# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel
## 3 Validation and Discussion
### Validation
#### 3.1.2 Validation Based on the EN50318-2018 Standard and FEM  
The present model is then validated based on the EN50318:2018 standard [30], which is a European standard for pantograph-catenary interaction simulation validation of the AC stitched catenary and its corresponding pantograph. Note that the present model is firstly validated by the measurement data from SYT7.0/9.8, which was developed before 2018, and the original EN50318:2018 standard is more suitable. In addition, the recent publications about the pantograph-catenary interaction modeling still use the traditional EN50318:2018 standard to validate the model. Thus, the original EN50318:2018 standard is used for validation. In the present validation process, the double pantograph is considered, the length of the reduced catenary model is 360 m, \(d_{S}\) is 19 m, and \(K^{\prime}_{S}\) is \(7\times 10^{5}\) N/m. These values are decided by the pre-analysis method. The number of modes considered in the modeling is \(n=360\). Other parameters of both the pantograph and catenary in the reduced pantograph-stitched-catenary model are set based on the requirement of EN50318:2018 (like tension and dropper distance). The time histories of the pantograph-catenary contact forces based on the EN50318:2018 standard are shown in Figure 5, where a similar model is also calculated, and the same results are presented in [30]. The corresponding statistical results are shown in Table 2. As shown in Figure 5 and Table 2, the results from the present model are reasonable, and its corresponding statistical results meet the demand of Table A.7 in EN50318-2018. Based on these results, the accuracy of the reduced pantograph-stitched-catenary interaction model can be validated, and the present stitch wire model \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Frequency Span** & \multicolumn{2}{c}{**0–2 Hz**} & \multicolumn{2}{c}{**0–5 Hz**} & \multicolumn{2}{c}{**5–20 Hz**} \\ \cline{2-9}  & **Train Operation** & **Pesent** & **Test** & **Results** & **Present** & **Test** & **Present** & **Total** \\  & **Speed** & **Model** & **Results** & **Model** & **Results** & **Model** & **Results** \\ \hline Contact force & & & & & & & \\ (N) & 222 km/h & 91.24 & 90.85 & 97.22 & 97.85 & 7.32 & 6.81 \\ \hline Standard deviation & 222 km/h & 11.43 & 11.98 & 16.19 & 16.76 & 23.62 & 24.21 \\ \hline \end{tabular}
\end{table} 
Table 1: Contact force sorted according to frequency span from different models and train speeds. Figure 4: Time histories and frequency spectra of the pantograph–catenary contact force at \(V\) = 222 km/h: (**a**) time histories at \(V\) = 222 km/h and (**b**) frequency spectra at \(V\) = 222 km/h. can accurately present the dynamic behavior of the stitch wire parts. Note that the results shown in Figure 5 are similar to those shown in [30]. This is caused by the fact that the MSM-based pantograph-catenary model in [30] is validated by the same standard EN50318:2018 with the same pantograph and catenary parameters. Thus, the measurement data are further used in Section 3.1.1 to validate the present model. The FEM model developed by [PERSON] et al. [10] is further considered to validate the present model. The static shape of the contact wire is considered, and both the FEM model and the present model are used to calculate it. The results are shown in Figure 6, where the results from both models are compared with each other. It can be seen from Figure 1 that the results from the present model are also in good agreement with those from the FEM model, and the maximum relative difference between these two results is no more than 2.7%, which further validates the accuracy of the present model.