## 3 Simulation Calibration Pre-Test
### Significance Parameter Range Determination Test  
To reach the optimal region for each significant factor as quickly as possible, the steepest climb was applied to the cylinder-lifting simulation test based on the Plackett-Burman test. The significance parameters were incrementally increased according to the selected step size, with factors' values determining the step change. Parameter values gradually increased from small to large according to parameter range values. After reaching a minimum value, the relative error for the angle of repose obtained from the test and simulation gradually increased.  
Table 5 shows the steep climb test design and results. This result shows that the angle of repose increases gradually with the increase in wheat-wheat rolling friction coefficient and wheat-wheat static friction coefficient. Furthermore, the relative error between the angle of repose of the wheat grain pile in the real test and the simulation first decreases, then increases. This relative error is minimized at level no. 3, showing that the optimum value interval is near level no. 3. Therefore, the range near level no. 3 was selected for the design of the subsequent response surface.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameter** & **Mean Square** & **F** & **\(p\)-Value** & **Significance** \\ \hline X1 & 0.0062 & 10.28 & 0.0491 & - \\ X2 & 0.0002 & 0.3509 & 0.5953 & - \\ X3 & 0.0018 & 3.02 & 0.1807 & - \\ X4 & 0.0001 & 0.1836 & 0.6972 & - \\ X5 & 0.0309 & 50.90 & 0.0057 & ** \\ X6 & 0.1489 & 244.94 & 0.0006 & ** \\ X7 & 0.0050 & 8.15 & 0.0649 & - \\ X8 & 0.0094 & 15.38 & 0.0295 & * \\ \hline \hline \end{tabular} Note: ** indicates highly significant, * indicates generally significant.  
\end{table}
Table 4: Statistical analysis of Plackett–Burman test parameters.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**Serial Number** & **X1** & **X2** & **X3** & **X4** & **X5** & **X6** & **X7** & **X8** & **X9** & **X10** & **X11** & **Angle of Repose Tangent** \\ \hline
1 & 1 & 1 & \(-1\) & 1 & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 0.3905 \\
2 & \(-1\) & 1 & 1 & \(-1\) & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & 0.5016 \\
3 & 1 & \(-1\) & 1 & 1 & \(-1\) & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 0.3029 \\
4 & \(-1\) & 1 & \(-1\) & 1 & \(-1\) & 1 & 1 & 1 & \(-1\) & \(-1\) & 0.2017 \\
5 & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 1 & \(-1\) & 1 & 1 & \(-1\) & 0.3934 \\
6 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 1 & \(-1\) & 1 & 1 & 0.3386 \\
7 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & 1 & \(-1\) & 1 & 1 & 1 & 0.1313 \\
8 & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 1 & \(-1\) & 1 & 0.2239 \\
9 & 1 & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 1 & \(-1\) & 0.1283 \\
10 & \(-1\) & 1 & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 1 & 0.0618 \\
11 & 1 & \(-1\) & 1 & 1 & \(-1\) & \(-1\) & \(-1\) & 1 & \(-1\) & 1 & 0.1687 \\
12 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 1 & 0.1223 \\ \hline \hline \end{tabular} Note: ** indicates highly significant, * indicates generally significant.  
\end{table}
Table 3: Plackett–Burman experimental design and results.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Serial Number** & **Wheat–Wheat Static** & **Wheat–Wheat Rolling** & **Angle of Repose Tangent** & **Relative Error/\%** \\  & **Friction Coefficient** & **Friction Coefficient** & **Angle of Repose Tangent** & **Relative Error/\%** \\ \hline
1 & 0.01 & 0.002 & 0.072 & 76.2 \\
2 & 0.03 & 0.005 & 0.293 & 10.1 \\
3 & 0.05 & 0.008 & 0.311 & 3.7 \\
4 & 0.07 & 0.011 & 0.394 & 25.2 \\
5 & 0.09 & 0.014 & 0.418 & 35.4 \\
6 & 0.11 & 0.017 & 0.436 & \(38.1\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Steepest climbing test design and results.