CN103353904B - Active interlayer microstrip antenna and the comprehensive data-driven method for designing of electromagnetism and antenna - Google Patents

Abstract

The invention discloses a kind of active interlayer microstrip antenna structure and the comprehensive data-driven method for designing of electromagnetism and antenna, solve prior art and can not realize structure and the comprehensive Integrated design problem of electromagnetism, step is: (1), according to electrical performance indexes, determines the material of radio-frequency enabled layer, size, panel and cell dimensions; (2) by mechanical analysis, the data such as the wavefront distortion of acquisition antenna structure and stress; (3) pre-service wavefront distortion data, obtain the site error of each radiating element; (4) coupling model of data-driven is utilized to calculate the far-field pattern of interlayer microstrip antenna; (5) wave penetrate capability under consideration panel and honeycomb impact is calculated; (6) interlayer microstrip antenna structure and electromagnetism Synthetical Optimization model is built; (7) solve this mathematical optimization models, obtain optimal synthesis result.Optimal design while the present invention can realize active interlayer microstrip antenna structure and electromagnetism, shortens the lead time, improves the power electrical property of product.

Description

Data drive design method for integrating active interlayer microstrip antenna and electromagnetism and antenna

Technical Field

The invention belongs to the technical field of antennas, and particularly relates to a data driving design method for integrating an active interlayer microstrip antenna structure and electromagnetism.

Background

The active interlayer microstrip antenna is characterized in that a feed network, a beam control unit and a microstrip antenna array of an integrated T/R assembly are embedded into a skin structure of a weapon platform, and high electromagnetic performance is realized on the premise of meeting the mechanical property of the platform structure. The active interlayer microstrip antenna can be applied to various future sea, land and air weapon equipment such as variant airplanes, unmanned planes, airship early warning machines, intelligent chariot, stealth warships and the like, and is a key technology for realizing stealth, multifunction, intelligence and high maneuverability of a weapon platform.

At present, some scientific research institutes at home and abroad have realized the importance of the active interlayer microstrip antenna in new generation weaponry, and have carried out some related researches, and the research conditions at home and abroad are introduced below.

(1) In the early 90 s of the last century, the united states has first conducted relevant research in the world in order to achieve antenna conformability to aircraft structures. For example, Boeing company designs a skin antenna conformal to the wing, and researches the change condition of the radiation performance of the microstrip antenna in the fatigue failure process of the wing. NASA has also developed a wing of long-range unmanned aerial vehicle, and its microstrip antenna array, solar cell array and wing structure are completely integrated into one body. Flight experiments show that the electrical properties are affected by the torsion and swing induced front surface stress. These results are described In the literature "LockyerAJ, AltKH, Coughlin DP, et. Designationdevelopmentaaconformaload-bearing smart-skinnantnenna: overviewWifAFRLsmart @ construction technology evaluation (S3TD). In: proceedingsofSPIE; 1999 410-424. Their research found that service environment loads such as aerodynamic, vibration and fatigue-induced front surface stress can affect the electrical performance, however, they do not give a mathematical model describing their influence relationship to guide the structural, electromagnetic, electromechanical integration design.

(2) The dutch national aerospace laboratory researches the change rule of the electrical property of the microstrip antenna conformal with the wings of the unmanned aerial vehicle in a vibration environment, and germany proposes a microstrip antenna structure applied to an intelligent chariot and points out that mechanical physical quantities (such as rigidity, strength, damage limit, manufacturing stress, lightning stroke environmental stress and the like) can cause antenna electromagnetic wave beam disorder and internal level signal change. These results are reported in the literature "Paul J.Callus.Conformalload-bearing anti-structural for Australian induced development for aircraft [ R ]. Australia: Australian GovermentDepartmentof Defence, 2007". Although the influence relationship of the mechanical structure on the electrical property of the microstrip antenna is found through an experimental method, an electromechanical comprehensive design method for ensuring the optimal comprehensive structural property and electrical property is not provided.

(3) The research group of korea, the science and technology university, used an adhesive method to embed microstrip antennas into composite structures. To improve the antenna gain, ChisangYou gives a method for improving the antenna gain by using the transmission line theory. This study is reported in the literature "Chisangyou, Woonbong Hwang. Designofload-bearing construction technology of microstatic compositions and structures. composition Structure, 2005 (3-4): 378-382". Subsequently, ChisangYou utilizes a mathematical statistics tool to research a gain-based optimal structure and electromagnetic collaborative design method. This method is reported in the literature "Chisangyou, Staicus, Laramatin, ethyl. anovelytic/mechanical engineering-domain modeling, fine knowledge method and stability for co-design optimization of RF-integrated mechanical structure. International journal of numerical modeling: electronic network, Devicesandfields.2007,21(1-2): 91-101". However, the design method only considers the optimization of the structure performance and the gain performance, the optimal design of the structure and the antenna far-field pattern is not realized, and the collaborative design method only aims at the passive interlayer microstrip antenna and is not suitable for the active interlayer microstrip antenna design urgently needed by the new generation of weapon equipment.

(4) The micro-strip antenna is embedded into the three-dimensional woven fabric by the textile technology at the national Donghua university, and the influence relationship of different weaving modes, composite materials, dielectric materials and the like on the mechanical and electrical properties of the antenna is researched by experimental samples. This study is reported in the literature "FujunXu, LanYao, Dazhao, et al, Performance and two demamage of the three dimensional integrated microstructuring of the important structural structure. Compositrestrestresucres.2010, 93(1): 193-197". The research institute of composite materials of Harbin Industrial university has developed the sample of the buried microstrip antenna laminated structure, and has studied the law of influence of dielectric parameter and honeycomb thickness on the antenna mechanical and electrical properties. The result is reported in the literature "Dy-electro-mechanical property analysis of embedded microstrip antenna honeycomb sandwich structure, composite material academic report 2011,28(2): 231-. Although relevant research has been carried out domestically, the research objects of the antennas are passive interlayer microstrip antennas, and the design method of the active interlayer microstrip antenna for realizing the optimal structure and electromagnetic comprehensive performance is not researched.

The above technical scheme has the following defects: 1) although the above researches find that the service environment, the honeycomb, the panel, the adhesive, the dielectric material and other factors can influence the mechanical and electrical properties of the sandwich antenna, the factors do not establish a mathematical model of the influence of the factors on the electrical properties of the antenna, so that the optimal structural and electromagnetic comprehensive result cannot be obtained in the initial design stage. 2) The existing documents lack a design method of an active interlayer microstrip antenna structure and electromagnetic integration, and the existing engineering usually adopts an integrated method of electromechanical separation, namely, according to electrical performance indexes, an excitation current of a radiation unit and the geometric size, shape, topology and the like of the structure are designed by respectively utilizing an antenna integrated technology and a mechanical principle, and then the strength of the antenna structure and the electrical performance of the antenna are respectively checked, and the integration of the electromechanical separation is difficult to ensure that the designed interlayer microstrip antenna meets the requirement of optimal overall performance. 3) Because this type of antenna has integrated level height, material heterogeneity and multidisciplinary nature, prior art uses electromechanical separation design method at first, then realizes the electro-mechanical properties of expectation through the debugging of appearance piece, this electromechanical separation and design method according to experience lead to the product development cycle long, the yield is low, with high costs, can't obtain optimum structure and electromagnetic properties in order to satisfy the practical needs of engineering.

Disclosure of Invention

The invention aims to provide a data driving method for realizing structure and electromagnetism synthesis aiming at the electromechanical integration design problem of an active interlayer microstrip antenna so as to simultaneously obtain the active interlayer microstrip antenna with the optimal structure and electromagnetic performance, lay a foundation for the electromechanical synthesis design of the antenna, avoid the defects of the existing electromechanical separation and empirical design technology, reduce the development cost and improve the product performance consistency.

The embodiment of the invention is realized in such a way that an active interlayer microstrip antenna structure and electromagnetism integrated data drive design method is characterized by comprising the following steps of:

firstly, determining a radio frequency functional layer material, a geometric dimension and a layout of a front surface radiation unit in the interlayer microstrip antenna according to a given electrical performance index;

secondly, determining the geometric dimensions of the upper panel, the lower panel and the honeycomb according to the geometric dimensions of the radio frequency functional layer;

thirdly, obtaining array surface deformation data and maximum stress sigma of the antenna structure through mechanical analysis_maxAnd maximum deformation v_maxData;

fourthly, preprocessing the deformation data of the array surface to obtain the position error delta x of each radiation unit caused by the service load_ij(β,F)、Δy_ij(β, F) and Δ z_ij(β, F) which are functions of the structural design parameters β and the in-service load magnitude F;

fifthly, calculating the electrical performance of the antenna array under the joint influence of the array surface unit position error and the interlayer radiation units by using a data-driven coupling model according to the position errors of the radiation units;

sixthly, calculating and considering the influence of the panel and the honeycomb on the gain of the sandwich microstrip antenna;

seventhly, according to the electric field far field data E of the interlayer microstrip antenna array obtained by the calculation in the fifth step_A(theta, phi), constructing an interlayer microstrip antenna structure and an electromagnetic comprehensive optimization model to determine structural design variables and the amplitude and phase of an excitation current of a microstrip radiation unit;

eighthly, solving the comprehensive optimization model by using an optimization algorithm, judging whether the result is converged, if not, updating the result obtained by solving to the initial value of the design variable, returning to the third step, and restarting the next solving, otherwise, obtaining the result of the optimal structural parameter and the excitation current which meet the power and electricity performance;

ninth, according to the obtained antenna electric field far field data E_A(theta, phi), determining sidelobe level and beam pointing electrical performance indexes, and calculating the gain of the interlayer microstrip antenna;

and tenth step, designing a feed network in the active interlayer microstrip antenna by using HFSS software according to the amplitude and the phase of the radiation unit excitation current obtained by the synthesis, and finally manufacturing the antenna by using an integrated molding process.

