## 6 Conclusions  
This study systematically investigates the sensitivity of longitudinal and lateral forces to the acceleration, strain, and displacement responses in different areas of the inner liner of a 205/55 R16 radial tire during rolling using the global sensitivity analysis and finite element simulation. The results indicate that, within the ground deformation area, acceleration and displacement responses exhibit higher sensitivity to longitudinal and lateral forces than strain responses. Specifically, when the tire enters and exits the contact \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model Number**} & \multicolumn{2}{c}{**Sensor**} & \multicolumn{2}{c}{**Structure of the RBF Neural Network Model**} \\ \cline{2-5}  & **Position** & **Quantity** & **Type of Input Vector** & **Size of Input Vector** \\ \hline
1 & Right sidewall & 1 & \(A_{1}\), \(A_{3}\) & \(16\times 200\) \\
2 & Left and right sidewalls & 2 & \(A_{1}\), \(A_{3}\), \(U_{3}\) & \(23\times 200\) \\
3 & Crown and left/right sidewalls & 3 & \(A_{1}\), \(A_{3}\), \(U_{2}\), \(U_{3}\) & \(29\times 200\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RBF neural network models with different input vectors. Figure 14: (a) Longitudinal force estimation of intelligent tires based on the RBF neural network. (b) Lateral force estimation of intelligent tires based on the RBF neural network. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Model Number**} & \multicolumn{2}{c}{**MRE**} \\ \cline{2-3}  & **Longitudinal Force (\%)** & **Lateral Force (\%)** \\ \hline
1 & 9.59 & 8.73 \\
2 & 5.83 & 3.69 \\
3 & 1.42 & 1.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Generalization performance of intelligent tire force estimation models. patch area, the longitudinal force shows extremely high sensitivity to the radial acceleration (\(A_{1}\)) in the sidewall area and the circumferential displacement (\(U_{2}\)) in the crown area. The effect of lateral force on sensitive response variables is primarily concentrated in the sidewall area, with significant asymmetry between the left and right sidewall areas: the lateral displacement (\(U_{3}\)) in the left sidewall area exhibits high sensitivity, while the lateral acceleration (\(A_{3}\)) in the right sidewall area exhibits similarly high sensitivity. Based on the global sensitivity analysis of tire forces, the characteristic values of sensitive response signal curves for longitudinal and lateral forces are extracted, and three intelligent tire force estimation models are established using the RBF neural network with different sensor-targeting configurations. The estimation results of the three models indicate that the MRE for intelligent tire force estimation remains below 10%. In particular, Model 3 achieves longitudinal and lateral force estimation errors of 1.42% and 1.10%, respectively, with an overall MRE below 2%, effectively verifying the generalization performance of the model. This study provides a theoretical foundation for the targeted configuration method of intelligent tire sensors and lays the groundwork for future research on accurate estimation methods of intelligent tire state parameters. However, there are some limitations in this study. The neural network based on the intelligent tire force estimation method is only applied under a single operating condition, and different sets of input features are used for force estimation in different directions. The coupling effects among sensitive response signals under complex operating conditions and different road surfaces are not fully considered. Therefore, future work should focus on optimizing the neural network to handle more complex and high-dimensional input features, enabling the simultaneous estimation of vertical, longitudinal, and lateral tire forces. This advancement is expected to further promote the development of vehicle intelligence through innovations in intelligent tire technology. Conceptualization, Y.Z. and G.W. ; methodology, Y.Z. and G.W. ; validation, J.Z., X.L. and X.W.