## 3 Results
### Storage Tank Pressure Optimization
\begin{tabular}{c} **W\({}_{\text{Comp}}\)** \\ **[kg]** \\ \end{tabular}  \\ \hline
1 & 250 & 205 & 130 & 218 & 9.46 & 0.1938 & 46.77 & 19.52 & 14.25 \\
2 & 250 & 185 & 110 & 214 & 9.43 & 0.1946 & 46.61 & 19.49 & 14.22 \\
3 & 250 & 165 & 90 & 221 & 9.41 & 0  
Table 7 presents the calculated S/N ratios of control factors at the levels determined through the Taguchi analysis. The difference between the highest and lowest S/N values for each factor, known as the _Delta_ value, indicates the factor's influence on the output parameter--a higher _Delta_ signifies a greater impact. As shown in the table, the _Delta_ values for \(n_{Vehicle}\) are very close. The \(\mathrm{P_{low}}\) factor has the highest influence (_Delta_ = 0.1984), followed by \(\mathrm{P_{medium}}\) (_Delta_ = 0.1982) and \(\mathrm{P_{high}}\) (_Delta_ = 0.1871). Over a 24 h period, \(\mathrm{P_{low}}\) and \(\mathrm{P_{medium}}\) pressures have a greater effect on the number of vehicles filled than \(\mathrm{P_{high}}\) pressure. The ranking in the table reflects the relative importance of each control factor in determining the number of vehicles filled within this period. The weighting coefficient for \(n_{Vehicle}\) is \(\mathrm{w}=48.82\%\). The impact of control factors on the average filled gas mass (\(\mathrm{m_{Average}}\)) was also analyzed using the Taguchi method, with results shown under the \(\mathrm{m_{Average}}\) row in Table 7. Here, the Delta values are even smaller, indicating a lower influence. As a result, the weighting factor for \(\mathrm{m_{average}}\) in the multi-objective optimization process is only 6.85%. Figure 12: (**a**) S/N ratios for \(n_{Vehicle}\) at the specified control factor levels during storage pressure optimization; (**b**) S/N ratios of control factors for the average gas mass (\(\mathrm{m_{Average}}\)) during storage pressure optimization. Figure 13: S/N ratios of control factors for the work performed by the compressor per unit mass filled (\(\mathrm{W_{Comp}}\)) at specified control factor levels during storage pressure optimization. Another design objective is minimizing the work performed by the compressor per unit mass filled (W\({}_{\text{Comp}}\)). The Taguchi analysis confirmed that P\({}_{\text{high}}\) pressure is the most significant factor in reducing W\({}_{\text{Comp}}\), as expected. The influence of W\({}_{\text{Comp}}\) on the objective function (weighting factor _w_) is 44.33%. Since the output parameters examined separately indicated different influential factors, they were integrated based on their respective weights and combined into a single objective function. The Taguchi-gray relational analysis method was employed to generate and analyze this function. The weighting coefficients used in the multi-objective optimization process were derived from the normalized Delta values presented in Table 7. These values represent the sensitivity of each output parameter to the control factors and were used to objectively assign relative importance. Although the entropy weight method was not explicitly applied, this approach serves a similar function by quantifying the information contribution of each response variable in a consistent, data driven manner. In this approach, the three output parameters listed under the \"Results\" column, calculated according to the orthogonal array in Table 6, are first normalized using Equations (7) and (8). The normalized results are then presented in Table 8. Next, these values are applied to Equations (9)-(12) to compute the gray relational coefficient (GRC) for each output parameter. Finally, the gray relational grade (GRG) is determined using Equation (13).