技術特征：

1.一種共形承載天線遠場功率方向圖的區(qū)間分析方法，其特征是：至少包括如下步驟：

1)確定防護結構中復合材料厚度的誤差區(qū)間；

實際厚度所處的區(qū)間為d∈[d^inf；d^sup]，角標inf和sup分別表示區(qū)間的上下邊界，d為材料實際厚度，d₀為理想設計厚度；

2)確定防護結構中復合材料參數的誤差區(qū)間：

實際相對介電常數的所在區(qū)間為ε′∈[ε′^inf；ε′^sup],磁損耗角的區(qū)間為tanδ∈[(tanδ)^inf；(tanδ)^sup],此時參數ε＝ε′(1-jtanδ)的區(qū)間為:

${\mathrm{\ϵ}}^{\mathrm{Re}}\⋐\[{\left({\mathrm{\ϵ}}^{\′}\right)}^{inf};{\left({\mathrm{\ϵ}}^{\′}\right)}^{sup}\]$

${\mathrm{\ϵ}}^{\mathrm{Im}}\⋐\[-{\left({\mathrm{\ϵ}}^{\′}\right)}^{sup}{\left(tan\mathrm{\δ}\right)}^{sup};-{\left({\mathrm{\ϵ}}^{\′}\right)}^{inf}{\left(tan\mathrm{\δ}\right)}^{inf}\]$

因為該參數為復數量，其實部和虛部的區(qū)間分別給出，用上角標Re和Im分別表示；

3)確定變量[Vd]區(qū)間的上下邊界；

4)引入變量：X＝cos(Vd),Y＝sin(Vd)，計算變量X和Y區(qū)間的上下邊界分別為：

(X^Re)^inf＝min{cos(Vd^Re)^inf·cosh(Vd^Im)^inf,cos(Vd^Re)^inf·cosh(Vd^Im)^sup,cos(Vd^Re)^sup·cosh(Vd^Im)^inf,cos(Vd^Re)^sup·cosh(Vd^Im)^sup}

(X^Re)^sup＝max{cos(Vd^Re)^inf·cosh(Vd^Im)^inf,cos(Vd^Re)^inf·cosh(Vd^Im)^sup,cos(Vd^Re)^sup·cosh(Vd^Im)^inf,cos(Vd^Re)^sup·cosh(Vd^Im)^sup}

(X^Im)^inf＝-max{sin(Vd^Re)^inf·sinh(Vd^Im)^inf,sin(Vd^Re)^inf·sinh(Vd^Im)^sup,sin(Vd^Re)^sup·sinh(Vd^Im)^inf,sin(Vd^Re)^sup·sinh(Vd^Im)^sup}

(X^Im)^sup＝-min{sin(Vd^Re)^inf·sinh(Vd^Im)^inf,sin(Vd^Re)^inf·sinh(Vd^Im)^sup,sin(Vd^Re)^sup·sinh(Vd^Im)^inf,sin(Vd^Re)^sup·sinh(Vd^Im)^sup}

(Y^Re)^inf＝min{sin(Vd^Re)^inf·cosh(Vd^Im)^inf,sin(Vd^Re)^inf·cosh(Vd^Im)^sup,sin(Vd^Re)^sup·cosh(Vd^Im)^inf,sin(Vd^Re)^sup·cosh(Vd^Im)^sup}

(Y^Re)^sup＝max{sin(Vd^Re)^inf·cosh(Vd^Im)^inf,sin(Vd^Re)^inf·cosh(Vd^Im)^sup,sin(Vd^Re)^sup·cosh(Vd^Im)^inf,sin(Vd^Re)^sup·cosh(Vd^Im)^sup}

(Y^Im)^inf＝min{cos(Vd^Re)^inf·sinh(Vd^Im)^inf,cos(Vd^Re)^inf·sinh(Vd^Im)^sup,cos(Vd^Re)^sup·sinh(Vd^Im)^inf,cos(Vd^Re)^sup·sinh(Vd^Im)^sup}

(Y^Im)^sup＝max{cos(Vd^Re)^inf·sinh(Vd^Im)^inf,cos(Vd^Re)^inf·sinh(Vd^Im)^sup,cos(Vd^Re)^sup·sinh(Vd^Im)^inf,cos(Vd^Re)^sup·sinh(Vd^Im)^sup}；

5)計算傳輸復數矩陣區(qū)間的上下邊界：其中

Aⁱⁿf^/sup＝C^inf/sup＝X^inf/sup

(B^Re)^inf＝min{(jZ₁)^Re·(Y^Re)^inf,(jZ₁)^Re·(Y^Re)^sup}-max{(jZ₁)^Im·(Y^Im)^inf,(jZ₁)^Im·(Y^Im)^sup}

