Variable-thickness interlayer antenna housing design method based on genetic algorithm

Abstract

The invention discloses a variable-thickness interlayer radome design method based on a genetic algorithm, and belongs to the technical field of radar radomes. According to the design method, related knowledge of electromagnetism, machine learning and intelligent optimization is comprehensively utilized, and the technical problems that in the prior art, a design method of a variable-thickness interlayer antenna housing is complex, and the implementation target is single are solved. According to the design process of the method, various preconditions such as antenna electromagnetic characteristics, antenna housing structure characteristics and material parameters are fully considered, the whole electromagnetic transmission process is analyzed, meanwhile, multi-parameter optimization design is carried out for multiple optimization targets, and variable-thickness interlayer antenna housing design under the complex multi-target condition is achieved. According to the method, the design mode of the antenna housing can be unified, and the modeling process is simplified; and in combination with an optimization algorithm, multi-parameter and multi-target rapid optimization is realized, and the design difficulty is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar radomes, and particularly relates to a design method for a variable-thickness sandwich radome based on a genetic algorithm. Background Art

[0002] Radar radomes were originally designed to protect antennas from the external environment, and at the same time, this structure ensures that the electrical and radiation performance of the internal antennas does not degrade significantly. They play an irreplaceable role on various antenna platforms such as ground-based, airborne, missile-borne, and space-borne. With the development of modern science and technology and the continuous changes in actual application requirements, the requirements for the electrical performance design of radomes are getting higher and higher. However, in actual situations, for example, for antennas on aircraft, when designing a radome, it is also necessary to consider aerodynamics and the stability of the radome structure in a harsh flight environment. Therefore, the designed radomes are not completely spherical but mostly have a streamline shape with a large length-to-diameter ratio, thus forming a very high electromagnetic wave incident angle. At this time, if a uniform constant-thickness radome design is adopted, when the antenna scans in the radome, the incident angle changes sharply, and the incident angles that the uniform constant-thickness radome wall design can adapt to are very limited, which has great limitations in actual applications and will greatly affect the normal radiation performance of the antenna. In order to be able to adapt to the aerodynamic shape design, enable the radome to adapt to different polarization angles and incident angle ranges, and at the same time hope to meet the wall structure parameters required by different positions of the internal antenna, a variable-thickness design is required to design a low-reflection and high-performance radome.

[0003] The patent application with the application number CN2023101324242 and the invention name "A Radome Design Method and Millimeter-Wave Radar" discloses a radome design method, which realizes the improvement of the antenna gain in the large-angle direction by adjusting the depression points of the radome. However, this design method requires manual adjustment, which consumes a large amount of time and labor costs, has a high design cost, insufficient controllability, and a single design means.

[0004] The patent application with the application number CN2020800822527 and the invention name "Radome Design" discloses a radome design method, particularly involving the design of a radome structure optimized for the transmission of broadband electromagnetic waves. However, this design method solves a single problem and lacks the feasibility of widespread use, and cannot solve technical problems such as aiming error and pattern distortion.

[0005] In summary, the two main problems currently encountered in the design of radomes in the prior art are: the design method is complex and difficult to promote and use; the problems solved are single, and it is difficult to design for multiple targets simultaneously. Summary of the Invention

[0006] The object of the present invention is to overcome the defects of the above-mentioned prior art and provide a design method for a variable-thickness sandwich radome based on a genetic algorithm.

[0007] The technical problem proposed by the present invention is solved as follows:

[0008] A design method for a variable-thickness sandwich radome based on a genetic algorithm, comprising the following steps:

[0009] Step 1: Set the outer wall size of the radome according to the design frequency band and the antenna aperture.

[0010] Step 2: Represent the continuity of the tangential components of the fields on both sides of the interface of two isotropic media as a 2×2 linear matrix transformation; the radome has a multi-layer structure, and determine that the characteristic matrix representation form of the radome is the form of the product of the interface characteristic matrices of adjacent two-layer structures and the characteristic matrices of each layer; calculate the reflection coefficient and transmission coefficient of the multi-layer structure with different thicknesses according to the characteristic matrix; fit the transmission efficiency curve of the radome changing with different thicknesses according to the reflection coefficient and transmission coefficient.

[0011] Step 3: According to the transmission efficiency curve of the radome changing with different thicknesses, the antenna station position, and the outer wall size of the radome, find the thickness corresponding to the best transmission efficiency at each point of the radome as the initial thickness model.

[0012] Step 4: Use the genetic algorithm to optimize the initial thickness model, set the optimization function according to the aiming error and the transmission coefficient, and iteratively optimize to obtain the best variable-thickness design model.

