# A Hybrid Model for Freight Train Air Brake Condition Monitoring
## 1 Introduction
In [21], a solution for automatising the brake test relying on pressure sensors is presented. It is shown that the introduction of the brake test system, along with the required automation, is anticipated to reduce the manual effort of the brake test, saving hours of work costs. The model implemented in this paper is part of a bigger research aiming at developing wireless, modular, and integrated onboard monitoring systems for freight train air brake systems. To optimise the algorithms for the detection of failures, the model should be characterised by low computation cost (for real-time diagnostics) and good accuracy (for recognising multiple brake malfunctions). As described in [22], models for air brake pneumatic components are classified into three main categories: fluid dynamics models, empirical models and fluid-empirical dynamics models. Fluid dynamics models describe the air brake system components relying on fluid dynamics theories. Those models can describe the dynamic behaviour of the brake systems but are slower in computational speed and are more complicated to develop, and a purely mathematical approach can overlook the mechanical behaviour and physical working principle of the air brake system. In [23], an approach for simulating air brake systems of long freight trains based on fluid dynamics theory is proposed. The fine spatial mesh along the length of the main brake pipe and the explicit time-stepping methods to stabilise the solution and manage the pressure wave oscillations accurately are important features for developing high-resolution and precise simulations. However, these methods introduce a significant computational overhead: the simulation process takes an average of some minutes to simulate just a few seconds of braking response, rendering it impractical for real-time application. In [24], a total number of 41 parameters were used to develop a detailed fluid dynamics air brake model, which includes subsystem models for pipes, wagons and locomotive brake valves. The average simulation time for the conventional sequential computing scheme is about 6.7 times slower than in real-time, making this model impractical for onboard diagnostics. Real-time simulations are achieved by parallel computing using eight computer cores: this hardware configuration will re quire high-performance computing (HPC) capabilities that are unsuitable for freight train onboard applications. Empirical models are simple and faster in computational speeds but have lower generalisation due to the high dependency on the experimental data used to develop the model. [25] shows the development of a strategy for the calculation of the air brake forces of European freight trains using an empirical exponential function. The model does not require the detailed simulation of the fluid dynamics in the brake pipe nor the precise knowledge of the main parameters of the braking system mounted on each vehicle. The model described in [26] uses a two-dimensional look-up table to determine the cylinder pressure in freight train air brakes. Cylinder pressures of the first and last vehicle of the convoy are used as reference pressures and identified from measured data, while the corresponding value of intermediate convoys is then interpolated by indexing the position of the vehicle. These two approaches are unsuitable for real-time diagnostic purposes since they lack the granularity to accurately simulate internal brake pressure variations in real-time contexts and show low generalizability since they are less adaptable to varying operational conditions. In the end, in [27], an example of a fluid-empirical dynamics model based on a lumped parameter scheme is presented. The model is adopted to represent the main brake pipe with the possibility of venting the pipe from different positions. Pressure build-up in brake cylinders is determined by the dynamics of pressure drop in the main brake pipe and by the crossing of pressure thresholds.