## 5 Experimental Validation
### Remarks  
Based on the proposed vehicle weight identification method discussed in Section 4, the weights of two 2-axle passenger cars and two 3-axle trucks were identified in the field test. Four tire force equations based on different footprint assumptions were compared. The results show that the proposed vision-based vehicle weight identification method can effectively identify the axle weight and gross weight of the vehicle. The identification error  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specification**} & \multirow{2}{*}{**Position**} & \multirow{2}{*}{**Estimated Pressure (MPa)**} & \multirow{2}{*}{**Deflection (mm)**} & \multirow{2}{*}{**Actual Weight (N)**} & \multicolumn{2}{c}{**Rectangular Equation**} & \multicolumn{2}{c}{**Huang Equation**} & \multicolumn{2}{c}{**Modified Equation**} \\ \cline{5-10}  & & & & **Calculated Weight (N)** & & **Calculated Weight (N)** & **Error** & **Calculated Weight (N)** & **Error** \\ \hline \multirow{5}{*}{12.00R20} & LF & 1.03 & 18.0 & 77,224 & 205,052 & 165.5\% & 94,299 & 22.1\% & 84,642 & 9.6\% \\  & LM & 1.03 & 20.2 & & & & & & \\  & RM & 1.03 & 22.0 & & & & & & \\  & LR & 1.03 & 19.6 & 170,618 & 432,364 & 153.4\% & 198,816 & 16.5\% & 179,242 & 5.1\% \\  & RR & 1.03 & 22.5 & & & & & & \\ \hline \multirow{5}{*}{11.00R20} & LF & 0.95 & 14.1 & \multirow{5}{*}{60,074} & \multirow{5}{*}{133,455} & \multirow{5}{*}{122.2\%} & \multirow{5}{*}{62671} & \multirow{5}{*}{4.3\%} & \multirow{5}{*}{56,501} & \multirow{5}{*}{6.0\%} \\  & RF & 0.95 & 15.9 & & & & & & \\  & LM & 0.95 & 20.5 & & & & & & \\  & RM & 0.95 & 16.3 & 127,890 & 326,401 & 155.2\% & 153,229 & 19.8\% & 138,143 & 8.0\% \\  & LR & 0.95 & 21.0 & & & & & & \\  & RR & 0.95 & 16.7 & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Axle weight identification results for trucks.  
Figure 21: Wear, tear, and perishing of the tire.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specification**} & \multirow{2}{*}{**Actual Weight (N)**} & \multicolumn{2}{c}{**Rectangular Equation**} & \multicolumn{2}{c}{**Huang Equation**} & \multicolumn{2}{c}{**Modified Equation**} \\ \cline{3-8}  & & **Calculated Weight (N)** & **Error** & **Calculated Weight (N)** & **Error** & **Calculated Weight (N)** & **Error** \\ \hline
12.00R20 & 413,070 & 1,070,811 & 159.2\% & 492,406 & 19.2\% & 443,554 & 7.4\% \\
11.00R20 & 324,086 & 794,109 & 145.0\% & 372,809 & 15.0\% & 336,105 & 3.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Gross weight identification results for trucks.  
of the axle weights and gross weights are both within 10%, regardless of passenger car tires or truck tires. In contrast, traditional footprint assumptions, such as oval, rectangular, and Huang's assumption are not accurate; therefore, the tire contact force equations have large errors. For the oval equation and rectangular equation, the errors in the axle and gross weight identification are all greater than 50%, and the errors for the Huang equation are about 20%. Thus, the equations based on the modified footprint are a significant improvement in vehicle weight estimation.