# Pantograph-Catenary Interaction Prediction Model Based on SCSA-RBF Network
## 4 Application in Optimization of Pantograph Parameters  
At a specific running speed and low-pass filtering frequency, the optimal solution of the decision vector was achieved using SCSA with the objective of minimizing the SDCF. According to trade standards EN50318:2018 [23] and EN50317:2012 [29], the time-domain signal of contact force should be filtered through a 20 Hz low-pass filter. The analysis of the time-domain signals of contact force from the 4200 sets of FEM results involved above indicates that 95.45 \(\pm\) 2.05% of the energy of the contact force signals is concentrated below 40 Hz. Therefore, two low-pass filtering frequencies, 20 and 40 Hz, were selected as the cut-off frequencies in the optimization. It is worth noting that the sampling frequency of the time-domain signal used in this paper is 200 Hz, which is five times higher than 40 Hz. According to the Nyquist-Shannon sampling theorem, such a sampling frequency is accurate enough to describe time-domain signals below 40 Hz. A total of nine speeds were selected with an interval of 25 km/h between 250 and 450 km/h; the decision vectors were set as **X** and **Y**, respectively, to study the effect of nonlinear stiffness panhead. The SDCF corresponding to the decision vector is given by the pantograph-catenary interaction prediction model. The value range of each decision variable in **X** and **Y** is the same as that in Section 3.3, and the maximum number of iterations is 200. The time-domain signal of the contact force at the optimal solution and the reference point are shown in Figure 6, where the reference point represents the parameters of the existing DSA380 pantograph in service [7]. Compared with the reference point, the fluctuation degree of the time-domain signal at the optimal solution is significantly reduced, and the optimization effect varies at different speeds and low-pass filtering frequencies. In addition, under the same working condition, most of the peak-valley values of the time-domain signals are slightly lower in the case of nonlinear panhead stiffness compared to those in the case of linear panhead stiffness. The decreased value of the SDCF of the optimal solution compared with the reference point \(\Delta\sigma\) was used as the quantitative index of the optimization effect. As the speed increases, the optimization effect tends to increase from about 5 N at medium speed to 18 N at higher speed (Figure 7a). However, the optimization effect has a local minimum at 375 km/h because the excitation frequency of the moving contact force at the nearby speed points, that is, 350 km/h and 400 km/h, is equal to the natural frequency of the catenary. This leads to the resonance of the pantograph and catenary, resulting in relatively high SDCF at 350 km/h and 400 km/h and relatively low SDCF at 375 km/h. Therefore, the optimization space at 375 km/h is relatively small, leading to the small size of \(\Delta\sigma\). In \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Test Set**} & \multicolumn{3}{c}{**Determination Coefficient (\%)**} & \multicolumn{3}{c}{**Model Error (N)**} \\ \cline{2-7}  & \multicolumn{2}{c}{\(\tilde{\mathbf{z}}_{3}(t)\)} & \multicolumn{2}{c}{\(F_{\mathbf{c}}(t)\)} & \multirow{2}{*}{\(\sigma\)} & **Interval within** & \multirow{2}{*}{**Probability of 0.95**} \\ \cline{2-2} \cline{5-7}  & **Mean Value** & **Interval within** & & & **Interval within** & \\  & **Probability of 0.95** & & & & **Probability of 0.95** & \\ \hline C & 97.7 & (92.8, 100\textgreater{}) & 97.4 & (91.0, 100\textgreater{}) & 98.2 & \(<\)\(-\)2.35, 3.60\textgreater{} \\ D & 97.1 & (92.5, 100\textgreater{}) & 97.3 & (91.5, 100\textgreater{}) & 98.2 & \(<\)2.01, 4.11\textgreater{} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Generalization ability of pantograph–catenary interaction prediction model. Figure 5: \(\sigma_{q}\) and \(\sigma_{q}\) of test set samples.