(B^Re)^sup＝max{(jZ₁)^Re·(Y^Re)^inf,(jZ₁)^Re·(Y^Re)^sup}-min{(jZ₁)^Im·(Y^Im)^inf,(jZ₁)^Im·(Y^Im)^sup}

(B^Im)^inf＝min{(jZ₁)^Re·(Y^Im)^inf,(jZ₁)^Re·(Y^Im)^sup}+min{(jZ₁)^Im·(Y^Re)^inf,(jZ₁)^Im·(Y^Re)^sup}

(B^Im)^sup＝max{(jZ₁)^Re·(Y^Im)^inf,(jZ₁)^Re·(Y^Im)^sup}+max{(jZ₁)^Im·(Y^Re)^inf,(jZ₁)^Im·(Y^Re)^sup}

(C^Re)^inf＝min{(j/Z₁)^Re·(Y^Re)^inf,(j/Z₁)^Re·(Y^Re)^sup}-max{(j/Z₁)^Im·(Y^Im)^inf,(j/Z₁)^Im·(Y^Im)^sup}

(C^Re)^sup＝max{(j/Z₁)^Re·(Y^Re)^inf,(j/Z₁)^Re·(Y^Re)^sup}-min{(j/Z₁)^Im·(Y^Im)^inf,(j/Z₁)^Im·(Y^Im)^sup}

(C^Im)^inf＝min{(j/Z₁)^Re·(Y^Im)^inf,(j/Z₁)^Re·(Y^Im)^sup}+min{(j/Z₁)^Im·(Y^Re)^inf,(j/Z₁)^Im·(Y^Re)^sup}

(C^Im)^sup＝max{(j/Z₁)^Re·(Y^Im)^inf,(j/Z₁)^Re·(Y^Im)^sup}+max{(j/Z₁)^Im·(Y^Re)^inf,(j/Z₁)^Im·(Y^Re)^sup}；

6)引入變量T₁＝A+B/Z_∞+CZ_∞+D，并計算其區(qū)間的上下邊界，

(T₁^Re)^inf＝(A^Re)^inf+(B^Re)^inf/Z_∞+(C^Re)^inf·Z_∞+(D^Re)^inf

(T₁^Re)^sup＝(A^Re)^sup+(B^Re)^sup/Z_∞+(C^Re)^sup·Z_∞+(D^Re)^sup

(T₁^Im)^inf＝(A^Im)^inf+(B^Im)^inf/Z_∞+(C^Im)^inf·Z_∞+(D^Im)^inf

(T₁^Im)^sup＝(A^Im)^sup+(B^Im)^sup/Z_∞+(C^Im)^sup·Z_∞+(D^Im)^sup

其中，

7)計算變量區(qū)間的上下邊界；

${\left(T_1^{2\mathrm{Re}}\right)}^{inf}=\left\{\begin{array}{c}min\{{\left({\left(T_1^{\mathrm{Re}}\right)}^{inf}\right)}^2,{\left({\left(T_1^{\mathrm{Re}}\right)}^{sup}\right)}^2\}\\ 0\end{array}\right.,\begin{array}{c}0\∈\[X\]\\ 0\∉\[X\]\end{array}$

${\left(T_1^{2\mathrm{Re}}\right)}^{sup}=max\{{\left({\left(T_1^{\mathrm{Re}}\right)}^{inf}\right)}^2,{\left({\left(T_1^{\mathrm{Re}}\right)}^{sup}\right)}^2\}$

${\left(T_1^{2\mathrm{Im}}\right)}^{inf}=\left\{\begin{array}{c}min\{{\left({\left(T_1^{\mathrm{Im}}\right)}^{inf}\right)}^2,{\left({\left(T_1^{\mathrm{Im}}\right)}^{sup}\right)}^2\}\\ 0\end{array}\right.,\begin{array}{c}0\∈\[X\]\\ 0\∉\[X\]\end{array}$

${\left(T_1^{2\mathrm{Im}}\right)}^{sup}=max\{{\left({\left(T_1^{\mathrm{Im}}\right)}^{inf}\right)}^2,{\left({\left(T_1^{\mathrm{Im}}\right)}^{sup}\right)}^2\}$

8)計算透射系數T區(qū)間的上下邊界：

${\left(T^{\mathrm{Re}}\right)}^{inf}=2min\{\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}}\}$

${\left(T^{\mathrm{Re}}\right)}^{\sup }=2\max \{\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}}\}$

${\left(T^{\mathrm{Im}}\right)}^{inf}=2min\{\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}},\frac{{\left(T_1^{\mathrm{Re}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}}\}$

