Unmanned aerial vehicle conformal aperture performance limit analysis method based on polarization decomposition

Abstract

The invention discloses an unmanned aerial vehicle conformal aperture performance limit analysis method based on polarization decomposition, and belongs to the technical field of electromagnetic wave propagation. The method can be applied to the field of unmanned aerial vehicle conformal antenna design, including but not limited to design of communication chain antennas, inter-machine chain antennas, airborne radars and novel electromagnetic devices. According to the method, the optimization model is constructed and solved based on the polarization decomposition method, and rapid prediction of the conformal aperture performance limit under complex constraints can be realized. According to the method, the physical feasibility of design indexes is ensured, the cost of unmanned aerial vehicle conformal antenna design can be saved, and the method is also a basis for successful design of a novel electromagnetic device.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic wave propagation technology, specifically relating to a method for analyzing the performance limits of conformal aperture of unmanned aerial vehicles based on polarization decomposition. Background Technology

[0002] Currently, unmanned aerial vehicles (UAVs), as one of the most transformative technologies of the new century, have permeated all aspects of human life, reshaping modern production methods. Compared to manned aircraft, UAVs have significant advantages such as lower cost and smaller size. The ever-evolving technology of UAVs places higher demands on airborne antennas. As a core component of UAV avionics systems, airborne antennas not only need to perform numerous functions such as communication, navigation, identification, and electronic warfare, but also need to meet additional requirements such as aerodynamics and stealth, further increasing the design complexity of airborne antennas.

[0003] To address the challenges of airborne antenna design, conformal antennas have been proposed and applied to modern avionics systems. UAVs are small and irregularly shaped, and the limited conformal aperture on board prevents the achievement of arbitrary design goals. In reality, designers often have to rely on experience to guess the performance range achievable with conformal apertures, significantly increasing the difficulty of designing UAV conformal antennas. Therefore, the design of UAV conformal antennas particularly faces the challenge of predicting the highest performance achievable with a given conformal aperture—the "performance limit" of the conformal aperture. However, currently, the engineering community still lacks a standardized definition and methodology for solving the performance limit problem of airborne conformal antennas.

[0004] The academic community has long considered the performance limits of antennas, and a considerable number of performance limit analysis methods have been proposed to date. However, most of these methods can only be applied to small-sized, regularly shaped models, and they tend to be inefficient and prone to errors when dealing with the performance limits of conformal apertures.

[0005] Antenna current optimization (ACO) is a novel approach to solving performance limit problems that has emerged in recent years. This method treats the performance limit problem as a convex optimization problem of current distribution on an arbitrary curved surface, which fits well with the conformal aperture model. However, a drawback is that for frequently moving UAVs, non-convex constraints such as axial ratio need to be considered, and ACO cannot yet handle such conditions.

[0006] Based on the above analysis, the existing technology has the following technical problems and defects:

[0007] (1) The design space on UAVs is limited, and conformal antennas are required, which raises the issue of performance limits. However, the engineering community still lacks a standardized definition and methodology for addressing the performance limits of airborne conformal antennas.

[0008] (2) Most performance limit analysis methods are only applicable to small-sized, regularly shaped models. They are inefficient and have large errors when dealing with the performance limit problems of UAVs with conformal apertures.

[0009] (3) The UAV antenna needs to consider non-convex constraints such as axial ratio, which is a huge challenge for the performance limit analysis method based on convex optimization.

[0010] In summary, UAV design engineering urgently needs to provide a standardized definition of the performance limits of airborne conformal antennas and develop an efficient and accurate methodology to solve this problem. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for performance limit analysis of conformal aperture of unmanned aerial vehicles based on polarization decomposition.

