## 4 Case Studies
### Case Study 1: Prestressed Concrete Box-Shape Girder Bridge  
The first bridge chosen for the validation was Hongjaecheon Viaduct, an 8-span continuous prestressed concrete box-shape girder bridge. The bridge has a total length of 380 m (40 + 6 \(\times\) 50 + 40) and a width of 12.5 m. The sensors were installed in the sixth span, of which the span length is 50 m. The installed sensors are FBG strain sensors, which measured the longitudinal strain at 21 points over 2 h with a sampling frequency of 100 Hz (Figure 3). Figure 4 presents the results obtained by applying pre-cleaning criteria to the candidate modes secured by SSI. The horizontal axis in the charts displays the mode index, which corresponds to the serial number attributed to the frequencies of the candidate modes in ascending order. In the charts, the red dots stand for the modes satisfying the pre-cleaning criteria whereas the grey dots represent the modes that do not. \begin{table}
\begin{tabular}{c c} \hline \hline
**Pre-cleaning Criteria** &
\begin{tabular}{c} **Criteria for Clustering and** \\ **Removal of Outliers** \\ \end{tabular} \\ \hline \(f\geq\frac{f_{k}}{2}\) & \\ \(\text{CV}_{f}=\frac{\sigma_{f}}{\mu_{f}}\leq 0.1\) & \(p=0.99\) \\ \(\xi\leq 0.1\) & \(n_{min}=3\) \\ \(\mu_{MAC}\geq 0.8\) & \\ \(\sigma_{MAC}\leq 0.2\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Criteria for automated modal analysis. Figure 4: Pre-cleaning results for Hongjaecheon Viaduct (The red dots indicate the modes satisfying the pre-cleaning criteria). Figure 3: Shape and sensor layout of Hongjaecheon Viaduct. The presence of a series of modes with definite values can be observed around zero for the coefficient of variation for the frequency, the damping ratio and the standard deviation of the MAC index. Modes preserving constant values are also scattered near the MAC index of 1. In addition, the modes exhibiting definite values with regard to specific parameters are also seen to preserve these values for other parameters. These modes maintaining constant values of each parameter can be recognized as real modes. Note that the charts display not only the modes maintaining constant values but also other modes. Consequently, the values chosen for each of the parameters appear to not be so tight as to remove real modes. Figure 5a plots the stabilization diagram for the SSI results. The circles in grey represent the modes removed by pre-cleaning, the circles in black are the potential real modes, the colored crosses designate identical modes with the same color, and the solid, colored circles represent the representative modes. Error bars have also been added to indicate the standard deviation of the frequency of each candidate mode. The potential real modes sorted out through the pre-cleaning process are seen to have been accurately selected in the form of poles despite the loose setting of the criteria. Figure 5: Hongjaecheon Viaduct: (**a**) stabilization diagram; (**b**) modal check diagram. However, it is still difficult to verify that clusters of identical modes have been appropriately constructed by means of the stabilization diagram only. Therefore, Figure 5b plots the modes pre-cleaned with regard to the frequency, damping ratio and MAC index (these diagrams are referred to as Modal Check Diagrams hereafter). Similar to Figure 4, the horizontal axis is the mode index. The dots in the charts distinguish the clusters of identical modes by color. In the charts related to frequency and damping ratio, the modes that can be identified as pertaining to clusters of identical modes are seen to lay in practically horizontal segments. On the other hand, these clusters appear in rectangular blocks in the MAC index chart. The modes exhibiting constant frequency also show a nearly constant damping ratio as well as a rectangular block pattern in the MAC index chart, which indicates that the clusters of identical modes were constructed rationally.