${\left(T^{\mathrm{Im}}\right)}^{\sup }=2min\{\frac{{\left(T_1^{\mathrm{Im}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Im}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{inf}+{\left(T_1^{2Im}\right)}^{sup}},\frac{{\left(T_1^{\mathrm{Im}}\right)}^{inf}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}},\frac{{\left(T_1^{\mathrm{Im}}\right)}^{sup}}{{\left(T_1^{2\mathrm{Re}}\right)}^{\sup }+{\left(T_1^{2Im}\right)}^{inf}}\};$

9)計算天線表面單個單元的遠場場值x分量F_xi的區(qū)間上下邊界，

10)計算天線表面全部單元場值x分量F_x的區(qū)間上下邊界：

${\left(F_x^{\mathrm{Re}}\right)}^{inf/sup}=\underset{i=1}{\overset{n}{\Σ}}({\mathrm{\ΔS}}_i\·{\left(F_{xi}^{\mathrm{Re}}\right)}^{\inf /sup})$

${\left(F_x^{\mathrm{Im}}\right)}^{inf/sup}=\underset{i=1}{\overset{n}{\Σ}}({\mathrm{\ΔS}}_i\·{\left(F_{xi}^{\mathrm{Im}}\right)}^{\inf /sup})$

n是天線表面離散單元的數量；

11)計算功率方向圖區(qū)間上下邊界

其上邊界為：

當時，下邊界為

當時，下邊界為

當且時，下邊界為

其余情況下，其下邊界為：

2.根據權利要求1所述的一種共形承載天線遠場功率方向圖的區(qū)間分析方法，其特征是：所述的步驟3)確定變量[Vd]區(qū)間的上下邊界包括：

當存在厚度誤差區(qū)間時，其邊界為：

(Vd^Re)^inf＝min((V^Re)d^inf,(V^Re)d^sup)

(Vd^Re)^sup＝max((V^Re)d^inf,(V^Re)d^sup)

(Vd^Im)^inf＝min((V^Im)d^inf,(V^Im)d^sup)

(Vd^Im)^sup＝max((V^Im)d^inf,(V^Im)d^sup)

當存在材料參數誤差區(qū)間時，其邊界為：

${\left({\mathrm{Vd}}^{\mathrm{Re}}\right)}^{inf}=\frac{2\mathrm{\π}}{\mathrm{\λ}}d{({\mathrm{\ϵ}}^{\′inf}-{\sin }^2\mathrm{\γ})}^{1/2}$

${\left({\mathrm{Vd}}^{\mathrm{Re}}\right)}^{sup}=\frac{2\mathrm{\π}}{\mathrm{\λ}}d{({\mathrm{\ϵ}}^{\′sup}-{\sin }^2\mathrm{\γ})}^{1/2}$

${\left({\mathrm{Vd}}^{Im}\right)}^{inf}=-\frac{2\mathrm{\π}}{\mathrm{\λ}}d{\left({\left(tan\mathrm{\δ}\right)}^{sup}\right)}^{1/2}$

${\left({\mathrm{Vd}}^{Im}\right)}^{sup}=-\frac{2\mathrm{\π}}{\mathrm{\λ}}d{\left({\left(tan\mathrm{\δ}\right)}^{inf}\right)}^{1/2}$

其中，ε＝ε′(1-jtanδ)，γ為罩體表面入射角，λ為波長，下角標H和V分別表示電磁波的水平和垂直極化分量。

3.根據權利要求1所述的一種共形承載天線遠場功率方向圖的區(qū)間分析，其特征是：所述的步驟9)計算天線表面單個單元的遠場場值x分量F_xi的區(qū)間上下邊界通過如下算法完成，

$\begin{array}{c}{\left(F_{xi}^{\mathrm{Re}}\right)}^{\inf }=\min \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Re}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Re}}\right)}^{\sup }\}-\max \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Im}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Im}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}\\ +\min \{{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Re}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Re}}\right)}^{\sup }\}-\max \{{\left(C_{xi}^{\′}\right)}^{Im}\·{\left(T_V^{Im}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{Im}\·{\left(T_V^{Im}\right)}^{\sup }\}\end{array}$

$\begin{array}{c}{\left(F_{xi}^{\mathrm{Re}}\right)}^{\inf }=\min \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Re}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Re}}\right)}^{\sup }\}-\min \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Im}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Im}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}\\ +\max \{{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Re}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Re}}\right)}^{\sup }\}-\min \{{\left(C_{xi}^{\′}\right)}^{Im}\·{\left(T_V^{\mathrm{Im}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Im}}\·{\left(T_V^{Im}\right)}^{\sup }\}\end{array}$