[0012] The technical problem addressed by this invention is solved as follows:

[0013] A method for performance limit analysis of conformal aperture of unmanned aerial vehicles based on polarization decomposition includes the following steps:

[0014] Step 1: Set the design parameters for the conformal antenna of the UAV;

[0015] In the context of UAV conformal antenna design, design parameters are set for performance limit calculations, including those related to aperture. ,frequency Radiation direction Gain and shaft ratio The indicator requirements; among them are , The desired target gain;

[0016] Step 2: Construct a current optimization model;

[0017] Given a conformal aperture Source points Frequency domain current distribution at [location] As an intermediate variable; in drones, Received Limitations, and produce gains and shaft ratio performance Thus, it is constructed Model;

[0018] based on The model will conform to the aperture. Discretize into a triangular mesh model, and then distribute the frequency domain current. Expanded into a linear combination of RWG basis functions on a triangular mesh, the coefficients of this linear combination constitute the current matrix. Define far-field pattern parameters, and extract far-field pattern, radiation intensity, radiated power, power loss, gain, axial ratio, and current matrix. Based on the relationship between them, construct a current optimization model;

[0019] Step 3: Solve the current optimization model;

[0020] The current optimization model is solved using the Lagrange analytical method to obtain the relationship between the gain performance limit and far-field polarization.

[0021] Step four, feature decomposition;

[0022] By performing eigenvalue decomposition on the intermediate parameters introduced during the Lagrange analytical solution process, the optimal polarization can be obtained. and worst polarization ;Will and Substituting each value into the current optimization model, we obtain the gain performance limit corresponding to the worst polarization. The gain performance limit corresponding to optimal polarization ;also, and The difference can be used as a quantitative indicator to reflect the dynamic range of the performance limit in polarization;

[0023] like If the design parameters in step one are feasible, then directly determine that the design parameters in step one are feasible; otherwise, proceed to step five.

[0024] Step 5: Construct a polarization optimization model;

[0025] Utilizing optimal polarization and worst polarization The linear combination of represents arbitrary polarization, and the current optimization problem is rewritten to obtain the polarization optimization model;

[0026] Step 6: Solve the polarization optimization model using the interior point method to obtain... and The optimal solution of the linear combination is used to reconstruct the limiting performance. ,like If the design parameters in step one are found to be feasible, then the design parameters in step one are deemed feasible; otherwise, they are deemed infeasible.

[0027] Furthermore, in step 1, , Conformal aperture refers to the area that can be used to design conformal antennas; , and These are the lowest and highest frequencies in the operating band of the conformal antenna; , and These are the azimuth and elevation radiation ranges of the conformal antenna, respectively. , The desired target gain; , This represents the maximum axial ratio of the conformal antenna's radiation field.

[0028] Furthermore, the specific process of step two is as follows:

[0029] Frequency domain current distribution Expanded into a triangular mesh model RWG basis functions Linear combinations formed:

[0030]

[0031] Where N is a positive integer, ; The coefficients corresponding to the nth RWG basis function are called current coefficients, which form the current matrix. ; Represents the source point The function value of the nth RWG basis function at point n;

[0032] In the far-field region of a conformal antenna, At the scene The electric field generated at that point is denoted as ; and yes The two reference polarization directions, and the azimuth angle and pitch angle Determined direction of propagation Vertical, satisfying ;

[0033] Define the far-field pattern for:

[0034]

[0035] in, express The length of , where j is the imaginary number sign. For wave number, c is the speed of light; and These represent the far-field radiation patterns at... and Components in direction;

[0036] Radiation intensity for:

[0037]

[0038] in, It is the impedance of the vacuum wave;

[0039] The radiated power generated in the far-field region is denoted as . ,exist The upper part is composed of surface resistance The resulting power loss is denoted as Then the gain Represented as:

[0040]

[0041] Shaft ratio Represented as:

[0042]

[0043] in, Indicates taking the absolute value;

[0044] Define two far-field component matrices and and radiation resistance matrix Its elements are:

[0045]

[0046]

[0047]

[0048] in, and Representing the far-field component matrices respectively and The nth element, express The trace components; Represents the radiation resistance matrix The element in the m-th row and n-th column, ; and Let them represent the inner integral and the outer integral, respectively. The trace components; , , ; and Let represent the source points of the inner and outer integrals, respectively; and They represent the source point respectively and The Laplace operator;

