CN106469850B - A kind of Thickness Design Method of antenna house - Google Patents

Abstract

The invention relates to a thickness design method of a radome, comprising the following steps: (1) discretizing the thickness of the radome according to the height direction of the cover body; (3) Calculate the statistical value according to the thickness value at discrete points, (4) Calculate the far field of the antenna, and extract the electrical performance indicators such as gain G ₁ and main beam position B ₁ from it; (5) ) using transmission line theory to calculate the transmission coefficient of the cover , (6) Calculate the far-field F′(θ, φ) of the antenna system with the cover, draw the far-field pattern, (7) Establish the optimal design model; (8) Determine the electrical performance index and thickness of the radome obtained after optimization Whether the distribution meets the preset requirements. It improves the electrical performance index of the radome.

Description

A kind of thickness design method of radome

technical field

The invention belongs to the technical field of radar antennas, in particular to a method for designing the thickness of a radome, which can be used for structural design of an aircraft radome.

Background technique

A radome is a wave-transparent shell that protects an antenna from the natural environment, a covering made of natural or man-made dielectric materials, or a specially shaped electromagnetic window made of a dielectric shell supported by a truss. A well-designed radome, in addition to its functions of protection, conductivity, reliability, concealment and decoration, can also prolong the service life of each part of the entire system, reduce life costs and operating costs, simplify design, and reduce maintenance costs. , Ensure the accuracy of the antenna surface and position, and create a good working environment for the antenna operator. However, the radome also affects the electromagnetic radiation of the ideal antenna, which reduces the electrical performance of the ideal antenna.

In order to meet the aerodynamic requirements of the aircraft radome, a streamlined cover is often used, which causes the radome to have too much influence on the electrical performance of the internal antenna. It is necessary to optimize the design of the radome to improve its electrical performance. The traditional equal-thickness optimization technology can improve the electrical performance of the radome to a limited extent. By discretizing the thickness of the radome along the height direction of the cover, and optimizing the design of variable thickness, the electrical performance of the streamlined cover can be greatly improved.

Fan Xueping used genetic algorithm to optimize the aiming error of two-dimensional phased array radome in his 2011 paper "Optimization of Two-dimensional Radome Aiming Error Based on Genetic Algorithm". It is divided into different areas, the wall thickness value of each area is used as the optimization variable, and the maximum aiming error in the antenna scanning process is used as the optimization target, the optimal wall thickness distribution is solved by using the genetic algorithm, which effectively reduces the radome. aiming error. The disadvantage of this method is that it does not consider the constraint of the wall thickness distribution, which leads to the drastic change of the wall thickness of the obtained radome, which is difficult to process and realize, and also does not consider the gain loss of the radome, an important electrical performance index.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for designing the thickness of the radome, which can improve the electrical performance index of the radome and reduce the manufacturing difficulty of the radome in view of the above-mentioned deficiencies of the prior art.

In order to achieve the above purpose, the technical solution of the present invention is: a thickness design method of a radome, comprising the following steps:

(1) Discretize the thickness of the radome according to the height direction of the cover;

Along the height of the cover body, a coordinate system O-xyz is established with the center of the bottom surface of the radome as the origin and the bottom surface as the xy plane. The height of the cover body is along the z direction, and 10 discrete points are uniformly selected along this direction, and their coordinates are marked as z ₁ ,z ₂ ,…,z ₁₀ ;

(2) According to the requirements of the radome's structural performance and electrical performance, determine the value range of the thickness value, and assign the initial value to the thickness at discrete points;

(3) Calculate the statistical value according to the thickness value at the discrete point, including the variance, the maximum slope and the variance of the slope.

(4) Calculate the far field of the antenna, and extract the electrical performance indicators such as gain G ₁ and main beam position B ₁ from it.

(5) According to the structural parameters and material parameters of the radome, use the transmission line theory to calculate the transmission coefficient of the cover body And according to the known antenna aperture field E(x,y), calculate the aperture field after passing through the radome:

(6) According to the aperture field E'(x, y) after passing through the radome, calculate the far field F'(θ, φ) of the antenna system with the cover, draw the far field pattern, and use the far field pattern from the far field pattern. The electrical performance indicators such as gain G ₂ and main beam position B ₂ are extracted, and then the gain loss TL and aiming error BSE caused by the radome are determined.

