Method and device for obtaining wideband characteristic parameters of electrically large conductor platform antenna based on FDM-PO and CAT

Abstract

The application discloses a kind of based on FDM-PO and CAT's electric large conductor platform antenna broadband characteristic parameter acquisition method and device, it is related to electromagnetic simulation technique technical field, can satisfy the engineering demand of electric large conductor platform antenna broadband characteristic parameter fast acquisition.The method comprises: obtaining the platform geometric model of electric large size conductor carrier platform, is divided into methodical quantity law area and physical optics area and is carried out discrete profile division;Define base function in methodical quantity law area to represent unknown surface current, establish current approximation model in physical optics area;Select several sampling frequency points, establish joint matrix equation, and introduce fast dipole method, calculate the interaction inside methodical quantity law area and the coupling interaction between methodical quantity law area and physical optics area, obtain surface current solution;Using Chebyshev approximation method, construct current reconstruction model;Current reconstruction model is used to calculate electromagnetic response parameter.

Description

Technical Field

[0001] This application relates to the field of electromagnetic simulation technology, and further to the field of radar electromagnetic calculation technology, and in particular to a method and apparatus for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT. Background Technology

[0002] As modern communication and detection systems continue to evolve towards higher power, higher gain, and wider bandwidth, the engineering applications of platform-based antennas require accurate performance evaluation over a broad frequency range. The presence of electrically large conductor platforms significantly alters the electromagnetic radiation and scattering characteristics of antennas, and the electromagnetic coupling effect between the antenna and the platform cannot be ignored. Therefore, the complex electromagnetic interactions between the antenna and the platform must be considered simultaneously during the analysis, which places higher demands on the computational efficiency and storage capacity of numerical calculation methods.

[0003] In related technologies, the broadband electromagnetic characteristic analysis of an ideal conductor carrier platform first involves decomposing the platform into regions. A common virtual dividing surface is introduced between adjacent unclosed sub-regions, dividing the platform and its equipment into several closed sub-regions with complete outer surfaces. Subsequently, the outer surfaces of each closed sub-region are divided into triangular patches, and the incident wave electric field of each sub-region is obtained based on this. The corresponding matrix equations are established, and the unknown coefficients are solved using the Gauss-Seidel iterative method. Finally, the Padé approximation method is used to broadband reconstruct the induced current, thereby obtaining the broadband radar cross section of the ideal conductor carrier platform.

[0004] However, the applicant recognizes that the relevant technology has at least the following technical problems in its implementation: When dealing with real antenna-platform systems containing local fine structures or multi-region coupling, the scale of unknowns increases rapidly, making it difficult to effectively address complex electromagnetic coupling problems. Furthermore, in broadband analysis, although Padé approximation reduces the direct solution of some frequency points, it is still necessary to establish and solve matrix equations at multiple representative frequency points. When the analysis bandwidth is wide or the model size is large, the computation time and storage resource consumption are still significant, making it difficult to meet the engineering requirements for rapid acquisition of broadband characteristic parameters of modern electrically large conductor platform antennas. Summary of the Invention

[0005] In view of this, this application provides a method and apparatus for obtaining broadband characteristic parameters of electrically large conductor platform antennas based on FDM-PO and CAT, the main purpose of which is to solve the problem that it is currently difficult to meet the engineering requirements of rapid acquisition of broadband characteristic parameters of modern electrically large conductor platform antennas.

[0006] According to the first aspect of this application, a method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT is provided, the method comprising: A platform geometric model of an electrically large conductor carrier platform is obtained. The computational region of the platform geometric model is divided into a method of moments region and a physical optical region. The surfaces of the method of moments region and the physical optical region are discretized respectively. The platform geometric model is used to characterize the platform structure of the electrically large conductor carrier platform and the antenna structure of the antenna loaded on the electrically large conductor carrier platform. A basis function is defined in the method of moments region to characterize the unknown surface current, and an approximate current model is established in the physical optics region. The broadband frequency range to be analyzed is determined, several sampling frequency points are selected in the broadband frequency range, and a joint matrix equation is established at each sampling frequency point. The fast dipole method is introduced to calculate the interaction within the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point. The Chebyshev approximation method is used to approximate the frequency response of the surface current solution at each sampling frequency point to construct the current reconstruction model in the broadband frequency range. The surface current distribution corresponding to any sampling frequency point within the broadband frequency range is obtained using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband range.

