# A Hybrid Model for Freight Train Air Brake Condition Monitoring
## 4 Conclusions and Future Developments  
The increase in safety and reliability of freight trains can be achieved through the implementation of real-time onboard monitoring systems that are able to use models and diagnostic algorithms to identify possible malfunctions in the system. A hybrid air brake model relying on both empirical and fluid-dynamic equations has been developed in this paper for freight train air brake system monitoring. Compared to fluid-dynamic models, the low computational cost for real-time application has been achieved through the reduction of the air brake system parameters and by the feed-forward approach for estimating the brake cylinder pressure from the main brake pipe pressure. The block schematisation of the main air brake components, each with its own transfer function, enables model generalisation to wagons with different air brake systems. A new model of the first braking phase based on the correlation between the brake cylinder pressure and the distributor pressure has been developed. As shown from the experimental comparison, the model is able to correctly replicate the different braking phases of the brake cylinder at different braking actions and wagon loading configurations. The high accuracy reached by the model in replicating nominal air brake conditions makes it well-suited for the future development of model-based diagnostic algorithms. For a final and complete validation of the air brake model presented in this paper, future tests in the confined environment of the RFI San Donato test circuit have been planned to account for different braking modes.  
Figure 20: Comparison between the braking time calculated in [27] and the braking time coming from the model.  
Moreover, real-world braking defects such as leakage in the weighing valve and auxiliary reservoir will be replicated, and the air brake model will be adopted to develop a diagnostic algorithm for the detection of malfunctions in freight train air brake systems. Additionally, to better address the accuracy of the model, future validation of each component using FEM simulations could be adopted.  
Conceptualisation, A.G.; methodology, F.Z. and G.T.; software, A.G.; validation, A.G. and F.Z.; formal analysis, A.G.; investigation, A.G.; resources, A.G., F.Z. and G.T.; data curation, A.G. and F.Z.; writing--original draft preparation, A.G.; writing--review and editing, F.Z. and G.T.; visualisation, F.Z.; supervision, G.T.; project administration, G.T.; funding acquisition, G.T. All authors have read and agreed to the published version of the manuscript.  
This study was carried out within the MOST--Sustainable Mobility National Research Centre and received funding from the European Union Next-GenerationEU (PIANO NAZIONALE DI RIPRESA E RESILENZA (PNRR--NATIONAL RECOVERY AND RESILENCE PLAN)--MISISORE 4 COMPONENTE 2, INVESTIMENTO 1.4 (MISSION 4 COMPONENT 2, INVESTMENT 1.4)--D.D. 1033 17/06/2022, CN0000023). This manuscript reflects only the authors' views and opinions; neither the European Union nor the European Commission can be considered responsible for them.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
This work has been carried out in collaboration with Mercitalia Intermodal (Polo Mercitalia--Gruppo FS Italiana).  
The authors declare no conflicts of interest.