## 2 Numerical Simulation
### Parameter Setting for Numerical Simulation  
The parameters of the vehicle and bridge are shown in Tables 1 and 2. The vehicle model adopted in this numerical simulation is assumed to be a 10-ton truck. The vehicle parameters are adjusted to have a vehicle mass of 10 tons so as to maintain the dynamic characteristics of the vehicle models used in the previous studies [29; 33; 34]. The vehicle runs over the bridge at a constant speed of 10 m/s. The bridge is a 30 m span beam-like structure. The bridge parameters are based on a rough design process shown in the existing studies [35]. The old design procedure is adopted because old bridges are expected targets of the PRE method. It is noted that these values are decided according to the existing studies but not based on actual data. In order to avoid adopting parameters that may affect generality, such as the center of gravity being in the geometric center of the vehicle body, all parameters are also changed slightly within the range that does not significantly change their dynamic characteristics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parts**} & \multirow{2}{*}{
\begin{tabular}{c} **Mechanical** \\ **Parameters** \\ \end{tabular} } & \multirow{2}{*}{**Symbol**} & \multicolumn{2}{c}{**Value**} & \multirow{2}{*}{**Unit**} \\ \cline{3-4} \cline{6-6}  & & & & **Front** (\(i=1\)) & & **Rear** (\(i=2\)) \\ \hline \multirow{2}{*}{Vehicle body} & Mass & \(m_{s}\) & & 8310 & kg \\  & Distance from G & \(d_{i}\) & 1.215 & 3.185 & m \\ \hline \multirow{2}{*}{Suspensions} & Stiffness & \(k_{si}\) & 456,000 & 410,000 & kg/s\({}^{2}\) \\  & Damping & \(c_{si}\) & 24,200 & 29,000 & kg/s \\ \hline \multirow{2}{*}{Wheels} & Unsprung-mass & \(m_{ui}\) & 469.0 & 751.0 & kg \\  & Stiffness & \(k_{ui}\) & 4,790,000 & 4,310,000 & kg/s\({}^{2}\) \\ \hline \multirow{2}{*}{(General)} & Speed & \(v\) & 10.0 & m/s \\ \end{tabular}
\end{table} 
Table 1: The vehicle parameters. In Scenarios 2 to 12, the bridge model is simulated by globally or partially reducing the flexural rigidity \(EI(x)\), as shown in Table 3. In this numerical simulation, twelve patterns are prepared to consist of 1 model without stiffness reduction and 11 models with stiffness reduction cases. The bold font in this table indicates stiffness reduction. Scenario 1 is provided as the standard bridge model with spatially constant stiffness. Scenario 2 and Scenario 3 indicate global stiffness reduction of the beam. The stiffness reduction ratios due to the global structural changes are set at 10% and 20%, respectively. The assumed abnormality of global stiffness reduction can include corrosion on bridges near the coast. Scenario 4, Scenario 5, and Scenario 6 provide the bridge models with different local stiffness reductions at the midspan. These scenarios can assume bending cracks on RC bridges. This kind of damage may develop for long periods without detection. Thus, the stiffness reductions in these scenarios are set at 10%, 30%, and 60%, respectively. Scenario 7, Scenario 8, and Scenario 9 indicate partial area stiffness reduction. These scenarios include the deterioration of concrete slabs. Since horizontal cracks in slabs cannot be visually detected, the vibration-based SHM is strongly expected to be used for detecting slab cracks. Scenario 10, Scenario 11, and Scenario 12 indicate local stiffness reduction at the edge. It is well known that the most common abnormality in steel girders is edge fatigue cracks. It should be noted that these scenarios with different stiffness reductions are provided just for a parametric study and are determined independently from any actual bridge structural abnormality. The used road unevenness \(R(x)\) is shown in Figure 3. This road unevenness is generated by Monte Carlo simulation based on the actual road profile characteristics shown in the previous study [29].