Further, according to the given electrical performance index, the method for determining the radio frequency functional layer material, the geometric dimension and the array surface radiation unit layout of the integrated microstrip antenna comprises the following steps:

according to the electrical performance design indexes such as gain, side lobe, center frequency, beam width and beam width, the shape, number and array layout of the microstrip radiating units and the geometric dimension of the microstrip antenna array such as length L are determined by the existing antenna theory_mWidth W_m(ii) a In order to reduce the manufacturing difficulty, the length and the width of the specified radio frequency functional layer are the same as those of the microstrip antenna array; height H in the radio frequency functional layer_mThe thickness of the microstrip antenna dielectric plate, the feed network circuit of the integrated T/R component and the thickness of the signal control and processing circuit are determined; the material of the radio frequency function layer is selected from polytetrafluoroethylene and low temperature co-fired ceramic (LTCC), and the microstrip radiation unit array is etched on the dielectric plate to realize the required electrical performance.

Further, according to the geometric dimension of the radio frequency functional layer, the method for determining the geometric dimensions of the upper panel, the lower panel and the honeycomb comprises the following steps:

the geometric dimensions of the upper and lower panels and the honeycomb are generally determined by the installation space of the weapon platform; selecting the lengths L of the upper and lower surface plate layers and the honeycomb layer and the radio frequency functional layer_mAnd width W_mThe same is true.

Further, the array surface deformation data and the maximum stress sigma of the antenna structure are obtained through mechanical analysis_maxAnd maximum deformation v_maxThe specific implementation process of the data is as follows:

3a) establishing a mechanical analysis model of the sandwich microstrip antenna under the action of service environment load such as pneumatic load or temperature load:

K＝F

in the formula, K is a structural rigidity matrix which is a function of a structural design parameter beta and a physical property parameter and represents a finite element node displacement array, F is a node load array which represents pneumatic load and temperature load and can also be a load array obtained by combining the pneumatic load and the temperature load;

3b) according to the determined geometric dimensions of the skin, the honeycomb and the radio frequency functional layer, an Ansys command stream is utilized to establish an initial interlayer microstrip antenna statics analysis model, and the specific process is as follows:

3b1) determining equivalent material parameters such as density, elastic modulus and Poisson ratio of the skin, the honeycomb and the microstrip antenna layer, wherein the regular hexagonal honeycomb core is equivalent to a plate with orthotropic property by utilizing a Y model, and the equivalent physical property parameters are calculated as follows:

$E_{cx}=E_{cy}=\frac{4}{\sqrt{3}}{E}_s(1-3\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}$

$E_{cz}=\frac{2}{\sqrt{3}}{E}_s\frac{t_c}{l_c}$

$G_{cxy}=\frac{\sqrt{3}}{3}{E}_s(1-\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}$

$G_{cxz}=G_{cyz}=\frac{\sqrt{3}}{3}{\mathrm{rG}}_s\frac{t_c}{l_c}$

in the formula,E_cx,E_cyand E_czRespectively, the equivalent elastic modulus, G, of the honeycomb along the x, y and z directions_cxy,G_cxzAnd G_cyzDenotes the equivalent shear modulus in the xy, xz, yz directions, respectively, E_sDenotes the modulus of elasticity, G, of the honeycomb material_sIs the shear modulus, t, of the honeycomb material_c、l_cThe wall thickness and the side length of the regular hexagonal honeycomb are respectively, r is a correction coefficient and depends on the manufacturing process, and a theoretical value is 1;

3b2) in Ansys, defining the cell type used by each layer, wherein the upper panel and the lower panel use Solid45 entity cell type, and the bonding layer uses Inter205 interface cell type for simulation;

3b3) applying service load, and obtaining data of antenna structure array surface deformation, maximum stress and maximum deformation under the influence of the service load by using Ansys software.

Further, preprocessing the deformation data of the array surface to obtain the position error delta x of each radiation unit caused by the service load_ij(β,F)Δy_ij(β, F) and Δ z_ij(β, F) which are functions of the structural design parameter β and the service load size F, and the concrete implementation process is as follows:

(4a) extracting position coordinates { (x) of each radiation unit after deformation from the array surface deformation data subjected to service load analysis_ij,y_ij,z_ij) 1,2,., M, j ═ 1,2,.., N }, where x is_ij,y_ijRepresenting the horizontal coordinate of the deformed wavefront, z, of the ijth radiation element_ijThe height coordinate of the deformed array surface is shown, and M and N respectively represent the total number of the interlayer microstrip radiating units along the x direction and the y direction;

(4b) extracting expected position coordinates of each radiation unit from a finite element model without applied service load ${\mathrm{\Γ}}^o=\{(x_{ij}^o,y_{ij}^o,z_{ij}^o),i=1,2,...,M,j=1,2,...,N\},$ Wherein,representing the desired horizontal coordinate at the center of the ijth radiating element,representing the desired height coordinates at the center of the radiating element, their desired position coordinates being determined by antenna synthesis techniques in accordance with electrical performance specifications;

(4c) obtaining the expected position coordinates of each radiation unit^oAnd the position coordinates of each radiation unit after deformation, and calculating the position error of the ijth radiation unit relative to the expected position under the action of the service load, wherein the calculation is as follows:

${\mathrm{\Δx}}_{ij}(\mathrm{\β},F)=x_{ij}-x_{ij}^o$

${\mathrm{\Δy}}_{ij}(\mathrm{\β},F)=y_{ij}-y_{ij}^o$

${\mathrm{\Δz}}_{ij}(\mathrm{\β},F)=z_{ij}-z_{ij}^o$

in the formula,. DELTA.x_ij(β,F)、Δy_ij(β, F) and Δ z_ij(β, F) represents the coordinate position variation of the ijth radiating element, which is a function of the structural design parameter β and the service load size F, and the larger the load, the larger the position variation.

Further, according to the position error of each radiation unit, the data-driven coupling model is used for calculating the antenna array electrical property E under the condition of considering the joint influence of the position error of the array surface unit and the interlayer radiation unit_A(θ,φ)：

In the formula, M and N respectively represent the number of microstrip radiating elements along the x-axis and y-axis directions of a horizontal coordinate system, and the space between each radiating element is d_xAnd d_y，I_mnAnd phi_mnRespectively representing the amplitude and phase of the excitation current of the mn-th radiating element, k-2 pi/lambda₀Denotes the free space wave constant, λ₀Which represents the wavelength in free space, is,respectively, the antenna beam pointing directions, j denotes the complex imaginary part,an active interlayer radiation unit far field under the influence of a structural factor x;

the above formula is calculated using a data-driven modeling methodThe data-driven hybrid modeling method is concretely implemented as follows:

5a) firstly, the radiation unit far field of the microstrip radiation unit is calculated by using the existing calculation formula of the microstrip antenna radiation unit without considering the influence of skin, honeycomb, coating and bonding structural factorsThe calculation formula is as follows:

in the formula, L_d、W_dAnd h_dRespectively showing the length, the width and the thickness of the dielectric plate of the rectangular radiating element;

5b) and calculating the correction quantity of the influence of the thicknesses of the skin, the honeycomb, the coating and the bonding structural factors on the far field of the radiation unit by using a data-driven model, wherein the data-driven model is described as follows:

ΔF_E(x)＝Re(ΔF(x))+jIm(ΔF(x))

in the formula, the structural factor x ═ x₁,x₂,x₃,x₄]^TIs represented by the panel thickness x₁Adhesive thickness x₂Honeycomb thickness x₃And thickness x of the coating₄Formed vector, Δ F_E(x) The correction quantity of the far field of the sandwich microstrip radiating unit is a complex number and consists of a real part Re (delta F (x)) and an imaginary part Im (delta F (x)), and the real part Re (delta F (x)) and the imaginary part Im (delta F (x)) are both nonlinear functions of a structural factor x;

5c) according to the structural factor x ═ x₁,x₂,x₃,x₄]^TCalculating far field of sandwich microstrip radiating element including skin, honeycomb, coating and bonding factor influenceThe mathematical expression is as follows:

in the far-field calculation formula of the sandwich microstrip antenna radiation unit, the data driving model in the step 5b) is specifically realized by the following steps:

5b1) aiming at the microstrip radiating unit, before designing the interlayer microstrip antenna array, processing L interlayer microstrip radiating unit experiment samples by using a uniform experiment design method, wherein the samples can reflect the influence degree of the thicknesses of different panels, honeycombs, coatings and bonding layers on the interlayer microstrip radiating unit;

5b2) measuring the radiation unit far fields of the manufactured L experimental samples by using an antenna near field test system and a three-dimensional coordinate test instrument to obtain different structural factors x and L numbers corresponding to the radiation unit far fieldsAccording to the sample set { (x)_i,F_i),x_i∈R,F_i∈ C, i ═ 1.., L }, where the vector x ═ x ·, L }, where x ═ x₁,x₂,x₃,x₄]^TRepresenting a structural factor, F representing corresponding radiating element far field data;

5b3) from the above-mentioned radiation unit far-field data F and the conventional microstrip radiation unit far-field data calculated in 5a)Calculating the variation of the far field of the radiation unit under the influence of skin, honeycomb, coating and bonding structural factors:

5b4) the method comprises the steps of respectively calculating the variable quantities of L experimental samples with different structures and far fields corresponding to radiation units by using the formula, carrying out normalization processing on data, and further obtaining an experimental data set psi { (x)_i,ΔF_i),x_i∈R,ΔF_i∈ C, i 1.., L }, R and C respectively representing a real set and a complex set;

5b5) splitting the normalized data set Ψ into two subsets Ψ₁And Ψ₂And using omega { (x) in combination_i,t_i) I 1.. L } to represent the two subsets collectively, where t_iRepresenting real and imaginary data in a complex phasor Δ F;