[0013] Further, in Step 2, the characteristic matrix representation form of the multi-layer structure is the form of the product of the interface characteristic matrices of adjacent two-layer structures and the characteristic matrices of each layer, specifically:

[0014] The total electric field excited by the incident plane wave in any layer includes the forward-traveling and backward-traveling plane waves, and the total electric field E(z) at any plane z is expressed as:

[0015]

[0016] Among them, E + (z) and E - (z) respectively represent the complex amplitudes of the forward-traveling and backward-traveling plane waves in the plane z;

[0017] For the electric fields E(z′) and E(z″) at different planes z′ and z″, they are related by a 2×2 transformation matrix:

[0018]

[0019] Among them, is the 2×2 transformation matrix between E(z′) and E(z″);

[0020] The above equation is simplified and denoted as:

[0021] E(z′) = T·E(z″) (3)

[0022] where T is the characteristic matrix of the multi-layer structure between plane z′ and plane z″;

[0023] Denote the adjacent interface z of the (j - 1)-th layer structure and the j-th layer structure j on both sides as plane z j -0 and plane z j +0. When plane z′ and plane z″ are respectively located at plane z j -0 and plane z j +0, equation (3) is expressed as:

[0024] E(z j -0) = I (j-1)j ·E(z j +0) (4)

[0025] where I (j+1)j represents the 2×2 characteristic matrix of the adjacent interface z j of the (j - 1)-th layer structure and the j-th layer structure;

[0026] Denote the two interfaces of the j-th layer structure as plane z j +0 and plane z j +d j -0, d j is the thickness of the j-th layer structure. When plane z′ and plane z″ are respectively located at plane z j +0 and plane z j +d j -0, then equation (3) is expressed as:

[0027] E(z j +0) = L j ·E(z j +d j -0) (5)

[0028] where L j is the characteristic matrix of the j-th layer structure itself;

[0029] For an m-layer structure, denote the adjacent interface of the air layer and the first layer structure as plane z1 - 0, and denote the adjacent interface of the m-th layer structure and the air layer as plane z m+1 +0. When plane z′ and plane z″ are respectively located at plane z1 - 0 and plane z m+1 +0, then equation (3) is expressed as:

[0030] E(z1-0) = T·E(z m+1 +0) (6)

[0031] Express the characteristic matrix T as the product of the interface characteristic matrix and the layer characteristic matrix arranged in order, specifically as follows:

[0032] T = I 01 L1I 12 L2......L m I m(m+1) (7)

[0033] Among them, m represents the number of layers of the multi-layer structure, and L1~L m represents the characteristic matrix of the 1st~mth layer itself, and I 01 , I 12 ~I m(m+1) represent the characteristic matrices of the adjacent interfaces between the air layer and the 1st layer structure, the adjacent interfaces between the 1st layer structure and the 2nd layer structure~the adjacent interfaces between the mth layer structure and the air layer, respectively.

[0034] Furthermore, in step two, in the characteristic matrix of the multi-layer structure, the representation of the interface characteristic matrix is specifically as follows:

[0035] For any two adjacent media a and b in the multi-layer structure, the intermediate interface characteristic matrix I ab is used to connect the electric fields between the two media and is expressed as:

[0036]

[0037] Among them, and are the complex amplitudes of the forward and backward traveling plane waves in medium a respectively, and are the complex amplitudes of the forward and backward traveling plane waves in medium b respectively, is the 2×2 order interface characteristic matrix between medium a and medium b;

[0038] Let There is:

[0039]

[0040] In the formula, t ab and r ab represent the transmission coefficient and reflection coefficient of the Fresnel complex amplitude from medium a to medium b respectively;

[0041] Let There is:

[0042]

[0043] Substitute \(I\) in equations (9) and (10) 11 and \(I\) 12 into equations (11) and (12), we get:

[0044]

[0045] where \(r\) ba and \(t\) ba represent the reflection coefficient and transmission coefficient of the Fresnel complex amplitude from \(b\) to \(a\), respectively;

[0046] Using the relationship between the Fresnel coefficients of the two propagation interfaces, that is:

[0047] \(r\) ab = - \(r\) ba (15)

[0048]

[0049] The expression of the interface characteristic matrix \(I\) ab is:

[0050]

[0051] Furthermore, in step two, in the characteristic matrix of the multi-layer structure, the representation of the layer characteristic matrix is specifically:

[0052] For a uniform layer structure with refractive index \(N\) and thickness \(d\), the relationship of wave propagation in the uniform layer structure is expressed as:

[0053]

[0054] where and are the complex amplitudes of the forward and backward traveling plane waves at the beginning of the uniform layer structure, respectively, and are the complex amplitudes of the forward and backward traveling plane waves at the end of the uniform layer structure, respectively, \(\beta\) is the phase shift, and \(i\) is the imaginary part symbol;

[0055] The phase shift \(\beta\) is expressed as:

[0056]

[0057] where is the angle between the wave propagation direction and the interface normal, and \(\lambda\) is the wavelength;

[0058] The layer characteristic matrix \(L\) of the uniform layer structure is expressed as:

[0059]

[0060] Further, in step two, the process of calculating the reflection coefficient and transmission coefficient of multilayer structures with different thicknesses based on the characteristic matrix is as follows:

[0061] Multiply the interface characteristic matrix I and the layer characteristic matrix L obtained from equations (17) and (20) successively according to equation (7), and then the total characteristic matrix T of the multilayer structure can be obtained.

