## 4 Structural Performance Optimization of Storage Tank
### Optimization Process of Structural Performance Parameters  
According to the analysis results in Section 3, the improved storage tank with a square column structure has less compressive stress, a greater volume utilization rate, a lighter weight, and more room for improvement; therefore, we select and optimize the improved storage tank with the square column structure. Owing to the precision limit of 3D metal printing, the precision fluctuation is in the range of \(-0.3\)-\(0.3\) mm during the process of printing. When the accuracy is limited, the fluctuation can become 0-0.2 mm. In order to prevent the optimized parameters from not printing as well as convenient optimization, we select \(d\) in the range of 0.5-1.5 mm, \(n_{x}\), \(n_{y}\), and \(n_{z}\) in the range of 11-21, \(T\) in the range of 0.3-0.8 mm, and \(D\) in the range of 2-7 mm. According to the ranges of factors affecting the performance of the storage tank structure, the parameter level table is established, as presented in Table 7. Without considering the interaction among various factors, the parameter level table of six factors and 11 levels is established. Eleven types \begin{table}
\begin{tabular}{c c c} \hline
**Structural Performance** & **Before Optimization** & **After Optimization** \\ \hline \(\sigma\) (Compression stress) & 416 MPa & \(\leq\)400 MPa \\ \(v\) (Volume utilization ratio) & 63.22\% & \(\geq\)94\% \\ \(m\) (Weight) & 600 g & \(\leq\)400 g \\ \hline \end{tabular}
\end{table} 
Table 6: Optimization target of structural performance of the improved storage tank with a square column structure. of storage tank models are built and inputted into ABAQUS FEA software. The parameter level table, calculation, and simulation results are listed in Table 8.  
Most of the experimental design methods usually use the variance and regression analysis to process the data. The test of the uniform design is relatively small. In order to not realize the analysis of variance, the regression analysis is the main method of uniform design. If the factor level is greater than the number of test factors, two regression analyses can be used. This paper can only use multiple linear regression analysis, so the \(\sigma\), \(v\), and \(m\) of the linear regression equations can be expressed as:  
\[\sigma = 3495.159-1052.56d+11.322n_{x}-32.522n_{y}-41.299n_{z}-986.523T-52.676D \tag{8}\] \[v = 120.027-13.227d-0.335n_{x}-0.272n_{y}-0.302n_{z}-1.719T+0.219D\] (9) \[m = -882.686+583.4421d+14.679n_{x}+12.058n_{y}+13.549n_{z}+350.334T-9.784D \tag{10}\]  
We want to know which factors influence the target values significantly. In order to determine the influence of each factor on the target value, we must analyze the statistic of the regression coefficient, that is, \(p\) value analysis. When the \(p\) value is lower than the significance level 0.05, indicating that the factors are related to the target value, a lower \(p\) value indicates a stronger effect on the target value. The analysis results are shown in Table 9.  
From Table 9, we can obtain the effect of the \(p\) values of six factors on \(\sigma\), \(v\), and \(m\). The orders of the six factors affecting \(\sigma\), \(v\), and \(m\) are \(d>T>n_{z}>n_{y}>D>n_{x}\), \(d>n_{x}>n_{z}>n_{y}>D>T\) and \(d>T>n_{x}>n_{z}>n_{y}>D\), respectively. This shows that \(d\) most strongly affects \(\sigma\), \(v\), and \(m\), and \(d\) is related to the three target values, having the strongest dependency between \(d\) and \(v\). Moreover, \(T\) also affects \(m\), and \(T\) is related to \(m\). Other factors have weaker effects and dependencies on these three target values.