## 5 Wind-Traffic-Bridge Coupled System  
In order to simulate the stress environment of the suspension cable wire more realistically, we adopt the stress-time history of the suspension cable obtained from the wind-traffic-bridge coupled system analysis [22] as the loading condition in this paper. The wind-traffic-bridge coupled system refers to a time-varying system under the action of dual random excitations (traffic and pulsating wind). It mainly involves two aspects of coupling: the fluid-structure coupling between strong wind and the bridge, and the solid contact coupling between traffic and the bridge. The wind-traffic-bridge coupled system [22] used in this study is based on a simulation platform established using the finite element method. This platform systematically considers the dynamic interactions between the bridge structure, random wind, and traffic. The system mainly consists of two subsystems: vehicle-bridge and wind-bridge. The entire simulation process involves three steps: first, the numerical models of the bridge and vehicles are established to obtain the mass and stiffness matrices in ANSYS; second, the simulation of stochastic wind field and traffic conditions is conducted to calculate the wind loads acting on the bridge and vehicles, as well as the interaction forces between them; finally, the control equations for the wind-traffic-bridge coupled vibration system are established, as shown in Equation (10), and the dynamic analysis of the wind-traffic-bridge coupled system is carried out in MATLAB 2019b. \[\left[ \begin{array}{cccc}M_{b}&0&\cdots&0\\ 0&M_{v1}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&M_{vm}\\ \end{array} \right]\left\{ \begin{array}{cccc}\hat{q}_{b}\\ \hat{q}_{v1}\\ \vdots\\ \hat{q}_{vm}\\ \end{array} \right\}+\left[ \begin{array}{cccc}C_{b}&0&\cdots&0\\ 0&C_{v1}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&C_{vm}\\ \end{array} \right]\left\{ \begin{array}{cccc}\hat{q}_{b}\\ \hat{q}_{v1}\\ \vdots\\ \hat{q}_{vm}\\ \end{array} \right\}+\left[ \begin{array}{cccc}K_{b}&0&\cdots&0\\ 0&K_{v1}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&K_{vm}\\ \end{array} \right]\left\{ \begin{array}{cccc}q_{b}\\ q_{v1}\\ \vdots\\ q_{vm}\\ \end{array} \right\}= \tag{10}\]  
\begin{table}
\begin{tabular}{c c where \(n\) represents the total number of vehicles in the traffic flow; \(q\) represents the displacement vector; \(M\) represents the mass matrix of the structure; \(C\) represents the damping matrix; \(K\) represents the stiffness matrix; \(F\) is the force matrix; subscripts b and \(vi\) (\(i\) = 1, 2, 3,..., \(n\)) represent the bridge system and the \(i\)-th vehicle, respectively; superscripts \(G\), \(R\), \(C\), \(W\), \(Se\), and \(Bu\) represent the excitation loads corresponding to gravity, road roughness excitation, vehicle-bridge coupled interaction, static wind, self-excitation, and buffeting force. By solving the wind-traffic-bridge coupled control equations, the stress vector can be further calculated based on the deflection-strain relationship and the stress-strain relationship, as shown in the following equation:  
\[[S]=[E][B]\{q_{b}\} \tag{11}\]  
where \([S]\) is the predicted stress vector; \([E]\) is the stress-strain relationship matrix; \([B]\) is the stress-deflection relationship matrix derived from the shape functions of the element; \(q_{b}\) is the displacement vector.