$\begin{array}{c}{\left(F_{xi}^{\mathrm{Im}}\right)}^{\inf }=\min \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}+\max \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}\\ +\min \{{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Im}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Im}}\right)}^{\sup }\}+\max \{{\left(C_{xi}^{\′}\right)}^{Im}\·{\left(T_V^{\mathrm{Im}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{Im}\right)}^{\sup }\}\end{array}$

$\begin{array}{c}{\left(F_{xi}^{\mathrm{Im}}\right)}^{\sup }=\min \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}+\max \{{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\inf },{\left(B_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_H^{\mathrm{Im}}\right)}^{\sup }\}\\ +\max \{{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Im}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Im}}\right)}^{\sup }\}+\max \{{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{\mathrm{Im}}\right)}^{\inf },{\left(C_{xi}^{\′}\right)}^{\mathrm{Re}}\·{\left(T_V^{Im}\right)}^{\sup }\}\end{array}$

其中，

$B_x=(A_{ex}^x{E}_t{t}_{bx}+A_{ey}^x{E}_t{t}_{by}+A_{ez}^x{E}_t{t}_{bz}+A_{hx}^x{H}_b{n}_{bx}+A_{hy}^x{H}_b{n}_{by}+A_{hz}^x{H}_b{n}_{bz})e^{{\mathrm{jk}}_0(xsin\mathrm{\θ}cos\mathrm{\φ}+ysin\mathrm{\θ}\sin \mathrm{\φ}+zcos\mathrm{\θ})}$

$C_x=(A_{ex}^x{E}_b{n}_{bx}+A_{ey}^x{E}_b{n}_{by}+A_{ez}^x{E}_b{n}_{bz}+A_{hx}^x{H}_t{t}_{bx}+A_{hy}^x{H}_t{t}_{by}+A_{hz}^x{H}_t{t}_{bz})e^{{\mathrm{jk}}_0(xsin\mathrm{\θ}cos\mathrm{\φ}+ysin\mathrm{\θ}\sin \mathrm{\φ}+zcos\mathrm{\θ})}$

$A_{ex}^x=-{\mathrm{cos\θn}}_{rz}-{\mathrm{sin\θsin\φn}}_{ry},A_{ey}^x={\mathrm{sin\θsin\φn}}_{rx},A_{ez}^x={\mathrm{cos\θn}}_{rx},$

$A_{hx}^x=\sqrt{{\mathrm{\μ}}_0/{\mathrm{\ϵ}}_0}({\mathrm{sin\θcos\θcos\φn}}_{ry}-{\sin }^2{\mathrm{\θsin\φcos\φn}}_{rz})$

$A_{hy}^x=\sqrt{{\mathrm{\μ}}_0/{\mathrm{\ϵ}}_0}(-{\sin }^2{\mathrm{\θsin}}^2{\mathrm{\φn}}_{rz}-{\cos }^2{\mathrm{\θn}}_{rz}-{\mathrm{sin\θcos\θcos\φn}}_{rx})$

$A_{hz}^x=\sqrt{{\mathrm{\μ}}_0/{\mathrm{\ϵ}}_0}({\sin }^2{\mathrm{\θsin\φcos\φn}}_{rx}+{\sin }^2{\mathrm{\θsin}}^2{\mathrm{\φn}}_{ry}+{\cos }^2{\mathrm{\θn}}_{ry})$

E_b和E_t為天線罩內表面電場和磁場在切平面上的分量，

$E_b=E_x^{in}{n}_{bx}+F_y^{in}{n}_{by}+E_z^{in}{n}_{bz}$

$E_t=E_x^{in}{t}_{bx}+E_y^{in}{t}_{by}+E_z^{in}{t}_{bz}$

$H_b=H_x^{in}{n}_{bx}+H_y^{in}{n}_{by}+H_z^{in}{n}_{bz}$

$H_t=H_x^{in}{t}_{bx}+H_y^{in}{t}_{by}+H_z^{in}{t}_{bz}$

天線罩內表面的電場Eⁱⁿ和磁場Hⁱⁿ為已知量，由天線基本尺寸參數可計算得到，其分量形式：

$E^{in}={\mathrm{iE}}_x^{in}+{\mathrm{jE}}_y^{in}+{\mathrm{kE}}_z^{in}$

$H^{in}={\mathrm{iH}}_x^{in}+{\mathrm{jH}}_y^{in}+{\mathrm{kH}}_z^{in}$

n_b和t_b分別標示天線罩外表面切平面上兩個互相垂直的分量，下標i表示天線表面離散后的第i個單元，ρ,φ,θ是球坐標下的半徑、方位角和俯仰角。