[0049] Based on surface resistance Define the loss resistance matrix Its element in row m and column n for:

[0050]

[0051] Far-field matrix Radiance matrix resistance matrix ; , , superscript Indicates non-conjugate transpose, superscript Indicates conjugate transpose;

[0052] Based on the frequency and radiation direction in step one, calculate , , , Matrix; given any far-field radiation intensity value The following optimization model is constructed:

[0053]

[0054] The above model is denoted as " "Current optimization model"; among which,

[0055]

[0056]

[0057]

[0058] The current optimization model represents: a fixed far-field radiation intensity value And the axis ratio is required to be no greater than Through optimization To obtain the optimal solution To achieve total power Minimum, i.e., let the gain be the minimum. Reaching the maximum value ;

[0059] pass Optimal solution of current optimization model Calculate the maximum gain for:

[0060]

[0061] Does the maximum gain satisfy the condition? To determine the set gain index To determine whether it is feasible, and thus complete the performance limit analysis;

[0062] Construct the following optimization model:

[0063]

[0064] The above model is denoted as " "Current optimization model";

[0065]

[0066] in, For any given far-field pattern, and These represent the far-field radiation patterns. corresponding Value and value.

[0067] Furthermore, in step two, the RWG basis functions are expressed as:

[0068]

[0069] in, For the length of the shared edge, and This represents two triangular mesh cells connected by a shared edge; Represents a triangle area, From Vertex pointing to that is not connected to a shared edge The vector, From point to Vectors of vertices not connected to shared edges.

[0070] Furthermore, the specific process of step three is as follows:

[0071] Solving based on the Lagrange analytical method Current optimization model; calculation of intermediate parameters and ,but Performance Limits of Current Optimization Model Represented as:

[0072] .

[0073] Furthermore, the specific process of step four is as follows:

[0074] For intermediate parameters Perform eigenvalue decomposition:

[0075]

[0076] in, and They are respectively The maximum and minimum eigenvalues ​​are given, and their corresponding eigenvectors are respectively... and ;Will and Substitute them separately The current optimization model is obtained. and ;

[0077] At this time, if If the design parameters in step one are deemed feasible, then step five is executed.

[0078] Furthermore, the specific process of step five is as follows:

[0079] Utilizing optimal polarization and worst polarization linear combination To represent arbitrary polarization, the coefficients of this linear combination are given by... and Sure, Indicates weight, , Indicates phase, ;

[0080] Construct the following optimization model:

[0081]

[0082] The above model is denoted as " Polarization optimization model.

[0083] Furthermore, the specific process of step six is ​​as follows:

[0084] Solving the polarization optimization model using the interior point method yields the following results: Optimal solution of polarization optimization model and To restore the performance limit Represented as:

[0085]

[0086] At this time, if If the design parameters in step one are found to be feasible, then the design parameters in step one are deemed feasible; otherwise, they are deemed infeasible.

[0087] The beneficial effects of this invention are:

[0088] The method described in this invention supports rapid calculation of performance limits under non-convex design conditions. Facing non-convex design conditions (such as axial ratio) that are difficult to handle with traditional ACO, this invention transforms the current optimization model into a polarization optimization model, reducing the difficulty of solving the performance limit problem; compared to ACO, polarization decomposition has significant advantages in both accuracy and speed.

[0089] The method described in this invention provides a shortcut for determining the feasibility of design specifications. Utilizing polarization decomposition, this invention can obtain the worst-case polarization. Performance limits .when Higher than target gain If the design specifications are feasible, then no further calculations are needed.

[0090] The method described in this invention can calculate the dynamic range of the performance limit with respect to polarization. Using polarization decomposition, this invention can obtain the optimal polarization. and worst polarization and their corresponding performance limits. and . and The difference can be used as a quantitative indicator to reflect the performance limit. Dynamic range in polarization.

