## 5 Results
### Prediction Model Establishment  
#### 5.2.1 Result and Analysis of DCCD-RSM  
DCCD enables rapid identification of the optimal experimental range even without prior experience. The development and application of this method lay the foundation for faster process optimization, conserving resources, and avoiding frequent, time-consuming trial-and-error experiments typically needed to achieve the desired experimental range. This method addresses the practical challenges of selecting experimental ranges in aluminum alloy processing effectively.  
Based on the results collected from DCCD, parameter ranges were selected as shown in Table 2, and three Discrete \(N\) (400, 600, 800) were selected for testing to conduct response analysis and determine the relationship between various factors and surface roughness. Through this designed DCCD-RSM, the model of surface roughness was developed in Equation (12):  
\[\begin{split} y&=3.2141-1.8614\times 10^{-1}F+9.0322 \times 10^{-2}v_{f}-7.7827\times 10^{-4}v_{s}\\ &\quad+7.4796\times 10^{-4}N+2.1104\times 10^{-2}F^{2}+2.7717\times 10^{- 5}FN\\ &\quad-8.6737\times 10^{-6}v_{f}v_{s}-1.5783\times 10^{-5}v_{f}N+5.572 0\times 10^{-8}v_{s}^{2}\\ &\quad-2.6393\times 10^{-8}v_{s}N-4.7448\times 10^{-7}N^{2}\end{split} \tag{12}\]  
According to the fitting results above, the response surface plots and the contour plots of the grinding process are shown in Figure 6. The strategy used for the remaining two variables is to fix them at their midpoint values. Figure 6a,d depict the response surface and contour plots of \(F\) and \(v_{f}\) on surface roughness. Surface roughness increases with increasing \(v_{f}\) and initially decreases with increasing \(F\) before increasing again. There is a minimum value of surface roughness when \(F\) is around 3.5 N at a given \(v_{f}\). Figure 6b,e illustrate the response surface and contour plots of \(v_{s}\) and \(F\). Surface roughness decreases initially with both \(v_{s}\) and \(F\) before increasing again. When \(F\) is around 3.5 N, and \(v_{s}\) is approximately 7700 rpm, the surface roughness reaches a minimum. Figure 6c,f present the response surface and contour plots of \(v_{s}\) and \(v_{f}\). Surface roughness increases with increasing \(v_{f}\). When \(v_{s}\) is around 5000 rpm, there is a significant reduction in surface roughness, while the reduction is less pronounced when \(v_{s}\) is around 9000 rpm. A minimum value of surface roughness is observed when \(v_{s}\) is approximately 7400 rpm at a given \(v_{f}\).  
\begin{table}
\begin{tabular}{l l} \hline
**Feature Type** & **Selected Features** \\ \hline Constant Term & 1 \\ Linear Terms & \(F\), \(v_{f}\), \(v_{s}\), \(N\) \\ Quadratic Terms & \(F^{2}\), \(v_{s}^{2}\), \(N^{2}\) \\ Interaction Terms & \(F\cdot N\), \(v_{f}\cdot v_{s}\), \(v_{f}\cdot N\), \(v_{s}\cdot N\) \\ \hline \end{tabular}
\end{table}
Table 1: Selected features after selection.  
\begin{table}
\begin{tabular}{l c c c} \hline
**Factor** & **Coded Symbol** & **Low Level** & **High Level** \\ \hline Grinding force (N) & \(F\) & 2.5 & 5 \\ Feed rate (mm/s) & \(v_{f}\) & 5 & 10 \\ Wheel speed (rpm) & \(v_{s}\) & 6000 & 8000 \\ Grit size & \(N\) & \(\star\) & \(\star\) \\ \hline \end{tabular} \({}^{a\star\star\star\star}\) means the discrete variable N has no high or low levels here  
\end{table}
Table 2: Parameter symbols and levels of DCCD.