# A Feasibility Study of the Drive-By Method for Damage Detection in Railway Bridges
## 3 Plan of the Simulations
### Data Processing Techniques  
Figure 11 compares the accelerations of the center of gravity of the leading bogie in the case of the damaged bridge (dashed orange line) and of the healthy bridge (continuous blue line). Figure 11 reports the time domain signals, as a function of position along the bridge. To make the diagram layout adoptable for bridges of different span length, and to ease the comparison of results of damage localization between different bridges, the horizontal axis is rescaled into a dimensionless range from 0 to 1, representing respectively, the initial and final sections of the bridge. Figure 11b reports the power spectral density (PSD). The results refer to bridge #2, the TSR train type, a speed of 100 km/h, damage level D40 (i.e., 40% reduction of flexural stiffness). In the time domain signals of Figure 11a, the position of the defective element is highlighted by two vertical red lines. A difference is visible, starting just before the location of the defects, and continuing further after its end. In the PSD of Figure 11b, three main frequency ranges are identifiable:  
* a low-frequency range, including the acceleration of the trajectory related to the quasi-static response due to the bridge deflection under the train load. This value depends both on the amplitude of bridge deflection, and on the period for crossing the bridge.
* A second contribution at around 5.5 Hz, corresponding to the first natural frequency of the bridge (which is a bit lowered by the presence of the train mass).
* A third frequency contribution at 46.3 Hz, generated by the wheelsets crossing the sleepers. The latter are equally spaced in all the bridge models developed (\(l_{sl}\) = 0.6 m), so that the sleeper passing frequency depends only on the speed of the train \(v\), according to the formula \(f_{sl}=v/l_{sl}\)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bridge Type**} & \multirow{2}{*}{**Bridge Length [m]**} & \multicolumn{2}{c}{**Damage Position (at Mid Span)**} & \multicolumn{1}{c}{**Damage Position (at Quarter Span)**} \\  & & & **Dimensionless Range** & **Dimensionless Range** \\ \hline \#1 & 13.2 & [0.409; 0.5] & [0.182; 0.273] \\ \#2 & 21.6 & [0.444; 0.5] & [0.25; 0.306] \\ \#3 & 46.8 & [0.474; 0.5] & [0.205; 0.231] \\ \#4 & 72 & [0.483; 0.5] & [0.25; 0.267] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dimensionless damage locations for each type of bridge.  
Since the considered defect is related to deck damage, its presence does not increase the amplitude of the sleeper passing frequency in any of the cases analyzed.  
Two different approaches for data-processing are investigated, basically differing in the frequency range taken into account for accelerations. In a first approach (see Section 3.4.1), the acceleration data are low-pass filtered to cancel the dynamic component due to the bridge first mode of vibration. The remaining signal is representative, in terms of acceleration, of the quasi-static deflection of the bridge in response to the moving loads. A second approach (see Section 3.4.2) also considers the first natural frequency of the bridge, as well as other natural frequencies that are related to bogie dynamics (vertical and pitch), if excited. Sleeper passing frequency is excluded from this range of analysis, since for the type of defects considered, it does not contain the relevant information to discern between damaged and healthy bridges.