# A New Method for Finding the Shape of the Main Cable in the Special Cable Plane
## 5 Analysis of the Main Cable Curve of Spatial Special-Shaped Suspension Bridge
### Differences between Different Calculation Models  
In order to study the difference between the four-coordinate constraint model proposed in this paper and the three-coordinate calculation model proposed by [PERSON], this paper selects several representative classical algorithms in the main cable shape-finding process and an improved heuristic algorithm with strong nonlinear computing capability. See Table 3 for the specific representation. For comparability, the convergence criteria of the two methods are uniformly taken as \(\max(\mid ey1\mid,\mid ey2\mid,\mid ez3\mid,\mid ez4\mid)<\text{eps}\), where \(\text{eps}=10^{-3}\) m. This paper refers to the parabola theory proposed by [PERSON] to estimate the space special-shaped main cable (\(H_{x0}\), \(H_{z0}\), \(V_{0}\)) = (4800 kN, 1180 kN, 2400 kN). This paper uses the estimated value as the initial point of iteration to carry out the iterative calculation of the influence matrix method and the modified least squares method. By comparing the forces of the spatial main cable and the spatial special-shaped main cable, it is found that the vertical force and the transverse force of the two bridge types have little difference, while the stress along the bridge direction has a large difference. Based on the parabola theory, the transverse and vertical force components are magnified 1.15 times, and the longitudinal force components are magnified 1.6 times. Therefore, the initial search interval of the heuristic algorithm proposed in this paper is \(H_{x0}\) = (4080-5520 kN), \(H_{z0}\) = (472-1888 kN) and \(V_{0}\) = (2040-2760 kN).  
Figure 3 shows the calculation results using the traditional calculation model, and Figure 4 shows the calculation results using the new calculation model. The calculation results in Figure 3 show that the calculation results of the existing calculation models have no obvious regularity, and the calculation error is large. Among them, the calculation results of the influence matrix method and those of [PERSON] [12] have the same regularity. They both become larger first and then tend to a larger error. The reason for this phenomenon is that the traditional Newton-like iterative method has weak computing power for strong nonlinear problems and cannot obtain correct results.  
Figure 2: Schematic Diagram of Bridge.  
The calculation results in Figure 4 show that the calculation results of the calculation model proposed in this paper have an obvious downward trend, and the hybrid heuristic  
Figure 4: Calculation Results of Four-coordinate Calculation Model.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Calculation Model** & \begin{tabular}{} **Influence Matrix** \\ **Method** \\ \end{tabular} & \
\begin{tabular}{} **Modified** \\ **Least Squares** \\ **Squares** \\ **Method** \\ \end{tabular} &
\begin{tabular}{} **Dproved** \\ **Quantum** \\ **Geetic** \\ **Geetic** \\ **Geetic** \\ **Algorithm** \\  
algorithm is obviously better than the single heuristic optimization algorithm. This phenomenon occurs because the heuristic algorithm has relatively weak optimization ability in the later stage and is not easy to jump out of the matrix optimal solution. However, the hybrid heuristic algorithm uses the modified least squares method in the later stage of the calculation, and the modified least squares method has a strong ability to search the local optimal solution.