# A Hybrid Model for Freight Train Air Brake Condition Monitoring
## 1 Introduction
This model is particularly suitable for onboard real-time diagnostics of railway brake systems due to its balance of accuracy, computational efficiency and generalisability. The model is highly accurate in simulating the dynamics of the main brake pipe, but it has significant limitations in modelling the dynamics of the brake system itself since critical components such as the weighing valve, the kink valve and the relay valve are not considered. Furthermore, the model does not account for the release phase, which is essential for identifying specific failures, such as improper brake detachment from the wheel, which can lead to wear of the brake pad, material build-up and overheating. Additionally, the model is restricted to simulating emergency braking and does not include service braking, which is the predominant braking action during nominal operations, where the brake cylinder response is more influenced by the gradual depression of the main brake pipe rather than the brake mode. Simulation experience indicates that a fluid dynamic air brake model can be 100 times slower than its empirical counterpart, that is, in general, faster than real-time [22]. Therefore, a fluid-empirical dynamic model can be used to achieve real-time monitoring, and this approach has been selected for the brake system modelled in this paper. Compared to fluid dynamics models ([23; 24]), the model presented in this paper is characterised by a total of 18 parameters. Moreover, thanks to the feed-forward approach in estimating the brake cylinder pressure from the main brake pipe pressure, bypassing the need for feedback from the auxiliary reservoir and the evaluation of the brake cylinder build-up pressure from the brake mode saturation in the relay valve, the computational cost is significantly reduced. Compared to the fluid-empirical dynamics model presented in [27], the model presented in this paper contains a new approach for the simulation of the first braking phase. It is not based on threshold settings but on the correlation between the brake cylinder pressure and the distributor pressure variation derived by the activation of the accelerated chambers. While most of the models found in the literature are focused on replicating the brake cylinder steady state condition, the higher accuracy reached in simulating the first braking phase allows for improving the ability of the diagnostic model to recognise malfunctions that are usually very difficult to detect (i.e., push-rod out of adjustment, higher stroke of the brake cylinder piston, variation of the stiffness of the brake cylinder spring and manual brake activation during train moving condition). Moreover, compared to [27], the simulation of different brake components, such as the weighing valve, the kink valve, the relay valve and the brake release valve, enables an increase in the efficiency of the model. With the main brake pipe pressure as an input parameter,the air brake model can also simulate service braking action rather than focusing only on emergency braking, as in [27]. As shown in the Results Section, the model's accuracy in replicating the air brake system mechanism makes it well-suited for future evaluations of model-based algorithms designed for air brake fault detection. This paper presents the description of a hybrid air brake model that uses both simplified fluid-dynamic models and empirical models to estimate the transfer function between the main brake pipe pressure and the brake cylinder pressure. In Section 2, the air brake model is presented, focusing the attention on the description of the T3000e wagon brake system configuration used as a reference for modelling and validating the air brake model, the algorithms for pre-processing the input variables and the model of the air brake main components. In Section 3, the main parameters used for modelling the air brake system are presented, and the model validation through experimental dataset comparison from the campaign reported in [28] is shown.