(7) Take the thickness value at the discrete point in step (1) as the design variable, take the variance of the thickness, the maximum slope, the variance of the slope in step (3) and the electrical performance index in step (6) as the design target, An optimization design model is established, and the particle swarm optimization algorithm is used to solve the model to obtain the thickness distribution of the radome;

(8) Judging whether the electrical performance index and thickness distribution of the radome obtained after optimization meet the preset requirements, if so, the radome structural design scheme is qualified; otherwise, modify the discretization method and optimization algorithm parameters of the radome, and repeat Steps (1) to (8) are carried out until a design scheme in which the electrical performance index and thickness distribution meet the preset requirements is obtained.

The step (2) is to determine the value range of the thickness value according to the requirements of the radome's structural performance and electrical performance, and proceed as follows:

(2a) The integrally formed aircraft radome usually adopts half-wavelength wall thickness, and the calculation formula of half-wavelength wall thickness is:

where λ is the wavelength, ε _r is the relative permittivity of the radome material, and α is the angle of incidence of the incident electromagnetic wave to the hood wall.

(2b) Determine n according to the structural performance requirements of the cover. The larger the n, the thicker the cover wall, the better the structural performance and the worse the electrical performance. Therefore, take the smallest value of n that can meet the structural performance requirements.

(2c) Calculate the minimum value α _min and the maximum value α _max of the incident angle of the electromagnetic wave radiated by the antenna to the cover wall during the scanning process of the internal antenna.

(2d) Determine the minimum value d _min and the maximum value d _max of the thickness value as follows:

Described step (4) concrete realization step is:

(4a) The components in the x, y, and z directions of the coordinate system established in step (1) are represented by i, j, and k respectively, and the distance of the antenna is calculated according to the known antenna aperture field distribution E(x, y). Field value F(θ,φ):

Among them, θ, φ are the spherical coordinate angles of the observation point in O-xyz, λ is the wavelength of the antenna, according to the antenna operating frequency f and the speed of light c, through the formula Calculated, s is the area of the integral unit;

(4b) Draw the antenna's far-field pattern according to the far-field F(θ,φ) of the ideal antenna, and extract the electrical performance indicators such as gain G ₁ and main beam position B ₁ from the pattern.

Described step (5) concrete realization step is:

(5a) For the coordinate system established in step (1), the components in the x, y, and z directions are represented by i, j, and k, respectively, and the known antenna aperture field distribution is recorded as E(x, y).

(5b) In the commercial model analysis software, the geometric model of the radome is established according to the structural form of the radome, and the grid side length is set to 0.2λ, where λ is the wavelength of the antenna, and the model is meshed;

(5c) According to the structural parameters and material parameters of the radome, the transmission line theory is used to calculate the transmission coefficient at each point on the skin

(5c1) According to the geometric shape of the radome and the incident aperture field, obtain the incident angle α and polarization angle β at each point on the radome, that is, the angle between the electromagnetic wave incident ray and the normal at the incident point is recorded as the incident angle α, the angle between the polarization direction of the electromagnetic wave and the incident plane is recorded as the polarization angle β, where the incident plane is composed of the electromagnetic wave incident ray and the normal at the incident point;

(5c2) According to the thickness values d ₁ ,d ₂ ,….,d ₁₀ at discrete points, use cubic B-spline interpolation to obtain the thickness profile of the smooth radome:

d(z)=f _{cubic-B-spline} (d ₁ ,...,d ₁₀ )

(5c3) According to the thickness d, relative permittivity ε _r , and loss tangent tanδ of the radome, calculate the transmission coefficient of the horizontal polarization component at each point on the skin and the vertical polarization component transmission coefficient

in, Z _H = cosα, These parameters are all intermediate variables; _TH and _TV are respectively The modulus value of , η _H and η _V are respectively phase;

(5c4) Transmission coefficient according to horizontal polarization component and the vertical polarization component transmission coefficient Obtain the transmission coefficient of the principal polarization component:

in, is an intermediate variable;

(5d) Multiply the aperture field incident on the radome by the transmission coefficient at the corresponding point to calculate the aperture field after passing through the skin:

Described step (6) concrete realization step is:

(6a) According to the aperture field E′(x, y) obtained in step (1) after passing through the radome, calculate the far field F′(θ, φ) generated by the aperture field after passing through the radome as follows ):

Among them, θ and φ are the spherical coordinate angles of the observation point in the rectangular coordinate system O-xyz, and k ₀ is the free space propagation constant. According to the formula Calculate, λ is the wavelength of the antenna, according to the antenna operating frequency f and the speed of light c, through the formula Calculated, s is the area of the integral unit;

(6b) According to the far field F′(θ, φ) generated by the aperture field after passing through the radome, draw the antenna far-field pattern after adding the cover, and extract the gain G ₂ and the main beam position B ₂ from the pattern. Electrical performance index;

(6c) Calculate the gain loss TL and aiming error BSE caused by the radome according to the electrical performance index calculated in step (4) and step (5):

TL=G ₁ -G ₂

BSE=|B ₁ -B ₂ |

Described step (7) concrete realization step is:

(7a) Taking the thickness at the discrete points in step (1) as the design variables, taking the variance of the thickness, the maximum slope, the variance of the slope in step (3), and the gain loss and aiming caused by the radome in step (6) Taking the error as the design goal, the following optimization model for the variable thickness of the aircraft radome considering the thickness control is established:

where BSE _max is the maximum radome-induced aiming error under all operating conditions, TL _max is the maximum radome-induced gain loss under all operating conditions, vd is the variance of the design variable, and mds is the slope of the design variable The maximum value of , vds is the variance of the slope of the design variable, BSE ₀ , TL ₀ , vd ₀ , mds ₀ and vds ₀ are the normalization coefficients given according to the specific problem, d _min is the lower limit of the design variable, d _max is the upper limit of the design variable;

(7b) The particle swarm optimization algorithm (PSO) is used to solve the optimization model of aircraft radome variable thickness considering thickness control, and the optimal thickness distribution of the radome is obtained. The population size of the particle swarm optimization algorithm is 50 and the evolutionary algebra is 200, the inertia weight decreases linearly from 0.9 to 0.4 with the evolution algebra, and the acceleration constant is taken as 2.

Compared with the existing variable thickness design method, the present invention not only improves the electrical performance index of the radome, but also reduces the manufacturing difficulty of the radome because the thickness control factor is introduced and the gain loss of the radome is considered.

Description of drawings

Fig. 1 is the realization general flow chart of the present invention;

2 is a sub-flow diagram of calculating the aperture field after passing through the radome in the present invention;

3 is a schematic diagram of the relationship between an antenna and a radome used in the present invention;

4 is a schematic structural diagram of a certain aircraft radome used for simulation in the present invention;

5 is a comparison diagram of aiming errors obtained before and after the optimal design of a certain aircraft radome with the present invention;

Fig. 6 is a gain loss comparison diagram obtained before and after the optimal design of a certain aircraft radome with the present invention;

7 is a comparison diagram of the thickness distribution obtained before and after the optimal design of an aircraft radome using the present invention.

Detailed ways

The present invention will be described in further detail below with reference to the accompanying drawings.

1, the concrete steps of the present invention are as follows:

In step (1), the thickness of the radome is discretized according to the height direction of the cover body.

As shown in Figure 2, along the height of the cover body, a coordinate system O-xyz is established with the center of the bottom surface of the radome as the origin and the bottom surface as the xy plane. The height of the cover body is along the z direction, and 10 discrete points are uniformly selected along this direction. Its coordinates are marked as z ₁ , z ₂ , . . . , z ₁₀ , and θ _s in the figure represents the scanning angle of the antenna.

Step (2), determining the value range of the thickness value, and assigning an initial value to the thickness at the discrete points.

(2a) The integrally formed aircraft radome usually adopts half-wavelength wall thickness, and the calculation formula of half-wavelength wall thickness is:

where λ is the wavelength, ε _r is the relative permittivity of the radome material, and α is the angle of incidence of the incident electromagnetic wave to the hood wall.

(2b) Determine n according to the structural performance requirements of the cover. The larger the n, the thicker the cover wall, the better the structural performance and the worse the electrical performance. Therefore, take the smallest value of n that can meet the structural performance requirements.

