# Dynamic Coal Flow-Based Energy Consumption Optimization of Scraper Conveyor
## 5 Case Study and Validation
### Correlation Parameter Analysis  
To analyze the impact of decision variables on the objective functions, we used Response Surface Methodology (RSM). Common design methods include Central Composite Design (CCD) and Box-Behnken Design (BBD). BBD is especially suitable for estimating second-order response surfaces in experimental studies. Unlike CCD, which uses extreme factor levels, BBD carefully selects points at the center and midpoints of the experimental \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Optimization Type**} & \multicolumn{3}{c}{**Optimization Variable**} & \multicolumn{3}{c}{**Optimization Objective**} \\ \cline{2-7}  & \(V_{q}\) **(m/min)** & \(V_{j}\) **(m/min)** & \(n\) **(r/min)** & \(E\) **(K)** & \(S_{a}\) **(mm\({}^{2}\))** \\ \hline B/min (\(E\),\(S_{a}\)) & 6.1 & 31 & 50 & 1.2617 \(\times\) 10\({}^{9}\) & 4912 \\ C/min (\(E\)) & 7 & 30 & 41.6 & 1.0169 \(\times\) 10\({}^{9}\) & 9989 \\ A/min (\(S_{a}\)) & 4.5 & 32 & 49.8 & 1.8086 \(\times\) 10\({}^{9}\) & 2500 \\ Original value & 6 & 40 & 35 & 1.9034 \(\times\) 10\({}^{9}\) & 13,827 \\ \hline \hline \end{tabular}  
*Original value refers to the data before optimization, and *min(\(E\),\(S_{a}\))* represents the data before optimization.  
\end{table} 
Table 8: Comparison of variables and objectives before and after optimization. space, avoiding extreme combinations. This design reduces the number of experiments and minimizes the risk of failure due to extreme factor settings while ensuring model accuracy. In comparison to CCD's axial point design, BBD does not require additional axial points. This makes it more efficient, especially when there are many factors, as it significantly reduces the number of experiments needed. Therefore, BBD was chosen in this study to assess the impact of three variables on the objective functions. Based on the BBD principles, 13 experimental runs were carried out. The factor levels and experimental plan are shown in Tables 9 and 10. To evaluate the effect of each variable, regression models were analyzed using an analysis of variance (ANOVA). A \(p\)-value of less than 0.05 indicates that the variable significantly affects the objective function. The smaller the \(p\)-value, the greater the influence of the variable. If the \(p\)-value is large, the variable has a negligible effect on the objective. To clearly illustrate the different impacts of chain speed, traction speed, and drum speed on the objectives, an ANOVA was performed on the regression models of each variable. In this analysis, a \(p\)-value (\(p\)) less than 0.05 indicates that the parameter has a statistically significant effect on the objective. The smaller the \(p\)-value, the greater the significance of the variable's impact on the objective. Conversely, larger \(p\)-values suggest that the parameter has a negligible effect on the objective. From Table 11, it is evident that the traction speed of the mining machine and the scraper chain speed are key factors influencing the energy consumption of the scraper conveyor. These factors directly affect the coal flow rate, the dynamic load, and system efficiency. Firstly, the traction speed of the mining machine determines the rate and volume of coal entering the scraper conveyor. As the traction speed increases, more coal is transported per unit of time, causing the scraper conveyor to overcome greater resistance and resulting in higher energy consumption. Additionally, fluctuations in traction speed can lead to frequent starts, stops, and accelerations. During these phases, the motor must handle higher currents to overcome inertia and coal flow resistance, further increasing energy consumption. Secondly, the scraper chain speed plays a significant role in coal