[0007] According to a second aspect of this application, a device for acquiring broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT is provided, the device comprising: A partitioning module is used to obtain the platform geometric model of the electrically large conductor carrier platform, divide the computational region of the platform geometric model into a method of moments region and a physical optical region, and discretize the surfaces of the method of moments region and the physical optical region respectively. The platform geometric model is used to characterize the platform structure of the electrically large conductor carrier platform and the antenna structure of the antenna loaded on the electrically large conductor carrier platform. A definition module is used to define basis functions in the method of moments region to characterize the unknown surface current and to establish an approximate current model in the physical optics region. The solution module is used to determine the broadband frequency range to be analyzed, select several sampling frequency points in the broadband frequency range, establish a joint matrix equation at each sampling frequency point, and introduce the fast dipole method to calculate the interaction within the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point. The module is used to approximate the frequency response of the surface current solution at each sampling frequency point using the Chebyshev approximation method, and to construct the current reconstruction model in the broadband frequency range. The acquisition module is used to obtain the surface current distribution corresponding to any sampling frequency point within the broadband frequency range using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband frequency range.

[0008] According to a third aspect of this application, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in any of the first aspects above.

[0009] According to a fourth aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method described in any one of the first aspects above.

[0010] Based on the above technical solutions, this application provides a method and apparatus for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT. This application divides the antenna and local fine structures into a method of moments (MoM) region and the electrically large platform body into a physical optics region. It introduces the fast dipole method to accelerate the coupling calculation within the MoM region and between the MoM region and the physical optics region, effectively controlling the scale of unknowns and solving the problem of excessively large unknowns in existing methods when dealing with local fine structures. Secondly, it uses the Chebyshev approximation method to perform broadband reconstruction of the surface current at sampling frequency points. Only a few sampling points need to be established and solved for the joint matrix equation, avoiding frequency-by-frequency full-wave solution over a wide bandwidth, significantly reducing computation time and storage resource consumption, and overcoming the shortcomings of existing broadband analysis which still requires solving multiple representative frequency points and involves large computational loads. Simultaneously, the broadband reconstruction process is directly established on a unified solution framework of the MoM and physical optics hybrid model, closely linking frequency approximation and hybrid modeling, which can improve the overall efficiency of broadband response reconstruction, thereby meeting the engineering requirements for rapid acquisition of broadband characteristic parameters of electrically large conductor platform antennas.

[0011] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0012] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This paper illustrates a flowchart of a method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, according to an embodiment of this application. Figure 2 This illustration shows a schematic diagram of a platform geometric model provided in an embodiment of this application; Figure 3 This paper illustrates a schematic flowchart of another method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, provided in an embodiment of this application. Figure 4 This illustration shows a schematic diagram of a device for acquiring broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, according to an embodiment of this application. Figure 5 A schematic diagram of the device structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0013] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0014] This application provides a method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, such as... Figure 1 As shown, the method includes: S10: Obtain the platform geometric model of the electrically large conductor carrier platform, divide the computational region of the platform geometric model into the method of moments region and the physical optics region, and discretize the surfaces of the method of moments region and the physical optics region respectively.

[0015] This application embodiment can be applied to an electromagnetic characteristic analysis system. Specifically, it requires first obtaining a platform geometric model of an electrically large conductor carrier platform. This geometric model characterizes the platform structure and the antenna structure of the antenna loaded on the platform. Then, based on the structural electrical size characteristics, the computational region of the platform geometric model is divided into a Method of Moments (MoM) region and a Physical Optics (PO) region. The antenna and its surrounding local fine structures are divided into the MoM region; the main body of the carrier platform, with its large electrical size and relatively smooth surface, is divided into the PO region. Next, the electromagnetic characteristic analysis system discretizes the surfaces of the MoM and PO regions using triangular facets, providing a discrete basis for subsequent electromagnetic calculations.

[0016] Through the above process, the complex electrically large platform and the local fine antenna structure are decomposed into regions. Only the antenna and fine structure regions with concentrated unknowns are solved using a strict method of moments (MoM), while the platform body, which has a huge electrical size but a relatively smooth surface, is approximated using physical optics. This effectively controls the overall scale of unknowns and avoids the problem of computational resource explosion caused by global fine decomposition. For example, in a ship platform model, the helical antenna installed on the deck and its surrounding local platform surface are divided into MoM regions, and the ship body is divided into physical optics regions and discretized.

[0017] S20: Define basis functions in the method of moments region to characterize the unknown surface current, and establish an approximate current model in the physical optics region.

[0018] In this embodiment of the application, in the method of moments region, the electromagnetic property analysis system defines basis functions. The basis functions can be RWG (Rao-Wilton-Glisson) basis functions. RWG basis functions are vector basis functions defined on the triangular facet pairs obtained after discrete partitioning. They are used to characterize the tangential distribution of surface current, and their unknown current coefficients are the quantities to be solved.

