# Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains
## 6 Blind Tests
### Results with 4-Axle Railway Carriage Model  
The 4-axle railway carriage model used by UCD (Figure 1) is the same as that used by NTNU. Hence, the validation in this subsection does not address differences in the models. It does show the ability of the proposed approach to infer model parameter values from the simulated values provided by NTNU to UCD and an insensitivity to some potential sources of inaccuracy (vehicle global property values and bridge flexural rigidities). Using the off-bridge data and the fleet monitoring concept, the APs and vehicle local properties (masses, moments of inertia, and speeds) were calculated from the vertical accelerations and angular velocities. Figure 9 shows the calculated AP from one run under the 1 st axle over Profile 1. It is compared to the true AP, provided subsequently by NTNU. This result is for the bridge in State 7 (healthy), but this has no effect as the data are off-bridge. It shows an obvious difference between calculated AP and true AP in the initial value, which generates a constant difference in the whole signal. The calculated AP is shifted by the difference between the true and calculated AP at the start point (the 0 position). All the points of the calculated AP are shifted by subtracting this quantity. After shifting, there is a very close match between calculated APs after shifting and true APs. Figure 10 shows the calculated values for the local vehicle properties for each of the 50 trains in the batch for Profile 1, State 7. The calculated vehicle properties are generally close to the true values, with some small differences for particular vehicles. As can be seen in Figure 10c, the speeds given by NTNU are sometimes significantly different from the true values (e.g., Run 2), but the calculated speeds are quite accurate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Property** & **Type** & **Symbol** & **Unit** &
\begin{tabular}{c} **Value before** \\ **Random Noise** \\ \end{tabular} \\ \hline Carriage body mass & Local & \(m_{v}\) & kg & Varied \\ Carriage body moment of inertia & Local & \(l_{v}\) & kg m\({}^{2}\) & Varied \\ Speed & Local & \(v\) & m/s & Varied \\ Bogie mass & Global & \(m_{b}\) & kg & 2615 \\ Bogie moment of inertia & Global & \(l_{b}\) & kg m\({}^{2}\) & 1476 \\ Wheelset mass & Global & \(m_{w}\) & kg & 1813 \\ Primary suspension stiffness & Global & \(k_{p}\) & N/m & \(2.4\times 10^{6}\) \\ Secondary suspension stiffness & Global & \(k_{s}\) & N/m & \(0.86\times 10^{6}\) \\ Primary suspension damping & Global & \(c_{p}\) & N s/m & \(7\times 10^{3}\) \\ Secondary suspension damping & Global & \(c_{s}\) & N s/m & \(16\times 10^{3}\) \\ Distance between bogie centre of gravity and wheelsets & Global & \(L_{b}\) & m & 1.28 \\ Distance between main body centre of gravity and bogies & Global & \(L_{v}\) & m & 9.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Carriage vehicle properties in the blind test. Figure 10: _Cont._  
Figure 9: Calculated AP, calculated AP after shifting, and true AP (off-bridge) for Profile 1, State 7, and Run No. 1. The vehicle properties calculated using the off-bridge data are used to find the APs for the section of track on the bridge. For each run, the APs under each of the four wheels are found using the Inverse Newmark-\(\beta\) method from the signals provided by NTNU. The calculated AP of the bridge from one run over Profile 1, State 7, is shown in Figure 11. In this figure, the calculated AP is very close to the true one after shifting. The fundamental MR-IL of the first bogie is calculated from the APs under these two wheels using the method described in Section 5. Figure 12 presents box plots showing the mid-span MR-IL values for Profile 1 and different bridge damage states/damage levels. Each box represents data from 50 mid-span MR-IL values and one bridge state. Here, the State 7 is the healthy bridge and has the smallest MR-IL values. On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25 th and 75 th percentiles, respectively.