[0062] For, there is:

[0063]

[0064] Among them, is the complex amplitude of the plane wave traveling forward in the positive direction at plane z m+1 +0;

[0065] The reflection coefficient R and transmission coefficient S of the multilayer structure are respectively:

[0066]

[0067] Further, when the multilayer structure is a single-layer solid wall structure, its characteristic matrix representation is specifically:

[0068] The single-layer solid wall has only one layer structure and its adjacent air layer, and its corresponding characteristic matrix T is expressed as:

[0069] T = I 01 L2I 10 (24)

[0070] Among them

[0071]

[0072] Among them, r 01 and r 10 respectively represent the reflection coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the reflection coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air. t 01 and t 10 respectively represent the transmission coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the transmission coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air. β1 represents the phase shift, d1 represents the thickness of the single-layer solid wall structure, N1 represents the refractive index of the single-layer solid wall structure, λ represents the electromagnetic wave wavelength, represents the angle between the wave propagation direction and the interface normal;

[0073] The characteristic matrix representation of the single-layer solid wall structure is:

[0074]

[0075] The reflection coefficient R and transmission coefficient S of the single-layer solid wall structure are respectively:

[0076]

[0077] Furthermore, the normalized representation of the characteristic matrix of the single-layer solid wall structure is specifically as follows:

[0078] For the single-layer solid wall structure, the refractive index ε r1 is the relative permittivity of the single-layer solid wall structure;

[0079] According to Fresnel's law and Snell's law:

[0080]

[0081] In the formula, E ip and E is respectively represent the complex amplitudes of the electric field vector components of the incident wave and the reflected wave on one side of the single-layer solid wall structure, and E rp and E rs respectively represent the complex amplitudes of the electric field vector components of the incident wave and the reflected wave on the other side of the single-layer solid wall structure; r p and r s are the Fresnel complex amplitude reflection coefficients for p-polarization and s-polarization respectively; the refractive index of air N0 = 1; represents the angle between the propagation direction of the incident wave and the interface normal, represents the angle between the propagation direction of the transmitted wave and the interface normal;

[0082] The parallel polarization reflection coefficient r 01p and the perpendicular polarization r 01s are respectively:

[0083]

[0084] Denote Y0 and Y1 are the normalized admittances of the air layer and the single-layer solid wall structure in the case of s-polarization respectively; the normalized representations of the reflection coefficient and the transmission coefficient of the single-layer solid wall structure are respectively:

[0085]

[0086] Furthermore, the specific process of step three is as follows:

[0087] According to the antenna position, obtain the incident angle between the electromagnetic wave emitted from the antenna and the radome, and according to the transmission efficiency curve of the radome varying with different thicknesses, obtain the thickness corresponding to the best transmission efficiency at each point;

[0088] The radome is made of a single-layer solid wall structure, which is a tangent ogival radome, and the tangent ogival equation is expressed as:

[0089]

[0090] In the formula, L0 and D0 respectively represent the major axis and minor axis of the tangent ovoid structure, and (x0, y0) are the coordinates of each point on the tangent ovoid;

[0091] The tangent equation at (x0, y0) is:

[0092]

[0093] In the formula, x and y are the horizontal and vertical coordinate variables;

[0094] The angle A between the incident wave and the normal direction at (x0, y0) is:

[0095]

[0096] According to the incident angle and the transmission efficiency curve of the radome varying with different thicknesses, the thickness d corresponding to the best transmission efficiency at each point is obtained;

[0097] The coordinate distribution (x′, y′) of the inner wall points of the radome is obtained:

[0098] x′ = x0 - d′ * sinA (44)

[0099] y′ = y0 - d′ * cosA (45)

[0100] Thus, the inner wall curve of the radome corresponding to the initial best transmission coefficient thickness distribution is obtained.

[0101] Furthermore, in step four, the genetic algorithm uses binary coding, adopts roulette wheel selection, sets the crossover probability and mutation probability of the chromosome, retains the individual with the highest optimization function value in each iteration, and uses the roulette wheel method to select and replicate excellent individuals. The crossover operation is single-point crossover.

[0102] The beneficial effects of the present invention are:

[0103] The design method of the present invention comprehensively applies the relevant knowledge of electromagnetics, machine learning, and intelligent optimization, and solves the technical problems of complex design methods and single implementation objectives of variable-thickness sandwich radomes in the prior art. The design process of the method of the present invention fully considers various preconditions such as the electromagnetic characteristics of the antenna, the structural characteristics of the radome, and the material parameters, analyzes the entire electromagnetic transmission process, and simultaneously conducts multi-parameter optimization design for multiple optimization objectives to realize the design of variable-thickness sandwich radomes under complex multi-objective conditions. The method of the present invention can unify the design method of the radome, simplify the modeling process; combine with the optimization algorithm to realize the rapid optimization of multiple parameters and multiple objectives, and reduce the design difficulty. Description of the Drawings

[0104] Figure 1 Schematic diagram of the process of the method of the present invention;

[0105] Figure 2 Graph showing the variation of transmission efficiency with thickness in the method of the embodiment;

[0106] Figure 3 Schematic diagram of the optimization process of the genetic algorithm in the method of the embodiment;

[0107] Figure 4 Graph showing the distribution of the incident angle in the method of the embodiment;

[0108] Figure 5 Graph showing the distribution of the thickness corresponding to the optimal transmission efficiency in the method of the embodiment;

[0109] Figure 6 Comparison diagram between the variable-thickness radome and the traditional equal-thickness design in the method of the embodiment. Detailed implementation manner

[0110] The present invention will be further described below in conjunction with the drawings and embodiments.

