## 3 CapsNet-GA Method for Electromagnetic Characteristic Fitting
### Determine the Constraint Conditions  
Regarding the influence of different structures on the RCS distribution characteristics, the electromagnetic parameter fitting constraint conditions are established as follows:  
1. Constraint on the right-angle side length of the large-angle reflector: \[h_{1}(x)=a-a_{\mathrm{max}}\leq 0\] (9) \[h_{2}(x)=a_{\mathrm{min}}-a\leq 0\] (10) where \(a_{\mathrm{min}}\) and \(a_{\mathrm{max}}\) are the minimum and maximum values of the right-angle side length of the large-angle reflector, respectively, and the unit is mm.
2. Constraint on the right-angle side length of the small-angle reflector: \[h_{3}(x)=b-b_{\mathrm{max}}\leq 0\] (11) \[h_{4}(x)=b_{\mathrm{min}}-b\leq 0\] (12)  
Figure 6: Schematic diagram of electromagnetic characteristic parameter optimization scheme.  
where \(b_{\rm min}\) and \(b_{\rm max}\) are the minimum and maximum values of the right-angle side length of the small-angle reflector, respectively, and the unit is mm.
3. Constraint on the diameter of the Luneberg sphere: \[h_{5}(x)=c-c_{\rm max}\leq 0\] (13) \[h_{6}(x)=c_{\rm min}-c\leq 0\] (14) where \(c_{\rm min}\) and \(c_{\rm max}\) are the minimum and maximum values of the relative position of the Luneberg sphere, respectively, and the unit is mm.
4. Constraint on the relative position of the Luneberg sphere: \[h_{7}(x)=d_{1}-d_{1\rm max}\leq 0\] (15) \[h_{8}(x)=d_{1\rm min}-d_{1}\leq 0\] (16) where \(d_{1\rm min}\) and \(d_{1\rm max}\) are the minimum and maximum values of the relative position of the Luneberg sphere, respectively, and the unit is mm.
5. Constraint on the relative position of the small-angle reflector: \[h_{9}(x)=d_{2}-d_{2\rm max}\leq 0\] (17) \[h_{10}(x)=d_{2\rm min}-d_{2}\leq 0\] (18) where \(d_{2\rm min}\) and \(d_{2\rm max}\) are the minimum and maximum values of the relative position of the small-angle reflector, respectively, and the unit is mm.  
Then, determine the value ranges of the optimization parameters \(a\), \(b\), \(c\), \(d_{1}\), and \(d_{2}\). Take the right-angle side length of the large-angle reflector successively from 580 mm to 620 mm, with an interval of 5 mm; take the right-angle side length of the small-angle reflector successively from 240 mm to 360 mm, with an interval of 20 mm; take the radius of the Luneberg sphere successively from 20 mm to 60 mm, with an interval of 5 mm; the relative position distance \(d_{1}\) of the Luneberg sphere is taken successively from 0 to 100 mm, with an interval of 25 mm; the relative position distance \(d_{2}\) of the small-angle reflector is taken successively from 0 to 20 mm, with an interval of 5 mm.  
Through the establishment of the above objective function, the selection of design variables, and the determination of constraint conditions, the optimization mathematical model of the nose simulation combination can be obtained according to (8) as follows:  
\[\left\{\begin{array}{l}X=\left[a,b,c,d_{1},d_{2}\right]^{T}\\ \min(a,b,c,d_{1},d_{2})=\left|x_{1}-x_{1}{}^{\prime}\right|+\left|x_{2}-x_{2} {}^{\prime}\right|+\ldots+\left|x_{m}-x_{m}{}^{\prime}\right|\\ \\ s.t\left\{\begin{array}{l}a_{\rm min}\leq a\leq a_{\rm max},580\leq a\leq 6 20\\ b_{\rm min}\leq b\leq b_{\rm max},240\leq b\leq 360\\ c_{\rm min}\leq c\leq c_{\rm max},20\leq c\leq 60\\ d_{1\rm min}\leq d_{1}\leq d_{1\rm max},0\leq d_{1}\leq 100\\ d_{2\rm min}\leq d_{2}\leq d_{2\rm max},0\leq d_{2}\leq 100\end{array}\right.\end{array}\right. \tag{19}\]