# Pantograph-Catenary Interaction Prediction Model Based on SCSA-RBF Network
## 3 Pantograph-Catenary Interaction Prediction Model
### Performance Evaluation of Prediction Model  
The catenary parameters of the stitched catenary of Datong-Xi'an High-speed Railway Line [7] were adopted and set \(k_{1}=74\) N/m, \(c_{3}=50\) N\(\cdot\)s/m, and \(c_{2}=10\) N\(\cdot\)s/m. Each decision variable in \(\mathbf{X}\) used the same value range as in our team's previous article [21]. In the decision vector \(\mathbf{Y}\), the value range of \(k_{31}\) and \(k_{32}\) is \(<\)4000, 14,000\(\cdot\) N/m, and the value range of \(S_{0}\) is \(<\)130, 520\(\cdot\) N. The sample sizes of sets A, B, C, and D were 2200, 900, 900, and 200, respectively. For set C with linear panhead stiffness, Figure 2(a) shows the time-domain signals of the panhead acceleration and the pantograph-catenary contact force of the samples with the best and worst prediction effect among them. Figure 3(a) shows the distribution of the determination coefficient of the time-domain signals and model errors of all samples. The relevant statistical values are given in the second row of Table 1. It can be seen that the probability density of the determination coefficient between the model-predicted value and FEM-calculated value of the two kinds of time-domain signals presents a left-skewed distribution. The intervals within the probability of 0.95 of them are (92.8%, 100%\(\gtrsim\) and (91.0%, 100%\(>\), respectively, which means most of the values are greater than their mean values of 97.7% and 97.4%. Obviously, for the sample with the maximum determination coefficient, the model-predicted results of the two kinds of time-domain signals almost coincide with their FEM results. Even for the sample with the minimum determination coefficient, the prediction accuracy of the two kinds of time-domain signals is also high. In addition, the model-predicted values of the SDCF in these samples are basically the same as those of the FEM-calculated value (\(\square\) in Figure 5), and the determination coefficient between them is 98.2%. The probability density distribution of model errors is approximately symmetric, and the interval within the probability of 0.95 of the model errors is \(<\)\(-\)2.35, 3.60\(\cdot\)N.  
For set D with piecewise linear panhead stiffness, Figure 2(b) shows the time-domain signals of the panhead acceleration and the pantograph-catenary contact force of the samples with the best and worst prediction effect among them. Figure 3(b) shows the distribution of the determination coefficient of the time-domain signals and model errors of all samples. The relevant statistical values are given in the third row of Table 1. Similarly, the probability density of the determination coefficient between the model-predicted value and FEM-calculated value of the two kinds of time-domain signals presents a left-skewed distribution. The intervals within the probability of 0.95 of them are (92.5%, 100%\(>\) and (91.5%, 100%\(>\), respectively, which means most of the values are greater than their mean values of 97.1% and 97.3%. For the sample with the maximum or the minimum determination coefficient, the model-predicted results of the two kinds of time-domain signals are in good agreement with their FEM results. In addition, the model-predicted values of the SDCF in these samples are basically the same as those of the FEM-calculated value (\(\square\) in Figure 5), and the determination coefficient between them is 98.2%. The probability density distribution of model errors is approximately symmetric, and the interval within the probability of 0.95 of the model errors is \(<\)\(-\)2.01, 4.11\(\mathrm{>}\) N.  
Therefore, the pantograph-catenary interaction prediction model demonstrates strong generalization ability. In addition, the prediction model required only \(1\times 10^{-3}\) core hours, which is only \(1/10^{4}\) of the computational cost required for the FEM model in Section 2 when calculating a single pantograph-catenary interaction case.