## 5 Discussion
### Comparison with Conventional RVM Models  
In order to verify the advantages of the Gaussian and Sigmoid hybrid kernel functions adopted in this paper in balancing the global generalization and local learning abilities, Gaussian kernel (g-RVM), polynomial kernel (p-RVM), Sigmoid kernel (s-RVM), Gaussian and polynomial hybrid kernel (g-p-RVM), and Gaussian and Sigmoid hybrid kernel (g-s-RVM) models are selected to predict the local resistance coefficient, respectively. The boxplot of the prediction residual error of different kernel relevance vector machine models is shown in Figure 11, the prediction error index comparison of the different kernel RVM models is shown in Table 4, and the improvement rate of the prediction error index of the IAJS-HKRVM model compared with different kernel RVM models is shown in Figure 12.  
Figure 11: Boxplot of different kernel RVM model prediction residual error. As can be seen from Figure 11, among the single-kernel RVM models, the Gaussian kernel RVM model has the most concentrated prediction residual error distribution, and the median value is close to zero, which is close to the IAJS-HKRVM model, while the polynomial kernel RVM and Sigmoid kernel RVM model have a scattered prediction residual error distribution. In the hybrid kernel RVM model, the residual error distributions of the Gaussian + polynomial hybrid kernel RVM and Gaussian + Sigmoid hybrid kernel RVM are close, but the prediction accuracy is lower than that of the Gaussian kernel RVM model because the kernel parameters are determined according to experience, which agrees with the error indexes presented in Table 4. Therefore, the IAJS algorithm is used to optimize the kernel parameters of the HKKVM model, which further improves the prediction accuracy. As can be seen from Table 4, the error indexes of the IAJS-HKRVM prediction model are superior to other RVM models with different kernels, and the error indexes of the IAJS-HKRVM prediction model are \(R^{2}\) (0.9903), \(MAE\) (0.0013), and \(RMSE\) (0.0015), respectively. As can be seen from Figure 12, the numbers marked in red in Figure 12 show the highest improvement rate of each error index of the IAJS-HKRVM model compared with other RVM models with different kernel. The \(R^{2}\) of the IAJS-HKRVM model has the highest increase of 36.3% compared with the polynomial kernel RVM model, and the lowest increase of 2.1% compared with the Gaussian kernel RVM model. The \(MAE\) has the largest decrease of 81.0% compared with the polynomial kernel RVM model, and the lowest decrease of 38.1% compared with the Gaussian kernel RVM model. The \(RMSE\) has the largest decrease of 81.2% compared with the polynomial kernel RVM model, and the lowest decrease of 42.9% compared with the Gaussian kernel RVM model, which agrees with the data presented in Table 4. According to the comparative analysis results, it can be seen that single-kernel RVM models such as the Gaussian kernel, polynomial kernel, and Sigmoid kernel are difficult to be able to effectively mine complex nonlinear motion features. At the same time, it is difficult to guarantee the prediction accuracy and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & \(MAE\) & \(RMSE\) \\ \hline g-RVM & 0.9702 & 0.0021 & 0.0027 \\ p-RVM & 0.7264 & 0.0067 & 0.0081 \\ s-RVM & 0.7598 & 0.0069 & 0.0076 \\ g-p-RVM & 0.9662 & 0.0023 & 0.0029 \\ g-s-RVM & 0.9384 & 0.0033 & 0.0039 \\
**IAJS-HKRVM** & **0.9903** & **0.0013** & **0.0015** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of different kernel RVM model prediction error indexes. Figure 12: Comparison of different kernel RVM model prediction error index improvement rate. generalization performance of the model by determining the kernel parameters based on experience.