## 4 Applications to Real Measured Responses
### Application to a Two-Span Cable-Stayed Bridge  
The considered two-span bridge, illustrated in Figure 11, is situated on Freeway 3 in Taiwan and features a 34.5 m wide deck. Comprising a 330 m long steel main span and a 180 m long prestressed concrete side span, the bridge is supported by a 183.5 m tall pylon with an inverted Y-shaped reinforced concrete structure and a diaphragm wall foundation. The pylon's two legs are interconnected by a transverse beam. The bridge is supported by 60 steel cables in total, ensuring stability and structural integrity. A comprehensive monitoring system was installed to measure the dynamic responses of the bridge in the face of wind and earthquake forces. A portion of this monitoring system is presented in Figure 11, with other sensors placed along the cables omitted from the illustration, as they were not utilized in this study. Three-axis accelerometers (ACC) and one-axis velocity meters (VEL) were strategically placed, including at locations such as the abutment (ACC 02), within the box girder of the deck (VELs 04-15), near the cable on the deck slab (VELs 16-18), atop a pylon (VELs 01-03), on the foundation (ACCs 03 and 04), and at pier P2 (ACC 05). The positions of these sensors are marked by red dots in Figure 11.  
The proposed approach was employed to identify the modal parameters of the bridge in the transverse direction using earthquake measurements. Transverse acceleration measurements from ACCs 03 and 04 were averaged and treated as the transverse base excitations at P1. Additionally, the transverse acceleration measurements of ACCs 02 and 05 were considered base excitation inputs. Transverse velocity measurements of VELs 02, 04, 07, 10, and 17 were used as responses. Figure 12 illustrates the measurements from some of these sensors along with the corresponding Fourier spectra. The Fourier spectra of base excitations clearly indicate that the bridge was subjected to multiple base excitations. Figure 11: Arrangement of monitoring instruments on the cable-stayed bridge. Although not presented here, the first mode scalogram from the measurement of VEL 02 suggests that the bridge exhibited linear behavior during the considered earthquake. Data within the time interval of 20 to 30 s were processed using the proposed approach, identifying eight modes. The identified modal frequencies and damping ratios are provided in Table 2, while the identified modal shapes for the bridge deck are depicted in Figure 13. Table 2 and Figure 13 also include results obtained from a commercial finite element package based on design data and from an autoregressive (AR) time series model applied to the ambient vibration responses of the bridge [55]. The shown MAC values for the obtained modal shapes were computed with respect to those obtained from the finite element analysis. The present results align well with those from the finite element analysis and [PERSON] et al. [55]. Notably, the second and sixth modes identified from the present approach were not found by [PERSON] et al. [55] processing ambient vibration measurements along the bridge deck. This discrepancy is attributed to these two modes being dominated by the pylon, with the ratios of the identified modal component at the top of the pylon to the maximum modal component along the deck being approximately 41 and 6 for the second and sixth modes, respectively.