# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel
## 3 Validation and Discussion
### Discussion  
According to the modeling process, the accuracy of the proposed model is strongly influenced by three factors, including the length of the reduced stitched catenary model, the distance between every two spring-damping elements, and the stiffness of the spring-damping elements in the stitched wire model. These three aspects are discussed to further understand the present model. The influence of the length of the reduced stitched catenary model \(L\) on the calculation accuracy in different cases is firstly discussed here. The mean contact force and standard deviation of the pantograph-catenary contact force with respect to different \(L\) in both the test case and the EN50318-2018 case are shown in Figure 8, where \(L\) changes from 60 m (1 span) to 240 m (4 spans) in the original case and 240 m (4 spans) to 420 m (7 spans) in the EN50318-2018 case. It can be seen from Figure 8 that both the mean contact force and standard deviation approach the test results and standard range with increasing \(L\), but different cases have different corresponding convergence values. In the original case, when \(L\) is greater than 180 m, the corresponding mean contact force and standard deviation converge to the test results. However, the mean contact force and standard deviation in the EN50318-2018 case converge when \(L\) is larger than 360 m. This means that different pantograph-catenary-interaction cases have different suitable \(L\) values, which should be decided by the pre-analysis method before investigation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Models**} & **Reduced Pantograph–Stitched-Catenary Model** & **FEM Model ([PERSON] et al. [10])** & **MSM Model ([PERSON] et al. [18])** \\ \hline \multirow{4}{*}{Characteristics} & The long stitched catenary is reduced to a small region around the moving pantograph and modeled using the modal superposition method and ALE method, and only the reduced area of the catenary can be modeled. & The whole long catenary structure is considered and modeled using the finite element method, and most of the components are detail modeled. & The whole long catenary structure is considered and modeled using the modal superposition method, only the main parts of the catenary can be modeled. & The whole long catenary structure is considered and modeled using the modal superposition method, only the main parts of the catenary can be modeled. & The whole long catenary structure is considered and modeled using the modal superposition method, only the main parts of the catenary can be modeled. \\ \hline \multirow{4}{*}{Accuracy} & Accurate in main pantograph–catenary interaction dynamics but can not simulate component’s dynamic responses & Accurate in both the main pantograph–catenary interaction dynamics but can not simulate component’s dynamic responses & Accurate in main pantograph–catenary interaction dynamics but can not simulate component’s dynamic responses \\ \hline Efficiency & Fastest & Slowest & Middle \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of reduced pantograph–stitched-catenary model and other models. Figure 7: Comparison of the calculation efficiencies of the present and traditional pantograph–stitched-catenary interaction models: (**a**) number of DOFs of the pantograph–catenary model; (**b**) CPU times of the pantograph–catenary model. The influence of the distance between every two spring-damping elements \(d_{S}\) in the stitch wire model on the calculation accuracy is then discussed. Based on the same case, the mean contact force and standard deviation of the contact force at the lead pantograph with respect to different \(d_{S}\) are calculated and shown in Figure 9. Figure 9 shows that both the mean contact force and standard deviation converge to standard values at \(d_{S}\) = 19 m, and they quickly increase with increasing and decreasing \(d_{S}\).