[0111] This embodiment provides a variable-thickness sandwich radome design method based on a genetic algorithm, and its schematic diagram of the process is as Figure 1 shown, including the following steps:

[0112] Step 1: Determine the outer wall size of the radome according to the design frequency band and the antenna aperture;

[0113] Step 2: Calculate the transmission coefficient and reflection coefficient curves of the radome according to the operating frequency, incident angle, dielectric constant of the dielectric material, etc.;

[0114] For the transmission of electromagnetic waves in an isotropic medium, it is a linear equation. Therefore, the continuity of the tangential components of the fields on both sides of the interface between two isotropic media can be expressed as a 2×2 linear matrix transformation.

[0115] (1) Representation of the characteristic matrix of a multi-layer structure

[0116] The total electric field excited by an incident plane wave in any layer includes two plane waves: the forward-propagating plane wave marked with a (+) sign and the backward-propagating plane wave marked with a (-) sign. Assuming that all plane waves are p-polarized or s-polarized, the total electric field at any plane z can be described by the column vector E(z):

[0117]

[0118] where E + (z) and E - (z) respectively represent the complex amplitudes of the forward-propagating and backward-propagating plane waves in plane z;

[0119] For the electric fields E(z′) and E(z″) at different planes z′ and z″, due to the linear characteristics of the system, they can be related by a 2×2 transformation matrix:

[0120]

[0121] where, is a 2×2 transformation matrix;

[0122] The above equation is simplified and denoted as:

[0123] E(z′) = T·E(z″) (3)

[0124] In the formula, T is the characteristic matrix of the multi-layer structure between plane z′ and plane z″.

[0125] Denote the two sides of the adjacent interface z j of the (j - 1)-th layer structure and the j-th layer structure as plane z j -0 and plane z j +0 respectively. When plane z′ and plane z″ are located at plane z j -0 and plane z j +0 respectively, equation (3) is expressed as:

[0126] E(z j -0) = I (j-1)j ·E(z j +0) (4)

[0127] In the formula, I (j+1)j represents the 2×2 characteristic matrix of the adjacent interface z j of the (j - 1)-th layer structure and the j-th layer structure.

[0128] Denote the two interfaces of the j-th layer structure as plane z j +0 and plane z j +d j -0 respectively, where d j is the thickness of the j-th layer structure. When plane z′ and plane z″ are located at plane z j +0 and plane z j +d j -0 respectively, then equation (3) is expressed as:

[0129] E(z j +0) = L j ·E(z j +d j -0) (5)

[0130] In the formula, L j is the characteristic matrix of the j-th layer structure itself.

[0131] For an m-layer structure, the adjacent interface between the 0th layer structure (air layer) and the 1st layer structure is denoted as plane z1-0, and the adjacent interface between the mth layer structure and the (m + 1)th layer structure (air layer) is denoted as plane z m+1 +0. When plane z′ and plane z″ are respectively located at plane z1-0 and plane z m+1 +0, then Equation (3) is expressed as:

[0132] E(z1-0) = T·E(z m+1 +0) (6)

[0133] The above equation defines a characteristic matrix T representing the total reflection property and total transmission property of the multi-layer structure. The characteristic matrix T can be expressed as the product of the interface characteristic matrix I and the layer characteristic matrix L arranged in an appropriate order, specifically as:

[0134] T = I 01 L1I 12 L2......L m I m(m+1) (7)

[0135] where m represents the number of layers of the multi-layer structure, L1~L m represent the characteristic matrices of the 1st~mth layers themselves, and I 01 , I 12 ~I m(m+1) represent the characteristic matrices of the adjacent interfaces between the 0th layer structure (air layer) and the 1st layer structure, the 1st layer structure and the 2nd layer structure~the adjacent interface between the mth layer structure and the (m + 1)th layer structure (air layer) respectively.

[0136] (2) Representation of the interface characteristic matrix in the characteristic matrix of the multi-layer structure

[0137] To determine the characteristic matrix T of the multi-layer structure, it is necessary to calculate each interface characteristic matrix I and layer characteristic matrix L.

