Machine learning based conformal array antenna beam compensation method

Abstract

The present application relates to a kind of conformal array antenna beam compensation methods based on machine learning, including on the basis of establishing load-shape change-antenna performance, using the method of multi-objective programming to obtain a large number of load-element displacement and array surface deformation-phase compensation quantity sample step, on this basis, using machine learning agent model to quickly predict the phase compensation quantity required by conformal array antenna after deformation caused by current load, to improve the electrical performance of array antenna after deformation, finally further simulation verification the phase compensation quantity solved by it.The present application realizes that when array antenna is subjected to deformation load, the beam pointing error is controlled within 0.01, the gain loss is controlled within 0.5dB, and the time used is only within 1s, it is a kind of conformal array antenna beam phase compensation method, which can obtain antenna pattern main lobe and ideal state agree well, side lobe, lobe width etc. are kept in ideal state.

Description

Technical Field

[0001] This invention belongs to the field of antenna radar, specifically relating to a method for beam compensation by optimizing the excitation phase of array elements using machine learning. Background Technology

[0002] With the rapid development of aerospace technologies such as aircraft, missiles, and satellites, the technical requirements for wireless communication equipment, represented by radar, are constantly increasing. Antennas, as the transceiver system of radar, play a crucial role in wireless communication. Conformal carrier antennas are antennas or antenna arrays that maintain the same shape as the surface structure of the carrier and do not introduce additional burdens to the mounted object. Compared to traditional planar array radars, they offer numerous advantages such as better aerodynamics, increased antenna aperture, better stealth, and lighter weight.

[0003] Based on the aforementioned advantages, conformal antennas have been widely used in the aerospace and military fields, as well as in civilian fields such as vehicle radar, medical devices, wearable devices, and mobile communication equipment. However, because conformal antennas participate in the process of bearing the loads of the carrier during operation, environmental loads can directly cause changes in the antenna structure, which in turn affect the performance of the array antenna itself. How to eliminate or reduce the impact of environmental loads on antenna performance in real time and quickly is of great significance for enhancing the stability of conformal antennas and expanding their application scenarios. Therefore, it is necessary to establish the correspondence between environmental load, structural deformation, and antenna performance, and design reasonable compensation methods to accurately and quickly perform beam compensation on the deformed array antenna.

[0004] Currently, there are two main beam compensation methods to address the performance degradation caused by antenna deformation: mechanical compensation and electrical compensation. Mechanical compensation primarily reduces deformation under dynamic loads by increasing the strength and stiffness of the antenna structure or adding active adjustment devices, or by using a driving structure or special materials to restore the deformed antenna to its original shape after deformation. This method generally requires a continuous power supply, additional space, and complex control technology, undoubtedly adding extra weight to the antenna system and affecting the aerodynamics and lightweight design of the wing or fuselage. The electrical compensation method, proposed in recent years, directly adjusts the amplitude and phase of the antenna array elements using phase shifters to optimize the antenna pattern. In this method, antenna deformation information is extracted using external sensors such as cameras, laser measuring instruments, and fiber optic sensors. After extracting the antenna deformation information, a mathematical model between deformation and performance is established to achieve beam compensation. In past studies, researchers have focused on the deformation information of some special points on the antenna array, only considering the deformation of the array or the displacement of the array elements on the array surface, ignoring the impact of the deformation of the array elements themselves on the antenna's electrical performance, resulting in insufficient precision in information acquisition. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a conformal array antenna beam compensation method based on machine learning that is not affected by the sensor position arrangement when acquiring array information, and at the same time takes array element deformation as a factor affecting antenna electrical performance, and can quickly predict the amount of phase compensation required under the current load or the current array state, thereby improving the electrical performance of the deformed array antenna.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a conformal array antenna beam compensation method based on machine learning, comprising the following steps:

[0007] Step 1: Establish a calculation model for the antenna load and the element deformation and displacement of the conformal array antenna to obtain the array deformation curve of the conformal array antenna under environmental load conditions.

[0008] Step 2: Based on the array deformation curve, establish an electrical performance calculation model for the array deformation curve;

[0009] Step 3: Calculate the element excitation phase Ψ in the electrical performance model based on the array deformation curve. n As design variables, a non-dominated genetic algorithm is used to perform multi-objective programming on the electrical performance calculation model of the array deformation curve, thereby obtaining samples of the phase compensation amount of the electrical performance of the antenna load and the array deformation curve.