5b6) for the sample subset Ω { (x)_i,t_i) 1.. L }, respectively establishing a meta-model of the structural factor x to a real part Re (Δ F (x)) and an imaginary part Im (Δ F (x)) in Δ F by using a kernel machine learning algorithm, wherein the meta-model is described by using the following formula in a unified manner:

$t\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0$

where t (x) can represent the real part Re (Δ F (x)) and imaginary part Im (Δ F (x)) of Δ F, which is a nonlinear function of x, k (x, x)_i) The kernel function is expressed, the regression problem of nonlinear data is solved by introducing the kernel function, the difficulty of directly searching nonlinear mapping is avoided, and L represents the number of data samples, omega_iRepresenting the weight, ω, corresponding to the kernel function₀Is a bias term;

5b7) the unknown parameter omega of the meta-model in the step 5b6) is obtained_iAnd ω₀The method is characterized by using two machine learning algorithms of linear programming support vector regression and correlation vector regression, and the solving process is as follows:

(one) solving for the unknown parameter ω if support vector regression is used_iAnd ω₀The solving process is as follows:

① first specifies a kernel function and then based on the normalized data sample subset Ω { (x)_i,t_i) L, determining the kernel parameters, the compromise constant C and the error margin using a 5-fold cross-validation method;

② the parameters are obtained by solving the following support vector regression algorithm using a linear programming algorithm based on the pre-specified kernel function type, kernel parameters, compromise constant C and error marginAnd a slack variable ξ_j：

$Find:{\mathrm{\ω}}_i^{+},{\mathrm{\ω}}_i^{-},{\mathrm{\ξ}}_j,{\mathrm{\ω}}_0$

$Min:\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}+{\mathrm{\ω}}_i^{-})+2C\underset{j=1}{\overset{L}{\Σ}}{\mathrm{\ξ}}_j$

$s.t.\left\{\begin{array}{c}{t}_j-\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)-{\mathrm{\ω}}_0\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ \underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)+{\mathrm{\ω}}_0-t_j\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ {\mathrm{\ω}}_i^{+}\≥0,{\mathrm{\ω}}_i^{-}\≥0\\ {\mathrm{\ξ}}_j\≥0,(\∀j=1,2,...,L)\end{array}\right.$

③ obtained from the aboveCalculating the unknown parameter ω in the data model using the following formula_i：

${\mathrm{\ω}}_i={\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_i^{-}$

④ solving the above solution to ω_iAnd ω₀In the formula substitution, obtaining a data model of the influence of structural factors of the interlayer microstrip antenna on a real part Re (delta F (x)) or an imaginary part Im (delta F (x)) in a far field variable quantity delta F of a microstrip radiation unit;

(II) solving the unknown parameter omega in step 5b6) if a correlation vector regression algorithm is used_iAnd ω₀Then the influence of noise needs to be considered, i.e. the meta-model in step 5b6) is re-represented as:

t(x)＝y(x)+

$y\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0$

where y (x) represents a prediction output without considering the influence of noise, and represents output noise satisfying the mean of 0 squareThe difference is sigma²T (x) represents the actual prediction output, and satisfies the mean y (x) and the variance σ²And independent normal distribution, the probability distribution of which is described asWherein the operatorMean μ and variance σ²Is defined as follows:

according to the normalized data sample subset Ω { (x)_i,t_i) And calculating an unknown parameter omega in the meta-model by using a solving method of the conventional correlation vector machine algorithm_i、ω₀And σ²；

5b8) And combining the obtained real part correction quantity and imaginary part correction quantity two element models according to the principle that the complex number consists of a real part and an imaginary part to obtain a data model of the influence of structural factors on the far field variable quantity of the radiation unit.

Further, the influence of the panel and the honeycomb on the gain of the sandwich microstrip antenna is considered in the calculation, and the calculation formula is as follows:

$S=\frac{{\mathrm{\Γ}}_{01}-{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_1(x_1+x_4)}+{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_o(2x_2+x_3+H_m)}-e^{-2j\[k_1(x_1+x_4)-k_o(2x_2+x_3+H_m)\]}}{1-{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_1(x_1+x_4)}+{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_o(2x_2+x_3+H_m)}-{\mathrm{\Γ}}_{01}{e}^{-2j\[k_1(x_1+x_4)-k_o(2x_2+x_3+H_m)\]}}$

in the formula, S represents the reflection coefficient of the interlayer microstrip antenna which takes the influences of the panel, the honeycomb, the bonding and the coating thickness into consideration and meets the condition of opening,which represents the wavelength constant in the panel, ${\mathrm{\Γ}}_{01}=(\sqrt{{\mathrm{\μ}}_r}-\sqrt{{\mathrm{\ϵ}}_r})/(\sqrt{{\mathrm{\μ}}_r}+\sqrt{{\mathrm{\ϵ}}_r})$ representing the partial reflection coefficient from free space to the panel, $k_0={\mathrm{\ω}}_f\sqrt{{\mathrm{\ϵ}}_0{\mathrm{\μ}}_0}$ is the wave constant, ω, in free space_fWhich represents the angular frequency of the free space,₀and mu₀Respectively representing the dielectric parameter and the permeability in free space,_rand mu_rRespectively, the dielectric parameter and the relative permeability, H, in the panel_mThe thickness of the radio frequency functional layer is indicated.

Further, according to the calculated electric field far field data E of the sandwich microstrip antenna array_A(theta, phi), constructing an interlayer microstrip antenna structure and an electromagnetic comprehensive optimization model to determine a structural design variable x ═ x₁,x₂,x₃,x₄,t_c,l_c]^TAnd the excitation current amplitude I of the microstrip radiating element_mnAnd phase phi_mn：

Find:x,I_mn,Φ_mn

Min:||E_A(θ,φ)-E^*(θ,φ)||

$s.t.\left\{\begin{array}{c}S\≤\[\mathrm{\ϵ}\]\\ v_{\max }\≤\[v\]\\ {\mathrm{\σ}}_{max}\≤\[\mathrm{\σ}\]\\ x_l\≤x\≤x_h\end{array}\right.$

In the formula, E^*(θ, φ) represents the far field of a given desired electric field, v_maxAnd σ_maxMaximum deformation and maximum stress, respectively, determined by the result of the Ansys analysis in the third step, x_l,x_hMinimum and maximum values of the structural design variable, [ alpha ]]、[v]And [ sigma ]]Respectively, the allowable reflection coefficient, maximum deformation and maximum stress, which are given by the design index, t_c,l_cRespectively representing the side length and the cell wall thickness, x, of the regular hexagonal honeycomb cell₁,x₂,x₃,x₄The meaning of the parameters of (A) is as described above. .

Further, the far field data E of the antenna electric field is obtained_A(theta, phi), determining sidelobe level and beam pointing electrical performance indexes, and calculating the gain of the interlayer microstrip antenna by using the following formula:

another objective of the embodiments of the present invention is to provide an active interlayer microstrip antenna, which mainly comprises an upper panel, a honeycomb, a radio frequency functional layer and a lower panel, wherein the upper panel, the lower panel and the honeycomb belong to a packaging functional layer, and have mechanical bearing and thermal insulation protection functions, and a stealth coating is usually further coated on the surface of the upper panel; the radio frequency functional layer mainly comprises a microstrip antenna array, an integrated T/R assembly, a power distribution circuit, a feed network of a liquid cooling channel, a beam signal control processing unit and the like, and mainly adopts a low-temperature co-fired ceramic material; by using an integrated molding manufacturing process, a radio frequency functional layer of the integrated microstrip antenna is embedded into a platform structure formed by a panel and a honeycomb, so that the integration of the structure and the electromagnetic function is realized.

Compared with the prior art, the invention has the following advantages:

1) the invention utilizes a data-driven modeling method to establish the structure and the electromagnetic coupling model of the active interlayer microstrip antenna, and the coupling model can analyze the position error of a array surface radiation unit caused by service load and the electrical property of the interlayer microstrip antenna under the influence of the interlayer radiation unit, thereby realizing the structure and electromagnetic integration analysis and overcoming the defect that the electromechanical integration design is difficult to realize by the current electromechanical separation method.

2) According to the method, two nuclear machine learning algorithms are used for establishing the data model of the far field influence of the panel, the honeycomb, the bonding, the coating and other factors on the interlayer radiation unit, the data model established by the algorithms is high in accuracy and sparse, the calculation complexity of the structure and electromagnetic comprehensive optimization design model is reduced, and the solving efficiency is improved.

(3) The structure and electromagnetism comprehensive design method not only utilizes the existing software such as Ansys to realize the accurate analysis of the mechanical property of the antenna structure, but also can realize the simultaneous optimal design of the active interlayer microstrip antenna structure and the electromagnetism, avoids the defects of the existing electromechanical separation and empirical design technology, shortens the development period, reduces the development cost and improves the mechanical and electrical properties of the product.