[0138] For any two adjacent media a and b in the multi-layer structure, the intermediate interface characteristic matrix I ab is used to connect the electric fields on both sides of it and is expressed as:

[0139]

[0140] where and are the complex amplitudes of the forward and backward traveling plane waves in medium a respectively, and are the complex amplitudes of the forward and backward traveling plane waves in medium b respectively, is the 2×2 order interface characteristic matrix between medium a and medium b;

[0141] Let Then, from Equation (8), we have:

[0142]

[0143] where t ab and r ab represent the transmission coefficient and reflection coefficient of the Fresnel complex amplitude from medium a to medium b, respectively;

[0144] Let Then, from Equations (9) and (10), we have:

[0145]

[0146] Substitute I 11 and I 12 in Equations (9) and (10) into Equations (11) and (12), we have:

[0147]

[0148]

[0149] where r ba and t ba represent the reflection coefficient and transmission coefficient of the Fresnel complex amplitude from b to a, respectively;

[0150] Finally, using the relationship between the Fresnel coefficients at the two propagation interfaces, i.e.:

[0151] r ab =-r ba (15)

[0152]

[0153] we can obtain the expression of the interface characteristic matrix I ab as:

[0154]

[0155] Using the local incident angle at the medium interface and the complex refractive indices of the two media, the Fresnel reflection coefficient and transmission coefficient at the interface in Equation (17) can be solved.

[0156] (3) Representation of the layer characteristic matrix in the characteristic matrix of the multi-layer structure

[0157] For a uniform layer structure with refractive index N and thickness d, the relationship for wave propagation in the uniform layer structure is expressed as:

[0158]

[0159] where and are the complex amplitudes of the plane waves traveling forward and backward at the start of the uniform layer structure, respectively, and are the complex amplitudes of the plane waves traveling forward and backward at the end of the uniform layer structure, respectively. β is the phase shift and i is the imaginary part symbol;

[0160] The phase shift β is given by the following formula:

[0161]

[0162] where is the angle between the wave propagation direction and the interface normal, and λ is the wavelength;

[0163] Therefore, the layer characteristic matrix L of the uniform layer structure is expressed as:

[0164]

[0165] (4) Representation of the total reflection coefficient and the total transmission coefficient of the multi-layer structure

[0166] Multiply the interface characteristic matrix I and the layer characteristic matrix L obtained from equations (17) and (20) successively according to equation (7), and the total characteristic matrix T of the multi-layer structure is obtained.

[0167] Expand equation (6), then there is:

[0168]

[0169] Further expand equation (21), the total reflection coefficient R and the total transmission coefficient S of the multi-layer structure are respectively:

[0170]

[0171] (5) Representation of the characteristic matrix of the single-layer solid wall structure

[0172] According to the above derivation, we can calculate and analyze the properties of the single-layer solid wall structure. Since the single-layer solid wall has only one layer structure and its adjacent air layer, the corresponding characteristic matrix T is expressed as:

[0173] T = I 01 L1I 10 (24)

[0174] where

[0175]

[0176] where, r 01 and r 10respectively represent the reflection coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the reflection coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air, t 01 and t 10 respectively represent the transmission coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the transmission coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air, β1 represents the phase shift, d1 represents the thickness of the single-layer solid wall structure, N1 represents the refractive index of the single-layer solid wall structure, λ represents the electromagnetic wave wavelength, represents the angle between the wave propagation direction and the interface normal.

[0177] Thus, the characteristic matrix of the single-layer solid wall structure can be expressed as:

[0178]

[0179] According to Eqs. (22) and (23), the reflection coefficient R and transmission coefficient S of the single-layer solid wall structure can be deduced as follows:

[0180]

[0181] (5) Normalized representation of the characteristic matrix of the single-layer solid wall structure

[0182] For the single-layer solid wall structure, ε r1 is the relative permittivity of the single-layer solid wall structure.

[0183] When the incident wave is parallel (p) polarized and perpendicular (s) polarized, according to the Fresnel's law and Snell's law:

[0184]

[0185] where, E ip and E is respectively represent the complex amplitudes of the electric field vector components of the incident wave and the reflected wave on one side of the single-layer solid wall structure, E rp and E rs respectively represent the complex amplitudes of the electric field vector components of the incident wave and the reflected wave on the other side of the single-layer solid wall structure; r p and r s are the Fresnel complex amplitude reflection coefficients for p polarization and s polarization respectively; the refractive index of air N0 = 1; represents the angle between the incident wave propagation direction and the interface normal, represents the angle between the transmitted wave propagation direction and the interface normal.

[0186] The parallel polarization reflection coefficient r 01p and the perpendicular polarization r 01s can be obtained as follows:

[0187]

[0188] At this time, denote Y0 and Y1 are the normalized admittances of the air layer and the single-layer solid wall structure when polarized in the s direction, respectively. Combining equations (30) and (31), the normalized representations of the total reflection coefficient and the total transmission coefficient of the single-layer solid wall structure are obtained as follows:

[0189]

[0190]

[0191] Draw the variation curve of the transmission efficiency of the multi-layer structure according to the transmission coefficient and the reflection coefficient. In this embodiment, the variation curve of the transmission efficiency of the single-layer solid wall structure with the thickness is shown in the appendix Figure 2 as shown.

[0192] Step 3: According to the calculated variation curve of the transmission efficiency in Step 2, combined with the antenna position, fit according to the outer shape curve of the radome to obtain the initial thickness model;

[0193] First, according to the variation curve of the transmission efficiency with the thickness calculated in Step 2, in the case of the proposed antenna position, obtain the angle between the electromagnetic wave emitted from the antenna and the radome, so as to obtain the thickness corresponding to the best transmission efficiency at this point when the incident angle is determined.

