## 5 Experimental Validation
### Weight Identification of Trucks  
One 3-axle truck equipped with 11.00R20 tries and the other with 12.00R20 tries were tested, as shown in Figure 19. For multi-axle trucks, except for the front axle, the other axles usually utilize a dual wheel system (DWS). Herein, it is assumed that the inner tire of the DWS has the same contact force as the outer tire [46,47]. It is noted that the middle and rear axles of the truck are DWSs.  
Figure 20 shows the measured and estimated inflation pressure, as well as the errors for each axle. Since most heavy trucks are not equipped with TPMS, the pressure detector was used to measure the inflation pressure of the tested trucks, which is the \"Measured Pressure (MP)\" in the figure. Meanwhile, the identified manufacturer-recommended inflation pressure value of each tire is 0.83 MPa (11.00R20) and 0.9 MPa (12.00R20), and the pressure estimated by the inflation pressure estimation method is the \"Estimated Pressure (EP)\" in the figure. The error is the average value of the left and right tires of each axle.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{
\begin{tabular}{c} **Actual** \\ **Weight (N)** \\ \end{tabular} } & \multicolumn{2}{c}{**Oval Equation**} & \multicolumn{2}{c}{**Modified Equation (N)**} \\ \cline{3-6}  & & **Calculated** & **Error** & **Calculated** & **Weight (N)** & **Error** \\ \hline Sedan & 15,631 & 32,617 & 108.6\% & 16,436 & 5.1\% \\ SUV & 18,130 & 34,687 & 91.3\% & 19,369 & 6.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Gross weight identification results for passenger cars.  
As can be seen in Figure 20, the estimated inflation pressure is 1.03 MPa and 0.95 MPa, and the measured inflation pressure value is in the range of 0.90\(\sim\)1.10 MPa. Most of the errors in the axle identification are within 10%, except for the front axle of the truck with 11.00R20 tires (=11.5%), which is slightly higher. Overall, the estimated value is close to the measured value.  
To evaluate the accuracy of the truck weight estimate, the axle and gross weights were identified by the rectangular equation (i.e., Equation (6)), the Huang equation (i.e., Equation (7)), and the modified equation (i.e., Equation (12)), respectively, as shown in Tables 7 and 8. The actual value of the weight is also listed in Tables 7 and 8. It is noted that the weight calculation is based on the estimated pressure in Figure 20. It can be seen that the modified equation shows better accuracy with the relative error in the range of 3.7\(\sim\)9.6%, while on the contrary, the rectangular equation and the Huang equation have a larger error of around 150% and 20%, respectively.  
Figure 19: Tested trucks and tires: (a) 11.00R20 tires; (b) 12.00R20 tires.  
Figure 20: The comparison of the inflation pressure.  
In addition, it is noted that the establishment of the theoretical equation was based on the ideal tire structure without consideration of the tire loss. In this test, some truck tires are in a relatively poor condition, as displayed in Figure 21, which might increase the identification error. The tire loss could be a critical issue that needs to be studied in the future.