Drawings

FIG. 1 is a schematic diagram of the composition of an active sandwich microstrip antenna structure of the present invention;

FIG. 2 is a flow chart of the structural and electromagnetic integrated design method of the present invention;

FIG. 3 is a schematic diagram of the composition and geometry of the radio frequency functional layer of the present invention;

FIG. 4 is a dimensional representation of the honeycomb layer and honeycomb cells of the present invention;

FIG. 5 is a dimensional representation of a panel of the present invention;

fig. 6 is a schematic diagram of a microstrip antenna array layout and microstrip radiating elements according to the present invention;

FIG. 7 is a radiating element data-driven hybrid modeling method of the present invention;

FIG. 8 is a structural design variable of the integrated design method of the present invention;

FIG. 9 is a CAD drawing of a sandwich microstrip antenna sample of the present invention;

FIG. 10 is a finite element analysis model of a sandwich microstrip antenna of the present invention;

FIG. 11 is a diagram of a sandwich microstrip antenna configuration variation of the present invention;

FIG. 12 is a composite resulting normalized electric field pattern for the case of the present invention;

fig. 13 is a far field electric field comparison graph for the present case.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Fig. 1 shows a schematic structural composition diagram of an active interlayer microstrip antenna designed by the present invention, which mainly comprises an upper panel 1, a honeycomb 2, a radio frequency functional layer 3, a lower panel 4, and the like, wherein the upper and lower panels and the honeycomb belong to a packaging functional layer, have mechanical bearing and thermal insulation protection functions, and are usually coated with a stealth coating on the upper panel surface; the radio frequency functional layer mainly comprises a microstrip antenna array, a feed network of an integrated T/R assembly, a beam signal control processing unit and the like, and is mainly made of low temperature co-fired ceramic (LTCC) materials. By using an integrated molding manufacturing process, a radio frequency functional layer of the integrated microstrip antenna is embedded into a platform structure formed by a panel and a honeycomb, so that the integration of the structure and the electromagnetic function is realized. Compared with the traditional antenna, the active interlayer microstrip antenna has the characteristic of high integration of structure/circuit, the weight and the space occupancy rate of the antenna are reduced, and the conformity and the lightweight unification of the antenna and the structure are realized.

The invention is described in further detail below with reference to fig. 2.

Firstly, determining the radio frequency functional layer material, the geometric dimension and the array surface radiation unit layout of the integrated microstrip antenna according to given electrical performance indexes.

In this step, according to the electrical property design index such as gain, side lobe, center frequency, beam width and beam width, the shape, number and array layout of the microstrip radiating elements and the geometric dimension of the microstrip antenna array such as length L are determined by the existing antenna theory_mWidth W_m. In order to reduce the manufacturing difficulty, the length and the width of the specified radio frequency functional layer are the same as those of the microstrip antenna array. FIG. 3 shows the structural composition and geometry of the RF functional layer, wherein the height H in the RF functional layer_mThe thickness of the microstrip antenna dielectric plate, a feed network circuit (comprising the T/R component, the power dividing circuit and the liquid cooling channel) of the integrated T/R component, and a signal control and processing circuit (comprising the beam signal processing circuit, the monitoring circuit and the power circuit) are used for determining the thickness of the microstrip antenna dielectric plate. The material of the radio frequency functional layer is selected from polytetrafluoroethylene such as RT/duroid5880 and low temperature co-fired ceramic (LTCC)The microstrip radiating element array is etched on the dielectric plate through the existing manufacturing process to realize the required electrical performance.

And secondly, determining the geometric dimensions of the upper panel, the lower panel and the honeycomb according to the geometric dimensions of the radio frequency functional layer.

In this step, the geometry of the upper and lower panels and the honeycomb is generally determined by the installation space of the weapon platform. However, to facilitate the following design method description, the lengths L of the upper and lower surface plate layers and the honeycomb layer and the RF functional layer are selected according to the present invention_mAnd width W_mThe same applies to fig. 4 and 5, wherein fig. 4 also shows the cell size of a regular hexagon, for example the side length l_cAnd honeycomb wall thickness t_cThey affect the mechanical properties of the sandwich microstrip antenna. In addition to this, the panel thickness x₁Adhesive thickness x₂Honeycomb thickness x₃And thickness x of the coating₄Also influences the mechanical and electrical properties of the sandwich microstrip antenna, and their design is determined by the following steps.

Thirdly, obtaining array surface deformation data and maximum stress sigma of the antenna structure through mechanical analysis_maxAnd maximum deformation v_maxAnd waiting data, and concretely realizing the following steps:

3a) establishing a mechanical analysis model of the sandwich microstrip antenna under the action of service environment load such as pneumatic load or temperature load:

K＝F(1)

where K is the structural stiffness matrix, which is the structural design parameter β (e.g., length L of the panel, honeycomb, and radio frequency functional layers)_mAnd width W_m) And physical parameters (e.g., modulus of elasticity, poisson's ratio, and density) representing a finite element nodal displacement array, and F being a nodal load array representing aerodynamic and temperature loads, as well as load arrays derived from combinations thereof.

3b) According to the determined geometric dimensions of the skin, the honeycomb and the radio frequency functional layer, an Ansys command stream is utilized to establish an initial interlayer microstrip antenna statics analysis model, and the specific process is as follows:

3b1) determining equivalent material parameters such as density, elastic modulus and Poisson ratio of the skin, the honeycomb and the microstrip antenna layer, wherein the regular hexagonal honeycomb core is equivalent to a plate with orthotropic property by utilizing a Y model, and the equivalent physical property parameters are calculated as follows:

$\begin{array}{c}{E}_{cx}=E_{cy}=\frac{4}{\sqrt{3}}{E}_s(1-3\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}\\ E_{cz}=\frac{2}{\sqrt{3}}{E}_s\frac{t_c}{l_c}\end{array}---\left(2\right)$

$\begin{array}{c}{G}_{cxy}=\frac{\sqrt{3}}{3}{E}_s(1-\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}\\ G_{cxz}=G_{cyz}=\frac{\sqrt{3}}{3}{\mathrm{rG}}_s\frac{t_c}{l_c}\end{array}---\left(3\right)$

in the formula, E_cx,E_cyAnd E_czRespectively, the equivalent elastic modulus, G, of the honeycomb along the x, y and z directions_cxy,G_cxzAnd G_cyzDenotes the equivalent shear modulus in the xy, xz, yz directions, respectively, E_sDenotes the modulus of elasticity, G, of the honeycomb material_sIs the shear modulus, t, of the honeycomb material_c、l_cThe wall thickness and the side length of the regular hexagonal honeycomb respectively are shown, r is a correction coefficient and depends on the manufacturing process, and the theoretical value is 1.

3b2) In Ansys, defining the cell type used by each layer, wherein the upper panel and the lower panel use Solid45 entity cell type, and the bonding layer uses Inter205 interface cell type for simulation;

3b3) applying a service load, and acquiring data such as antenna structure array surface deformation, maximum stress, maximum deformation and the like under the influence of the service load by using Ansys software;

fourthly, preprocessing the deformation data of the array surface to obtain the position error delta x of each radiation unit caused by the service load_ij(β,F)Δy_ij(β, F) and Δ z_ij(β, F) which are functions of the structural design parameter β and the service load size F, and the concrete implementation process is as follows:

(4a) extracting position coordinates { (x) of each radiation unit after deformation from the array surface deformation data subjected to service load analysis_ij,y_ij,z_ij) 1,2,., M, j ═ 1,2,.., N }, where x is_ij,y_ijRepresenting the horizontal coordinate of the deformed wavefront, z, of the ijth radiation element_ijThe height coordinate of the deformed array surface is shown, and M and N represent the total number of the interlayer microstrip radiating units along the x and y directions;

(4b) extracting expected position coordinates of each radiation unit from a finite element model without applied service load ${\mathrm{\Γ}}^o=\{(x_{ij}^o,y_{ij}^o,z_{ij}^o),i=1,2,...,M,j=1,2,...,N\},$ Wherein,representing the desired horizontal coordinate at the center of the ijth radiating element,representing the expected height coordinates at the center of the ijth radiating element, and the expected position coordinates of the ijth radiating element are determined by utilizing an antenna synthesis technology according to the electrical performance index;

(4c) obtaining the expected position coordinates of each radiation unit^oAnd the position coordinates of each radiation unit after deformation, and calculating the position error of the ijth radiation unit relative to the expected position under the action of the service load, wherein the calculation is as follows:

$\begin{array}{c}{\mathrm{\Δx}}_{ij}(\mathrm{\β},F)=x_{ij}-x_{ij}^o\\ {\mathrm{\Δy}}_{ij}(\mathrm{\β},F)=y_{ij}-y_{ij}^o\\ {\mathrm{\Δz}}_{ij}(\mathrm{\β},F)=z_{ij}-z_{ij}^o\end{array}---\left(4\right)$

in the formula,. DELTA.x_ij(β,F)、Δy_ij(β, F) and Δ z_ij(β, F) represents the coordinate position variation of the ijth radiating element, which is a function of the structural design parameter β and the service load size F, and the larger the load, the larger the position variation.

These changes in the position of the radiating elements reflect the inevitable impact of shock, temperature and aerodynamic loads on the weapon platform structure during rapid maneuvers. These loads can cause the structure to deform, which in turn can cause changes in the position of the microstrip antenna array elements embedded in the structure. The change of the position of the antenna radiation unit can cause the phase error of the radiation unit, and further cause the performance of an antenna array radiation directional diagram to generate larger change, namely the change of beam pointing and the increase of side lobe level can be caused, wherein the beam pointing directly influences the accuracy of antenna positioning, and for a synthetic aperture radar, the radar imaging quality is directly influenced; while an increase in the sidelobe level results in a decrease in the radar immunity.

Fifthly, according to the position errors of the radiation units, the data-driven coupling model is used for calculating the antenna array electrical property E under the joint influence of the position errors of the array plane units and the interlayer radiation units_A(θ,φ)：

Wherein M and N represent the number of microstrip radiating elements along the x-axis and y-axis directions of the horizontal coordinate system, respectively, and FIG. 6(a) shows that the microstrip radiating elements are arranged in an equidistant rectangular grid array, the array antenna has MN radiating elements in total, and is located on the oxy plane, and the distance between each radiating element is d_xAnd d_yEach unit is a rectangular microstrip radiating unit widely used in engineering, and a rectangular microstrip radiating unit structure is shown in figure 6(b), wherein L is shown in the figure_d、W_dAnd h_dRespectively showing the length, the width and the thickness of the dielectric plate of the rectangular radiating element; i is_mnAnd phi_mnRespectively representing the amplitude and the phase of the excitation current of the nth radiation unit; k 2 pi/lambda₀Denotes the free space wave constant, λ₀Which represents the wavelength in free space, is,respectively representing the pointing directions of the antenna beams; j represents the imaginary part of the complex number,showing the far field of the active sandwich radiating element under the influence of the structural factor x.