[0091] The method described in this invention can be applied to the design of conformal antennas for unmanned aerial vehicles (UAVs), including but not limited to communication link antennas, inter-aircraft link antennas, airborne radar, and the design of novel electromagnetic devices. The method constructs an optimization model and solves it based on polarization decomposition, enabling rapid prediction of the performance limits of conformal apertures under complex constraints, thus saving significant costs in conformal antenna design. For the design of novel electromagnetic devices, the method ensures the physical feasibility of design specifications by calculating the performance limits of a given aperture, which is fundamental to successful design. Attached Figure Description

[0092] Figure 1 This is a flowchart illustrating the method described in this invention;

[0093] Figure 2 The method described in the embodiment Model diagram;

[0094] Figure 3 This is a radiation model diagram from the method described in the embodiment;

[0095] Figure 4 This is a schematic diagram of the STL model in the method described in the embodiment, where (a) is a strip and (b) is a spherical shell;

[0096] Figure 5 The diagram shows the dynamic range distribution in the method described in the embodiment, where (a) is a strip and (b) is a spherical shell;

[0097] Figure 6 The performance limit of the method described in the embodiment Shaft ratio constraint The graphs show the changes, where (a) represents polarization decomposition and (b) represents direct optimization. Detailed Implementation

[0098] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0099] This embodiment provides a method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition, and its flowchart is shown below. Figure 1 As shown, it includes the following steps:

[0100] Step 1: Set the design parameters for the conformal antenna of the UAV;

[0101] In the context of UAV conformal antenna design, design parameters are set for performance limit calculations, including those related to aperture. ,frequency Radiation direction Gain and shaft ratio Requirements.

[0102] These design parameters are shown in Table 1. Conformal aperture, i.e., the area that can be used to design conformal antennas; and These are the lowest and highest frequencies in the operating band of the conformal antenna; and These are the azimuth and elevation radiation ranges of the conformal antenna, respectively. The desired target gain; This represents the maximum axial ratio of the conformal antenna's radiation field.

[0103] Table 1

[0104]

[0105] The ultimate goal of the method described in this embodiment is to determine whether the design specifications in Table 1 are feasible based on performance limits.

[0106] Step 2: Construct a current optimization model;

[0107] In order to conformal aperture and performance parameters (In this embodiment, gain is included) and shaft ratio This embodiment establishes a connection between ( ) and ( ). Source points Frequency domain current distribution at [location] As an intermediate variable. On drones, Received The limitations, in turn, led to performance issues. This kind of Model such as Figure 2 As shown.

[0108] from Starting with the model, we will use modeling methods to... The data is divided into discrete grids, and RWG basis functions are established on the grids, specifically as follows:

[0109] First, use modeling software to draw the conformal aperture. The 3D model is then divided into discrete triangular meshes using modeling software and exported as an STL file. The STL file contains the positions of each vertex of the triangular mesh and the connections between them, providing a concise and complete description of any triangular mesh model. In this embodiment, such a model is called an "STL model," such as... Figure 4 As shown, (a) is a strip and (b) is a spherical shell;

[0110] In the STL model, the current distribution Expanded from a triangular mesh model RWG basis functions Linear combinations formed:

[0111]

[0112] Where N is a positive integer, ; The coefficients corresponding to the nth RWG basis function are called current coefficients, which form the current matrix. , , express dimensional vector;

[0113] Defined as: for two triangular mesh cells connected by a shared edge and ,have:

[0114]

[0115] in, For the length of the shared edge, Represents a triangle area, From Vertex pointing to that is not connected to a shared edge The vector, From point to Vectors of vertices not connected to shared edges.

[0116] For the sake of clarity in the following discussion, this is based on Figure 3 The radiation model provides definitions for some performance parameters and intermediate parameters. In the far-field region of a conformal antenna, superior At the scene The electric field generated at that point is denoted as ; and yes The two reference polarization directions, and the propagation direction (from azimuth) and pitch angle (Definitely) perpendicular, satisfying ;

[0117] Define the far-field pattern for:

[0118]

[0119] in, express The length of , where j is the imaginary number sign. For wave number, c is the speed of light; and These represent the far-field radiation patterns at... and Components in direction;

[0120] Far-field pattern eliminates distance The influence of radiation intensity is... :

[0121]

[0122] in, It is the vacuum wave impedance.

