# Dynamic Deflection Measurement on Stiff Bridges with High Piers by Preloaded Spring Method
## 3 Parameter Analysis and Optimization
### Dynamic Responses and DLAs
When the stiffness of the compression spring is 50 N/m and the length of the stretched wire is less than 30 m, the minimum DLA of the PSM is also 0.180, which has the same maximum difference of 6.0% with the girder. (3) Initial Preload Force  
The section stiffness of the stretched wire was assumed to be 1.53 \(\times\) 10\({}^{5}\) N, while the stiffness of the compression spring was 200 N/m, and the DLAs of the girder and the PSM were obtained by changing the initial preload force as shown in Figure 12. When the lengths of the stretched wire are the same, DLAs obtained by the PSM are not affected by the initial preload force, a conclusion that is consistent with Equation (7). Under the same initial preload force conditions, the DLAs of the SWSS decrease with the length of the stretched wire, which is consistent with the conclusion in Figures 10 and 11. Figure 11: Dynamic load allowances (DLAs) of the PSM influenced by compression spring stiffness. Note: \(L\) is the length of the stretched wire or pier height; PSM is the preloaded spring method. (4) Material Point Mass  
The section stiffness of the stretched wire was assumed to be 1.53 \(\times\) 10\({}^{5}\) N, while the stiffness of the compression spring was 200 N/m with an initial preload of 20 N, and the DLAs of the girder and the PSM were obtained by changing the mass of the material point as shown in Figure 13. Under the same stretched-wire length conditions, the DLAs and their difference between the girder and the PSM increase linearly with the mass of the material point, which indicates that the mass of the material point contributes more to the accuracy of the measurement. When the mass of the material point is more than 0.2 kg, and the length of the stretched wire is 5 m, the DLA of the PSM is 0.185 at the minimum, and the maximum difference between the girder and the SWSS is 3.9%. When the mass of the material point is 2 kg and the length of the stretched wire is less than 25 m, the minimum DLA of the PSM is 0.172, which has a difference of 10.4% from the girder. Figure 12: Dynamic load allowances (DLAs) of the PSM influenced by preload force. Note: \(L\) is the length of the stretched wire or pier height; PSM is the preloaded spring method. Figure 10.0 Dynamic load allowances (DLAs) of the PSM influenced by material point mass. Note: \(L\) is the length of the stretched wire or pier height; PSM is the preloaded spring method. (5)  
In Figures 10-13, the DLAs and the difference between the PSM and the girder increase with the stretched-wire length while the stretched-wire section stiffness and the material point mass, or the compression spring stiffness, remain constant. In any case, a higher length may reduce the measurement accuracy, even with greater masses of the material point. In summary, the deflections and DLAs obtained by the PSM are influenced by factors such as the stretched-wire section stiffness, spring stiffness, and stretched-wire length, independent of the initial preload force. The errors of the DLAs of the PSM increase with the spring stiffness and stretched-wire length and decrease with the stretched-wire section stiffness and material point mass. The presence of preload force reduces the wind-induced measurement errors in the system to a certain extent.