# Pantograph-Catenary Interaction Prediction Model Based on SCSA-RBF Network
## 1 Introduction  
The \"CR450 technological innovation project\" of China State Railway Group proposes that the operating speed of electric multiple units (EMUs) should be 400 km/h, and the maximum speed should be 450 km/h [1]. For most completed high-speed rail lines, since the costs arising from changes in catenary parameters could be high, optimizing pantograph parameters to improve the current collection quality of the pantograph-catenary system at higher speeds, i.e., 400 km/h and above, is a more feasible and effective method. The numerical simulation of pantograph-catenary interaction is usually based on the finite element method (FEM) [2; 3; 4]. The classic approach is to simplify the pantograph to a reduced model consisting of only a few lumped masses and spring-damper elements and construct a model of the catenary that consists of more than 10,000 finite element elements. With the objective of improving pantograph-catenary interaction performance, the optimization of pantograph-catenary parameters may include 1 to more than 10 decision variables and involve thousands or even tens of thousands of simulation cases. If the pantograph-catenary finite element model is used, hundreds of thousands of core hours are needed to solve a single set of pantograph-catenary parameter optimization problems. For different optimization scenarios, such as different running speeds on different operating lines and optimization scheme designs for different types of pantographs, it is often necessary to solve multiple sets of pantograph-catenary parameter optimization problems, which results in huge computational costs. Therefore, it is an urgent issue to improve the numerical calculation efficiency and reduce the computational cost. The vast majority of the elements in the pantograph-catenary finite element model are located in the catenary model. The catenary finite element model adopts the geometric and material parameters of the real catenary, with a total structural length exceeding a thousand meters, containing tens of spans with repetitive structures. Rod or beam elements are often used to simulate contact wires, messenger wires, and stitch wires. The nonlinear spring elements, which only bear tension, are often used to simulate the droppers. The spring-lumped mass systems are used to simulate the steady arms, and the lumped masses are used to simulate various clumps [2, 5, 6, 7]. To reduce the computational cost of numerical simulation, methods that can be adopted include improving the finite element model of the catenary, simplifying the physical model of the catenary, and constructing the surrogate model of pantograph-catenary interaction. Firstly, for the finite element model, the number of meshes can be reduced, or its nonlinear terms can be ignored. With the moving mesh method, finer meshes are set around the area near the contact point of the contact line, and coarse fixed meshes are set in the other areas to reduce the number of finite element elements of the catenary model. At 300 km/h and below, the relative error of the obtained time-domain signal of the contact force is lower than 7%, and the computational cost is reduced to 1/3 of that before mesh optimization [8]. Correction forces are used to eliminate the nonlinear stiffness term arising from the slackening of the dropper or the loss of pantograph-catenary contact. The solution process is divided into the online stage and the offline stage. The large matrix in the finite element model is pre-decomposed using LU factorization, which can considerably decrease computational cost while ensuring reasonable calculation accuracy [9, 10]. Secondly, the structure of the catenary can be simplified with an equivalent method. However, the results of the simplified catenary model have a relatively large error compared with those of the finite element model.