The key feature of the above formula is that it is calculated using a data-driven modeling methodFig. 7 is a schematic diagram of a data-driven hybrid modeling method proposed by the present invention, and referring to fig. 7, the specific implementation process is as follows:

5a) firstly, the radiation unit far field of the microstrip radiation unit is calculated by using the existing calculation formula of the microstrip antenna radiation unit without considering the influence of skin, honeycomb, coating, bonding and other structural factorsThe calculation formula is as follows:

in the formula, L_d、W_dAnd h_dRespectively, the length, width and dielectric plate thickness of the rectangular radiating element are shown in fig. 6 (b).

5b) And calculating the correction quantity of the influence of the thickness of structural factors such as skin, honeycomb, coating, bonding and the like on the far field of the radiation unit by using a data-driven model, wherein the data-driven model is described as follows:

ΔF_E(x)＝Re(ΔF(x))+jIm(ΔF(x))(7)

in the formula, the structural factor x ═ x₁,x₂,x₃,x₄]^TIs represented by the panel thickness x₁Adhesive thickness x₂Honeycomb thickness x₃And thickness x of the coating₄Formed vector, Δ F_E(x) The correction quantity of far field of the sandwich microstrip radiating element is a complex quantity and consists of a real part Re (delta F (x)) and an imaginary part Im (delta F (x)))Composition, both of which are non-linear functions of the construction factor x.

5c) According to the structural factor x ═ x₁,x₂,x₃,x₄]^TCalculating far field of sandwich microstrip radiating element including skin, honeycomb, coating and bonding factor influenceThe mathematical expression is as follows:

in the far-field calculation formula of the sandwich microstrip antenna radiation unit, the key characteristic is that the data driving model in the step 5b) is specifically realized by the following steps:

5b1) aiming at the microstrip radiating unit, before designing the interlayer microstrip antenna array, processing L interlayer microstrip radiating unit experiment samples by using a uniform experiment design method, wherein the samples can reflect the influence degree of the thicknesses of different panels, honeycombs, coatings and bonding layers on the interlayer microstrip radiating unit;

5b2) measuring the radiation unit far fields of the manufactured L experimental samples by using an antenna near-field test system and a three-dimensional coordinate test instrument to obtain L data sample sets { (x) of different structural factors x and corresponding radiation unit far fields_i,F_i),x_i∈R,F_i∈ C, i ═ 1.., L }, where the vector x ═ x ·, L }, where x ═ x₁,x₂,x₃,x₄]^TRepresenting structural factors, F representing corresponding radiation unit far-field data, and R and C representing a real number set and a complex number set respectively;

5b3) from the above-mentioned radiation unit far-field data F and the conventional microstrip radiation unit far-field data calculated in 5a)Calculating skin, honeycomb, coating and adhesionThe change of the far field of the radiation unit under the influence of the following factors:

5b4) the method comprises the steps of respectively calculating the variable quantities of L experimental samples with different structures and far fields corresponding to radiation units by using the formula, carrying out normalization processing on data, and further obtaining an experimental data set psi { (x)_i,ΔF_i),x_i∈R,ΔF_i∈C,i＝1,...,L}；

5b5) Splitting the normalized data set Ψ into two subsets Ψ₁And Ψ₂And using omega { (x) in combination_i,t_i) I 1.. L } to represent the two subsets collectively, where t_iRepresenting real or imaginary data in a complex phasor Δ F;

5b6) for the sample subset Ω { (x)_i,t_i) 1.. L }, respectively establishing a meta-model of the structural factor x to a real part Re (Δ F (x)) and an imaginary part Im (Δ F (x)) in Δ F by using a kernel machine learning algorithm, wherein the meta-model is described by using the following formula in a unified manner:

$t\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0---\left(10\right)$

wherein t (x) represents a real part Re (Δ F (x)) or an imaginary part Im (Δ F (x)) in Δ F, which is a nonlinear function of x, k (x, x)_i) The kernel function is shown in table 1, the regression problem of nonlinear data is solved by introducing the kernel function, the difficulty of directly searching nonlinear mapping is avoided, and L represents the number of data samples, omega_iRepresenting the weight, ω, corresponding to the kernel function₀Is a bias term;

TABLE 1 Kernel function used in the invention

5b7) Combining the two element models of the correction quantity of the real part and the imaginary part to obtain a data model of the influence of the structural factors on the far field variation of the interlayer radiation unit in the step 5 b);

unknown parameter ω in the above-mentioned meta model_iAnd ω₀The following two kernel machine learning algorithms can be used for solving, and the specific solving processes of the two algorithms are as follows.

(one) solving for the unknown parameter ω in the model if support vector regression is used_iAnd ω₀The solving process is as follows:

① first specifies a kernel function and then based on the normalized data sample subset Ω { (x)_i,t_i) L, determining kernel parameters, compromise constant C and error margin using a 5-fold cross-validation method;

② solving the following support vector regression algorithm by using a linear programming algorithm according to the pre-specified kernel function type, kernel parameters, compromise constant C and error tolerance to obtain the parameters to be solvedAnd a slack variable ξ_j：

$\begin{array}{c}Find:{\mathrm{\ω}}_i^{+},{\mathrm{\ω}}_i^{-},{\mathrm{\ξ}}_j,{\mathrm{\ω}}_0\\ Min:\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}+{\mathrm{\ω}}_i^{-})+2C\underset{j=1}{\overset{L}{\Σ}}{\mathrm{\ξ}}_j\\ s.t.\left\{\begin{array}{c}{t}_j-\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)-{\mathrm{\ω}}_0\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ \underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)+{\mathrm{\ω}}_0-t_j\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ {\mathrm{\ω}}_i^{+}\≥0,{\mathrm{\ω}}_i^{-}\≥0\\ {\mathrm{\ξ}}_j\≥0,(\∀j=1,2,...,L)\end{array}\right.\end{array}---\left(11\right)$

③ calculated according to the aboveObtained byCalculating the unknown parameter ω in the data model using the following formula_i：

${\mathrm{\ω}}_i={\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_i^{-}---\left(12\right)$

④ solving the above solution to ω_iAnd ω₀In the formula, a data model of the influence of the structural factor of the sandwich microstrip antenna on the real part Re (delta F (x)) or the imaginary part Im (delta F (x)) in the far field variation delta F of the microstrip radiation unit is obtained.

(II) solving the unknown parameter ω in the model if correlation vector regression is used_iAnd ω₀The implementation process is as follows:

the relevance vector regression and the support vector regression belong to a kernel machine learning algorithm, and compared with the support vector regression, the model obtained by the relevance vector regression is simplest. In addition, the relevance vector regression can give not only the data model, but also the probability distribution of the predicted output of the model. Therefore, if the influence of the prediction output noise is considered, the model shown in equation (10) can also be expressed as:

$y\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0---\left(13\right)$

t(x)＝y(x)+(14)

where y (x) represents the predicted output without considering the influence of noise, represents the output noise error, and satisfies that the mean is 0 and the variance is σ²T (x) represents the actual prediction output, and they satisfy the mean y (x) and the variance σ²And independent normal distribution, the probability distribution of which is described asWherein the operatorMean μ and variance σ²Is defined as follows:

from the above analysis, the models shown in equations (13) and (14) can also be expressed using vectors as

t(x)＝Φω+(16)

In the formula, the time of omega is determined by the weight value omega_iThe component vector ω ═ ω₀,ω₁,ω₂…ω_L]^TΦ is a design matrix with dimension L × (L +1) obtained by substituting each structural factor x into the kernel function:

data sample subset with normalization Ω { (x)_i,t_i) I 1.. L } solving the variance of the unknown parameter ω and the output noise in the data model to σ²The specific solving process is as follows:

① Pre-selects the kernel function type and kernel function shown in the Table, initializes the predicted output noise variance σ²The weight value over-parameter α is [ α ]₀,α₁,α₂,…,α_L]^TAnd a maximum number of iterations;

② calculating weight ω ═ ω from the design matrix Φ and training data samples t given above₀,ω₁,ω₂…ω_N]^TThe posterior probability distribution of (a):

$p\left(\mathrm{\ω}\right|t,\mathrm{\α},{\mathrm{\σ}}^2)={\left(2\mathrm{\π}\right)}^{-\frac{L+1}{2}}{\left|\mathrm{\Σ}\right|}^{-\frac{1}{2}}\exp \[-\frac{{(\mathrm{\ω}-\mathrm{\μ})}^T{\mathrm{\Σ}}^{-1}(\mathrm{\ω}-\mathrm{\μ})}{2}\]---\left(18\right)$

the calculation formula of the mean value mu and the covariance Σ of the weight ω is as follows:

μ＝σ^-2ΣΦ^Tt(19)

Σ＝(σ^-2Φ^TΦ+A)^-1(20)

in the formula, the matrices Ω and a are mathematically expressed as follows:

Ω＝σ²I+ΦA^-1Φ^T(21)

in the formula, I represents an identity matrix, and other parameters are as described above.

③ according to the above-mentioned hyper-parameter α ═ α₀,α₁,α₂,…,α_L]^TAnd covariance matrix sigma, calculating an intermediate quantity parameter gamma_i：

γ_i＝1-α_iΣ_i,i(23)

In the formula, sigma_i,iIs the ith diagonal cell element, gamma, in the covariance matrix sigma of the a posteriori weights omega_i∈[0,1]Is a measure representing ω estimated by the training data_iDegree of credibility when α_iWhen the weight is very large, the weight omega_iDue to prior knowledgeCan lead to gamma_i0, otherwise, when α_iSmaller, gamma_i＝1；

④ the hyper-parameter vector α ═ α is estimated using the equation₀,α₁,α₂,…,α_L]^TAnd the predicted output variance σ²：

${\mathrm{\α}}_i^{new}=\frac{{\mathrm{\γ}}_i}{{\mathrm{\μ}}_i^2}---\left(24\right)$

${\left({\mathrm{\σ}}^2\right)}^{new}=\frac{\left|\right|t-\mathrm{\Φ}\mathrm{\μ}|{|}^2}{L-{\mathrm{\Σ}}_{i=0}^L{\mathrm{\γ}}_i}---\left(25\right)$

In the formula,andrespectively representing the hyper-parameter and the predicted output noise variance, mu, after iterative update using the above formula_iRepresenting the mean value of the ith unit in the weight vector omega;

⑤ orderAndthen return to step ② to restart the next iterative solution when max (log α) is satisfied_i)≤10^-3And when the time or the iteration times reach the times specified in advance, the iteration solution is finished.

