## 3 Orthogonal Experimental Data Analysis
### Analysis of Extreme Variance  
The analysis of extreme variance, encompassing all factors at each level, examines the difference between the maximum and minimum values derived from the orthogonal experimental results. This methodology evaluates the influence of various factors across all levels and identifies the optimal combination of multiple factors, thereby aiding in the formulation of an effective blowing strategy along with relevant data support [16].  
Initially, it is crucial to compute the sum of the experimental results for each factor Kx across all levels, as demonstrated below:  
\[\text{K}_{\text{x}}=\sum_{y=1}^{3}\text{L}_{\text{xy}} \tag{1}\]  
In Equation (1), let x denote the factor defined as A-G, while y represents the level, classified within the range of 1-3.  
Consequently, the ratio Kx to the total number of levels is calculated as kx, as demonstrated below:  
\[\text{k}_{\text{x}}=\text{K}_{\text{x}}/3 \tag{2}\]  
To deduct the mean of all orthogonal experiment results T from kx leads to the offset:  
\[\text{T}_{\text{x}}\text{=k}_{\text{x}}\text{-T} \tag{3}\]  
In Equation (3), Tx denotes the average of the total results obtained from the orthogonal experiments while signifying the offset between kx and T.  
For any given factor x, the extreme variance is determined by calculating the difference between its maximum and minimum value Tx, as illustrated below:  
\[\text{R}_{\text{x}}\text{= maxT}_{\text{x}}\text{-minT}_{\text{x}} \tag{4}\]  
In Equation (4), Rx denotes the extreme variance related to any factor x.  
After determining the extreme variance Rx for each factor, it becomes feasible to rank these factors according to their effect on the experimental results. A higher value signifies a more pronounced effect. Furthermore, optimal combinations of all factors across various levels can also be obtained. The data comprising 18 groups of the extreme variance data from orthogonal experiments are summarized in Table 4.  
In Table 4, the optimal combination of various factors has a significant impact on the drainage percentage of the ballast tank, as follows:  
* Firstly, factor D3 contributed 39.16%. A duration of 15 (s) corresponded to the maximum blowing, ensuring that gas was introduced into the ballast tank to its fullest capacity;
* Secondly, factor G1 accounted for 33.35%. A back pressure of 0.2 (MPa) represented the minimum threshold required to optimize the blowing efficiency [18];
* Thirdly, factor F3 contributed 10.94%, with the maximum blowing pressure from the cylinder group set at 20 (MPa), which further enhanced blowing effectiveness [3];
* Fourthly, factor C3 contributed 9.02%. A flowing area of 200 (mm), corresponding to the sea valve's aperture, could maximize the water discharge volume per unit time [19];* Fifthly, factor B1 constituted 6.42%, with a gas supply pipeline length limited to just 10 (m); this ensured sufficient gas mass flowed into the ballast tank within each time interval [17];
* Sixthly, factor A2 contributed 4.99%, where a volume of 500 (L) established an optimal balance between gas and water interactions in the ballast tank and facilitated adequate high-pressure gas for an improved blowing effect [3];
* Lastly, factor E3 accounted for a contribution of 3.62%, wherein the inner diameter of the gas supply pipe measuring 10 (mm) ensured maximum gas mass flow into the ballast tank during each period.  
Although the extreme variance analysis highlights contributions from these multi-factors toward drainage performance, it did not effectively establish correlations between the individual factors and the data.