The main deviation comes from the incomplete release of Figure 17c, where the model underestimates the experimental pressure. The reason for this incorrect behaviour can be found in a premature activation of the realising phase from the model. The model has also been validated on the datasets shown in Table 3, accounting for different braking actions and wagon loading conditions (Dataset 4 presents a full-loading condition, Dataset 5 presents an intermediate loading condition while Dataset 6 presents a tare loading condition). In Figure 18a-c, a detailed comparison of the model and the experimental brake cylinder pressure with the input parameters described in Table 3 accounting for different loading conditions is shown. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Brake Action** & \begin{tabular}{c} **Main Brake** \\ **Pipe Depression** \\ \end{tabular} & \
\begin{tabular}{c} **Mean Weighing** \\ **Pressure** \\ \end{tabular} &
\begin{tabular}{c} **Brake Mode** \\ \end{tabular} \\ \hline
1 & Service braking & 0.8 bar & 2.6 bar & G \\ \hline
2 & Service braking & 0.9 bar & 2.6 bar & G \\ \hline
3 &
\begin{tabular}{c} Consecutive \\ service braking \\ \end{tabular} & 0.74 bar & 2.6 bar & G \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dataset for model validation at different braking actions. Figure 17: Comparison between the model and the experimental brake cylinder pressure with input parameters from (**a**) Dataset 1, (**b**) Dataset 2 and (**c**) Dataset 3. Overall, the model is able to replicate correctly the brake cylinder pressure with different braking actions and wagon loading conditions. As shown in Figure 18c, the model is also able to replicate correctly emergency braking. Unfortunately, during the campaign described in [28], only datasets with freight brake mode (G) were monitored. Future experimental campaigns will provide further model validation accounting also for different brake modes. Figure 18: Comparison between the model and the experimental brake cylinder pressure with input parameters from (**a**) Dataset 4, (**b**) Dataset 5 and (**c**) Dataset 6.