⑥ at the end of the above iteration, the obtained superparameter α ═ α₀,α₁,α₂,…,α_L]^TPredicted output variance σ²The mean μ of the weight ω, and the covariance Σ, where some cells of the hyperparametric vector α will tend to infinity, corresponding to the weight ω according to equation (24)_iIs 0, which means that the corresponding basis function can be pruned, which is specified in the present invention as α_i≥10⁹And pruning the basis functions to further realize model sparseness.

⑦ substituting the mean value mu into ω to obtain new data x_*Corresponding output t_*Data driven model of

And

output t_*Probability distribution of (2):

y(x_*)＝μ^Tφ(x_*)(26)

in the formula, new data x_*Corresponding basis function vector phi (x)_*)＝[1,k(x_*,x₁),k(x_*,x₂),...,k(x_*,x_L)]^TPredicting the output t_*Satisfy the mean value of y (x)_*) And variance ofA Gaussian distribution of whereinIndicating that the final solution of the above step ⑥ yields the estimated noise variance σ²。

Sixthly, calculating and considering the influence of the panel and the honeycomb on the gain of the sandwich microstrip antenna, wherein the influence reflects the wave-transparent performance of electromagnetic waves, and the calculation formula is as follows:

$S=\frac{{\mathrm{\Γ}}_{01}-{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_1(x_1+x_4)}+{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_o(2x_2+x_3+H_m)}-e^{-2j\[k_1(x_1+x_4)-k_o(2x_2+x_3+H_m)\]}}{1-{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_1(x_1+x_4)}+{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_o(2x_2+x_3+H_m)}-{\mathrm{\Γ}}_{01}{e}^{-2j\[k_1(x_1+x_4)-k_o(2x_2+x_3+H_m)\]}}---\left(28\right)$

in the formula, S represents the reflection coefficient of the interlayer microstrip antenna which takes the influences of the panel, the honeycomb, the bonding and the coating thickness into consideration and meets the condition of opening,which represents the wavelength constant in the panel, ${\mathrm{\Γ}}_{01}=(\sqrt{{\mathrm{\μ}}_r}-\sqrt{{\mathrm{\ϵ}}_r})/(\sqrt{{\mathrm{\μ}}_r}+\sqrt{{\mathrm{\ϵ}}_r})$ representing the partial reflection coefficient from free space to the panel, $k_0={\mathrm{\ω}}_f\sqrt{{\mathrm{\ϵ}}_0{\mathrm{\μ}}_0}$ is the wave constant, ω, in free space_fWhich represents the angular frequency of the free space,_rand mu_rRespectively representing the dielectric parameters and the relative permeability within the panel,₀and mu₀Respectively representing the dielectric parameter and the magnetic permeability in free space, parameter x₁,x₂,x₃,x₄And H_mSee figure 8.

Seventhly, according to the electric field far field data E of the interlayer microstrip antenna array obtained by the calculation in the fifth step_A(theta, phi), constructing an interlayer microstrip antenna structure and an electromagnetic comprehensive optimization model to determine a structural design variable x ═ x₁,x₂,x₃,x₄,t_c,l_c]^TAnd the excitation current amplitude I of the microstrip radiating element_mnAnd phase phi_mn：

$\begin{array}{c}Find:x,I_{mn},{\mathrm{\Φ}}_{mn}\\ Min:\left|\right|E_A(\mathrm{\θ},\mathrm{\φ})-E^{*}(\mathrm{\θ},\mathrm{\φ})\left|\right|\\ s.t.\left\{\begin{array}{c}S\≤\[\mathrm{\ϵ}\]\\ v_{\max }\≤\[v\]\\ {\mathrm{\σ}}_{max}\≤\[\mathrm{\σ}\]\\ x_l\≤x\≤x_h\end{array}\right.\end{array}---\left(29\right)$

In the formula, E^*(θ, φ) represents the far field of a given desired electric field, v_maxAnd σ_maxMaximum deformation and maximum stress, respectively, determined by the result of the Ansys analysis in the third step, x_l,x_hMinimum and maximum values of the structural design variable, [ alpha ]]、[v]And [ sigma ]]Respectively, the allowable reflection coefficient, maximum deformation and maximum stress, given by the design specifications, the other parameters being as previously described.

And eighthly, solving the comprehensive optimization model by using the existing optimization algorithm, judging whether the result is converged, if not, updating the result obtained by the solution to the initial value of the design variable, returning to the third step, and restarting the next solution, otherwise, obtaining the result of the optimal structure parameter and the excitation current meeting the power and electricity performance.

Ninth, according to the obtained antenna electric field far field data E_A(theta, phi), determining electric performance indexes such as side lobe level and beam direction, and calculating the gain of the sandwich microstrip antenna by using the following formula:

and tenth step, designing a feed network in the active interlayer microstrip antenna by using HFSS software according to the amplitude and the phase of the radiation unit excitation current obtained by the synthesis, and finally manufacturing the antenna by using an integrated molding process.

The advantages of the present invention can be further illustrated by the following S-band sandwich microstrip antenna.

The effectiveness of the structure and the electromagnetic comprehensive design method is verified by taking the sandwich microstrip antenna with the center frequency of 2.5GHz as a case. The design indexes of the interlayer microstrip antenna are as follows: the gain is larger than 15dB, the bandwidth is larger than 50MHz, the side lobe is larger than 12dB, and the bending rigidity is larger than 160N/mm.

According to the electrical performance indexes, firstly, the layout and the geometric dimension of the microstrip antenna of the radio frequency functional layer are designed. In this sample, we designed 8 microstrip radiating elements, whose length and width are 800mm and 200mm, respectively. The CAD of the proof sample is shown in fig. 9, which also shows the initial thicknesses of the face sheet, honeycomb and radio frequency functional layer, which are 2.5mm, 22.5mm and 3mm, respectively, which are not the final design result.

By using the method of the present invention, the CAD model is imported into Ansys software to build a geometric model thereof, as shown in FIG. 10. In the case, the panel, the honeycomb and the radio frequency function layer are selected to use Solid45 entity unit types, and the interlayer bonding interface is simulated by adopting an Inter205 interface unit type. When the grid is divided, 40 nodes are taken in the length direction, 9 nodes are taken in the width direction, and 10 nodes are taken in the thickness direction. The distributed load 1000N is applied to the node of the symmetry line of the model, and displacement constraint in three directions is applied to the node of the two symmetric bottom edges of the model, as shown in the attached figure 10. In addition, some physical parameters need to be set in Ansys, in this case, the upper and lower panels use glass fiber reinforced plastic epoxy resin composite material plates, the radio frequency functional layer uses RT/duroid5880 material, the honeycomb layer uses regular hexagonal paper honeycomb, the initial values of wall thickness and side length are t_c0.6mm and l_c5mm, the modulus of elasticity of the honeycomb is E_s3600MPa and shear modulus G_s1900MPa, utilizeThe formula given in the third step of the present invention can calculate the equivalent parameters of the panel, the honeycomb layer and the radio frequency functional layer, as shown in table 2. The parameters are input into Ansys software, and then the mechanical property of the verification sample piece can be analyzed by applying load, so that data such as the deformation amount of the front surface, the maximum stress, the maximum deformation amount and the like can be obtained. Figure 11 shows the results of a structural deformation analysis in which the deformation front represents the deformation of the antenna array structure after application of a load, while the ideal front represents the desired array structure without application of a load.

TABLE 2 equivalent parameters used for mechanical analysis

According to the data-driven design method, the structural parameter x ═ x in the case is synthesized₁,x₂,x₃,x₄,t_c,l_c]^TAnd the excitation current amplitude I of each microstrip radiating element_mnAnd phase phi_mnSo that it meets the pre-given desired electric field far field, see the desired electric field curve in fig. 11. In the solving equation, in this case]、[v]And [ sigma ]]Is 1, 0.1mm and 300MPa, the minimum range x of x_lAnd a maximum range x_hAre each x_l＝[1,0.01,5,0.01,0.1,4]^Tmm，x_h＝[10,2,50,1,2,8]^Tmm. Solving the formula by using a particle swarm optimization algorithm to obtain a design result meeting the expected mechanical and electrical performance index. Solving to obtain the structural factor x ═ 2.31,0.32,7.25,0.56,0.74,5.3]^TThe excitation current amplitudes and phases of the 8 microstrip radiating elements are shown in table 3, the synthesized normalized far-field pattern is shown in fig. 12, and it can be seen from the figure that the far-field pattern synthesized by using the structure and the electromagnetism is almost the same as the expected electric field, especially the synthesized side lobe is 14.34dB, and the expected side lobe requirement is met.

TABLE 3 amplitude and phase of the integrated radiating element excitation current

And calculating the gain of the current excitation according to the integrated current excitation by using a formula. Fig. 13 shows the far field electric field after the sandwich microstrip antenna is synthesized, the maximum electric field strength, namely the gain, can be found from the figure to be 15.9dB, and the bending rigidity after the synthesis by the method of the invention can be calculated to be 176N/m through Ansys mechanical analysis. Table 4 shows the comparison between the electrical performance index obtained after the antenna is synthesized and the expected design index, and it can be seen from the table that the active interlayer microstrip antenna designed by the method of the present invention completely meets the expected design index.