[0010] Step 4: Establish a machine learning-based antenna phase prediction neural network that takes antenna array deformation as input and antenna phase compensation value as output. Use compensation amount samples within the maximum load range of the conformal array antenna to train the neural network to quickly predict the electrical performance phase compensation amount required by the conformal array antenna under the current load or current array state, thereby improving the electrical performance of the conformal array antenna after deformation.

[0011] Furthermore, the specific steps of step one are as follows:

[0012] (1) Based on the stiffness matrix Q of the conformal array antenna, the single-layer stiffness of the antenna and the strain curvature of each layer of the antenna are obtained sequentially, thereby further obtaining the tensile stiffness A of the conformal array antenna. ij Coupling stiffness B ij and bending stiffness D ij The stiffness matrix Q is defined in the 1-2-3 direction; the 1 direction is the vertical direction of the conformal array antenna radio frequency functional layer, the 2 direction is the horizontal direction of the conformal array antenna material fiber, and the 3 direction is orthogonal to the 1 direction and the 2 direction.

[0013] (2) Establish a spatial coordinate system for the conformal array antenna material's inherent properties, with the intersection of directions 1-2-3 as the origin, direction 1 as the y-axis, direction 2 as the x-axis, and direction 3 as the z-axis, and based on the obtained tensile stiffness A... ij Coupling stiffness B ij and bending stiffness D ij The formulas for calculating the internal forces, internal moments, and strain of the conformal array antenna are as follows:

[0014]

[0015]

[0016] In the formula, N x N y N xy M x M y M xy The internal forces and internal moments are represented respectively, thus obtaining the deformation curve calculation model of the antenna array deformation;

[0017] (3) Based on the deformation curve calculation model, the mid-surface deflection k of the conformal array antenna is obtained. x κ y k xy Then the displacement model of the antenna array is expressed as:

[0018]

[0019]

[0020]

[0021] In the formula, ω is the displacement of the conformal array antenna in the z direction, which gives the deformation curve of the conformal array antenna under environmental load conditions. At the same time, the deformation and displacement of the antenna elements are obtained from the deformation curve.

[0022] Furthermore, based on the stiffness matrix Q of the conformal array antenna, the formula for calculating the single-layer stiffness of the antenna is as follows:

[0023]

[0024]

[0025]

[0026] In the formula, E1 represents the elastic modulus of the material in direction 1, E2 represents the elastic modulus in direction 2, and G... 12 v represents the shear modulus on the plane formed by directions 1 and 2.12 V represents the Poisson's ratio in direction 2 when stress is applied in direction 1. 31 V represents the Poisson's ratio in direction 1 when stress is applied in 3 directions. 32 This represents the Poisson's ratio in direction 2 when stress acts in 3 directions;

[0027] The strain curvature of each conformal array antenna layer, that is, the stress of the k-th layer, is expressed by the strain and curvature of the mid-surface of the conformal array antenna as follows:

[0028]

[0029] In the formula, It is the mid-surface strain of the conformal array antenna, κ x κ y It is the mid-surface deflection curvature of the conformal array antenna; κ xy It is the mid-surface distortion rate; The stiffness matrix Q is the stiffness matrix after coordinate transformation from the 1-2 direction to the xy direction;

[0030] Then, the tensile stiffness A of the conformal array antenna is calculated according to the following formula. ij Coupling stiffness B ij Bending stiffness D ij for:

[0031]

[0032] Where z k This represents the displacement of layer k from the center of the antenna thickness.

[0033] Furthermore, step two specifically involves:

[0034] (1) Steps for establishing the array deformation curve array element radiation pattern calculation model;

[0035] (2) The step of superimposing the array deformation curve radiation pattern on the deformation element radiation pattern refers to the rotation of the antenna elements in the array deformation curve, that is, the actual spacing between the elements in the x-direction of the array deformation curve is displaced, and the displacement spacing is ΔS. x Simultaneously, the displacement spacing in the z-direction of the array deformation curve is ΔS. z Based on the superposition theorem and the array pattern, a calculation model for the electrical performance of the array deformation curve is obtained.

[0036] Wherein, the x-direction of the array deformation curve is the direction of the antenna element width extension; at the same time, the direction of the antenna element length extension is the y-direction, and the z-direction of the array deformation curve is the direction perpendicular to the xy plane.

