# Modeling and Parameter Calibration of Morchella Seed Based on Discrete Element Method
## 3 Results and Discussion
### Box-Behnken Design  
According to the results of the steepest ascent (SA) test, the Box-Behnken Design (BBD) test was carried out. Two levels were taken for each of the three significant factors. Five central points were selected for error estimation, and a total of 17 tests were carried out. The test results are shown in Table 6.  
As shown in Table 6, Box-Behnken Design and its results, the second-order regression model of Morchella cultivation spawn particle repose angle, and three significant parameters were established by using Design-Expert, as shown in Formula (7). \[\theta=39.41+64.95C-353.74D-98.91G+1240.00 CD+185.00 CG+2023.81 DG-191.10C^{2}+3221.11D^{2}+192.30G^{2}\]  
\[\text{Significance ranking:}\ C>D>DG>G>G^{2}>CD>D^{2}>CG>C^{2} \tag{7}\]  
The variance analysis results of the regression model are shown in Table 7. The JKR surface energy, seed-to-seed rolling friction coefficient, and seed-to-seed restitution coefficient had extremely significant effects on the repose angle of the seed particles. The model's \(p\)-value was less than 0.0001, indicating a highly significant relationship between the dependent and independent variables. The \(p\)-value for the lack of fit was 0.1943, suggesting a good fit for the equation. The determination coefficient \(R^{2}=0.9841\) and the adjusted \(R^{2}=0.9637\), both of which are close to 1, demonstrate the high reliability of the model. Additionally, a precision value of 24.05 further confirms the model's good accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run** & \(C\) & \(D\) & \(G\) & **Simulation Repose Angle/(\({}^{\circ}\))** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 6: Results of Box–Behnken Design test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(p\)**-Value** & **Significance** \\ \hline Model & 222.92 & 9 & 24.77 & 48.26 & \textless{}0.0001 & Very Significant \\ C & 127.76 & 1 & 127.76 & 248.91 & \textless{}0.0001 & Very Significant \\ \(D\) & 54.6 & 1 & 54.6 & 106.38 & \textless{}0.0001 & Very Significant \\ \hline \hline \end{tabular}
\end{table} 
Table 7: ANOVA of Box–Behnken Design quadratic model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Serial Number** & \multicolumn{3}{c}{**Factors**} & **Simulation Repose Angle \(\sigma\)/(\({}^{\circ}\))** & **Relative Error/\%** \\ \cline{2-5}  & \(C\) & \(D\) & \(G\) & \\ \hline
1 & 0.05 & 0.01 & 0.05 & 32.28 & 14.22 \\
2 & 0.1 & 0.025 & 0.12 & 35.42 & 5.87 \\
3 & 0.15 & 0.04 & 0.19 & 42.17 & 12.06 \\
4 & 0.2 & 0.055 & 0.26 & 48.99 & 30.19 \\
5 & 0.25 & 0.07 & 0.33 & 51.34 & 36.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Design and results of climbing test. For the Box-Behnken experiment results, variance analysis was conducted, where a larger F-value and a smaller \(p\)-value indicate a more significant effect of the factor. A \(p\)-value less than 0.01 indicates a highly significant effect, a \(p\)-value between 0.01 and 0.05 indicates a significant effect, and a \(p\)-value greater than 0.05 indicates a non-significant effect. As shown in Table 7, \(C\), \(D\), \(G\), and \(DG\) had a significant positive impact on the repose angle, while \(CD\) and \(G^{2}\) also had a significant influence. However, \(CG\), \(C^{2}\), and \(D^{2}\) did not have a significant effect on the repose angle. According to the variance analysis results, the interaction terms \(CD\) and \(DG\) have significant effects on the repose angle of Morchella seeds, indicating that multi-factor interactions play a key role in particle accumulation behavior. The \(CD\) interaction term shows that when both the seed-to-seed rolling friction coefficient and seed surface energy increase, the repose angle gradually rises, suggesting that these two factors together enhance the stability between particles. On the other hand, the \(DG\) interaction term (seed surface energy and seed-to-steel rolling friction coefficient) exhibits a nonlinear trend, initially decreasing and then increasing.