## 3 Analysis of Simulation Data Based on D-S Evidence Theory
### Data Analysis Based on D-S Evidence Theory  
Based on the establishment of a high-fidelity finite element model, the data from the simulation of multiple mechanical parameters of the structure were fused. The sensitivity of the mechanical parameters at each node of the cable under the effect of temperature was analyzed using the probabilistic treatment and D-S evidence theory. In this study, to verify the accuracy of the judgment based on the D-S evidence theory, the points where the simulated data are collected in the model are set to be the same as the locations of the monitored points arranged in the real cables. Upper radial cable 1 is the object of study, and there are seven monitored and simulated points arranged at the support and midspan positions of each section of the cable. The selection of the monitored and simulated points is the same as that in Figure 6.  
In the finite element model, a condition consistent with the real tensioning process was set, that is, a temperature rise of 55 \({}^{\circ}\)C. The simulated values of the cable force, strain, and deflection at each node were extracted from the model, and the sensitivity of the mechanical parameters at each point under the effect of temperature was calculated by probabilistic processing. In calculating the probability of the simulated values at each point, the analysis using the D-S evidence theory should ensure that the sum of the probabilities of parameter changes at each node is 1 when a single parameter is used as the discriminant. For example, when using the cable force as the basis for discrimination, the probability of the change in the cable force at each node is calculated using Equation (14). \[P_{i}^{*}=\frac{\left|C_{fi}-C_{fi}^{*}\right|}{C_{fi}} \tag{14}\]  
In Equation (14), \(C_{fi}\) indicates the value of the cable force at each node on the cable before the effect of temperature, \(C_{fi}^{*}\) and indicates the value of the cable force at each node on the cable after a temperature increase of 55 \({}^{\circ}\)C. To ensure that the sum of the damage probability of each node on the cable is 1 when the cable force is used as the basis for discrimination, the probability calculated by Equation (14) needs to be corrected. The  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \begin{tabular}{c} **Component Unit** \\ **Number** \\ \end{tabular}  & \begin{tabular}{c} **Monitoring Values of** \\ **the Structure** \\ **(N)** \\ \end{tabular}  & \begin{tabular}{c} **Simulation Value** \\ **before Correction** \\ **(N)** \\ \end{tabular}  & \begin{tabular}{c} **Simulation Value** \\ **after Correction** \\ **(N)** \\ \end{tabular}  & \ \begin{tabular}{c} **Error before** \\ **Correction** \\ \end{tabular}  & \begin{tabular}{c} **Error after** \\ **Correction** \\ \end{tabular}  \\ \hline Upper radial cable 1 & 4890 & 5572 & 4775 & 14\% & \(-\)2\% \\ Upper radial cable 3 & 5850 & 5563 & 5713 & \(-\)5\% & \(-\)2\% \\ Upper radial cable 5 & 5150 & 5570 & 5087 & 8\% & \(-\)1\% \\ Upper radial cable 7 & 5660 & 5569 & 5772 & \(-\)2  
probability (\(P_{i}\)) of the change in the cable force at each node after correction was calculated according to Equation (15):  
\[P_{i}=\frac{P_{i}^{*}}{\lambda} \tag{15}\]  
In Equation (15), \(\lambda\) denotes the coefficient of the correction of probability \(\lambda=\sum_{i=1}^{7}P_{i}^{*}\). The probabilities calculated accordingly can be used in the fusion analysis of the D-S evidence theory to discriminate the sensitivity of the mechanical parameters of each node. Similarly, the probability of change in the mechanical parameters at each point when strain and deflection are used as discriminators can be derived. Combining the D-S evidence theory to fuse various types of data and synthesize the sensitivity of each node can lead to the response of the cable to the effect of temperature. At the same time, the rate of change of the cross-sectional area of each point on the real structure is used as an important basis for the detected results of structural safety performance.