[0037] Furthermore, the specific steps for establishing the array deformation curve element radiation pattern calculation model are as follows:

[0038] The E-plane radiation pattern expression of a standard microstrip antenna element is as follows:

[0039]

[0040] The array element radiation pattern is determined by the following formula:

[0041]

[0042] Where Le represents the actual length of the array deformation curve;

[0043] f θ —A model of the relationship between beam pointing and deformation of array elements;

[0044] Δx and Δz represent the displacements in the x and z directions at the point of maximum deformation of the array element, respectively;

[0045] Then, the calculation model for the electrical performance of the array deformation curve obtained according to the superposition theorem is as follows:

[0046]

[0047] In the formula, T is the rotation angle of the array element, which is the displacement spacing ΔS in the z-direction of the array deformation curve. z The corresponding element displacement angle, ΔS e That is, Δx, Δz, and ΔS are the actual displacements of the array element in the x and z directions, respectively, and Ψ n For the excitation phase of the array element, I n The amplitude of the array element excitation.

[0048] Furthermore, step three specifically involves:

[0049] (31) The non-dominated genetic algorithm NSGA-II was used to perform multi-objective programming on the electrical performance calculation model of the array deformation curve. The optimization objective was:

[0050] Min.Г1(Ψ n ) = abs(θ0)

[0051] Max.Г2(Ψ n = abs(Gain)

[0052] ST -π≤Ψ n ≤π

[0053] θ0 is the beam pointing value, and Gain is the gain value; and the technical specifications that meet the service requirements are determined to be a gain value < 0.5 and a beam pointing value < 0.01;

[0054] (32) Determine the optimal individual ratio, population size, maximum number of iterations, and maximum cutoff time for NSGA-II parameters as 0.3, 200, 200, and 36000s, respectively.

[0055] (33) Collect the electrical performance phase compensation sample. Under the conditions of load variation range of 0 to 10 N, sampling interval of 0.02 N, and maximum displacement range of antenna array of 0 to 18.4048 mm, collect antenna load and array antenna deformation data. The array antenna deformation data includes array element deformation: Δx, Δz; array displacement: rotation angle T, x-direction displacement ΔS. x displacement ΔS in the z-direction z ; and the phase value Ψ of each antenna element n .

[0056] Furthermore, step four specifically involves:

[0057] (41) Randomly select at least 400 samples from the electrical performance phase compensation quantity samples as the training set of the antenna phase prediction neural network, and use the remaining samples as the test set.

[0058] (42) Divide the network structure. The number of input layers of the antenna phase prediction neural network is the feature that characterizes the deformation data of the array antenna. The output layer is the antenna phase compensation amount required under the current deformation. The structure of the antenna phase prediction neural network is determined according to the principle of decreasing network structure from input layer to output layer.

[0059] (43) Using the calculation model of the antenna load and the array element deformation and displacement of the array antenna, calculate the array deformation curve under the required load, and use the array element deformation and displacement information as network input to predict the phase compensation amount required by the array antenna under the load.

[0060] Furthermore, it also includes calculating the regression model evaluation indicators R², root mean square, and average correlation coefficient (MAE) of the test set and training set to see if they meet the requirements. The closer the MAE is to 0 or the closer the R² is to 1, the more accurate the model is in making predictions based on the deformation information of the array. If the prediction accuracy is insufficient, the network structure or network parameters are further adjusted until the evaluation indicators reach a good level. The formula is as follows.

[0061]

[0062]

[0063] in, This is the antenna phase prediction value. y is the average phase value of the antenna. i This represents the true value of the antenna phase.

[0064] Furthermore, it also includes establishing simulation models of the conformal array antenna before and after deformation using the HFSS simulation method, in order to verify the solution of the phase compensation amount step.

[0065] Furthermore, the conformal array antenna is composed of an upper skin, a honeycomb layer, a radio frequency functional layer, and a lower skin, with antenna microstrip patches arranged sequentially along the extension direction of the radio frequency functional layer.

[0066] The beneficial effects of this invention are as follows: The conformal array antenna beam compensation method based on machine learning proposed in this invention does not require a complex calculation process after establishing the environmental load-structural deformation-antenna performance. It obtains a large number of samples through a multi-objective programming method and then trains a neural network model to quickly predict the phase compensation amount. Furthermore, the accuracy of phase compensation is verified in the theoretical and simulation stages. At the same time, it also incorporates array and element deformation information, and the array surface information acquisition is not affected by the sensor placement. The deformation curve of the entire array surface can be obtained directly, resulting in more refined information acquisition while saving costs and additional equipment placement space.

[0067] The fast beam compensation technology for conformal array antennas proposed in this invention can quickly predict antenna performance changes under load and rapidly and accurately adjust the antenna phase to achieve beam compensation. During actual service of conformal antennas, for antenna deformation caused by airborne vibration, air resistance, etc., resulting in a decrease in antenna electrical performance, this invention can quickly and accurately predict the actual required compensation amount, enabling the antenna to meet service requirements.

