# Contact Force Surrogate Model and Its Application in Pantograph-Catenary Parameter Optimization
## 5 Conclusions and Future Work  
Based on Latin Hypercube Sampling and a validated finite element model of the pantograph-catenary, a database for the pantograph-catenary interaction examples was established. Using a feedforward neural network, a surrogate model for the SDCF with respect to operating speed and 14 pantograph-catenary parameters was constructed. This surrogate model exhibits strong generalization ability and can accurately predict the SDCF for unknown samples.  
With the surrogate model and the variance-based method, the first-order and total sensitivities of the SDCF to the pantograph-catenary parameters were calculated across the entire speed range and different frequency bands. Utilizing the k-means clustering algorithm, the pantograph-catenary parameters were categorized into Classes I to V. Among the pantograph-catenary parameters, \(T_{\text{c}}\) and \(A_{\text{c}}\) fall into Class I, as their impact on the SDCF is significantly higher than that of the other pantograph-catenary parameters, while \(k_{\text{1}}\), \(c_{\text{3}}\), and \(c_{\text{2}}\) fall into Class V, the influence of which can be neglected. Additionally, at speeds of 400 km/h and above, the coupling effects between catenary parameters need to be considered, and at speeds of 450 km/h, the influence of low-pass filtering frequency on the sensitivity of pantograph-catenary parameters also needs to be considered.  
Following a stepwise reduction in sensitivity class, 10 sets of decision vectors consisting of pantograph-catenary parameters, catenary parameters, and pantograph parameters were obtained. Using the surrogate model and the SCSA, optimization was performed  
Figure 8: SDCF at optimal solutions.  
across the entire speed range with the objective of minimizing the SDCF. At a medium speed of 250 km/h, it is sufficient to optimize the pantograph-catenary, catenary, or pantograph parameters at higher sensitivity classes to achieve the desired optimization results. However, at higher speeds and above, the number of optimized parameters needs to be increased. Furthermore, \(k_{1}\), \(c_{3}\), and \(c_{2}\) can be neglected under all operating conditions.  
In the future, a pantograph-catenary model that can more accurately predict its real dynamic performance is required to be obtained, such as a pantograph model that considers more degrees of freedom, medium-high frequency, and other low-frequency vibrations, and a three-dimensional catenary model that considers stagger.  
Data curation, R.Z.; Investigation, R.Z.; Methodology, R.Z.; Supervision, X.X.; Project administration, X.X.; Funding acquisition, X.X.; Writing--original draft, R.Z. and X.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Major Project of China Railway Co., Ltd., grant number K2021J004-A, and the Strategic Priority Research Program of the Chinese Academy of Sciences, grant number XDB22020201.  
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.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.