## 5 Validation Experiment and Discussion
### Validation Experiment
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Driver**} & \multicolumn{2}{c}{**Shoveling**} & \multicolumn{5}{c}{**Fuel Consumption**} & \multicolumn{5}{c}{**Average Fuel**} \\  & **Operation** & & & & & & & & **Consumption** & \\ \hline \multirow{2}{*}{Driver A} & Shoveling gravel & 71.67 & 64.06 & 92.31 & 72.56 & 75.38 & 71.89 & 63.60 & 71.72 & 76.12 & 66.70 & 72.60 \\  & Shoveling sand & 72.65 & 62.36 & 72.07 & 64.77 & 68.66 & 92.63 & 76.10 & 72.38 & 65.51 & 66.17 & 71.33 \\ \hline \multirow{2}{*}{Driver B} & Shoveling gravel & 84.85 & 65.72 & 74.56 & 77.76 & 72.16 & 74.00 & 65.73 & 68.77 & 96.22 & 78.53 & 75.83 \\  & Shoveling sand & 61.17 & 57.76 & 67.28 & 61.05 & 74.34 & 66.57 & 69.00 & 74.26 & 68.23 & 74.09 & 67.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Fuel consumption by manually controlled shoveling. Figure 13: Fuel consumption comparison. The average fuel consumption for the validation experiments of the three optimized trajectories decreased by 29.54%, 19.84%, and 42.33%, respectively, compared to driver A's control of shoveling gravel and by 30.39%, 21.42%, and 43.46%, respectively, compared to driver B. The average fuel consumption of the validation experiments for the three optimized trajectories decreased by 33.63%, 33.60%, and 23.76%, respectively, compared to driver A shoveling sand, and by 29.99%, 29.96%, and 19.58%, respectively, compared to driver B. The average fuel consumption for shoveling gravel with optimized trajectory with three engine speeds is 53.69 mL, which is 26.05% and 29.20% lower compared to Driver A and Driver B, respectively. And the average fuel consumption of shoveling sand with optimized trajectory with three engine speeds is 52.47 mL; compared with Driver A and Driver B, the average fuel consumption is reduced by 26.44% and 22.12%, respectively. The average fuel consumption for manually controlled shoveling of gravel is 74.22 mL, and the average fuel consumption for manually controlled shoveling of sand is 69.35 mL. The fuel consumption can be, on average, reduced by 27.66% when shoveling gravel with an optimized trajectory and by 24.34% when shoveling sand with an optimized trajectory. In conclusion, compared with the manually controlled shoveling operation, the shoveling operation, according to the optimized trajectory, can effectively reduce fuel consumption of shoveling operation. In order to test the significance of the reduction in fuel consumption for the optimized shoveling trajectory, a \(t\)-test is chosen to test it in this paper. The samples are selected from the fuel consumption of the optimized shoveling trajectory and the fuel consumption of drivers A and B shoveling gravel and sand, respectively. The \(t\)-test allows us to obtain statistical conclusions about the significance of the difference between the means of the two groups of samples and to determine their level of statistical significance. First, the hypothesis is established. The null hypothesis \(H_{0}\) is that there is no significant difference between the fuel consumption data of the optimized shoveling trajectory and the fuel consumption data of the manually controlled shoveling. The alternative hypothesis \(H_{1}\) is that the fuel consumption data from the optimized shoveling trajectory performs  
Figure 14: Parameters of the shoveling process for driver A and driver B. (**a**) Engine speed; (**b**) Initial velocity; (**c**) Displacement of wheel loader in insertion phase; (**d**) Displacement of wheel loader in scooping phase; (**e**) Operation time; (**f**) Shoveling weight. significantly better than the fuel consumption data from the manually controlled shoveling, as shown in Equation (22). After that, the significance level needs to be determined. In this paper, the significance level \(\alpha\) is chosen as 0.05. Finally, the T-value is calculated and compared with the critical value of the two-sided test, and the formula for calculating the T-value is shown in Equation (23).