[0068] The technical method proposed in this invention enables an array antenna to achieve beam pointing error within 0.01 and gain loss within 0.5 dB when receiving a load of 0–10 N, all within a time of less than 1 second. The obtained antenna pattern shows good agreement between the main lobe and the ideal state, while the side lobes and beamwidth remain within the ideal state. This demonstrates the effectiveness of the invention. Attached Figure Description

[0069] Figure 1 This is a flowchart of the conformal array antenna beam compensation method based on machine learning according to the present invention;

[0070] Figure 2 This is a schematic diagram of the conformal carrier antenna of the present invention;

[0071] Figure 3 This is a schematic diagram of the deformation of the array element itself in this invention;

[0072] Figure 4 This is a schematic diagram of the deformation of the array before and after being subjected to force according to the present invention;

[0073] Figure 5This refers to the element size of the present invention;

[0074] Figure 6 This is the simulation model of the undeformed HFSS array antenna of this invention;

[0075] Figure 7 This is a simulation model of the deformed HFSS array antenna of the present invention;

[0076] Figure 8 These are the antenna radiation patterns before deformation, after deformation, after optimization algorithm compensation, and after neural network predicted phase compensation, according to the present invention.

[0077] Figure 9 This is the R2 histogram of the neural network model performance index of this invention;

[0078] Figure 10 This is the MAE histogram, which represents the performance index of the neural network model of this invention.

[0079] Figure 11 The images show the radiation patterns before deformation, after deformation, and after neural network-predicted phase compensation under HFSS simulation of this invention. Detailed Implementation

[0080] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0081] Example 1: As Figure 2 As shown, the conformal array antenna consists of an upper skin 1, a honeycomb layer 2, an RF functional layer 3, and a lower skin 4. The antenna microstrip patches are arranged sequentially and installed in the extension direction of the RF functional layer 3.

[0082] like Figure 1 As shown, a conformal array antenna beam compensation method based on machine learning includes the following steps:

[0083] 001. Based on the stiffness matrix Q of the conformal array antenna, the single-layer stiffness of the antenna and the strain curvature of each layer are obtained sequentially, thus further obtaining the tensile stiffness A of the conformal array antenna. ij Coupling stiffness B ij and bending stiffness D ij The stiffness matrix Q is defined in the 1-2-3 direction; direction 1 is the vertical direction of the radio frequency functional layer of the conformal array antenna, direction 2 is the horizontal direction of the material fiber of the conformal array antenna, and direction 3 is orthogonal to direction 1 and direction 2.

[0084] Based on the stiffness matrix Q of the conformal array antenna, the formula for calculating the stiffness of a single layer of the antenna is as follows:

[0085]

[0086]

[0087]

[0088] In the formula, E1 represents the elastic modulus of the material in direction 1, E2 represents the elastic modulus in direction 2, and G... 12 v represents the shear modulus on the plane formed by directions 1 and 2. 12 V represents the Poisson's ratio in direction 2 when stress is applied in direction 1. 31 V represents the Poisson's ratio in direction 1 when stress is applied in 3 directions. 32 This represents the Poisson's ratio in direction 2 when stress acts in 3 directions;

[0089] The strain curvature of each conformal array antenna layer, which is the stress of the k-th layer, can be expressed using the strain and curvature of the mid-surface of the conformal array antenna as follows:

[0090]

[0091] In the formula, It is the mid-surface strain of the conformal array antenna, κ x ,κ y It is the mid-surface deflection of the conformal array antenna; κ xy It is the mid-surface distortion rate; The stiffness matrix Q is the stiffness matrix after coordinate transformation from the 1-2 direction to the xy direction;

[0092] Then, the tensile stiffness A of the conformal array antenna is calculated according to the following formula. ij Coupling stiffness B ij Bending stiffness D ij for:

[0093]

[0094] Where z k This represents the displacement of layer k from the center of the antenna thickness.

[0095] 002. Establish a spatial coordinate system for the conformal array antenna material's inherent properties, with the intersection of directions 1-2-3 as the origin, direction 1 as the y-axis, direction 2 as the x-axis, and direction 3 as the z-axis. Then, based on the obtained tensile stiffness A... ij Coupling stiffness B ij and bending stiffness D ij The formulas for calculating the internal forces, internal moments, and strain of a conformal array antenna are as follows:

[0096]

[0097]

[0098] In the formula, Nx N y N xy M x M y M xy The internal forces and internal moments are represented respectively, thus obtaining the deformation curve calculation model for the antenna array deformation;

[0099] 003. Based on the deformation curve calculation model, the mid-surface deflection k of the conformal array antenna is obtained. x κ y k xy Then the displacement model of the antenna array is expressed as:

[0100]

[0101]

[0102]

[0103] In the formula, ω is the displacement of the conformal array antenna in the z direction, which gives the deformation curve of the conformal array antenna under environmental load conditions. At the same time, the deformation and displacement of the antenna elements are obtained from the deformation curve.