(2c) Calculate the minimum value α _min and the maximum value α _max of the incident angle of the electromagnetic wave radiated by the antenna to the cover wall during the scanning process of the internal antenna.

(2d) Determine the minimum value d _min and the maximum value d _max of the thickness value as follows:

(2e) randomly select a group of numbers in the interval [d _min , d _max ] as the thickness values at the discrete points in step (1).

Step (3), according to the thickness value at the discrete point, calculate its variance, the maximum slope and the variance of its slope;

Calculate the variance vd of these numbers according to the thickness values d ₁ , d ₂ ,….,d ₁₀ at discrete points, and further calculate the slope values of adjacent discrete points according to their coordinates z ₁ , z ₂ ,…,z ₁₀ :

Calculate the maximum value mds of these slope values and its variance vds.

Step (4), calculate the far field of the antenna, and extract the electrical performance indicators of gain G ₁ and main beam position B ₁ therefrom;

(4a) The components in the x, y, and z directions of the coordinate system established in step (1) are represented by i, j, and k respectively, and the distance of the antenna is calculated according to the known antenna aperture field distribution E(x, y). Field value F(θ,φ):

Among them, θ, φ are the spherical coordinate angles of the observation point in O-xyz, λ is the wavelength of the antenna, according to the antenna operating frequency f and the speed of light c, through the formula Calculated, s is the area of the integral unit;

(4b) Draw the antenna's far-field pattern according to the far-field F(θ,φ) of the ideal antenna, and extract the electrical performance indicators such as gain G ₁ and main beam position B ₁ from the pattern.

Step (5), according to the structural parameters and material parameters of the radome, use the transmission line theory to calculate the transmission coefficient of the cover body And according to the known antenna aperture field E(x,y), calculate the aperture field after passing through the radome:

Referring to Fig. 3, the concrete realization of this step is as follows:

(5a) For the coordinate system established in step (1), the components in the x, y, and z directions are represented by i, j, and k, respectively, and the known antenna aperture field distribution is recorded as E(x, y).

(5b) In the commercial model analysis software, the geometric model of the radome is established according to the structural form of the radome, and the grid side length is set to 0.2λ, where λ is the wavelength of the antenna, and the model is meshed;

(5c) According to the structural parameters and material parameters of the radome, the transmission line theory is used to calculate the transmission coefficient at each point on the skin

(5c1) According to the geometric shape of the radome and the incident aperture field, obtain the incident angle α and polarization angle β at each point on the radome, that is, the angle between the electromagnetic wave incident ray and the normal at the incident point is recorded as the incident angle α, the angle between the polarization direction of the electromagnetic wave and the incident plane is recorded as the polarization angle β, where the incident plane is composed of the electromagnetic wave incident ray and the normal at the incident point;

(5c2) According to the thickness values d ₁ ,d ₂ ,….,d ₁₀ at discrete points, use cubic B-spline interpolation to obtain the thickness profile of the smooth radome:

d(z)=f _{cubic-B-spline} (d ₁ ,...,d ₁₀ )

(5c3) According to the thickness d, relative permittivity ε _r , and loss tangent tanδ of the radome, calculate the transmission coefficient of the horizontal polarization component at each point on the skin and the vertical polarization component transmission coefficient

in, Z _H = cosα, These parameters are all intermediate variables; _TH and _TV are respectively The modulus value of , η _H and η _V are respectively phase;

(5c4) Transmission coefficient according to horizontal polarization component and the vertical polarization component transmission coefficient Obtain the transmission coefficient of the principal polarization component:

in, is an intermediate variable;

(5d) Multiply the aperture field incident on the radome by the transmission coefficient at the corresponding point to calculate the aperture field after passing through the skin:

Step (6), according to the aperture field E′(x, y) after passing through the radome, calculate the far field F′ (θ, φ) of the antenna with the cover, draw the far field pattern, and use the far field pattern from the far field pattern. The electrical performance indicators such as gain G ₂ and main beam position B ₂ are extracted from the radome, and then the gain loss TL and aiming error BSE caused by the radome are determined.