[0194] The radome in this embodiment is a single-layer solid wall structure, which is a tangent-oval radome. The tangent-oval equation is expressed as:

[0195]

[0196] In the formula, L0 and D0 respectively represent the major axis and the minor axis of the tangent-oval structure, and (x0, y0) are the coordinates of each point on the tangent-oval.

[0197] The tangent equation at (x0, y0) is:

[0198]

[0199] In the formula, x and y are the horizontal and vertical coordinate variables;

[0200] The angle A between the incident wave and the normal direction at (x0, y0) is:

[0201]

[0202] After obtaining the incident angle, combined with the derivation in Step 2, we can obtain the thickness distribution d corresponding to the best transmission efficiency at each point.

[0203] The coordinate distribution (x′, y′) of the inner wall points of the radome can be obtained as follows:

[0204] x′ = x0 - d * sinA (44)

[0205] y′ = y0 - d * cosA (45)

[0206] Thus, the inner wall curve corresponding to the initial optimal transmission coefficient thickness distribution is obtained.

[0207] Step 4: According to the initial model obtained in Step 3, combined with the genetic algorithm, set the optimization function for optimization objectives such as aiming error, transmission coefficient, etc. In the formula, f1 and f2 are the minimum and maximum values of the operating frequency, and ω1 and ω2 are weights, which are responsible for adjusting the influence of antenna gain (gain) and aiming error (BE). For different optimization scenarios, appropriate adjustments can be made to achieve better optimization effects. For example, in a scenario where higher requirements are placed on the aiming error (BE), the value of ω1 can be appropriately increased to control the optimization direction to pay more attention to the aiming error (BE). Specific optimization parameters need to be designed according to the simulation duration and structure of the actual structure. Through iterative optimization, the best variable-thickness design curve is obtained.

[0208] In this step, as Figure 3 shown, after integrating the optimization objectives to design the optimization function, iterative optimization is carried out through the genetic algorithm. Binary coding is used, roulette wheel selection is adopted, the appropriate crossover probability of the chromosome is set, the individual with the highest fitness value in each generation is always retained, the roulette wheel method is used to select and copy excellent individuals, the crossover operation is single-point crossover, and a certain mutation probability is introduced, so as to realize the thickness change of the radome and finally obtain the radome parameters with the desired electromagnetic performance.

[0209] Step 5: According to the design curve obtained in Step 4, carry out modeling design to obtain the final variable-thickness radome design.

[0210] In this embodiment, a certain missile-borne radome is designed. The diameter of the radome is 300 mm and the height is 400 mm. The missile-borne radar operates at 5 GHz, and the antenna is an array antenna. During the radome design process, the design method described in the present invention is adopted and a sample radome is made. The measured results are consistent with the design, effectively improving the transmission coefficient and reducing the aiming error, and all performance indicators meet the requirements.

[0211] The specific design process is as follows:

[0212] Adopt the method described in Step 1 to determine that the radome is a tangent ogival structure, with an outer wall size of diameter 300 mm and height 400 mm.

[0213] Using the method described in Step 2, set the standing point of the antenna, and successively calculate the intersection points of the rays emitted from the center to the tangent ogival radome. Calculate the incident angle based on the normal line at the intersection point and the ray determined by the standing point. Taking the case where the antenna standing point is 35 mm as an example, the calculated incident angle distribution is as follows Figure 4 , according to the known incident angle distribution, and setting the relative permittivity of the designed radome dielectric material to 2.2, obtain the curve of the power transmission efficiency corresponding to each incident angle varying with the radome thickness.

[0214] Using the method described in Step 3, by screening out the thicknesses with high transmission efficiency corresponding to each incident angle, we can obtain the thickness distribution with high transmission efficiency at each point of the tangent ogival under the condition of determining our antenna standing point, as shown in Figure 5 . After calculating the corresponding thickness distribution, fit it with the structural curve to obtain the initial thickness model, whose inner wall diameter is 129 mm and height is 350 mm.

[0215] Using the method described in Step 4, based on the design of the initial thickness model, taking reducing the aiming error as the main optimization goal, using binary coding, using roulette wheel selection, setting the crossover probability of the chromosome to 90%, always retaining the individual with the highest fitness value in each generation, using the roulette wheel method to select and replicate excellent individuals, the crossover operation is single-point crossover, and introducing a mutation probability of 10% for optimization design. The final optimization result is that its inner wall diameter is 125 mm and height is 378 mm.

[0216] Using the method described in Step 5, complete the final radome design, and the simulation test results are as shown in Figure 6 . As shown, compared with the traditional equal-thickness radome design in terms of the antenna electrical performance, the radome transmission coefficient has a certain improvement, while reducing the aiming error, and solving the pattern distortion and suppressing the sidelobe elevation, and all electrical performance indicators meet the design requirements.

[0217] In summary, the present invention discloses a variable-thickness sandwich radome design method based on a genetic algorithm, which efficiently and rapidly completes the multi-objective variable-thickness sandwich radome design by simplifying the design method of variable-thickness design, thereby providing a solution to solve the current single and complex design methods of radomes.

