## 3 Orthogonal Experimental Data Analysis
### Analysis of Variance
For each factor, the corresponding degree of freedom belongs to the levels minus one and is calculated as follows:  
\[f_{x}=m-1 \tag{9}\]  
The degree of freedom for the error can be determined by subtracting the total of all factor degrees from \(f_{\text{total}}\) as freedom, as shown below:  
\[f_{\text{error}}=f_{\text{total}}-\sum_{x=A}^{G}f_{x} \tag{10}\]  
In Equation (10), the factor x ranges from A to G.  
The mean square is further calculated by dividing the factor variance \(S_{x}\) and error variance \(S_{\text{error}}\) by their respective degrees of freedom, which is determined as follows:  
\[\overline{S_{x}}=S_{x}/f_{x},\overline{S_{\text{error}}}=S_{\text{error}}/f_ {\text{error}} \tag{11}\]  
The F-ratio of each factor is further calculated, which reflects the extent to which different factor levels contribute to the experimental results at a certain confidence level, removing the interference of errors. Taking factor x as an example, its F-ratio is calculated as follows:  
\[F_{x}=\overline{S_{x}}/\overline{S_{\text{error}}} \tag{12}\]  
The F-ratio at a confidence level of \(\alpha=0.05\) was designated as the critical value. If \(F_{x}\) exceeded this critical value, the factor was deemed to have a significant effect on the experimental results; otherwise, it was considered to have an insignificant effect. Table 5 was generated by calculating all data groups along with the corresponding F critical value. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Parameters** & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline K\({}_{1}\) & 213.56\% & 263.62\% & 197.98\% & 105.98\% & 226.47\% & 189.25\% & 329.18\% \\ K\({}_{2}\) & 243.51\% & 225.09\% & 224.78\% & 227.95\% & 213.33\% & 230.70\% & 216.61\% \\ K\({}_{3}\) & 217.80\% & 260.53\% & 252.11\% & 340.94\% & 235.07\% & 254.92\% & 129.08\% \\ k\({}_{1}\) & 35.59\% & 43.94\% & 33.00\% & 17.66\% & 37.74\% & 31.54\% & 54.86\% \\ k\({}_{2}\) & 40.58\% & 37.52\% & 37.46\% & 37.99\% & 35.56\% & 38.45\% & 36.10\% \\ k\({}_{3}\) & 36.30\% & 43.42\% & 42.02\% & 56.82\% & 39.18\% & 42.49\% & 21.51\% \\ T\({}_{1}\) & \(-1.90\%\) & 6.44\% & \(-4.50\%\) & \(-19.83\%\) & 0.25\% & \(-5.95\%\) & 17.37\% \\ T\({}_{2}\) & 3.09\% & 0.02\% & \(-0.03\%\) & 0.50\% & \(-1.94\%\) & 0.96\% & \(-1.39\%\) \\ T\({}_{3}\) & \(-1.19\%\) & 5.93\% & 4.53\% & 19.33\% & 1.69\% & 4.99\% & \(-15.98\%\) \\ S\({}_{x}\) & 0.11\% & 1.25\% & 0.61\% & 11.80\% & 0.00\% & 1.06\% & 9.05\% \\ f\({}_{x}\) & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\ \(\overline{S_{x}}\) & 0.05\% & 0.62\% & 0.30\% & 5.90\% & 0.00\% & 0.53\% & 4.53\% \\ F-ratio & 0.03 & 0.35 & 0.17 & 3.27 & 0.00 & 0.29 & 2.51 \\ Critical value, & & & & & & & \\ \(\alpha=0.05\) & 3.24 & 3.24 & 3.24 & 3.24 & 3.24 & 3.24 & 3.24 \\ Effect & insignificant & insignificant & insignificant & significant & insignificant & insignificant & insignificant \\ \hline \end{tabular}
\end{table} 
Table 5: Table of variance data. It can be concluded that the blowing duration at a value of 3.27 and sea tank back pressure at a value of 2.51, as well as the gas blowing pressure of the cylinder group at 0.29, exert significant influences on the blowing effect, thereby reaffirming the conclusion drawn in Section 3.1 that the optimal blowing performance is achieved when the highest gas pressure and minimal back pressure flows into the ballast tank over an extended time period [18,22]. While variance analysis could illustrate each factor's sensitivity to the experimental results, further clarification of the specific correlation between the individual factors and results remains necessary.