[0123] set up The radiated power generated in the far-field region is ,exist Due to surface resistance The power loss caused is Then the gain Represented as:

[0124]

[0125] In addition, shaft ratio Represented as:

[0126]

[0127] in, This indicates taking the absolute value.

[0128] The above performance parameters ( and ) and intermediate parameters ( , , , and Both are related to current distribution Related, and can therefore be expressed as to Matrix operations.

[0129] The specific calculation method is given below:

[0130] After establishing the STL model and RWG basis functions, it is necessary to calculate the two far-field component matrices. ( ), ( ) and radiation resistance matrix ( ), whose elements are:

[0131]

[0132]

[0133]

[0134] in, and Representing the far-field component matrices respectively and The nth element, express The trace components; Represents the radiation resistance matrix The element in the m-th row and n-th column, ; and Let them represent the inner integral and the outer integral, respectively. The trace components; , , ; and Let represent the source points of the inner and outer integrals, respectively; and They represent the source point respectively and The Laplace operator.

[0135] when When it cannot be ignored, surface resistance also needs to be considered. Calculate the loss resistance matrix ( ), its m-th row and n-th column element for:

[0136]

[0137] Command Superscript Indicates non-conjugate transpose, superscript Representing the conjugate transpose, we can further derive the far-field matrix. ( ), radiation intensity matrix ( ), resistance matrix ( ).

[0138] Thus, we have the matrix form calculation formulas for each parameter. , , , .

[0139] Based on the frequency bands and radiation ranges in step one, this embodiment applies the following to various frequencies. and radiation direction Above, calculate , , , Matrix. Then, arbitrarily assign a far-field radiation intensity value. Construct a current optimization model:

[0140]

[0141] The above model is called " "Current optimization model".

[0142]

[0143]

[0144]

[0145] The significance of the current optimization model is that it fixes the far-field radiation intensity value. And the axis ratio is required to be no greater than Through optimization To obtain the optimal solution To achieve total power Minimum, i.e., let the gain be the minimum. Reaching the maximum value .

[0146] Thus, for the design indicators in step one, the caliber indicators It has been passed The RWG basis functions are automatically satisfied on the STL model. Frequency band indicators. and radiation range indicators Multiple sets were calculated by sampling within the interval. , , Parameters, construct and analyze multiple This is achieved through a current optimization model. Shaft ratio index. Then it is embedded as a constraint condition. Current optimization model. Finally, through... Optimal solution of current optimization model Calculate the maximum gain for:

[0147]

[0148] Does the maximum gain satisfy the condition? To determine the set gain index Whether it is feasible, thus completing the performance limit analysis. In this embodiment, the maximum gain The criteria for determining the optimal value and design feasibility are, in fact, the specific performance limits within the framework of the method described in this embodiment. Therefore, the method described in this embodiment will also... This is known as the "performance limit".

[0149] Further steps will be discussed. Solution of the current optimization model. To solve... The current optimization model described in this embodiment also requires the construction of an optimization model:

[0150]

[0151] Called " Current optimization model.

[0152]

[0153] in, It is an arbitrary, given far-field pattern. and These represent the far-field radiation patterns. corresponding Value and value.

[0154] make ,but This actually reflects the polarization in the far field. The significance of this optimization model is that it fixes... (i.e., the size and polarization of the far-field mode), through optimization To obtain the optimal solution To achieve total power Minimum, i.e., let the gain be the minimum. Reaching the maximum value .

[0155] Parallel computing methods can be applied to this step. In this step, the computation of some data is independent, such as the various RWG basis functions and... , The elements of the matrix. The method described in this embodiment uses a multi-core CPU to compute these data in parallel, significantly improving modeling efficiency.

[0156] Step 3: Solve the current optimization model;

[0157] The current optimization model is a non-convex optimization model, and it has many optimization parameters. Solving this problem using traditional ACO methods would be difficult. Therefore, the method described in this embodiment utilizes polarization decomposition to address this challenge.