[0104] 004. Establish a calculation model for the array deformation curve element radiation pattern:

[0105] The E-plane radiation pattern expression of a standard microstrip antenna element is as follows:

[0106]

[0107] The array element radiation pattern is determined by the following formula:

[0108]

[0109] Where Le represents the actual length of the array deformation curve;

[0110] f θ —A model of the relationship between beam pointing and deformation of array elements;

[0111] Δx and Δz represent the displacements in the x and z directions at the point of maximum deformation of the array element, respectively;

[0112] 005, such as Figure 3 , Figure 4 As shown, the array deformation curve pattern is calculated by superimposing the deformation element radiation pattern on the deformation element radiation pattern: that is, the antenna elements in the array deformation curve rotate, that is, the actual spacing between the elements in the x-direction of the array deformation curve is displaced, and the displacement spacing is ΔS. x Simultaneously, the displacement spacing in the z-direction of the array deformation curve is ΔS.z Based on the superposition theorem and the array pattern, a calculation model for the electrical performance of the array deformation curve is obtained.

[0113] In this context, the x-direction of the array deformation curve is the direction of the antenna element width extension; at the same time, the y-direction is the direction of the antenna element length extension. Therefore, the z-direction of the array deformation curve is the direction perpendicular to the xy plane.

[0114] The electrical performance calculation model for the array deformation curve obtained according to the superposition theorem is as follows:

[0115]

[0116] In the formula, T is the rotation angle of the array element, which is the displacement spacing ΔS in the z-direction of the array deformation curve. z The corresponding element displacement angle, ΔS e That is, Δx, Δz, and ΔS are the actual displacements of the array element in the x and z directions, respectively, and Ψ n For the excitation phase of the array element, I n The amplitude of the array element excitation.

[0117] 006. The excitation phase Ψ of the array elements in the electrical performance calculation model based on the array deformation curve. n As design variables, the non-dominated genetic algorithm NSGA-II is used to perform multi-objective programming on the electrical performance calculation model of the array deformation curve. The optimization objective is:

[0118] Min.Γ1(Ψ n ) = abs(θ0)

[0119] Max.Γ2(Ψ n = abs(Gain)

[0120] ST -π≤Ψ n ≤π

[0121] θ0 is the beam pointing value, and Gain is the gain value; and the technical specifications that meet the service requirements are determined to be a gain value < 0.5 and a beam pointing value < 0.01;

[0122] 007. Determine the optimal individual ratio for NSGA-II parameters as 0.3, population size as 200, maximum number of iterations as 200, and maximum cutoff time as 36000s;

[0123] 008. Conduct phase compensation sample collection for electrical performance. Under the conditions of load variation range of 0-10N, sampling interval of 0.02N, and maximum displacement range of antenna array surface of 0-18.4048mm, collect antenna load and array antenna deformation data. The array antenna deformation data includes element deformation: Δx, Δz; array displacement: rotation angle T, x-direction displacement ΔS. xdisplacement ΔS in the z-direction z ; and the phase value Ψ of each antenna element n ;

[0124] This means that the electrical performance phase compensation quantity samples of the antenna load and array deformation curves have been obtained.

[0125] 009. Randomly select at least 400 samples from the electrical performance phase compensation quantity samples as the training set for the antenna phase prediction neural network, and use the remaining samples as the test set.

[0126] 010. Divide the network structure. The number of input layers of the antenna phase prediction neural network is the feature representing the deformation data of the array antenna, and the output layer is the antenna phase compensation amount required under the current deformation. The structure of the antenna phase prediction neural network is determined according to the principle of decreasing network structure from input layer to output layer.

[0127] 011. Using the calculation model of antenna load and array element deformation and displacement of the array antenna, calculate the array deformation curve under the required load, and use the array element deformation and displacement information as network input to predict the phase compensation amount required by the array antenna under the load.

[0128] A machine learning-based antenna phase prediction neural network was established, which takes antenna array deformation as input and antenna phase compensation value as output. The neural network was trained using compensation amount samples within the maximum load range of the conformal array antenna to quickly predict the electrical performance phase compensation amount required by the conformal array antenna under the current load or the current array state, thereby improving the electrical performance of the conformal array antenna after deformation.

