## 5 Multi-Parameter Coupled Coordination Model  
### Coupling Coordination Degree  
An index system was established to characterize the optimal parameter composition of the overall static performance of the bridge. To this end, a three-parameter coupling and coordination model was constructed to measure the coupling degree and coupling coordination of 216 sets of data consisting of different parameters, including stiffness of the main girder, stiffness of the diagonal cable and length of the cable-free zone in the span, and to conduct a comparative analysis. Due to its small influence on the force and deformation of the bridge, the uncoupled zone at the bottom of the tower was not involved in comparative analyses. It provides new research ideas and references for exploring the mutual influence relationship between the stiffness of each member and the cable-free zone, realizing the joint consideration of the coordinated development of each parameter and optimizing the structural designs of the bridge.  
According to the live load ratio concept, the main girder stiffness should be considered in combination with axial stiffness of the cable-stayed cable, while length distribution of the cable-free zone of some cable-stayed bridges is associated with main girder stiffness [21; 22]. Therefore, based on relevant research results combined with the actual research, a three-parameter coupled coordination model was constructed to establish whether the three parameters promoted each other at high levels or constrained each other at low levels, and the specific calculation formula is  
\[C=\frac{3\sqrt[3]{U_{1}U_{2}U_{3}}}{U_{1}+U_{2}+U_{3}} \tag{4}\]  
\[D=\sqrt{C\times T} \tag{5}\]  
\[T=\alpha_{1}U_{1}+\alpha_{2}U_{2}+\alpha_{3}U_{3},\ \alpha_{1}+\alpha_{2}+ \alpha_{3}=1 \tag{6}\]  
whereby \(C\) denotes the coupling degree between the three parameters, the value range was \([0,1]\), the size of the C value was determined by evaluation value of structural stress caused by the settings for each parameter, and the larger the value, the stronger the interaction and influence between the parameters; \(U_{1}\), \(U_{2}\), \(U_{3}\) represent the comprehensive evaluation values of main girder stiffness, stayed cable stiffness and length of cable-free zone in the span, respectively, which are obtained by multiplying the standardized value with the weights determined by comprehensive evaluation [23]. The full arrangement of the 216 combinations was evaluated; \(D\) denotes the coupling coordination of the three parameters; the coefficients to be determined \((\alpha_{1},\ \alpha_{2},\ \alpha_{3})\) refer to the above calculation results; the degree of influence on the overall structural forces was determined as \(\alpha_{1}=0.35\), \(\alpha_{2}=0.35\), \(\alpha_{3}=0.30\). The degree of action between \(U_{1}\), \(U_{2}\) and \(U_{3}\) was calculated as  
\[C_{12}=\frac{2\sqrt{U_{1}U_{2}}}{U_{1}+U_{2}},\ \ C_{13}=\frac{2\sqrt{U_{1}U_{ 3}}}{U_{1}+U_{3}},\ \ C_{23}=\frac{2\sqrt{U_{2}U_{3}}}{U_{2}+U_{3}} \tag{7}\]  
Depending on the situation, the coefficients to be determined differed from each other; \(U_{1}\) was measured with \(U_{2}\)\(\alpha_{1}=\alpha_{2}=0.5\); \(U_{1}\) was measured with \(U_{3}\)\(\alpha_{1}=0.55\), \(\alpha_{3}=0.45\); and \(U_{2}\) was measured with \(U_{3}\)\(\alpha_{2}=0.55\), \(\alpha_{3}=0.45\).