## 3 Orthogonal Experimental Data Analysis
### Analysis of Variance  
An analysis of extreme variance provides the advantage of lower computational demands. However, it is unable to directly measure the changes resulting from different factor levels and experimental errors [19]. In contrast, an analysis of variance (ANOVA) employs mean square calculations for both variance and freedom degrees to partition the total sum of squares derived from experimental results into components attributable to factor and error deviation. This methodology constructs an F-ratio that can be compared to a critical value, thereby offering an intuitive insight into how various factors influence experimental results [20; 21]. Firstly, the total sum of squares represents deviations across all experimental results, i.e., the variance, and this is computed by aggregating the squared difference between \(\mathrm{k_{x}}\) and T, as demonstrated below:  
\[\mathrm{S_{total}}=\sum_{x=A}^{G}(\mathrm{k_{x}}-\mathrm{T})^{2} \tag{5}\]  
In Equation (5), the factor x ranges from A to G, with \(\mathrm{S_{total}}\) representing the total square sum of deviations across all the experimental results. For each factor x, its deviations can be calculated according to the following formula, which is defined by the square sum of differences between \(\mathrm{k_{x}}\) at all levels, specifically \(\mathrm{k_{xy}}\) and T, as follows:  
\[\mathrm{S_{x}}=3\cdot\sum_{y=1}^{3}\left(\mathrm{k_{xy}}-\mathrm{T}\right)^{2} \tag{6}\]  
In Equation (6), y corresponds to the values 1, 2, and 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameters** & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline \(\mathrm{K_{1}}\) & 213.56\% & 263.62\% & 197.98\% & 105.98\% & 226.47\% & 189.25\% & 329.18\% \\ \(\mathrm{K_{2}}\) & 243.51\% & 225.09\% & 224.78\% & 227.95\% & 213.33\% & 230.70\% & 216.61\% \\ \(\mathrm{K_{3}}\) & 217.80\% & 260.53\% & 252.11\% & 340.94\% & 235.07\% & 254.92\% & 129.08\% \\ \(\mathrm{k_{1}}\) & 35.59\% & 43.94\% & 33.00\% & 17.66\% & 37.74\% & 31.54\% & 54.86\% \\ \(\mathrm{k_{2}}\) & 40.58\% & 37.52\% & 37.46\% & 37.99\% & 35.56\% & 38.45\% & 36.10\% \\ \(\mathrm{k_{3}}\) & 36.30\% & 43.42\% & 42.02\% & 56.82\% & 39.18\% & 42.49\% & 21.51\% \\ \(\mathrm{T_{1}}\) & \(-\)1.90\% & 6.44\% & \(-\)4.50\% & \(-\)19.83\% & 0.25\% & \(-\)5.95\% & 17.37\% \\ \(\mathrm{T_{2}}\) & 3.09\% & 0.02\% & \(-\)0.03\% & 0.50\% & \(-\)1.94\% & 0.96\% & \(-\)1.39\% \\ \(\mathrm{T_{3}}\) & \(-\)1.19\% & 5.93\% & 4.53\% & 19.33\% & 1.69\% & 4.99\% & \(-\)15.98\% \\ \(\mathrm{R_{x}}\) & 4.99\% & 6.42\% & 9.02\% & 39.16\% & 3.62\% & 10.94\% & 33.35\% \\ Priority & & & & & D \textgreater{} G \textgreater{} F \textgreater{} C \textgreater{} B \textgreater{} A \textgreater{} E & & & \\ Optimal level & A2 & B1 & C3 & D3 & E3 & F3 & G1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Table of extreme variance data. On calculating all the factor variances, the sum of the squared error deviations is expressed as follows:  
\[S_{\text{error}}=S_{\text{total}}-\sum_{x=A}^{G}S_{x} \tag{7}\]  
In Equation (7), the factor x is taken from A to G.  
Upon calculating the variance of each factor and error, the total degree of freedom is further calculated as follows:  
\[f_{\text{total}}=m\cdot n-1 \tag{8}\]  
In Equation (8), m is the number of levels of each factor, which is taken as 3, and n is the number of orthogonal experiments, which is taken as 18.