[0129] 012. It also includes calculating the regression model evaluation indicators R², root mean square and average correlation coefficient MAE of the test set and training set to see if they meet the requirements. The closer the MAE is to 0 or the closer the R² is to 1, the more accurate the model is in making predictions based on the deformation information of the array. If the accuracy of the prediction results is not high enough, the network structure or network parameters are further adjusted until the evaluation indicators reach a good level. The formula is as follows.

[0130]

[0131]

[0132] in, This is the antenna phase prediction value. y is the average phase value of the antenna. i This represents the true value of the antenna phase.

[0133] 013. It also includes the use of HFSS simulation method to establish simulation models of two conformal array antennas before and after deformation, which are used to verify the solution of phase compensation amount steps.

[0134] Experimental examples, such as Figure 2 As shown, in this example, the thickness of the upper and lower skins is 1mm, the thickness of the honeycomb layer is 0.1mm, and the thickness of the radio frequency layer is 0.254mm; Figure 5 As shown, this example uses an array element dielectric substrate with a length of 30mm and a width of 25mm. The array element has a width of 14.82mm and a length of 12.48mm, a dielectric thickness of 0.254mm, a feed line length of 5mm, and a feed line width of 0.75mm. At the junction of the feed line and the patch unit, two 0.51mm × 3.6mm slots extend into the rectangular area of ​​the patch. The method of this invention is verified as follows:

[0135] This experimental example determined the following technical specifications to meet the service requirements:

[0136]

[0137] The parameters for NSGA-II are set as follows:

[0138]

[0139] By comparing the solution results under multiple conditions, we can evaluate whether the requirements are met.

[0140] Based on this, samples were collected with a load variation range of 0–10 N, a sampling interval of 0.02 N, and a maximum antenna array displacement range of 0–18.4048 mm. Load and array antenna deformation information were collected, including element deformation (Δx, Δz), array displacement (rotation angle T, x-direction displacement, z-direction displacement), and the phase value Ψ of each element. n A total of 501 samples were used to train the machine learning model.

[0141] Then, samples are randomly selected from the sample library, with 80% used as the training set and 20% as the test set.

[0142] The network structure is divided into several layers. The input layer consists of 40 features representing the deformation information of the array antenna, and the output layer contains the phase compensation amount required under the current deformation. Following the principle of decreasing network layer number from input to output, the network structure is determined to be {[40, 20, 10, 8]}.

[0143] Further, configure the network parameters:

[0144]

[0145] Furthermore, a phase prediction method based on machine learning is used to quickly predict the required phase compensation value by inputting deformation information under the current load.

[0146] like Figure 6-11As shown, the advantages of this invention can be further illustrated by theoretical calculations and HFSS simulation experiments. HFSS simulation is used to verify the accuracy of the phase value predicted by machine learning, and it is necessary to establish two models, one before deformation and one after deformation.

[0147] (1) Establish the model before deformation: The model before deformation is Figure 6 The rectangular microstrip antennas shown form an eight-element uniform linear array, with no deformation of the array elements.

[0148] (2) Establishing the deformed model: Based on step one, the deformed model can be established according to the deformation curve of the conformal array antenna when F = 10N. Figure 7 The antenna model shown is first plotted in HFSS by drawing a single-sided deformation curve on the xoz plane. Boolean operations are then used to connect the deformation curves into a closed curve. The coverline function is then used to connect the closed curves into a closed surface. The sweep function is then used to raise the surface by 0.254 mm. Finally, the warpsheet function is used to conformally fit the microstrip lines to the upper surface of the model.

[0149] (3) Simulation parameters

[0150] The array antenna operates at a frequency of 8 GHz, uses Rogers 5880 dielectric material, has a dielectric thickness of 0.254 mm, and the microstrip antenna dimensions are as follows. Figure 5 As shown, the array antenna in the ideal state and when F = 10N is as follows: Figure 6 As shown in the figure. To compare the simulation results, Table 1 lists the excitation parameter values ​​for the three cases: ideal state, after deformation, and after deformation compensation.

[0151] Table 1

[0152]

[0153]

[0154] (4) Simulation results

[0155] Simulations were performed on three models in HFSS. After completion, the radiation patterns of the phi=0 profile were exported. To compare the differences in the radiation patterns, the profile radiation patterns were extracted with a step size of 0.1° and plotted as follows. Figure 11 As shown, the antenna pattern of the deformed array antenna exhibited a 4.4° deflection, which was corrected to 0° after compensation. The gain after compensation was also improved compared to the deformed state.

[0156] (5) Analysis of the results of this study:

[0157] Conclusion 1: From Figure 8Theoretical calculations have verified the compensation effect of the NSGA-II algorithm when the array antenna is subjected to a concentrated force of 10N. It can correct the radiation pattern and improve the gain to a certain extent. However, each optimization algorithm takes 3200 seconds.

