# Contact Force Surrogate Model and Its Application in Pantograph-Catenary Parameter Optimization
## 4 Multi-Parameter Joint Optimization of Pantograph-catenary  
Using the Selective Crow Search Algorithm (SCSA) [19] with the optimization objective of minimizing the SDCF, the optimal solutions for 10 sets of decision vectors (Table 5) and their corresponding SDCFs were iteratively searched (Figure 1c). These iterations were conducted under two low-pass filtering frequencies and five operating speeds. Specifically, Case 1 includes all pantograph-catenary parameters, while Case 2 to Case 5 successively reduce the number of pantograph-catenary parameters. Case 6 encompasses all catenary parameters, with Case 7 and Case 5 progressively reducing the number of catenary parameters. Case 8 represents all pantograph parameters, with Case 9 and Case 10 gradually reducing the number of pantograph parameters. To ensure the generalization ability of the optimization scheme, 100 random values were sampled for the other pantograph-catenary parameters outside the decision variables within their respective ranges using Latin Hypercube Sampling. Firstly, the relevant parameters of SCSA are set as follows: the maximum number of iterations is 500, the population size is 50, the flight length is 2, and the awareness probability is 0.1. The values of decision variables are shown in Table 1. Next, initialize the decision vector of all populations in the first generation and calculate the SDCF of all populations. Then, update the decision vector by the regulation of SCSA and calculate the corresponding SDCF repetitively until the number of iterations reaches the maximum value. Finally, the optimal solution is the decision vector with the smallest SDCF. The SDCF of the samples during the iteration process was computed using the surrogate model from Section 2. Figure 8 provides the mean and standard deviation of SDCF at the optimal solutions for 100 samples in each operating condition. Compared to the optimization effects of jointly optimizing all 14 pantograph-catenary parameters at 250 km/h, the optimization results for 5 catenary parameters, or 6 pantograph parameters at Classes II-IV, or 4 pantograph-catenary parameters at Classes I-II, as well as combinations of these parameters, show similar performance. At 300 km/h and above, the optimization effects for 11 pantograph-catenary parameters, excluding (\(c_{3}\), \(c_{2}\), \(k_{1}\)), are comparable. However, the optimization performance of other parameter combinations is notably inadequate, and the performance gap widens as the operating speed increases or the number of decision variables decreases. To further elaborate, in comparison to optimizing the five catenary parameters at speeds of 300 km/h and below, optimizing the two Class I catenary parameters (\(T_{\text{c}}\), \(A_{\text{c}}\)) yields similar effects. As the speed increases, it becomes necessary to consider simultaneously optimizing the three catenary parameters for Classes II-III. In comparison to optimizing the nine pantograph parameters across all speed ranges, optimizing the six pantograph parameters (\(m_{3}\), \(c_{1}\), \(m_{1}\), \(m_{2}\), \(k_{3}\), \(k_{2}\)) at Classes II-IV produces similar results, and the Class V parameters (\(c_{3}\), \(c_{2}\), \(k_{1}\)) can be ignored.