## 5 Application Analysis
### Measured Responses and Analysis  
During the 4-month-long monitoring period, data on vehicle speed and weight were obtained through piezoelectric thin film sensors, totaling 18,820 valid samples. The frequency histogram and probability density function for vehicle speed and weight are shown in Figures 9 and 10, respectively. Apparently, the maximum vehicle speed does not exceed 30 m/s, and the maximum vehicle weight does not exceed 50 tons, meaning that  
Figure 8: Layout of instruments. Figure 6: Illustration of the piezoelectric thin film sensor: (**a**) piezoelectric thin film sensor installation and (**b**) sealing. Figure 7: Fiber Bragg grating strain sensors mounted at the bottom of the beam. the maximum value of the effective uniform load hardly exceeds 10 ton/m. Therefore, the analysis of the coupled vibration of the vehicle group-bridge system considers both normal and extreme conditions of vehicle speed and weight. The corresponding results will provide effective support for the optimization strategy of bridge health monitoring. In addition, based on the strain data from the midspan compression zone, the equivalent three-dimensional stress spectrum is calculated by using the rain-flow counting method. The results are presented in Figure 11, providing valuable insights for the optimal strategy. Figure 10: Frequency histogram of vehicle weight and probability density function. Figure 9: Frequency histogram of vehicle speed and probability density function. The power spectrum of the measured acceleration is shown in Figure 12. The compare between the actual expected bridge frequency and the obtained measured frequency is shown in Table 1. As shown in Table 1, the measured frequency is basically consistent with the FEM frequency. Using the numerical analysis method proposed in this work for vehicle-bridge coupling analysis, we investigate the influence of traffic loads on the dynamic characteristics of the bridge. The coupling ratio of the vehicle group, defined by the mass density \(V_{cm}\), is the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **FEM Frequency/Hz** & **Measured Frequency/Hz** & **Error/\%** & **Description** \\ \hline
1 & 5.56 & 5.76 & 3.60 & 1 st vertical bending \\
2 & 18.10 & 16.50 & 8.84 & 1 st longitudinal bending (symmetric) \\
3 & 24.44 & 26.11 & 6.83 & 2 nd longitudinal bending of \\
4 & 41.48 & 41.02 & 1.11 & 2 nd vertical bending \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of measured and calculated values. Figure 11: Results of fiber Bragg grating strain sensors. Figure 12: Power spectrum of the acceleration: (**a**) mid span; (**b**) beam end. ratio of the coupling uniform mass density to the total mass density of the vehicle group. In the initial theoretical analysis, \(V_{cm}\) is assumed as 0.3 or 0.15, the main body has a uniform mass density of 10 ton/m, and the vehicle speed is 15 m/s. The acceleration responses, with or without consideration of the coupling mass of the vehicle group, are shown in Figure 13. The results show that the dynamic response of the bridge, considering the coupling mass of the vehicle group, is slightly reduced, but the difference is not significant. Based on experience and monitoring data, the actual coupling mass ratio can be set to 0.15 for normal analysis. With the gradual deterioration of the pavement layer, road surface roughness becomes a crucial consideration in dynamic analysis and the estimation of response range. According to the Chinese national standard, there are eight grades for road roughness, with grade C assumed to be suitable for this bridge according to visual inspection, indicating good surface condition. The average value of the displacement power spectral density coefficient \(G_{q}(n_{0})\) is 256 \(\times\) 10\({}^{-6}\) m\({}^{-1}\). Based on the triangular series superposition method, the simulated road roughness curve is obtained, as shown in Figure 14, assuming a vehicle group speed of 10 m/s.