Claims

1. A variable thickness sandwich radome design method based on genetic algorithm, characterized in that: The following steps are involved: Step 1: Set the outer wall size of the radome according to the designed frequency band and antenna aperture; Step 2: The continuity of the tangential component of the field on both sides of the interface of the two isotropic media is expressed as a 2×2 linear matrix transformation; the radome is a multi-layer structure, and the characteristic matrix representation of the radome is determined to be the product of the interface characteristic matrix of the two adjacent layers and the characteristic matrix of each layer; The reflection coefficient and transmission coefficient of multilayer structures with different thicknesses are calculated based on the characteristic matrix; the transmission efficiency curve of the radome with different thicknesses is fitted based on the reflection coefficient and transmission coefficient; Step 3: According to the transmission efficiency curve of the radome with different thicknesses, the antenna position and the outer wall size of the radome, find the thickness corresponding to the best transmission efficiency at each point of the radome as the initial thickness model; Step 4: Use genetic algorithm to optimize the initial thickness model, set the optimization function according to the aiming error and transmission coefficient, and iterate the optimization to obtain the best variable thickness design model.

2. The variable thickness sandwich radome design method based on genetic algorithm according to claim 1, characterized in that: In step 2, the characteristic matrix representation of the multilayer structure is the product of the interface characteristic matrix of the two adjacent layers and the characteristic matrix of each layer, specifically: The total electric field excited by the incident plane wave in any layer includes the plane waves traveling in the forward direction and the plane waves traveling in the reverse direction. The total electric field E(z) at any plane z is expressed as: Among them, E + (z) and E - (z) denotes the complex amplitudes of the plane waves traveling in the forward and reverse directions in plane z, respectively; The electric fields E(z′) and E(z″) at different planes z′ and z″ are related by a 2×2 order transformation matrix: in, is the 2×2 transformation matrix between E(z′) and E(z″); The above formula is simplified as: E(z′)=T·E(z″) (3) Where T is the characteristic matrix of the multilayer structure between plane z′ and plane z″; Let the adjacent interface z between the (j-1)th layer structure and the jth layer structure be j The two sides are plane z j -0 and plane z j +0, when plane z′ and plane z″ are located on plane z j -0 and plane z j When +0, formula (3) is expressed as: E(z j -0)=I (j-1 )j·E(z j +0) (4) In the formula, I (j+1)j represents the adjacent interface z between the (j-1)th layer structure and the jth layer structure j 2×2 order characteristic matrix; The two boundary surfaces of the j-th layer structure are plane z j +0 and plane z j +d j -0,d j is the thickness of the j-th layer structure, when plane z′ and plane z″ are located on plane z j +0 and plane z j +d j -0, then formula (3) is expressed as: E(z j +0)=L j ·E(z j +d j -0) (5) Where, L j is the characteristic matrix of the j-th layer structure itself; For an m-layer structure, the adjacent interface between the air layer and the first layer is plane z1-0, and the adjacent interface between the m-th layer and the air layer is plane z m+1 +0, when plane z′ and plane z″ are located on plane z1-0 and plane z respectively m+1 When +0, equation (3) is expressed as: E(z1-0)=T·E(z m+1 +0) (6) The characteristic matrix T is expressed as the multiplication of the interface characteristic matrix and the layer characteristic matrix in order, specifically: T=I 01 L1I 12 L2......L m L m(m+1) (7) Where m represents the number of layers in the multilayer structure, L1~L m Represents the characteristic matrix of the 1st to mth layers, I 01 ,I 12 ~I m(m+1 ) represent the characteristic matrices of the adjacent interfaces between the air layer and the first layer structure, the adjacent interfaces between the first layer structure and the second layer structure, and the adjacent interfaces between the mth layer structure and the air layer, respectively.

3. The variable thickness sandwich radome design method based on genetic algorithm according to claim 2, characterized in that: In step 2, in the characteristic matrix of the multilayer structure, the interface characteristic matrix is ​​specifically represented as: For any two adjacent layers of media a and b in a multilayer structure, the interface characteristic matrix I ab Used to connect the electric field between two layers of media, expressed as: in, and are the complex amplitudes of the plane waves traveling forward and backward in medium a, respectively, and are the complex amplitudes of the plane waves traveling forward and backward in medium b, respectively, is the 2×2 order interface characteristic matrix between medium a and medium b; make have: Where, t ab and r ab denote the transmission coefficient and reflection coefficient of the Fresnel complex amplitude from medium a to medium b respectively; make have: Let I in equations (9) and (10) 11 and I 12 Substituting into equations (11) and (12), we have: In the formula, r ba and t ba denote the reflection coefficient and transmission coefficient of the Fresnel complex amplitude from b to a respectively; Using the relationship between the Fresnel coefficients of the two propagation interfaces, namely: r ab ＝-r ba (15) Get the interface characteristic matrix I ab The expression is:

