# Pantograph-Catenary Interaction Prediction Model Based on SCSA-RBF Network
## 5 Conclusions  
In this paper, a data-physics coupling model that can quickly predict the pantograph-catenary interaction was proposed. In the process of obtaining the time-domain signal of the pantograph-catenary contact force, the time-consuming finite element solution process of the pantograph-catenary dynamic equation was avoided, and the time-domain signal of the panhead acceleration was taken as the boundary condition to directly solve the pantograph dynamic equation. The computational cost of this prediction model was only \(1\times 10^{-3}\) core hours, which is only \(1/10^{4}\) of that of the traditional pantograph-catenary finite element model. The application prospect of this model includes the following two aspects:  
Figure 6: Time-domain signal of contact force with low-pass filtering frequency of 20 Hz (**a**) and 40 Hz (**b**). Figure 7: Optimization effect (**a**) and its influencing factors (**b**). Firstly, whether in existing line tests or on the operational high-speed railway, compared with the real-time monitoring of the pantograph-catenary contact force, which requires changes in the panhead structure and installation of sensors, the non-contact test technology for panhead displacement is more mature and feasible. Based on the time-domain signal of panhead displacement, the time-domain signal of panhead acceleration can be obtained. Then, the time-domain signal of the contact force can be obtained using the pantograph-catenary interaction prediction model. Secondly, for the multi-parameter joint optimization of the pantograph-catenary system, a greater number of decision variables leads to a more favorable optimization effect. However, the number of cases involved will increase sharply, and the computational cost required for the calculation based on the pantograph-catenary FEM model is extremely higher as the number of decision variables increases. In addition to greatly improving computational efficiency, the pantograph-catenary interaction prediction model can effectively predict the time-domain signal of the dynamic response of the pantograph-catenary system. In this paper, under different speeds, the prediction model was applied to the multi-parameter joint optimization of six pantograph dynamic parameters and nine pantograph dynamic parameters considering the nonlinear panhead stiffness. The optimization strategies outlined in this paper led to a significant 34.62% reduction in the SDCF. Based on all the working conditions concerned in this paper, it is suggested that \(m_{3}\) and \(m_{1}\) should be reduced to their lower limits; \(k_{3}\) should be increased, the increase depending on specific working conditions; \(m_{2}\) should be reduced at medium and higher speeds and increased at other speeds; \(k_{2}\) should be reduced to its lower limit at medium and high speeds, and increased at 375 km/h and above; and \(c_{1}\) should be reduced at medium speed and increased to its upper limit at the other speeds. Conceptualization, M.W. and X.X. ; Methodology, M.W. and J.W. ; Software, M.W. ; Validation, H.Z. and R.Z. ; Formal analysis, M.W., H.Z. and R.Z. ; Investigation, M.W., H.Z. and R.Z. ; Data Curation, M.W. and X.X. ; Writing--Original Draft, M.W. ; Writing--Review & Editing, X.X. and J.W. ; Visualization, M.W. and X.X. ; Supervision, X.X. and J.W. ; Project administration, X.X. and J.W. ; Funding acquisition, X.X. and J.W. All authors have read and agreed to the published version of the manuscript. This work was supported by the Major Project of China Railway Co., Ltd., Beijing, China, (K2021)004-A) and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22020201). The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.