(6a) According to the aperture field E′(x, y) obtained in step (1) after passing through the radome, calculate the far field F′(θ, φ) generated by the aperture field after passing through the radome as follows ):

Among them, θ and φ are the spherical coordinate angles of the observation point in the rectangular coordinate system O-xyz, and k ₀ is the free space propagation constant. According to the formula Calculate, λ is the wavelength of the antenna, according to the antenna operating frequency f and the speed of light c, through the formula Calculated, s is the area of the integral unit.

(6b) According to the far field F′(θ, φ) generated by the aperture field after passing through the radome, draw the antenna far-field pattern after adding the cover, and extract the gain G ₂ and the main beam position B ₂ from the pattern. Electrical performance indicators.

(6c) Calculate the gain loss TL and aiming error BSE caused by the radome according to the electrical performance index calculated in step (4) and step (5):

TL=G ₁ -G ₂

BSE=|B ₁ -B ₂ |

Step (7), establish and solve the optimal design model.

(7a) Taking the thickness at the discrete points in step (1) as the design variables, taking the variance of the thickness, the maximum slope, the variance of the slope in step (3), and the gain loss and aiming caused by the radome in step (6) Taking the error as the design goal, the following optimization model for the variable thickness of the aircraft radome considering the thickness control is established:

where BSE _max is the maximum radome-induced aiming error under all operating conditions, TL _max is the maximum radome-induced gain loss under all operating conditions, vd is the variance of the design variable, and mds is the slope of the design variable The maximum value of , vds is the variance of the slope of the design variable, BSE ₀ , TL ₀ , vd ₀ , mds ₀ and vds ₀ are the normalization coefficients given according to the specific problem, d _min is the lower limit of the design variable, d _max is the upper limit of the design variable.

(7b) The particle swarm optimization algorithm (PSO) is used to solve the optimization model of the variable thickness of the aircraft radome considering the thickness control, and the optimal thickness distribution of the radome is obtained. The population size of the particle swarm optimization algorithm is taken as 50, the evolutionary algebra is taken as 200, the inertia weight decreases linearly from 0.9 to 0.4 with the evolutionary algebra, and the acceleration constant is taken as 2.

In step (8), it is judged whether the electrical performance index and thickness distribution of the radome obtained after optimization meet the preset requirements.

According to the change of the electrical performance index allowed by the antenna, it is judged whether the change of the electrical performance index of the system after adding the cover and the optimal design of the radome, and whether the thickness distribution of the radome meets the preset requirements, if so, the structure design of the radome The scheme is qualified; otherwise, modify the discretization method and optimization parameters of the radome, and repeat steps (1) to (8) until the results meet the requirements.

The advantages of the present invention can be further illustrated by the following simulation experiments:

1. Simulation parameters

An aircraft radome, the shape is shown in Figure 4, the diameter of the bottom surface is 0.5 meters, the height is 1 meter, the radome material is FRP material, the relative permittivity of the material is 4, the magnetic loss tangent is 0.015, and the diameter of the antenna inside the cover is 0.015. It is 0.22 meters, the working frequency is 9.4GHz, its aperture field is equal amplitude and in-phase distribution, and the scanning angle of the antenna ranges from 0° to 90°.

2. Simulation content and results

Using the present invention to consider the thickness control of the above aircraft radome is the thickness optimization design.

In Fig. 5, Fig. 6 and Fig. 7, design 1 represents the design scheme of equal thickness, design 2 represents the design scheme obtained by using the traditional variable thickness design method, and design 3 represents the design scheme obtained by using the variable thickness design method considering thickness control provided by the present invention Design.

Table 1 Electrical performance index of the system

It can be seen from the above data that after the traditional variable thickness design is adopted, the electrical performance of the radome is significantly improved, but the cost is that the thickness of the radome changes drastically, which causes great difficulties in the processing and manufacture of the radome. After the design method, not only the improvement effect of the electrical performance index is ensured, but also the thickness of the radome changes smoothly, which is convenient for processing and manufacturing.

The above simulation data experiments prove that the present invention can effectively improve the electrical performance of the aircraft radome, and at the same time can reduce the manufacturing difficulty.

