# Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains
## 4 Monitoring Track Using Self-Calibrating Batches of Vehicles  
In the previous section, it is shown that the AP can be calculated from measured vertical accelerations and angular velocities if the properties of the train are known. Trains often make multiple runs on the same route. Hence, an instrumented carriage will provide data from multiple runs for which some 'global' vehicle properties, such as spring stiffnesses and damping coefficients, are the same but other 'local' properties, such as speed, mass, and moment of inertia are not. In this study, the global properties are assumed to have been determined in a global calibration exercise to some degree of accuracy. A self-calibration process is presented for calculation of the local properties, which are taken to be different for every run of the train. As first proposed by [PERSON] et al. [40] for 2-axle vehicles, batches of runs of the same vehicle will be used to calculate profiles and to determine the local properties. However, in this case, unlike [PERSON] et al., the track is supported on springs. [PERSON]'s concept is that every vehicle is subjected to the same (rigidly supported) surface profile. Hence, whatever the vehicle properties, processing its measurements should give the same surface profile as all other runs. [PERSON] et al. use this phenomenon to self calibrate the system, finding the surface profile and the properties for every vehicle in the batch. CE optimization is used to find those train properties that imply the same profile for all runs in the batch. In this article, the fleet monitoring concept is extended to 4-axle railway carriages passing over tracks on spring supports. As the surface profile is no longer on rigid supports, the track deflects under the weight of the train. From the vehicle's perspective, it is excited by an AP made up of the unloaded surface profile and deflection components due to deformation of the track under its own weight. The hypothesis is that the system can be calibrated by forcing all calculated APs to be the same (for all trains). Like the Genetic Algorithm, CE is a population-based method of optimization which considers multiple feasible solutions in each generation (or iteration) of the process [41]. Firstly, a population of trial values of the vehicle parameter vector is generated. For calibration of a particular batch, global train-specific parameters (such as vehicle stiffnesses) are assumed to be known and only local run-specific parameters are needed. In this case, the local parameter vector has three components: carriage mass (\(m_{b}\)), moment of inertia (\(I_{b}\)), and speed (\(v\)). In the CE process, a population of parameter vectors is randomly generated from a normal distribution using Monte Carlo simulation. Using the generated masses, moments of inertia, speeds, and known global properties, the AP is calculated from the bogie vertical accelerations and angular velocities using the Inverse Newmark-\(\beta\) method. This process is repeated for all vehicles so the total number of unknown local properties in the vector is \(3\;n_{b}\), where \(n_{b}\) is the number of runs in the batch. In the first generation of solutions, the \(n_{b}\) generated APs will not be correct as the (run-specific) train properties will not generally be correct. However, better trials of the \(3\;n_{b}\) parameters can be identified as those for which the calculated APs are closest to each other. Thus, an 'elite set' of the trials with the best property vectors can be identified using an objective function that captures similar APs within the batch. While more sophisticated measures of'similarity' of APs are possible, a simple approach is adopted here, and the objective function is defined as the sum of squared differences between each AP and the mean of all calculated APs. Hence, the objective function for the \(j\)th trial solution, \(O_{j}\), is the sum of squared differences of the AP generated by this trial vector of \(3\;n_{b}\) properties and the mean AP generated by all vehicles.