# Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains
## 7 Conclusions  
This article presents a numerical investigation of a novel method to determine AP and detect bridge damage using bogie vertical accelerations and angular velocities measured in batches of passing trains. Firstly, an Inverse Newmark-\(\beta\) method is developed to calculate the AP of the railway track using train accelerations. A 4-axle railway carriage and train/track/bridge dynamic interaction model is used here to generate vehicle bogie vertical accelerations and angular velocities, the simulated measurements. The result shows that the calculated AP is the same as the 'true' AP and this method is efficient. Combining the Inverse Newmark-\(\beta\) method with CE optimisation, the APs of the track and vehicle properties can be calculated accurately using batches of trains.  
The work is expanded to introduce a new method to determine the moving reference influence line from moving reference deflections. A 2-axle half-car and track beam model is tested with different bridge damage levels. The results show that the moving reference influence line is a good indicator of the bridge damage level.  
Finally, the results are validated in a blind test with an independent research group. For this, the analysis is carried out using the same 4-axle railway carriage model that generated the data and a simpler 2-axle half-car. For both cases, the moving reference influence lines are determined using measurements from the train. Furthermore, the damage levels of the bridge are inferred by the calculated moving reference influence lines with very good accuracy.  
The idea of the fleet monitoring concept is developed in this article. As it will monitor the bridge through time, it will average out the effects through a variety of environmental conditions, including temperature. This mitigates against 'contamination' by changes in environmental conditions. The fleet monitoring concept has the potential to monitor bridges by combining drive-by data from a large number of in-service trains. To analyse large amounts of data, the fleet monitoring concept can be further developed using machine learning strategies. A passenger carriage is simulated here. It is expected that using freight carriages with one level of suspension would tend to improve the accuracy of the calculated  
Figure 13: Box plot of mid-span fundamental MR-IL values of half-car model for Profile 1, organised by (**a**) bridge state number and (**b**) damage level.  
AP. The train used in this article is modelled simply as a 2D model. Further work is needed to extend this to a 3D train model and to allow for non-linearity in the vehicle. Ultimately, field testing will be needed to validate the concept.  
Conceptualization, methodology, formal analysis, Y.R., E.J.O. and J.K.; software, Y.R.; validation, Y.R.; writing--original draft preparation, Y.R.; writing--review and editing, Y.R., E.J.O., D.C. and J.K.; supervision, E.J.O., J.K. and D.C. developed the model used in the 'blind' test and subsequently provided the acceleration and velocity signals for the test. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the joint scholarship between University College Dublin and Chinese Scholarship Council, grant number is '201708300005'.  
Not applicable.  
All of the data reported in the paper are presented in the main text. Any other data will be provided on request.  
[PERSON] acknowledges the Ph.D. scholarship awarded jointly by University College Dublin and the China Scholarship Council.  
The authors declare no conflict of interest.