[0158] Conclusion 2: From Figure 8 as well as Figure 9 , 10 As can be seen, the direction of training the neural network model can quickly and accurately predict the amount of compensation required for the current deformation. Training the network takes less than 5 seconds, and predicting new data takes less than 1 second. The prediction results obtained by randomly sampling forces from 1 to 10 N are shown in Table 2.

[0159] Table 2

[0160]

[0161]

[0162] Conclusion 3: To verify the accuracy of the theoretical calculations, the array antenna was simulated in HFSS. With a load of 10N, the beam pointing in HFSS was 4.4°, while the theoretical calculation result was 4.3°. Furthermore, the beam pointing returned to 0° after compensation. The error between the theoretical calculation and the simulation verification was only 0.1°.

[0163] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A conformal array antenna beam compensation method based on machine learning, characterized in that, Includes the following steps: Step 1: Establish a calculation model for the antenna load and the element deformation and displacement of the conformal array antenna to obtain the array deformation curve of the conformal array antenna under environmental load conditions. Step 2: Based on the array deformation curve, establish an electrical performance calculation model for the array deformation curve. The specific steps are as follows: (1) Steps for establishing the array deformation curve array element pattern calculation model; (2) The step of superimposing the array deformation curve radiation pattern on the basis of the deformation element radiation pattern: refers to the rotation of the antenna elements in the array deformation curve, that is, the array deformation curve... The actual spacing between array elements in the direction is shifted, and the shift spacing is... Meanwhile, in the array deformation curve The displacement spacing in the direction is Based on the superposition theorem and the array pattern, a calculation model for the electrical performance of the array deformation curve is obtained. Among them, the array deformation curve The direction is the direction of the antenna element width extension; simultaneously, the direction of the antenna element length extension is... Direction, then, array deformation curve Direction is The direction perpendicular to the plane; Step 3: Calculate the element excitation phase in the electrical performance model based on the array deformation curve. As design variables, a non-dominated genetic algorithm is used to perform multi-objective programming on the electrical performance calculation model of the array deformation curve, thereby obtaining samples of the phase compensation amount of the electrical performance of the antenna load and the array deformation curve. The specific steps are as follows: (31) The non-dominated genetic algorithm NSGA-II was used to perform multi-objective programming on the electrical performance calculation model of the array deformation curve. The optimization objective was: ， This is the beam pointing value. The values ​​were determined, and the technical specifications that meet the service requirements were defined as gain value <0.5 and beam pointing value <0.

01. (32) Determine the optimal individual ratio for NSGA-II parameters as 0.3, population size as 200, maximum number of iterations as 200, and maximum cutoff time as 36000s; (33) Collect the electrical performance phase compensation sample. Under the conditions that the load variation range is 0 to 10 N, the sampling interval is 0.02 N, and the maximum displacement range of the antenna array is 0 to 18.4048 mm, collect the antenna load and array antenna deformation data. The array antenna deformation data includes the element deformation: ; Array displacement: rotation angle T , Directional displacement , Directional displacement ; and the phase values ​​of each antenna element. ; Step 4: Establish a machine learning-based antenna phase prediction neural network that takes antenna array deformation as input and antenna phase compensation value as output. Use compensation amount samples within the maximum load range of the conformal array antenna to train the neural network to quickly predict the electrical performance phase compensation amount required by the conformal array antenna under the current load or current array state, thereby improving the electrical performance of the conformal array antenna after deformation.

2. The conformal array antenna beam compensation method based on machine learning as described in claim 1, characterized in that, The specific steps of step one are as follows: (1) Based on the stiffness matrix of the conformal array antenna The single-layer stiffness of the antenna and the strain curvature of each antenna layer are obtained sequentially, thereby further obtaining the tensile stiffness of the conformal array antenna. Coupling stiffness and bending stiffness The stiffness matrix mentioned above Herein lies the stiffness matrix defined in the 1-2-3 directions; direction 1 is the vertical direction of the radio frequency functional layer of the conformal array antenna, direction 2 is the horizontal direction of the fiber of the conformal array antenna material, and direction 3 is orthogonal to directions 1 and 2. (2) Taking the intersection of the 1-2-3 directions as the origin, and direction 1 as... Axis, 2 directions are Axis, 3 directions Establish a spatial coordinate system based on the axis and the inherent properties of the conformal array antenna material, and then determine the tensile stiffness based on the obtained tensile stiffness. Coupling stiffness and bending stiffness The formulas for calculating the internal forces, internal moments, and strain of the conformal array antenna are as follows: ， In the formula, The internal forces and internal moments are represented respectively, thus obtaining the deformation curve calculation model of the antenna array deformation; (3) Based on the deformation curve calculation model, the mid-surface deflection of the conformal array antenna is obtained. The displacement model of the antenna array is then expressed as: ， In the formula, For conformal array antennas in The displacement in the direction is obtained, that is, the deformation curve of the conformal array antenna under environmental load conditions. At the same time, the deformation and displacement of the antenna elements are obtained from the deformation curve.

