## 4 Case Studies
### Case Study 2: Reinforced Concrete Rigid-Frame Bridge  
The second bridge selected for the validation was Gajwa Bridge, a 3-span continuous reinforced concrete rigid-frame bridge (Figure 6). The bridge spans a total length of 47 m (\(15.45+16.10+15.45\)) with a width of 21 m. A total of 6 accelerometers were installed in the vertical direction with 1 accelerometer at the center and ends of each span. Measurement was conducted over 4 h at a sampling rate of 100 Hz. This case differs by type of bridge, type of sensor and measured quantities compared to Hongiaecheon Viaduct.  
Figure 6: Shape and sensor layout of Gajwa Bridge (The red dots indicate sensor locations).  
Figure 7 presents the results obtained by applying pre-cleaning criteria to the candidate modes secured by SSI. Sections where the parameters maintain constant values can be distinguished along the frequency arranged in ascending order. It appears that these sections where specific parameters maintain constant values also exhibit constant values for other parameters. The modes contained in these sections can be regarded as real modes. Considering that each individual pre-cleaning criterion does not preclude additional modes, apart from those recognized as being real modes, it can be stated that the pre-cleaning criteria for each separate parameter have been set loosely.  
Figure 8 arranges the results provided by the clustering of pre-cleaned modes and the removal of outliers by means of the stabilization diagram and modal check diagram. The pre-cleaned modes indicated in the stabilization diagram appear in the form of poles and show that the pre-cleaning process was appropriately conducted. Here also, the sole stabilization diagram is insufficient to assess the identicality of the mode shapes. Therefore, the modal check diagram plotting the frequency, damping ratio and MAC index of the pre-cleaned modes has been drawn to verify whether the clustering process was appropriately performed. The modes pertaining to clusters of identical modes maintain a  
Figure 7: Pre-cleaning results for Gajwa Bridge (The red dots indicate the modes satisfying the pre-cleaning criteria).  
constant frequency and also exhibit a high MAC index, from which it is easy to conclude that the constructed clusters are indeed clusters of identical modes.  
Even if the damping ratio of the first mode is distributed over a very broad range between 2% and 6%, it is recognized as a cluster of identical modes. This recognition can be done because the assessment was conducted based upon the uncertainty of each mode obtained by SSI without unilaterally setting a range for the identification of clusters of identical modes over the whole set of modes. In other words, if there is large uncertainty about the individual modes obtained by SSI, the range for the recognition of identical modes will also enlarge, whereas a small uncertainty will lead to a narrower range. This fact makes it possible to apply the approach to ranges of clusters of identical modes that can vary according to the bridge type or mode.  
Figure 8: Gajwa Bridge: (**a**) stabilization diagram; (**b**) modal check diagram.  
Since Gajwa Bridge is a different bridge type than Hongjaecheon Viaduct, it will have different dynamic characteristics. Moreover, the noise is also different because another type of sensor was used and the measured quantities were different. Despite all these differences, the present case study shows that the proposed AOMA performed successfully using the criteria listed in Table 1.