4. The variable thickness sandwich radome design method based on genetic algorithm according to claim 3 is characterized in that: In step 2, in the characteristic matrix of the multi-layer structure, the layer characteristic matrix is ​​specifically represented as: For a uniform layer structure with a refractive index of N and a thickness of d, the relationship for wave propagation within the uniform layer structure is expressed as: in, and are the complex amplitudes of the plane waves traveling forward and backward at the beginning of the uniform layer structure, and are the complex amplitudes of the plane waves traveling forward and backward at the terminal of the uniform layer structure, β is the phase shift, and i is the sign of the imaginary part; The phase shift β is expressed as: In the formula, is the angle between the wave propagation direction and the interface normal, λ is the wavelength; The layer characteristic matrix L of a uniform layer structure is expressed as:

5. The variable thickness sandwich radome design method based on genetic algorithm according to claim 4, characterized in that: In step 2, the process of calculating the reflection coefficient and transmission coefficient of multilayer structures of different thicknesses based on the characteristic matrix is ​​as follows: The interface characteristic matrix I and the layer characteristic matrix L obtained by equation (17) and equation (20) are multiplied in sequence according to equation (7) to obtain the total characteristic matrix T of the multilayer structure. For, there are: in, For plane z m+1 The complex amplitude of the plane wave traveling in the positive direction at +0; The reflection coefficient R and transmission coefficient S of the multilayer structure are:

6. The variable thickness sandwich radome design method based on genetic algorithm according to claim 5, characterized in that: When the multi-layer structure is a single-layer solid wall structure, its characteristic matrix is ​​expressed as follows: A single-layer solid wall has only one layer of structure and its adjacent air layer, and its corresponding characteristic matrix T is expressed as: T=I 01 L1I 10 (24) in Among them, r 01 and r 10 They represent the reflection coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the reflection coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air, respectively. 01 and t 10 They represent the transmission coefficient of the Fresnel complex amplitude from air to the single-layer solid wall structure and the transmission coefficient of the Fresnel complex amplitude from the single-layer solid wall structure to air, β1 represents the phase shift, d1 represents the thickness of the single-layer solid wall structure, N1 represents the refractive index of the single-layer solid wall structure, λ represents the wavelength of the electromagnetic wave, It represents the angle between the wave propagation direction and the interface normal; The characteristic matrix of a single-layer solid wall structure is expressed as: The reflection coefficient R and transmission coefficient S of a single-layer solid wall structure are:

7. The variable thickness sandwich radome design method based on genetic algorithm according to claim 6, characterized in that: The normalized representation of the characteristic matrix of a single-layer solid wall structure is: For a single-layer solid wall structure, the refractive index ε r1 is the relative dielectric constant of a single-layer solid wall structure; According to Fresnel's law and Snell's law: In the formula, E ip and E is denote the complex amplitudes of the electric field vector components of the incident and reflected waves on one side of the single-layer solid wall structure, E rp and E rs represent the complex amplitudes of the electric field vector components of the incident wave and the reflected wave on the other side of the single-layer solid wall structure; r p and r s are the Fresnel complex amplitude reflection coefficients for p-polarization and s-polarization respectively; The refractive index of air is N0 = 1; represents the angle between the incident wave propagation direction and the interface normal, It represents the angle between the propagation direction of the transmitted wave and the interface normal; Parallel polarization reflection coefficient r 01p and vertical polarization r 01s They are: remember Y0 and Y1 are the normalized admittances of the air layer and the single-layer solid wall structure under s-polarization, respectively; the normalized expressions of the reflection coefficient and transmission coefficient of the single-layer solid wall structure are:

8. The variable thickness sandwich radome design method based on genetic algorithm according to claim 1, characterized in that: The specific process of step three is: The incident angle of the electromagnetic wave emitted from the antenna to the radome is obtained according to the antenna position, and the thickness corresponding to the best transmission efficiency at each point is obtained according to the transmission efficiency curve of the radome with different thicknesses; The radome adopts a single-layer solid wall structure, which is a tangent oval radome. The tangent oval equation is expressed as: Where L0 and D0 represent the major axis and minor axis of the tangent oval structure, respectively, and (x0, y0) are the coordinates of each point on the tangent oval; The equation of the tangent line at (x0, y0) is: In the formula, x and y are horizontal and vertical coordinate variables; The angle A between the incident wave and the normal direction at (x0, y0) is: According to the transmission efficiency curve of the incident angle and the radome with different thicknesses, the thickness d corresponding to the best transmission efficiency at each point is obtained; Get the coordinate distribution (x′, y) of the inner wall points of the radome: x′=x0-d'*sinA (44) y′=y0-d′*cosA (45) Thus, the inner wall curve of the radome corresponding to the initial optimal transmission coefficient thickness distribution is obtained.

9. The variable thickness sandwich radome design method based on genetic algorithm according to claim 1, characterized in that: In step 4, the genetic algorithm uses binary coding and roulette wheel selection to set the crossover probability and mutation probability of chromosomes. In each iteration, the individual with the highest optimization function value is retained, and the roulette wheel method is used to select and copy excellent individuals. The crossover operation is a single-point crossover.

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