## 4 Realization of the Optimization of the Measurement Points of the Deck Modal Test of STTGB
### Comparison of the Experiments Results of the Two-Measurement Point Arrangement Method  
The analysis in Section 4.2 shows that the number of measurement points of the IPSOARW distribution method is 28 and the number of measurement points of the uniform pointing method U (a, b) is 50. In comparison, the number of measurement points optimized by the proposed improved particle swarm algorithm is reduced by 44%, indicating that the IPSOARW is more efficient than the traditional uniform distribution method. A comparison of the frequencies of the bridge deck based on the two methods is shown in Table 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Order**} & \multicolumn{2}{c}{**Frequency [Hz]**} & \multicolumn{2}{c}{**Error [\%]**} & \multicolumn{2}{c}{**Mean Error [\%]**} \\ \cline{2-7}  & **FEA** & **U (a, b)** & **IPSOARW** & **U (a, b)** & **IPSOARW** & **U (a, b)** & **IPSOARW** \\ \hline
1 & 18.037 & 17.042 & 17.031 & 5.5 & 5.6 & & \\
2 & 27.455 & 28.156 & 28.091 & 2.6 & 2.3 & & \\
3 & 37.271 & 40.614 & 40.774 & 8.9 & 9.4 & & \\
4 & 53.726 & 51.152 & 52.112 & 4.8 & 3.0 & 5.33 & 4.06 \\
5 & 79.738 & 79.151 & 79.120 & 0.7 & 0.8 & & \\
6 & 85.554 & 93.662 & 90.814 & 9.5 & 6.1 & & \\
7 & 95.439 & - & 96.546 & - & 1.2 & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison of the frequency of the bridge deck based on two methods.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Order** & **Frequency [Hz]** & **Modal Vibration Pattern** & **Description of the Vibration Pattern** \\ \hline
1 & 17.031 & 1 st order bending \\
2 & 28.091 & 1 st order twisting \\
3 & 40.774 & 2 nd order bending \\
4 & 52.112 & 2 nd order twisting \\
5 & 79.120 & 3 rd order twisting \\
6 & 90.814 & 4 th order bending \\
7 & 96.546 & Combined 1 st-order bending and torsion deformation \\ \hline \hline \end{tabular}
\end{table}
Table 9: Modal frequency and vibration pattern of the bridge deck based on the IPSOARW distribution method.  
As shown in Table 10, it can be obtained that:  
* The modal test on the bridge deck based on the uniform distribution method identified a total of six orders of modes, and compared to the FEA, the modal frequencies around 90 Hz were lost and a lost mode condition occurred, while the test on the bridge deck based on the IPSOARW distribution method identified a total of seven orders of modes and no lost modes.
* The mean error between the frequency obtained by the uniform distribution method and the FEA frequency of the bridge deck was 5.33%, while that of the bridge deck based on the IPSOARW distribution method was 4.06%. Obviously, the modal parameters obtained by the IPSOARW distribution method are consistent with the FEA modal parameters, and the modes of each order are basically the same.  
In conclusion, in the aspect of mode shape identification, the distribution method based on the IPSOARW can identify the modes in the dense segment of frequency, and it is not easy to lose the modes. Therefore, the distribution method based on the IPSOARW has high feasibility in the arrangement of the modal measurement points of the bridge deck.