[0158] Polarization decomposition requires solving first. Current optimization model. Based on the Lagrange method, this model has an analytical optimal solution. Its calculation method is as follows: first, calculate the intermediate parameters... and ,but Performance Limits of Current Optimization Model Represented as:

[0159]

[0160] Step four, feature decomposition;

[0161] according to As can be seen from the expression, With polarization Change. Therefore, The current optimization model has an optimal polarization. Corresponding to various Under the highest performance limit Similarly, there also exists a worst-case polarization. Corresponding to various Minimum performance limit . and In the following text, it will be abbreviated as and .

[0162] In order to obtain and For intermediate parameters Perform eigenvalue decomposition:

[0163]

[0164] in, and They are respectively The maximum and minimum eigenvalues ​​are given, and their corresponding eigenvectors are respectively... and .Will and Substitute them separately The current optimization model is obtained. and .

[0165] At this time, if If the design parameters in step one are feasible, then proceed directly to step five to solve the problem. Current optimization model, and then based on performance limits judge.

[0166] also, and The difference It can be used as a quantitative indicator to reflect performance limits. In polarization The dynamic range of the above.

[0167] Step 5: Construct a polarization optimization model;

[0168] Regulation Then optimal polarization can be adopted. and worst polarization linear combination To represent arbitrary polarization, the coefficients of this linear combination are given by... and Sure, Indicates weight, , Indicates phase, .

[0169] Construct the following optimization model:

[0170]

[0171] The above model is called " The "polarization optimization model" is more difficult to optimize than... The current optimization model is greatly reduced.

[0172] Step 6: Solve the polarization optimization model;

[0173] The polarization optimization model is an optimization model with very few parameters (only a few). and This embodiment addresses a simple nonconvex optimization problem, which is solved using the interior-point method. The interior-point method is a well-established nonconvex optimization algorithm, and the `fmincon` function in MATLAB provides a complete solution for it.

[0174] Step 7, Post-processing;

[0175] according to Optimal solution of polarization optimization model and To restore the performance limit Represented as:

[0176]

[0177] At this time, if If the design parameters in step one are found to be feasible, then the design parameters in step one are deemed feasible; otherwise, they are deemed infeasible.

[0178] This embodiment demonstrates the effectiveness of the conformal aperture performance limit analysis method for UAVs based on polarization decomposition, using spherical shell and strip models as examples. Taking the case of [time period] as an example, the STL model of the strip and the spherical shell at this frequency is as follows: Figure 4 (a) and Figure 4 As shown in (b). Where the rectangular coordinates Spherical coordinates The transformation relationship is as follows:

[0179]

[0180] Table 2

[0181]

[0182] Under the design parameters in Table 2, this embodiment calculated the dynamic range of the strip and the spherical shell. The distribution, such as Figure 5 As shown, (a) is a stripe, and (b) is a spherical shell. The stripe exhibits a higher [missing information - likely a specific characteristic]. Especially in the radial directions off-center. The spherical shell This can be ignored. Dynamic range This has important guiding significance in conformal antenna design, such as evaluating the degree to which the performance of conformal apertures is affected by polarization. This embodiment introduces quantization calculation for the first time. The method.

[0183] Table 3

[0184]

[0185] Due to the high quality of the strip The values, in the examples, under the design parameters in Table 3, were obtained by polarization decomposition to solve for the stripes under different conditions. Performance limits This visually demonstrates the impact of shaft ratio on performance limits, as shown in the following results. Figure 6 As shown in (a). In addition, , and target gain It was also marked. Figure 6 (a) In the results, Below Therefore, it is necessary to base it on Determine whether the design specifications are feasible. Higher than This indicates that in various tests Under these conditions, all design parameters are feasible.

[0186] Finally, to demonstrate the advantages of polarization decomposition, the examples also solved the stripe polarization using a direct optimization method (i.e., the ACO method) under the design parameters in Table 3. Current optimization model, The results are as follows Figure 6 As shown in (b). Wherein, the error...

