## 4 Experimental Verification
### Experimental Results and Discussion  
Because of uncertainty, the identification of modal parameters for a real structure is more challenging than a numerical model. To verify the performance of above identification methods, the modal parameters generated by the classical input-output modal analysis algorithm (frequency response function method, FRF) are introduced as a reference. Through the peak-picking technology (PP), six modes could be accurately obtained within the range of 0-30 Hz. As usual, the damping ratios were more uncertain. Thus, both the FRF and the BSS methods could only get an estimation of the damping ratio. The identification accuracy of damping ratio can be referred to the simulation results in Section 3.2.  
Figure 9: The identification results by generalized eigen decomposition with different sample lengths of the system responses of the bridge system: (**a**) frequency; (**b**) damping ratio; (**c**) MAC.  
The modal parameters were identified using the methodology described in this study. Table 4 shows the identified modes for the mock-up using the CP and GED methods. It also shows the correlation of the output-only identification results with the input-output identification results. It is clear that the maximum identified frequency error between the BSS methods and FRF method was less than 1.5%; the mode shape correlation using the modal assurance criterion (between the identified modal vector and theoretical modal vector) was high, close to unity for most of the modes. In addition, the CPU time for CP and GED was only dependent on the length of the response signal; the computation time of GED was shorter than that of the CP method, taking only 2.6 s.  
In Table 4, under the laboratory environment, the CP method missed mode 4, and the performance of GED was better than CP, but the identification accuracy of mode 4 decreased significantly. Here, the most reasonable explanation for this case is that mode 4 was not well excited (mode 4 corresponds to mode 3 rd B in Table 1, the actuator close to the fixed node of mode 4). Overall, the identified natural frequencies from the GED method were in excellent agreement with the reference (FRF method), and the mode shapes were within reasonable agreement with the theoretical mode shapes. Figure 12 illustrates several representative modes identified using GED.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Input-Output (FRF)**} & \multicolumn{2}{c}{**Identified by CP**} & \multicolumn{4}{c}{**Identified by GED**} \\ \cline{2-9}  & \(f\) **(Hz)** & \(f\) **(Hz)/Error** & \(\xi\)**(\%)** & **MAC** & \(f\) **(Hz)/Error** & \(\xi\)**(\%)** & **MAC** \\ \hline
1 (1 st B) & 5.12 & 5.13/0.20\% & 0.28 & 0.96 & 5.14/0.39\% & 0.29 & 0.96 \\
2 (2 nd B) & 5.78 & 5.82/0.69\% & 1.48 & 0.86 & 5.80/0.35\% & 1.43 & 0.87 \\
3 (1 st T) & 10.14 & 10.12/0.20\% & 0.60 & 0.82 & 10.15/0.10\% & 0.59 & 0.99 \\
4 (3 rd B) & 11.76 & — & — & — & 11.62/1.19\% & 0.36 & 0.81 \\
5 (2 nd T) & 13.20 & 13.18/0.15\% & 0.25 & 0.96 & 13.20/0\% & 0.19 & 0.98 \\
6 (4 nd B) & 19.06 & 19.07/0.05\% & 0.21 & 0.96 & 19.06/0\% & 0.21 & 0.96 \\  & CPU Time & & 5.47 s & & & 2.6 s & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Identification results by BSS methods in experimental test.  
Figure 11: Layout of the accelerometers over the bridge deck (four accelerometers and multiple measurements): (**a**) accelerometer (circled by blue circles); (**b**) measuring position on the deck (one point near each hanger).  
Figure 10: Laboratory mock-up of the suspension bridge.