# Optimization Design of Space Camera Enclosure Based on Bionics
## 2 Biomimetic Structural Design
### Structure Design
Optimization of Structural Parameters for Biomimetic Stiffened Plates Based on Response Surface Methodology  
After completing the initial design of the stiffened plate structure, it is necessary to further explore the relationship between factors such as base plate thickness, stiffener height, and stiffener width, as well as the maximum deformation, total weight, and first-order natural frequency of the box, in order to find the optimal design parameters for achieving a biomimetic structural design with high stiffness, high lightweight, and high fundamental frequency. To achieve this objective, this article proposes the use of the response surface analysis method. Response surface analysis, also referred to as response surface methodology (RSM) [25; 26], is a statistical method that primarily employs multivariate quadratic regression equations to model the relationship between independent and dependent variables. It aims to identify the optimal parameters while analyzing the regression equation, making it highly suitable for solving multivariate optimization problems [27; 28]. Response optimization analysis is a method used to optimize complex systems, especially in multi-variable scenarios. It involves establishing a mathematical model that describes the relationship between design variables and response variables, and then finding the optimal design parameters based on this model. The general process is as follows: First, define the design variables such as Stiffener Height, Stiffener Width, and Substrate Thickness. Second, define the response variables such as First-order natural frequency and Maximum deformation. Third, design experiments using the intermediate composite design method provided by the software. Fourth, the computer automatically builds the response surface. Response surface analysis first requires deriving the regression Equation (3). The observed value \(y\) can be expressed as:  
\[y=f(x_{1},x_{2},\dots,x_{n})+\varepsilon \tag{3}\]  
Among them, \(f(x_{1},x_{2},\dots,x_{n})\) represents the function expression of the independent variable \(x_{1},x_{2},\dots,x_{n}\), while \(\varepsilon\) denotes the error term. Figure 5: Parameter meaning representation. Then, by optimizing the independent variables and selecting reasonable values, the optimal value can be obtained. \[\hat{g}=f(x_{1},x_{2},\ldots,x_{n}) \tag{4}\]  
To explore the relationship between the aforementioned structural parameters and the weight, first-order natural frequency, and maximum deformation of the box, as well as to determine the optimal structural parameters, the experimental content is designed as shown in Table 2. Each experiment evaluated 100 sets of data points, with the selection of data points automatically completed by the computer. Each set of data points contained information about the variables. The response cloud map generated by the aforementioned experiment is illustrated in Figure 6.  
The comprehensive analysis indicates that, despite the interaction among the three variables, the substrate thickness and stiffener height exert the greatest influence on the two response values. Additionally, it is straightforward to comprehend that these three variables are positively correlated with the box's weight, hence they were excluded from the response surface analysis. Simultaneously, for the response requirements of maximizing the first-order natural frequency, minimizing the maximum deformation, and reducing the box weight, optimal solutions are available for these three variables. \begin{table}
\begin{tabular}{c c c} \hline \hline
\begin{tabular}{c} First-order natural \\ frequency \\ Maximum deformation \\ \end{tabular} } \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental design. Figure 6: _Cont._  
Consequently, this is a typical multi-objective optimization problem, aiming to identify an optimal solution that strikes a balance between multiple objectives within an optimization framework. The model for multi-objective optimization problems is typically represented as:  
\[\left\{