# Possibility of Bridge Inspection through Drive-By Vehicles
## 4 Drive-By Inspection through 3D Virtual Simulations
### STFT of Vehicle Responses and Its Relationship with Damage  
To demonstrate the effectiveness of STFT in 3D bridge damage detections, a simply supported short bridge was used to filter out the effect of internal supports. The bridge has the properties shown in Table 6.  
When the tire moves on the damaged bridge, the vehicle's vibration will be changed, which would cause the STFT results to show multiple high energy frequencies between 20 Hz to 50 Hz (Figure 16) between 0-7 s. Similar changes will occur when the front tire drives out of the bridge or the rear tire drives in the bridge. The acceleration data were collected from the rear tire because the frequency changes caused by the front tire driving out the bridge are smaller than those caused by the rear tire on the damaged bridge. The underlying reason could be explained as the front tire acts as an actuator while the rear tire acts as a sensor to pick up the signal excited and accumulated through time.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Length** & **15 m** & **Young’s Modulus** & **3E10 N/m2** \\ \hline Width & 10 m & Poisson’s modulus & 0.2 \\ Thickness & 1 m & Density & 2500 Kg/m3 \\ Damping & 2\% & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Properties of the simulated short bridge.  
Figure 16: STFT result of the bridge deck with a 10 cm damage at 5 m through the drive-by front tire acceleration time history (Energy leaked zones).  
A 10% energy difference of the frequency range between 47 Hz to 50 Hz is set as the threshold for damage identification to identify the damage.  
To simulate different damage locations, a 10 cm segment with 80% original Young's modulus was set to 5.0, 7.5, and 10 m of the bridge. The predicted locations are listed in Table 7 for comparison.  
Table 7 shows that the damage location has been identified successfully through the vehicle's vertical acceleration history.  
To reflect the effect of the damage severities, a 10 cm segment with 20%, 40%, and 60% loss of original Young's modulus was set at 7.5 m. The change of frequency energy can be plotted with the modulus loss, as shown in Figure 17.  
Figure 17 shows that the energy change for each spectrum frequency has a linear relationship with the bridge deck's damage level.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multirow{2}{*}{\begin{tabular}{c} **Real Mid** \\ **Location(m)** \\ \end{tabular} } & \multicolumn{4}{c}{**Identified Results**} \\ \cline{3-8}  & & \begin{tabular}{c} **Start** \\ **Location** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **End** \\ **Location** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **Mid** \\ **Location** \\ **(m)** \\ \end{tabular} &
\begin{tabular}{c} **Error (m)** \\ **(dB/Hz)** \\ \end{tabular} \\ \hline
0.1 m damage at 5 m location & 5.05 & 4.81 & 5.3 & 5.05 & 0 & \(-\)88.06 \\ \hline
0.1 m damage at 7.5 m location & 7.55 & 7.21 & 7.85 & 7.53 & 0.02 & \(-\)87.73 \\ \hline
0.1 m damage at 10 m location & 10.05 & 9.05 & 10.95 & 10.0 & 0.05 & \(-\)106.87 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the predicted and real damage locations.  
Figure 17: STFT energy results for different damage levels.