## 4 Practical Engineering Validation  
Shijiazhuang Yutong Stadium canopy is a cantilevered cone-shaped steel mesh frame with welded hollow ball nodes, divided into two symmetrical pieces, located on the east and west sides of the site. The shape of the grid is a slightly curved rectangle with a length of 120.28 m, a width of 41.4 m, and an area of about 5000 square meters. The outer side of the grid is supported on two rows of 47 concrete columns along the long side, and the elevation of a cantilevered roof is 47 m. A schematic diagram of the cantilevered mesh frame of the stadium in the east area is shown in Figure 7.  
The lower chord node numbering and sensor arrangement are shown in Figure 8, with 12 vertical sensors and 2 additional sensors each for the horizontal and vertical directions, totaling 16 sensors. Photographs of the sensor arrangement and on-site acquisition are shown in Figures 9 and 10. Figure 8: Layout of measuring points. Figure 7: Stadium east suspension grids. Figure 9: Photograph of sensor arrangement. According to the design information, the self-oscillation characteristics of the stadium were analyzed by Midas software (Midas Gen 2024v1.1), and the first six orders of theoretical frequencies and vibration patterns of the structure are shown in Figure 11.  
During the measurement, high winds caused non-stationary excitation, and the response signal at measurement point 4 is shown in Figure 12.  
The modal parameters of the response signal are identified using the improved RDT-SSI method. The frequency identification results are shown in Table 2, and the first six orders of the vibration mode are shown in Figure 13. \begin{table}
\begin{tabular}{c c c c} \hline
**Modal Order** & **Theoretical Frequency (f/Hz)** & **SSI-COV (f/Hz)** & **Improved RDT-SSI (f/Hz)** \\ \hline
1 & 1.904 & 2.1338 & 1.986 \\ \hline
2 & 1.978 & 2.3827 & 2.215 \\ \hline
3 & 2.220 & 2.9960 & 3.044 \\ \hline \end{tabular}
\end{table} 
Table 2: Stadium modal frequency identification results. Figure 11: Theoretical frequencies and modes of vibration of the first 6 orders. Figure 10: Acquisition equipment collecting data on-site. As shown in Table 2 and Figures 13 and 14, the frequency recognition results of the two methods are relatively close, yet the damping ratios of certain orders are different. The measured frequency of the structure is higher than the theoretical analysis frequency. This is because the theoretical analysis did not consider the contributions of actual engineering components, such as purlins and roof panels, to the structural stiffness, which resulted in a smaller theoretical stiffness and a lower frequency. This paper determines the order of the measured modes by utilizing the correlation between the measured and theoretical mode shapes. The measured mode shapes identified by the improved RDT-SSI method are in good agreement with the theoretical mode shapes. The modal parameters of Shijiazhuang Yutong Stadium under high wind excitation can be effectively identified, and the computational efficiency is significantly improved. The traditional stochastic subspace method assumes that the environmental excitation is stationary white noise, which may result in false modes under non-stationary white noise excitation, leading to inaccurate recognition results. In the improved RDT-SSI method proposed in this article, the collected response signals are first processed using the random decrement method under non-stationary excitation, and then the modal parameter identification is carried out using the covariance-driven stochastic subspace method, which to some extent mitigates the problem of false modes. The overall recognition results of the two methods are not significantly different, but the improved RDT-SSI in low-order modes is slightly more accurate than the traditional SSI-COV method and reduces computation time by nearly 45%.