Table 4 comprehensive optimization results of active sandwich microstrip antenna

In order to further verify the effectiveness of the method, the case also uses the traditional electromechanical separation design method to design the case antenna from the structural and electromagnetic disciplines. FIG. 13 shows the far field electric field pattern after the two methods are combined, and it can be seen from the figure that the gain obtained by the method of the present invention is more than 0.5dB than the gain obtained by the electromechanical separation method, and through mechanical analysis, the maximum deformation of the antenna array surface structure under load is 0.035mm, and the maximum deformation of the electromechanical separation method is 0.15mm, which means that the bending rigidity is poor, which indicates that the rigidity of the antenna structure obtained by the method of the present invention is better than that of the conventional method.

Through experiments in the case, the invention can realize the optimal design of the structure and the electromagnetism of the active interlayer microstrip antenna at the same time, avoid the defects of the traditional electromechanical separation and empirical design method, shorten the development period and improve the mechanical and electromagnetic properties of the product.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (3)

1. A data drive design method for integrating an active interlayer microstrip antenna structure and electromagnetism is characterized by comprising the following steps of:

firstly, determining a radio frequency functional layer material, a geometric dimension and a layout of a front surface radiation unit in the interlayer microstrip antenna according to a given electrical performance index;

secondly, determining the geometric dimensions of the upper panel, the lower panel and the honeycomb according to the geometric dimensions of the radio frequency functional layer;

thirdly, obtaining array surface deformation data and maximum stress sigma of the antenna structure through mechanical analysis_maxAnd maximum deformation v_maxData;

fourthly, preprocessing the deformation data of the array surface to obtain the position error delta x of each radiation unit caused by the service load_ij(β,F)、Δy_ij(β, F) and Δ z_ij(β, F) which are functions of the structural design parameters β and the in-service load magnitude F;

fifthly, according to the position errors of the radiation units, calculating far field data of an antenna array electric field under the joint influence of the array plane unit position errors and the interlayer radiation units by using a data-driven coupling model;

sixthly, calculating and considering the influence of the panel and the honeycomb on the gain of the sandwich microstrip antenna;

seventhly, according to the electric field far field data E of the interlayer microstrip antenna array obtained by the calculation in the fifth step_A(theta, phi), constructing an interlayer microstrip antenna structure and an electromagnetic comprehensive optimization model to determine structural design variables and the amplitude and phase of an excitation current of a microstrip radiation unit;

eighthly, solving the comprehensive optimization model by using an optimization algorithm, judging whether the result is converged, if not, updating the result obtained by solving to the initial value of the design variable, returning to the third step, and restarting the next solving, otherwise, obtaining the result of the optimal structural parameter and the excitation current which meet the power and electricity performance;

ninth, according to the obtained antenna electric field far field data E_A(theta, phi), determining sidelobe level and beam pointing electrical performance indexes, and calculating the gain of the interlayer microstrip antenna;

tenth step, according to the amplitude and phase of the radiation unit exciting current obtained by the synthesis, designing a feed network in the active interlayer microstrip antenna by using HFSS software, and finally manufacturing the antenna by using an integrated molding process;

the method for determining the radio frequency functional layer material, the geometric dimension and the array surface radiation unit layout of the interlayer microstrip antenna according to the given electrical performance index comprises the following steps:

based on the electrical performance design criteria such as gain, sidelobe, center frequency and beam width,firstly, the shape, number and array layout of the microstrip radiating elements and the geometric dimension of the microstrip antenna array, such as the length L, are determined by utilizing the existing antenna theory_mWidth W_m(ii) a In order to reduce the manufacturing difficulty, the length and the width of the specified radio frequency functional layer are the same as those of the microstrip antenna array; height H in the radio frequency functional layer_mThe thickness of the microstrip antenna dielectric plate, the feed network circuit of the integrated T/R component and the thickness of the signal control and processing circuit are determined; the material of the radio frequency functional layer is polytetrafluoroethylene and low-temperature co-fired ceramic, and the microstrip radiating element array is etched on the dielectric plate to realize the required electrical performance;

according to the geometric dimension of the radio frequency functional layer, the method for determining the geometric dimensions of the upper panel, the lower panel and the honeycomb comprises the following steps:

the geometric dimensions of the upper and lower panels and the honeycomb are generally determined by the installation space of the weapon platform; selecting the lengths L of the upper and lower surface plate layers and the honeycomb layer and the radio frequency functional layer_mAnd width W_mThe same;

obtaining array surface deformation data and maximum stress sigma of antenna structure through mechanical analysis_maxAnd maximum deformation v_maxThe specific implementation process of the data is as follows:

3a) establishing a mechanical analysis model of the sandwich microstrip antenna under the action of service environment load such as pneumatic load or temperature load:

K＝F

in the formula, K is a structural rigidity matrix which is a function of a structural design parameter beta and a physical property parameter and represents a finite element node displacement array, F is a node load array which represents pneumatic load and temperature load and can also be a load array obtained by combining the pneumatic load and the temperature load;

3b) according to the determined geometric dimensions of the skin, the honeycomb and the radio frequency functional layer, an Ansys command stream is utilized to establish an initial interlayer microstrip antenna statics analysis model, and the specific process is as follows:

3b1) determining equivalent material parameters such as density, elastic modulus and Poisson ratio of the skin, the honeycomb and the microstrip antenna layer, wherein the regular hexagonal honeycomb core is equivalent to a plate with orthotropic property by utilizing a Y model, and the equivalent physical property parameters are calculated as follows:

$E_{cx}=E_{cy}=\frac{4}{\sqrt{3}}{E}_s(1-3\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}$

$E_{cz}=\frac{2}{\sqrt{3}}{E}_s\frac{t_c}{l_c}$

$G_{cxy}=\frac{\sqrt{3}}{3}{E}_s(1-\frac{t_c^2}{l_c^2})\frac{t_c^3}{l_c^3}$

$G_{cxz}=G_{cyz}=\frac{\sqrt{3}}{3}{\mathrm{rG}}_s\frac{t_c}{l_c}$

in the formula, E_cx,E_cyAnd E_czRespectively, the equivalent elastic modulus, G, of the honeycomb along the x, y and z directions_cxy,G_cxzAnd G_cyzDenotes the equivalent shear modulus in the xy, xz, yz directions, respectively, E_sDenotes the modulus of elasticity, G, of the honeycomb material_sIs the shear modulus, t, of the honeycomb material_c、l_cThe wall thickness and the side length of the regular hexagonal honeycomb are respectively, r is a correction coefficient and depends on the manufacturing process, and a theoretical value is 1;

3b2) in Ansys, the cell type used by each layer is defined, Solid45 entity cell types are used by the upper panel and the lower panel, and an Inter205 interface cell type is used by the bonding layer for simulation;

3b3) applying a service load, and acquiring data of array surface deformation, maximum stress and maximum deformation of the antenna structure under the influence of the service load by using Ansys software;

preprocessing array surface deformation data to obtain each radiation unit caused by service loadPosition error Δ x_ij(β,F)Δy_ij(β, F) and Δ z_ij(β, F) which are functions of the structural design parameter β and the service load size F, and the concrete implementation process is as follows:

(4a) extracting position coordinates { (x) of each radiation unit after deformation from the array surface deformation data subjected to service load analysis_ij,y_ij,z_ij) 1,2,., M, j ═ 1,2,.., N }, where x is_ij,y_ijRepresenting the horizontal coordinate of the deformed wavefront, z, of the ijth radiation element_ijThe height coordinate of the deformed array surface is shown, and M and N respectively represent the total number of the interlayer microstrip radiating units along the x direction and the y direction;

(4b) extracting expected position coordinates of each radiation unit from a finite element model without applied service load ${\mathrm{\Γ}}^o=\{(x_{ij}^o,y_{ij}^o,z_{ij}^o),i=1,2,...,M,j=1,2,...,N\},$ Wherein,representing the desired horizontal coordinate at the center of the ijth radiating element,representing the desired height coordinates at the center of the radiating element, their desired position coordinates being determined by antenna synthesis techniques in accordance with electrical performance specifications;

(4c) according to the obtained expected position coordinates of each radiation unit^oAnd the position coordinates of each radiation unit after deformation, and calculating the position error of the ijth radiation unit relative to the expected position under the action of the service load, wherein the calculation is as follows:

${\mathrm{\Δx}}_{ij}(\mathrm{\β},F)=x_{ij}-x_{ij}^o$

${\mathrm{\Δy}}_{ij}(\mathrm{\β},F)=y_{ij}-y_{ij}^o$

${\mathrm{\Δz}}_{ij}(\mathrm{\β},F)=z_{ij}-z_{ij}^o$

in the formula,. DELTA.x_ij(β,F)、Δy_ij(β, F) and Δ z_ij(β, F) represents the coordinate position variation of the ijth radiating element, which is a function of the structural design parameter β and the service load size F, wherein the position variation is larger when the load is larger;

according to the position errors of the radiation units, calculating far field data E of the antenna array electric field under the joint influence of the position errors of the array surface units and the interlayer radiation units by using a data-driven coupling model_A(θ,φ)：

In the formula, M and N respectively represent the number of microstrip radiating elements along the x-axis and y-axis directions of a horizontal coordinate system, and the space between each radiating element is d_xAnd d_y，I_mnAnd phi_mnRespectively representing the amplitude and phase of the excitation current of the mn-th radiating element, k-2 pi/lambda₀Denotes the free space wave constant, λ₀Which represents the wavelength in free space, is,respectively, the antenna beam pointing directions, j denotes the complex imaginary part,an active interlayer radiation unit far field under the influence of a structural factor x;

the above formula is calculated using a data-driven modeling methodThe data-driven hybrid modeling method is concretely implemented as follows:

