# Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains
## 6 Blind Tests  
The concept of monitoring railway bridge condition using batches of instrumented trains was assessed in a series of blind tests. A team from the Norwegian University of Science and Technology (NTNU) used the advanced model described in Section 2 to simulate batches of train carriages crossing a railway track and a culvert. The vertical accelerations and angular velocities from two bogies were generated by NTNU for various cases of the bridge condition. University College Dublin (UCD) analysed these signals to calculate the AP, determine the train properties, and detect the bridge damage level using the methods described above.  
In these tests, the 'off-bridge' length of track used for calibration was 120 m (unknown to UCD) and the length of the bridge was 10.2 m. Data were analysed for 7 different bridge damage states, including one perfectly healthy state. Global damage was simulated but, for each damaged bridge, there were small random differences (5% standard deviation) between element flexural rigidities (stiffness), reflecting the natural variation in a corroded bridge. For each state, data from 50 different train journeys were used. In each run, all properties were kept constant except for the local properties of mass (\(m_{v}\)), moment of inertia (\(I_{v}\)), and speed (\(v\)) (Table 4). For each batch of runs, NTNU used Monte Carlo simulation to randomly generate these properties for each of the 50 vehicles in the fleet. The individual vehicle local property values were not made known to UCD but the means were provided, on the basis that these mean values are repeatable and can be determined for a particular site. UCD was provided with the approximate speed (\(v\)) which was slightly different from  
Figure 8: Mean calculated MR-ILs with different damage at different speed: (a) 10 m/s; (b) 20 m/s.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & True damage level & 0\% & 5\% & 10\% \\ \hline \multirow{2}{*}{10 m/s} & _Damage Indicator_ 1 & 0\% & 5\% & 11\% \\  & _Damage Indicator_ 2 & 0\% & 5\% & 10\% \\ \hline \multirow{2}{*}{20 m/s} & _Damage Indicator_ 1 with filter & 0\% & 5\% & 12\% \\  & _Damage Indicator_ 1 without filter & 0\% & 7\% & 15\% \\  & _Damage Indicator_ 2 & 0\% & 5\% & 10\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Inferred damaged indicators and true damage levels.  
the true value (to represent inaccuracy in a Global Positioning System (GPS) measurement). NTNU applied random noise (5% standard deviation) to other global vehicle properties when generating the signals to represent inaccuracy resulting from a global calibration process. Reference global property values were used by UCD, which is shown in Table 4.  
For the railway track, variable stiffness at the ballast and sub-ballast levels were generated randomly using a 'Gaussian process' algorithm, which allows small incremental changes. To confirm that the method is not sensitive to the profile assumed, the entire process (healthy and 6 damage states) was repeated for two different track profiles, making a total of 14 batches of runs. To help establish the baseline, the two batches for which the bridge was healthy were identified to UCD as such. To separate the track and bridge parts, the starting point of the bridge in each run was provided. For application in the field, it is proposed that the location of the bridge relative to the data can be estimated with a GPS and can be found more accurately using an optimisation algorithm. In this blind test, UCD used the 4-axle railway carriage model and the 2-axle 2-degree-of-freedom half-car model to analyse these signals.