Claims (6)

1. A thickness design method of an antenna housing is characterized by comprising the following steps: the method comprises the following steps:

(1) discretizing the thickness of the antenna housing according to the height direction of the housing body;

establishing a coordinate system O-xyz by taking the bottom surface center of the radome as an origin and the bottom surface as an xy plane along the height of the radome, uniformly selecting 10 discrete points along the direction along the height of the radome along the z direction, and recording the coordinates as z₁,z₂,…,z₁₀；

(2) Determining the value range of the thickness value according to the requirements of the structural performance and the electrical performance of the antenna housing, and assigning an initial value to the thickness at the discrete point;

(3) calculating the statistical values including the variance, the maximum slope and the variance of the slope according to the thickness value at the discrete point, and calculating the statistical values according to the thickness value d at the discrete point₁,d₂,…,d₁₀The variance vd of these numbers is calculated and further based on its coordinates z₁,z₂,…,z₁₀Calculating the slope values of the adjacent discrete points:

calculating the maximum value mds of the slope values and the variance vds thereof;

(4) calculating the far field of the antenna and extracting the gain G therefrom₁And main beam position B₁These electrical performance metrics;

(5) calculating the transmission coefficient of the cover body by using a transmission line theory according to the structural parameters and the material parameters of the antenna coverAnd according to the known antenna aperture field E (x, y), calculating the aperture field after penetrating through the antenna housing:

(6) calculating the far field F '(theta, phi) of the antenna system with the radome according to the aperture field E' (x, y) after the antenna radome is penetrated, drawing a far field directional diagram, and extracting the gain G from the far field directional diagram₂And main beam position B₂The gain loss TL and the aiming error BSE caused by the antenna housing are further determined according to the electrical performance indexes;

(7) establishing an optimal design model by taking the thickness value at the discrete point in the step (1) as a design variable, the variance of the thickness, the maximum slope, the variance of the slope in the step (3) and the electrical performance index in the step (6) as design targets, and solving the model by using a particle swarm optimization algorithm to obtain the thickness distribution of the radome;

(8) and (3) judging whether the electrical performance index and the thickness distribution of the antenna housing obtained after optimization meet preset requirements, if so, judging that the antenna housing structural design scheme is qualified, otherwise, modifying the discretization method and the optimization algorithm parameters of the antenna housing, and repeating the steps (1) to (8) until obtaining the design scheme that the electrical performance index and the thickness distribution meet the preset requirements.

2. The method for designing the thickness of the radome of claim 1, wherein: and (2) determining the value range of the thickness value according to the requirements of the structural performance and the electrical performance of the antenna housing, and performing the following steps:

(2a) the integrally formed aircraft radome adopts a half-wavelength wall thickness, and the calculation formula of the half-wavelength wall thickness is as follows:

where λ is the wavelength, ∈_rIs the relative dielectric constant of the radome material, α is the angle of incidence of the incident electromagnetic wave on the radome wall;

(2b) determining n according to the structural performance requirement of the cover body, wherein the larger n, the thicker the cover wall, the better the structural performance, and the poorer the electrical performance, so that the minimum n value capable of meeting the structural performance requirement is obtained;

(2c) the minimum value α of the angle of incidence of the electromagnetic wave radiated by the antenna on the shield wall during scanning of the internal antenna is calculated_minAnd maximum value α_max，

(2d) Determining the minimum value d of the thickness value according to the following formula_minAnd maximum value d_max：

3. The method for designing the thickness of the radome of claim 1, wherein: the step (4) is realized by the following steps:

(4a) respectively representing the components in the x, y and z directions of the coordinate system established in the step (1) by i, j and k, and calculating the far-field value F (theta, phi) of the antenna according to the known antenna aperture field distribution E (x, y):

wherein theta and phi are the spherical coordinate angles of the observation point in O-xyz,λ is the wavelength of the antenna, according to the antenna operating frequency f and the speed of light c, by the formulaCalculating to obtain s as the area of the integral unit;

(4b) drawing an antenna far-field directional diagram according to the far-field F (theta, phi) of the ideal antenna, and extracting the gain G from the directional diagram₁And main beam position B₁These electrical properties are indicative.