5a) firstly, the radiation unit far field of the microstrip radiation unit is calculated by using the existing calculation formula of the microstrip antenna radiation unit without considering the influence of skin, honeycomb, coating and bonding factorsThe calculation formula is as follows:

in the formula, L_d、W_dAnd h_dRespectively showing the length, the width and the thickness of the dielectric plate of the rectangular radiating element;

5b) and calculating the correction quantity of the skin, the honeycomb, the coating and the bonding thickness on the far field influence of the radiation unit by using a data-driven model, wherein the data-driven model is described as follows:

ΔF_E(x)＝Re(ΔF(x))+jIm(ΔF(x))

in the formula, the structural factor x ═ x₁,x₂,x₃,x₄]^TIs represented by the panel thickness x₁Adhesive thickness x₂Honeycomb thickness x₃And thickness x of the coating₄Formed vector, Δ F_E(x) The correction quantity of the far field of the sandwich microstrip radiating unit is a complex number and consists of a real part Re (delta F (x)) and an imaginary part Im (delta F (x)), and the real part Re (delta F (x)) and the imaginary part Im (delta F (x)) are both nonlinear functions of a structural factor x;

5c) according to the structural factor x ═ x₁,x₂,x₃,x₄]^TCalculating far field of sandwich microstrip radiating element under influence of skin, honeycomb, coating and bonding factorsThe mathematical expression is as follows:

in the far-field calculation formula of the sandwich microstrip antenna radiation unit, the data driving model in the step 5b) is specifically realized by the following steps:

5b1) aiming at the microstrip radiating unit, before designing the interlayer microstrip antenna array, processing L interlayer microstrip radiating unit experiment samples by using a uniform experiment design method, wherein the samples can reflect the influence degree of the thicknesses of different panels, honeycombs, coatings and bonding layers on the interlayer microstrip radiating unit;

5b2) measuring the radiation unit far fields of the manufactured L experimental samples by using an antenna near-field test system and a three-dimensional coordinate test instrument to obtain L data sample sets { (x) of different structural factors x and corresponding radiation unit far fields_i,F_i),x_i∈R,F_i∈ C, i ═ 1.., L }, where the vector x ═ x ·, L }, where x ═ x₁,x₂,x₃,x₄]^TRepresenting a structural factor, F representing corresponding radiating element far field data;

5b3) from the above-mentioned radiation unit far-field data F and the conventional microstrip radiation unit far-field data calculated in 5a)Calculating the variation of the far field of the radiation unit under the influence of skin, honeycomb, coating and bonding structural factors:

5b4) the method comprises the steps of respectively calculating the variable quantities of L experimental samples with different structures and far fields corresponding to radiation units by using the formula, carrying out normalization processing on data, and further obtaining an experimental data set psi { (x)_i,ΔF_i),x_i∈R,ΔF_i∈ C, i 1.., L }, R and C respectively representing a real set and a complex set;

5b5) splitting the normalized data set Ψ into two subsets Ψ₁And Ψ₂And using omega { (x) in combination_i,t_i) I 1.. L } to represent the two subsets collectively, where t_iRepresenting real or imaginary data in a complex phasor Δ F;

5b6) for the sample subset Ω { (x)_i,t_i) 1.. L }, respectively establishing a meta-model of the structural factor x to a real part Re (Δ F (x)) and an imaginary part Im (Δ F (x)) in Δ F by using a kernel machine learning algorithm, wherein the meta-model is described by using the following formula in a unified manner:

$t\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0$

where t (x) may represent the real part Re (Δ F (x)) or imaginary part Im (Δ F (x)) of Δ F, which is a non-linear function of x, k (x, x)_i) The kernel function is expressed, the regression problem of nonlinear data is solved by introducing the kernel function, the difficulty of directly searching nonlinear mapping is avoided, and L represents the number of data samples, omega_iRepresenting the weight, ω, corresponding to the kernel function₀Is a bias term;

5b7) the unknown parameter omega of the meta-model in the step 5b6) is obtained_iAnd ω₀The method is characterized by using two algorithms of support vector regression and correlation vector regression, and the solving process is as follows:

(one) solving for the unknown parameter ω if support vector regression is used_iAnd ω₀The solving process is as follows:

① first specifies a kernel function and then based on the normalized data sample subset Ω { (x)_i,t_i) L, determining the kernel parameters, the compromise constant C and the error margin using a 5-fold cross-validation method;

② are solved by linear programming algorithm according to pre-specified kernel function type, kernel parameters, compromise constant C and error toleranceSupport vector regression algorithm of face to obtain parametersω₀And a slack variable ξ_j：

$Find:{\mathrm{\ω}}_i^{+},{\mathrm{\ω}}_i^{-},{\mathrm{\ξ}}_j,{\mathrm{\ω}}_0$

$Min:\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}+{\mathrm{\ω}}_i^{-})+2C\underset{j=1}{\overset{L}{\Σ}}{\mathrm{\ξ}}_j$

$s.t.\left\{\begin{array}{c}{t}_j-\underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)-{\mathrm{\ω}}_0\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ \underset{i=1}{\overset{L}{\Σ}}({\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_j^{-})k(x_i,x_j)+{\mathrm{\ω}}_0-t_j\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_j\\ {\mathrm{\ω}}_i^{+}\≥0,{\mathrm{\ω}}_i^{-}\≥0\\ \begin{array}{cc}{\mathrm{\ξ}}_j\≥0& (\∀j=1,2,...,L)\end{array}\end{array}\right.$

③ obtained from the aboveCalculating the unknown parameter ω in the data model using the following formula_i：

${\mathrm{\ω}}_i={\mathrm{\ω}}_i^{+}-{\mathrm{\ω}}_i^{-}$

④ solving the above solution to ω_iAnd ω₀In the formula substitution, obtaining a data model of the influence of structural factors of the interlayer microstrip antenna on a real part Re (delta F (x)) or an imaginary part Im (delta F (x)) in a far field variable quantity delta F of a microstrip radiation unit;

(II) solving the unknown parameter omega in step 5b6) if a correlation vector regression algorithm is used_iAnd ω₀Then the influence of noise needs to be considered, i.e. the meta-model in step 5b6) is re-represented as:

t(x)＝y(x)+

$y\left(x\right)=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\ω}}_{i}k(x,x_i)+{\mathrm{\ω}}_0$

where y (x) represents a prediction output without considering the influence of noise, and represents output noise satisfying the condition that the mean is 0 and the variance is σ²T (x) represents the actual prediction output, and satisfies the mean y (x) and the variance σ²And independent normal distribution, the probability distribution of which is described asWherein the operatorMean μ and variance σ²Is defined as follows:

according to the normalized data sample subset Ω { (x)_i,t_i) And calculating an unknown parameter omega in the meta-model by using a solving method of the conventional correlation vector machine algorithm_i、ω₀And σ²；

5b8) And combining the obtained real part correction quantity and imaginary part correction quantity two element models according to the principle that the complex number consists of a real part and an imaginary part to obtain a data model of the influence of structural factors on the far field variable quantity of the radiation unit.

2. The active interlayer microstrip antenna structure and electromagnetic integrated data-driven design method according to claim 1, characterized in that the influence of panel and honeycomb on the interlayer microstrip antenna gain is considered in the calculation, and the calculation formula is as follows:

$S=\frac{{\mathrm{\Γ}}_{01}-{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_1\left(x_1+x_4\right)}+{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_o\left(2x_2+x_3+H_m\right)}-e^{-2j\[k_1\left(x_1+x_4\right)-k_o\left(2x_2+x_3+H_m\right)\]}}{1-{\mathrm{\Γ}}_{01}^2{e}^{-2{\mathrm{jk}}_1\left(x_1+x_4\right)}+{\mathrm{\Γ}}_{01}{e}^{-2{\mathrm{jk}}_o\left(2x_2+x_3+H_m\right)}-{\mathrm{\Γ}}_{01}{e}^{-2j\[k_1\left(x_1+x_4\right)-k_o\left(2x_2+x_3+H_m\right)\]}}$

in the formula, S represents the reflection coefficient of the interlayer microstrip antenna which takes the influences of the panel, the honeycomb, the bonding and the coating thickness into consideration and meets the condition of opening,which represents the wavelength constant in the panel,representing the partial reflection coefficient from free space to the panel,is the wave constant, ω, in free space_fWhich represents the angular frequency of the free space,₀and mu₀Respectively representing the dielectric parameter and the permeability in free space,_rand mu_rRespectively, the dielectric parameter and the relative permeability, H, in the panel_mThe thickness of the radio frequency functional layer is indicated.

3. The active interlayer microstrip antenna structure and electromagnetic integration data driven design method of claim 1 wherein the interlayer microstrip antenna array electric field far field data E is calculated based on the above_A(theta, phi), constructing an interlayer microstrip antenna structure and an electromagnetic comprehensive optimization model to determine a structural design variable x ═ x₁,x₂,x₃,x₄,t_c,l_c]^TAnd the excitation current amplitude I of the microstrip radiating element_mnAnd phase phi_mn：

Find:x,I_mn,Φ_mn

Min:||E_A(θ,φ)-E^*(θ,φ)||

$s.t.\left\{\begin{array}{c}S\≤\[\mathrm{\ϵ}\]\\ v_{\max }\≤\[v\]\\ {\mathrm{\σ}}_{max}\≤\[\mathrm{\σ}\]\\ x_l\≤x\≤x_h\end{array}\right.$

In the formula, E^*(θ, φ) represents the far field of a given desired electric field, v_maxAnd σ_maxRespectively, the maximum deformation amount and the maximum stress, which are determined from the result of Ansys analysis in the third step,x_l,x_hminimum and maximum values of the structural design variable, [ alpha ]]、[v]And [ sigma ]]Respectively, the allowable reflection coefficient, maximum deformation and maximum stress, which are given by the design index, t_c,l_cRespectively representing the side length and the cell wall thickness of the regular hexagonal cell.