## 7 Example with Sectional Model of Bridge Deck in Wind Tunnel Tests  
In order to further investigate the reliability of the proposed method for flutter derivative identification through wind tunnel tests, experimental data for a sectional model of a bridge deck were used. Free-vibration wind tunnel tests were carried out in the CRIACIV laboratory. Figure 11 shows the cross-section view of the model. It has a width \(B\) of 450 mm and a depth \(H\) of 70 mm. The model was suspended elastically by eight helical springs, allowing for vertical and torsional motions, while suppressing the sway motion in the wind flow direction by long cables. Vertical and torsional initial conditions were set through a device consisting of cables and electromagnets. More details concerning the model, the setup, and the wind tunnel test can be found in [19; 35]. The free vibration tests were repeated 10 times for each wind speed. The sample population for bootstrap sampling consisted of 10 sets of data. All eight flutter derivatives of the bridge deck model were identified by the proposed method, in which the control parameters in the MABC-Powell algorithm for numerical optimization are the same as in the numerical examples in the previous sections. The number of data sets in each bootstrap sample is still three. In total, 100 bootstrap samples are extracted from the sample population of 10 data sets. The comparison between the flutter derivatives identified by the proposed method and the reference results [19] is shown in Figure 12. At a certain testing wind speed, the real frequencies were used for the calculation of reduced wind velocities \(U/B\). It can be seen that the flutter derivatives identified by the proposed method agree with the reference results and exhibit consistent statistical properties. \(H_{3}^{*}\), \(A_{2}^{*}\), and \(A_{3}^{*}\) have small standard deviations while the other derivatives are more dispersed. The standard deviations at higher wind speed are generally larger than those at lower wind speed, especially near flutter onset. The possible reasons for this phenomenon are presented in point (3) of the discussion part. It should also be noted that the reference results present only 10 samples, which is insufficient to obtain accurate statistics. To improve statistical inference, the bootstrap scheme with 100 samples is adopted. At the wind speed of 8.6 m/s, the histogram of flutter derivatives identified using only the original 10 data sets and the histogram of flutter derivatives identified using 100 bootstrap samples are shown in Figure 13a,b, respectively. It can be seen that the distribution in Figure 13b is more concentrated, while Figure 13a is very scattered. The convergence lines for the weighting factors for one bootstrap sample at a wind speed of 10.64 m/s are shown in Figure 14. Additionally, in this case, the weighting factors for torsional signal residuals are smaller than those for the vertical bending ones, which are similar to the results of the  
Figure 11: Cross-section geometry of the model tested in the wind tunnel (in mm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Derivatives** & **Theoretical Value** & **Mean** & \(\sigma\) & **CV** & **95\%-CI** \\ \hline \(A_{1}^{*}\) & 0.7486 & 0.7478 & 0.0152 & 0.0204 & [0.7164, 0.7764] \\ \(A_{2}^{*}\) & \(-\)0.1848 & \(-\)0.1877 & 0.0074 & 0.0392 & [\(-\)0.2035, \(-\)0.1752] \\ \(A_{3}^{*}\) & 0.4532 & 0.4508 & 0.0071 & 0.0157 & [0.4366, 0.4639] \\ \(A_{4}^{*}\) & 0.2165 & 0.2134 & 0.0178 & 0.0834 & [0.1769, 0.2443] \\ \(H_{1}^{*}\) & \(-\)2.9942 & \(-\)2.9614 & 0.1061 & 0.0358 & [\(-\)3.1792, \(-\)2.7573] \\ \(H_{2}^{*}\) & \(-\)0.7305 & \(-\)0.695 & 0.3475 & 0.5 & [\(-\)1.3308, \(-\)0.0377] \\ \(H_{3}^{*}\) & \(-\)1.7147 & \(-\)1.9039 & 0.3233 & 0.1698 & [\(-\)2.6665, \(-\)1.3561] \\ \(H_{4}^{*}\) & \(-\)0.0808 & \(-\)0.024 & 0.0841 & 3.5045 & [\(-\)0.1595, 0.1705] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Bootstrap statistics of identified flutter derivatives with 10% noise level (\(U\) = 8 m/s). numerical example.