[0187]

[0188] The direct optimization results showed a lot of jitter, which demonstrates the advantage of polarization decomposition in terms of accuracy.

[0189] Table 4 summarizes the time costs of polarization decomposition and direct optimization (in terms of...). (Taking a single solution as an example). It can be seen that polarization decomposition also has a significantly faster speed while maintaining higher accuracy.

[0190] Table 4

[0191]

[0192] The results of this embodiment show that: (1) there is a high The value model requires designers to consider the impact of polarization on performance limits. (2) Direct optimization has poor speed and accuracy, showing that due to the introduction of non-convex conditions such as shaft ratio, Current optimization models are difficult to handle by traditional ACO methods. (3) Polarization decomposition significantly improves the quality and efficiency of evaluating the performance limits of conformal antennas.

[0193] This invention can be applied to the design of conformal antennas for unmanned aerial vehicles (UAVs), including but not limited to communication link antennas, inter-aircraft link antennas, airborne radar, and the design of novel electromagnetic devices. For UAV conformal antennas, traditional design methods often rely on the designer's experience to guess the performance range achievable by the conformal aperture, frequently requiring extensive trial and error and iteration. However, the polarization decomposition method provided by this invention can rapidly predict the performance limits of conformal apertures under complex constraints, saving significant costs in conformal antenna design. For the design of novel electromagnetic devices, this invention ensures the physical feasibility of design specifications by calculating the performance limits of a given aperture, which is the foundation for successful design.

[0194] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for limit analysis of conformal aperture performance of unmanned aerial vehicles based on polarization decomposition, characterized in that, Includes the following steps: Step 1: Set the design parameters for the conformal antenna of the UAV; In the context of UAV conformal antenna design, design parameters are set for performance limit calculations, including those related to aperture. ,frequency Radiation direction Gain and shaft ratio The indicator requirements; among them are , The desired target gain; Step 2: Construct a current optimization model; Given a conformal aperture Source points Frequency domain current distribution at [location] As an intermediate variable; in drones, Received Limitations, and produce gains and shaft ratio performance Thus, it is constructed Model; based on The model will conform to the aperture. Discretize into a triangular mesh model, and then distribute the frequency domain current. Expanded into a linear combination of RWG basis functions on a triangular mesh, the coefficients of this linear combination constitute the current matrix. Define far-field pattern parameters, and extract far-field pattern, radiation intensity, radiated power, power loss, gain, axial ratio, and current matrix. Based on the relationship between them, construct a current optimization model; Step 3: Solve the current optimization model; The current optimization model is solved using the Lagrange analytical method to obtain the relationship between the gain performance limit and far-field polarization. Step four, feature decomposition; The optimal polarization is obtained by eigenvalue decomposition of the intermediate parameters introduced in the Lagrange analytical method. and worst polarization ;Will and Substituting each value into the current optimization model, we obtain the gain performance limit corresponding to the worst polarization. The gain performance limit corresponding to optimal polarization ; like If the design parameters in step one are feasible, then directly determine that the design parameters in step one are feasible; otherwise, proceed to step five. Step 5: Construct a polarization optimization model; Utilizing optimal polarization and worst polarization The linear combination of represents arbitrary polarization, and the current optimization problem is rewritten to obtain the polarization optimization model; Step 6: Solve the polarization optimization model using the interior point method to obtain... and The optimal solution of the linear combination is used to reconstruct the limiting performance. ,like If the design parameters in step one are found to be feasible, then the design parameters in step one are deemed feasible; otherwise, they are deemed infeasible.

2. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 1, characterized in that, In step one, , Conformal aperture refers to the area that can be used to design conformal antennas; , and These are the lowest and highest frequencies in the operating band of the conformal antenna; , and These are the azimuth and elevation radiation ranges of the conformal antenna, respectively. , The desired target gain; , This represents the maximum axial ratio of the conformal antenna's radiation field.

3. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 2, characterized in that, The specific process of step two is as follows: Frequency domain current distribution Expanded into a triangular mesh model RWG basis functions Linear combinations formed: ； Where N is a positive integer, ; The coefficients corresponding to the nth RWG basis function are called current coefficients, which form the current matrix. ; Represents the source point The function value of the nth RWG basis function at point n; In the far-field region of a conformal antenna, At the scene The electric field generated at that point is denoted as ; and yes The two reference polarization directions, and the azimuth angle and pitch angle Determined direction of propagation Vertical, satisfying ; Define far-field pattern for: ； in, express The length of , where j is the imaginary number sign. For wave number, c is the speed of light; and These represent the far-field radiation patterns at... and Components in direction; Radiation intensity for: ； in, Vacuum wave impedance; The radiated power generated in the far-field region is denoted as . ,exist The upper part is composed of surface resistance The resulting power loss is denoted as Then the gain Represented as: ； Shaft ratio Represented as: ； in, Indicates taking the absolute value; Define two far-field component matrices and and radiation resistance matrix Its elements are: ； ； ； in, and Representing the far-field component matrices respectively and The nth element, express The trace components; Represents the radiation resistance matrix The element in the m-th row and n-th column, ; and Let them represent the inner integral and the outer integral, respectively. The trace components; , , ; and Let represent the source points of the inner and outer integrals, respectively; and They represent the source point respectively and The Laplace operator; Based on surface resistance Define the loss resistance matrix Its element in row m and column n for: ； Far-field matrix Radiance matrix resistance matrix ; , , superscript Indicates non-conjugate transpose, superscript Indicates conjugate transpose; Based on the frequency and radiation direction in step one, calculate , , , Matrix; given any far-field radiation intensity value The following optimization model is constructed: ； The above model is denoted as " "Current optimization model"; among which, ； ； ； The current optimization model represents: a fixed far-field radiation intensity value And the axis ratio is required to be no greater than Through optimization To obtain the optimal solution To achieve total power Minimum, i.e., let the gain be the minimum. Reaching the maximum value ; pass Optimal solution of current optimization model Calculate the maximum gain for: ； Does the maximum gain satisfy the condition? To determine the set gain index To determine whether it is feasible, and thus complete the performance limit analysis; Construct the following optimization model: ； The above model is denoted as " "Current optimization model"; ； in, For any given far-field pattern, and These represent the far-field radiation patterns. corresponding Value and value.

4. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 3, characterized in that, In step two, the RWG basis functions are expressed as follows: ； in, For the length of the shared edge, and This represents two triangular mesh cells connected by a shared edge; Represents a triangle area, From Vertex pointing to that is not connected to a shared edge The vector, From point to Vectors of vertices not connected to shared edges.

5. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 3, characterized in that, The specific process of step three is as follows: Solving based on the Lagrange analytical method Current optimization model; calculation of intermediate parameters and ,but Performance Limits of Current Optimization Model Represented as: 。 6. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 5, characterized in that, The specific process of step four is as follows: For intermediate parameters Perform eigenvalue decomposition: ； in, and They are respectively The maximum and minimum eigenvalues ​​are given, and their corresponding eigenvectors are respectively... and ;Will and Substitute them separately The current optimization model is obtained. and ; At this time, if If the design parameters in step one are deemed feasible, then step five is executed.

7. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 6, characterized in that, The specific process of step five is as follows: Utilizing optimal polarization and worst polarization linear combination To represent arbitrary polarization, the coefficients of this linear combination are given by... and Sure, Indicates weight, , Indicates phase, ; Construct the following optimization model: ； The above model is denoted as " Polarization optimization model.

8. The method for limit analysis of conformal aperture performance of UAVs based on polarization decomposition according to claim 7, characterized in that, The specific process of step six is ​​as follows: Solving the polarization optimization model using the interior point method yields the following results: Optimal solution of polarization optimization model and To restore the performance limit , is represented as: ； At this time, if If the design parameters in step one are found to be feasible, then the design parameters in step one are deemed feasible; otherwise, they are deemed infeasible.

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