3. The conformal array antenna beam compensation method based on machine learning as described in claim 2, characterized in that, According to the stiffness matrix of the conformal array antenna The formula for calculating the single-layer stiffness of an antenna is as follows: ， ， ， In the formula, This represents the elastic modulus of the material in the 1 direction. Represents the elastic modulus in the 2-direction. This represents the shear modulus in the plane formed by directions 1 and 2. This represents the Poisson's ratio in direction 2 when stress is applied in direction 1. This represents the Poisson's ratio in direction 1 when stress is applied in 3 directions. This represents the Poisson's ratio in direction 2 when stress acts in 3 directions; The strain curvature of each conformal array antenna layer, that is, the stress of the k-th layer, is expressed by the strain and curvature of the mid-surface of the conformal array antenna as follows: ， In the formula, , It is the mid-surface strain of the conformal array antenna. It is the surface deflection of the conformal array antenna. It is the mid-surface distortion rate; The stiffness matrix From direction 1-2 to Stiffness matrix after coordinate transformation in the direction; Furthermore, the tensile stiffness of the conformal array antenna is calculated using the following formula. Coupling stiffness Bending stiffness for: ， in express The displacement of the layer from the center of the antenna thickness.

4. The conformal array antenna beam compensation method based on machine learning as described in claim 1, characterized in that, The specific steps for establishing the array deformation curve element radiation pattern calculation model are as follows: The E-plane radiation pattern expression of a standard microstrip antenna element is as follows: ， The array element radiation pattern is determined by the following formula: ， in Le —The actual length of the array deformation curve; —A model of the relationship between beam pointing and deformation of array element deflection; These represent the points where the array element undergoes the greatest deformation. direction and Displacement in the direction; Then, the calculation model for the electrical performance of the array deformation curve obtained according to the superposition theorem is as follows: ， In the formula, T The rotation angle of the array element is the array deformation curve. Displacement spacing in the direction The corresponding array element displacement angle, That is, the aforementioned , For the actual array element direction and Displacement in the direction, For the excitation phase of the array element, The amplitude of the array element excitation.

5. The conformal array antenna beam compensation method based on machine learning as described in claim 1, characterized in that, The fourth step is specifically as follows: (41) Randomly select at least 400 samples from the electrical performance phase compensation quantity samples as the training set of the antenna phase prediction neural network, and use the remaining samples as the test set; (42) Divide the network structure. The number of input layers of the antenna phase prediction neural network is the feature representing the deformation data of the array antenna, and the output layer is the antenna phase compensation amount required under the current deformation. The structure of the antenna phase prediction neural network is determined according to the principle of decreasing network structure from input layer to output layer. (43) Using the calculation model of the antenna load and the array element deformation and displacement of the array antenna, calculate the array deformation curve under the required load, and use the array element deformation and displacement information as network input to predict the phase compensation amount required by the array antenna under the load.

6. The conformal array antenna beam compensation method based on machine learning as described in claim 5, characterized in that, It also includes calculating the regression model evaluation indicators R², root mean square and average correlation coefficient (MAE) of the test set and training set to see if they meet the requirements. The closer the MAE is to 0 or the closer the R² is to 1, the more accurate the model is in making predictions based on the deformation information of the array. If the prediction accuracy is insufficient, the network structure or network parameters are further adjusted until the evaluation indicators reach a good level. The formula is as follows. ， ， in, This is the antenna phase prediction value. This is the average phase value of the antenna. This represents the true value of the antenna phase.

7. The conformal array antenna beam compensation method based on machine learning as described in any one of claims 1-6, characterized in that, It also includes establishing simulation models of the conformal array antenna before and after deformation using the HFSS simulation method, to verify the solution of the phase compensation amount.

8. The conformal array antenna beam compensation method based on machine learning as described in any one of claims 1-6, characterized in that, The conformal array antenna is composed of an upper skin (1), a honeycomb layer (2), a radio frequency functional layer (3) and a lower skin (4), with antenna microstrip patches arranged sequentially in the extension direction of the radio frequency functional layer (3).

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