4. The method for designing the thickness of the radome of claim 1, wherein: the step (6) is realized by the following steps:

(5a) regarding the coordinate system established in the step (1), respectively representing components in x, y and z directions by i, j and k, and recording known antenna aperture field distribution as E (x, y);

(5b) in commercial model analysis software, a geometric model of the radome is established according to the structural form of the radome, the side length of a grid is set to be 0.2 lambda, wherein lambda is the wavelength of an antenna, and the model is subjected to grid division;

(5c) according to the structural parameters and the material parameters of the antenna housing, the transmission coefficient of each point on the covering is calculated by using the transmission line theory

(5c1) According to the geometric shape of the antenna housing and an incident aperture field, an incident angle α and a polarization angle β at each point on the antenna housing are obtained, namely, an included angle between an incident ray of electromagnetic waves and a normal line at the incident point is recorded as an incident angle α, and an included angle between a polarization direction of the electromagnetic waves and an incident plane is recorded as a polarization angle β, wherein the incident plane is formed by the incident ray of the electromagnetic waves and the normal line at the incident point;

(5c2) according to the thickness value d at discrete points₁,d₂,…,d₁₀Obtaining a smooth thickness profile of the radome by using a cubic B spline interpolation method:

d(z)＝f_{cubic-B-spline}(d₁,...,d₁₀)

(5c3) according to the thickness d and the relative dielectric constant epsilon of each part of the antenna housing_rLoss tangent tan delta, calculating the transmission coefficient of horizontal polarization component at each point on the skinAnd vertical polarization component transmission coefficient

Wherein, Z_H＝cosα，these parameters are all intermediate variables; t is_H、T_VAre respectively asModulus of (d), η_H、η_VAre respectively asThe phase of (d);

(5c4) transmission coefficient according to horizontal polarization componentAnd vertical polarization component transmission coefficientObtaining the transmission coefficient of the main polarization component:

wherein,is an intermediate variable;

(5d) multiplying the aperture field incident on the antenna housing by the transmission coefficient of the corresponding point, and calculating the aperture field after penetrating the skin:

5. the method for designing the thickness of the radome of claim 1, wherein: the step (6) is realized by the following steps:

(6a) calculating a far field F '(θ, Φ) generated by the aperture field after passing through the radome according to the aperture field E' (x, y) after passing through the radome obtained in the step (1) by the following formula:

where θ and φ are spherical coordinate angles of the observation point in the rectangular coordinate system O-xyz, and k₀For free space propagation constant, by formulaCalculating, lambda is the wavelength of the antenna, according to the working frequency f and the speed of light c of the antenna, through a formulaCalculating to obtain s as the area of the integral unit;

(6b) drawing a far-field directional diagram of the covered antenna according to a far-field F' (theta, phi) generated by a caliber field penetrating through the antenna cover, and extracting a gain G from the directional diagram₂And main beam position B₂These electrical performance metrics;

(6c) calculating gain loss TL and aiming error BSE caused by the antenna housing according to the electrical performance indexes calculated in the step (4) and the step (5):

TL＝G₁－G₂

BSE＝|B₁－B₂|。

6. the method for designing the thickness of the radome of claim 1, wherein: the step (7) is realized by the following steps:

(7a) and (3) establishing an aircraft radome variable thickness optimization model considering thickness control by taking the thickness value at the discrete point in the step (1) as a design variable, and taking the variance of the thickness, the maximum slope and the slope in the step (3) and the gain loss and the aiming error caused by the radome in the step (6) as design targets:

wherein d is_min≤d_i≤d_max,i＝1,...,10

Wherein BSE_maxIs the maximum value of the aiming error caused by the antenna housing under all working conditions, TL_maxIs the maximum value of the gain loss caused by the radome under all working conditions, vd is the variance of the design variable, mds is the maximum value of the slope of the design variable, vds is the variance of the slope of the design variable, BSE₀,TL₀,vd₀,mds₀And vds₀Is a normalized coefficient given according to a specific problem, d_minIs the lower limit of the design variable, d_maxIs the upper value limit of the design variable;

(7b) the aircraft radome variable thickness optimization model considering thickness control is solved by adopting a particle swarm optimization algorithm to obtain the optimal radome thickness distribution, the population scale of the particle swarm optimization algorithm is 50, the evolution algebra is 200, the inertia weight is linearly decreased to 0.4 from 0.9 along with the evolution algebra, and the acceleration constant is 2.