# Optimization Design of Space Camera Enclosure Based on Bionics
## 2 Biomimetic Structural Design
### Structure Design
\begin{array}{l}find:x\in D\\ \mathit{obj}:minf_{1}(x),minf_{2}(x),\ldots,minf_{n}(x)\\ \mathit{s.t}:g_{1}(x)\leq 0,g_{2}(x)\leq 0,\ldots,g_{n}(x)\leq 0\end{array}  \right\} \tag{5}\]  
Among them, \(x\) represents the design variable; \(D\) represents the decision space; \(minf_{1}(x),minf_{2}(x),\ldots,minf_{n}(x)\) represents the optimization objective; \(f_{n}(x)\) represents the nth optimization objective, which can be related performance parameters such as weight, strength, stiffness, etc. \(g_{1}(x)\leq 0,g_{2}(x)\leq 0,\ldots,g_{n}(x)\leq 0\) represents the constraint condition. The Multi-Objective Genetic Algorithm (MOGA) is a widely used method for seeking global optimal solutions [29]. By employing genetic operators for fitness-based selection, recombination, and mutation, it is well-suited for handling multiple objectives and  
Figure 6: Response cloud maps of three sets of experiments to first-order natural frequency and maximum deformation. (**a**) The influence of substrate thickness and stiffener width on the first-order natural frequency. (**b**) The influence of stiffener height and substrate thickness on the first-order natural frequency. (**c**) The influence of substrate thickness and stiffener width on maximum deformation. (**d**) The influence of substrate thickness and stiffener height on maximum deformation. (**e**) The influence of stiffener width and stiffener height on the first-order natural frequency. (**f**) The influence of stiffener width and stiffener height on maximum deformation. constraints, offering high efficiency. Hence, this paper employs the MOGA for optimization [30,31]. Additionally, as indicated by the aforementioned response surface analysis, substrate thickness and stiffener height are crucial factors influencing the results; hence their importance is designated as \"higher\". The objectives and constraints are outlined in Table 3.  
After conducting 592 evaluations, the results converged, as illustrated in Figure 7. The different colored lines in the figure represent the optimization results of different independent variables including reinforcement width, height, and rib plate thickness when selecting different data combinations. Based on these results, three sets of candidate points were identified, as presented in Table 4. The selection of candidate points is determined through computer calculations based on optimization methods. It is necessary to set parameters such as the initial population size, the number of samples per iteration, the maximum allowable Pareto percentage, and the convergence stability percentage. Finally, the final result is obtained through calculation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Type** & **Parameter Name** & **Parameter Description** & **Set Value** \\ \hline \multirow{3}{*}{Constraint} & DS\_JTG & Stiffener height & 3–15 \\  & DS\_JTK & Stiffener width & 4–10 \\  & DS\_JBH & Substrate thickness & 2–5 \\ \hline \multirow{3}{*}{Target} & P4 & Box’s weight & minimize \\  & P5 & Maximum deformation & minimize \\  & P6 & first-order natural frequency & 200–300 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Goal and constraint settings. Figure 7: Evaluation results. Comparing the three candidate points, it is evident that candidate point 1 exhibits a smaller maximum deformation and a lower box weight. Although its first-order natural frequency is marginally lower than that of the other two schemes, it is still acceptable. Hence, this paper opts for candidate point 1 for the structural design of the spatial camera enclosure.