# A Feasibility Study of the Drive-By Method for Damage Detection in Railway Bridges
## 3 Plan of the Simulations
### Sensor Location on the Train  
The best positioning of acceleration sensors on the vehicle depends on several aspects: capability to reveal the defect, signal-to-noise ratio, and effort required for maintenance. The latter aspect is also relevant, since sensors are thought to be used on an operating train fleet. Sensor locations considered  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & \multicolumn{2}{c}{**Excitation Frequency Related to Vehicle Length**} & \multicolumn{2}{c}{**Span Passing Frequency**} \\  & & & \multicolumn{2}{c}{**f\({}_{\text{exc}}\) = v/l\({}_{\text{Span}}\) [Hz]**} & & \multicolumn{2}{c}{**f\({}_{\text{exc}}\) = v/l\({}_{\text{span}}\) [Hz]**} & \\ \cline{3-8}  & & & **CSA Train** & **TSR Train** & **Bridge \#1** & **\#2** & **\#3** & **Bridge \#4** \\ \hline
**v\({}_{1}\)** & 80 & 22.2 & 1.52 & 0.84 & 1.68 & 1.03 & 0.47 & 0.31 \\
**v\({}_{2}\)** & 100 & 27.8 & 1.90 & 1.06 & 2.10 & 1.29 & 0.59 & 0.39 \\
**v\({}_{3}\)** & 120 & 33.3 & 2.28 & 1.27 & 2.53 & 1.54 & 0.71 & 0.46 \\
**v\({}_{4}\)** & 140 & 38.9 & 2.65 & 1.48 & 2.95 & 1.80 & 0.83 & 0.54 \\ \hline \end{tabular}
\end{table}
Table 3: Simulation speeds and bridge excitation frequency due to bogie passing.  
in the present analysis are on bogies and wheelsets, since a previous work [5] showed that carbody acceleration signals are not sensitive enough to detect a defect on the bridge. A second issue is related to the location of the sensor along the train. In principle, it can be considered that differences may be found between accelerations at the front and at the rear of the train, since the leading bogies interact with an unperturbed bridge, whereas the middle and rear part of a train find a bridge already excited by the passage of the first part of the train. For this reason, the comparison between accelerations corresponding to the first and fourth bogies are considered in the present analysis. In addition, for each bogie, vertical accelerations corresponding to different positions on the bogie frame are calculated. These positions, regarded as virtual measuring points, are indicated in Figure 9, with numbers from 1 to 4.  
For each of the two bogies (i.e., first and fourth of the train), accelerations corresponding to the leading wheelsets are considered. The accelerations at left and right wheels are also calculated, based on the degrees of freedom that are related to the vertical motion of the center of gravity (\(z_{w}\)) and roll rotation (\(\rho_{w}\)) of the wheelset. These measuring points are investigated to evaluate the performances of sensors on axleboxes, which is another feasible position for where acceleration sensors for diagnostic purposes can be placed [16]. Figure 10 shows a scheme of a wheelset, with indications of the degrees of freedom (\(z_{w}\) and \(\rho_{w}\)) adopted for calculation.  
The evaluation of the best location for sensors is performed through simulations without track irregularity, to neglect differences in accelerations due to random effects, and to focus only on  
Figure 10: Wheelset structure. Degrees of freedom adopted for the evaluation of vertical accelerations at points 1 and 2.  
Figure 9: Bogie frame structure. Degrees of freedom adopted for the evaluation of vertical accelerations at points from 1 to 4.  
systematic differences that are related to the dynamic interaction between the train and the defective bridge. Clearly, simulation results show that on straight track with no irregularity, and with a defect covering the entire bridge width, the roll motion is not excited. On the other hand, the effect of the defect on bogie pitch is visible. In the following Section 4, the analysis is therefore focused on the results of vertical acceleration on bogie center of mass \(z_{B}\), bogie frame edges \(z_{B1}\), and \(z_{B3}\) (see Figure 9), and the wheelset center of gravity \(z_{w}\) (see Figure 10).