## 4 Realization of the Optimization of the Measurement Points of the Deck Modal Test of STTGB
### Optimization of Bridge Deck Measurement Points Location Based on the IPSOARW  
Firstly, the modal confidence matrix in Equation (9) is introduced, and Equation (10) is used as the fitness function; then, the parameters of PSO are set. The particle dimension is set as 28 according to the optimized number of measurement points; the population size is set as 50 and the maximum number of iterations is set as 300 according to the particle dimension and structural characteristics of the STTGB deck. The calculation formula of inertia weight is shown in Equation (3), and the learning factor and particle velocity are generally empirical values. The final parameter settings are shown in Table 4.  
With the bridge deck vibration pattern data obtained in Section 4.1 as the training data, the IPSOARW was used to optimize the location of the measurement points. When the iteration reaches the maximum iteration number of 300, the cycle ends and 28 optimal values are output, namely, the node numbers of the optimal locations of the bridge deck measurement points. The results are shown in Table 5.  
After inputting these node numbers into the finite element model of the bridge deck, the optimized distribution of measurement points on the bridge deck is obtained, as shown in Figure 7. The two-dimensional coordinates of the optimized measurement points are shown in Table 6.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Population** & **Particle Dimension** & **Maximum Number of Iterations** & **Learning Factor** & **Particle Velocity** \\
**Size** & **Particle Dimension** & **of Iterations** & \(c_{1}c_{2}\) & \(v_{\min}v_{\max}\) \\ \hline
50 & 28 & 300 & 2 2 & \(-20\) 20 \\ \hline \end{tabular}
\end{table}
Table 4: IPSOARW parameter selection.  
Figure 6: Variation curve of the maximum non-diagonal elements of the \(MAC\) matrix versus the number of measurement points.  
The analysis of Figure 8 can be obtained as follows:  
* When IPSOARW is used to optimize the location of measuring points, the fitness function value decreases with the increase in the number of iterations.
* After the number of iterations of the optimization algorithm reaches 240, when the number of iterations continues to increase, the fitness function value does not change, and the optimization algorithm reaches convergence.
* According to the criterion of modal confidence, the final convergence result of the fitness function value in the figure can reach 0.006, indicating that the proposed IPSOARW-based point distribution method of the bridge deck can meet the optimization goal of measurement point positions.  
Validation of Optimization Strategy for STTGB Bridge Deck Measurement Points Based on Experimental Modal Analysis  
An STTGB bridge deck modal test system was built, the bridge deck measurement points were arranged according to the uniform distribution method and the IPSOARW distribution method, and a modal test was carried out. The random subspace modal parameter identification method was used for parameter identification, and the modal parameters obtained based on the two distribution schemes were compared and analyzed. The feasibility and superiority of the proposed IPSOARW-based modal test measurement point arrangement were verified.