## 3 Results and Discussion
### Multi-Factor Optimization Experiment Based on Response Surface Method  
Based on the above research, the effects of process parameters A (molding pressure, MPa), B (mixing water, %) and C (particle size of aluminum ash, mesh) on Y in the process of preparing non-fired bricks with aluminum dress were investigated by using Box-Behnken response surface scheme and Y (compressive strength, MPa) as the response value. The specific ranges of the aluminum dress particle size are 50-100 mesh, 100-150 mesh and 150-200 mesh. The experimental factors and level encoding values of the response surface method are shown in Table 2.  
The specific test plan and test data are shown in Table 3.  
Design Expert (Version number: 11, Stat-Ease in Minneapolis) software is used to process the data in Table 3. The fitted multivariate quadratic regression equation is as follows:  
\[\text{Y}=22.63+2.07\text{A}+0.7087\text{B}-0.9225\text{C}+0.4925\text{AB}-0. 0850\text{AC}-0.6000\text{BC}-0.4621\text{A}^{2}-1.18\text{B}^{2}-1.96\text{C} ^{2} \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Level**} \\ \cline{2-4}
**Element** & \(-\)**1** & **0** & **1** \\ \hline A (forming pressure/MPa) & 12 & 15 & 18 \\ B (mixing-water amount/\%) & 12 & 14 & 16 \\ C (aluminum dress particle size/mesh) & 50 & 100 & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Factors and level encoding of response surface development experiment. Figure 12: XRD analysis results of aluminum dress non-fired bricks with different aluminum dress particle sizes. Figure 13: SEM images of non-fired bricks with different aluminum dress particle sizes: (**a**) 100–150 mesh; (**b**) more than 250 mesh. \[ \begin{split}\text{Y}=-60.15833+1.13736\text{A}+7.99771\text{B}+0.230817 \text{C}+0.082083\text{AB}-0.000567\text{AC}-0.006000\text{BC}-0.051343\text{A} ^{2}\\ -0.295521\text{B}^{2}-0.000784\text{C}^{2}\end{split}  \tag{3}\]  
The variance analysis of the quadratic regression equation is shown in Table 4. It can be seen from Table 4 that the model is significant (\(p<0.05\)), while the lack of fit is not significant (\(p>0.05\)). It can be seen from Table 5 that the adjusted R\({}^{2}\) value is 0.9696, the predicted R\({}^{2}\) value is 0.8544 and the difference is less than 0.2. Therefore, the model is able to accurately predict the experimental results. The model can be used for analysis and optimization of process parameters. In addition, it can be concluded from Table 4 that A, B, C, AB, BC, B\({}^{2}\) and C\({}^{2}\) are the significant terms of the model, while AC and A\({}^{2}\) are insignificant terms. The size of the F value can reflect the degree of influence of the corresponding factors on the response value (Y). Therefore, the influence of different process parameters on the compressive strength of aluminum dress non-fired bricks is as follows: forming pressure > aluminum dress particle size > mixing-water amount. \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 & 65.84 & 9 & 7.32 & 50.60 & 0.0002 & significant \\ A & 34.24 & 1 & 34.24 & 236.80 & \textless{}0.0001 & significant \\ B & 4.02 & 1 & 4.02 & 27.79 & 0.0033 & significant \\ C & 6.81 & 1 & 6.81 & 47.09 & 0.0010 & significant \\ AB & 0.9702 & 1 & 0.9702 & 6.71 & 0.0488 & significant \\ AC & 0.0289 & 1 & 0.0289 & 0.1999 & 0.6735 & not significant \\ BC & 1.44 & 1 & 1.44 & 9.96 & 0.0252 & significant \\ A\({}^{2}\) & 0.7884 & 1 & 0.7884 & 5.45 & 0.0668 & not significant \\ B\({}^{2}\) & 5.16 & 1 & 5.16 & 35.68 & 0.0019 & significant \\ C\({}^{2}\) & 14.18 & 1 & 14.18 & 98.06 & 0.0002 & significant \\ Residual & 0.7229 & 5 & 0.1446 & none & none & none \\ Lack of fit & 0.5867 & 3 & 0.1956 & 2.87 & 0.2690 & none \\ Pure Error & 0.1363 & 2 & 0.0681 & none & none & none \\ Cor Total & 66.57 & 14 & none & none & none & none \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of variance (ANOVA) for quadratic model.