[0019] In the physical optics region, the electromagnetic property analysis system establishes a current approximation model based on the physical optics approximation. That is, it assumes that the surface current in the physical optics region is determined only by the incident magnetic field, ignoring the mutual coupling between currents inside the physical optics region, thus eliminating the need to introduce additional unknowns.

[0020] Through the above processing, the unknowns of the entire electromagnetic calculation problem only come from the RWG basis functions in the method of moments region. The current coefficients in the physical optics region are not independent unknowns, but are explicitly determined by the incident field and the current coefficients in the method of moments region, and are updated synchronously with the current coefficients in the method of moments region during the iteration process, which can significantly reduce the dimension of the matrix equations. At the same time, the physical optics current model can reflect the reflection and diffraction effects of electrically large platforms on the antenna radiation field with low computational cost, and can achieve effective control of the computational scale while ensuring engineering accuracy.

[0021] Continuing with the above example, suppose 73 RWG basis functions are defined on the surface of the helical antenna in the method of moments region. Each basis function corresponds to a pair of triangular patches with common sides, and their unknown coefficients constitute the current vector to be determined. A physical optical current model is established on the surface of the ship's main body in the physical optical region. This model directly calculates the surface current based on the incident magnetic field without generating new unknowns, so that the total number of unknowns is only 73, which is much smaller than the tens of thousands of unknowns that may be generated by performing a method of moments partitioning on the entire platform.

[0022] S30: Determine the broadband frequency range to be analyzed, select several sampling frequency points within the broadband frequency range, establish a joint matrix equation at each sampling frequency point, and introduce the fast dipole method to calculate the internal interaction of the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point.

[0023] In this embodiment, the electromagnetic characteristic analysis system determines the broadband frequency range to be analyzed, for example, starting from the starting frequency. to the termination frequency Within this wide frequency range, several Chebyshev sampling frequency points are selected. The number of sampling frequency points can be determined based on the wide frequency range and the required approximation accuracy, specifically 5 to 10. At each sampling frequency point, the electromagnetic characteristic analysis system establishes a joint matrix equation based on the hybrid model of the method of moments (MoM) and physical optics. The joint matrix equation includes the self-impedance matrix of the MoM region, the mutual impedance matrix between the MoM region and the physical optics region, and the excitation vector. Simultaneously, the Fast Dipole Method (FDM) is introduced to transform the far-field interactions within the MoM region and between the MoM region and the physical optics region into a aggregation-translation-deaggregation form for accelerated calculation. For near-field interactions, the traditional MoM method or the equivalent dipole moment method is still used to directly fill the gaps. An iterative solver, such as the stable double conjugate gradient method, is used to solve the joint matrix equation at each sampling frequency point, obtaining the surface current coefficient vector of the MoM region corresponding to each sampling frequency point.

[0024] Through the above process, full-wave solutions are performed only at a small number of sampling frequency points. The computational complexity of the far-field matrix-vector product is significantly reduced by utilizing the fast dipole method, thus significantly decreasing the computation time per solution. Compared to the traditional frequency-by-frequency sweep method, the number of sampling points is greatly reduced, effectively controlling the overall computational burden. For example, assuming a broadband frequency range of 350 MHz to 550 MHz, and taking 5 Chebyshev sampling points, the corresponding 5 sampling frequency points are calculated according to the corresponding sampling point formula. Furthermore, at each sampling frequency point, a moment method region self-impedance matrix of corresponding dimension and a moment method region-physical optics region mutual impedance matrix of corresponding dimension are established. The fast dipole method is used to accelerate the calculation of far-field interactions, and the BiCGSTAB iterative solver converges within 20 steps, obtaining 73 current coefficients on the surface of the helical antenna at each sampling frequency point.

[0025] S40: Using the Chebyshev approximation method, the frequency response of the surface current solution at each sampling frequency point is approximated and modeled to construct a current reconstruction model in the broadband frequency range.

[0026] In this embodiment, the electromagnetic characteristic analysis system uses the surface current coefficients of the region obtained at each sampling frequency point as sample data, and introduces the Chebyshev Approximation Technique (CAT) to perform broadband modeling of the frequency response of the surface current. Specifically, the current coefficients are expressed as wave values. The Chebyshev series form, within the standardized wavenumber interval, utilizes the discrete orthogonality of Chebyshev polynomials to calculate the expansion coefficients of each order from the current coefficient values ​​at the sampling frequency points. Each sampling point is constructed to... The order expansion and series form can approximate the real current response with an exponential convergence rate over the entire wideband frequency range.

[0027] Through the above modeling process, the electromagnetic characteristic analysis system compresses the continuous current response over a wide frequency range into a finite-order Chebyshev series. Once the expansion coefficients are obtained, the surface current at any frequency point within the wide frequency range can be quickly calculated without resolving any matrix equations. Compared to piecewise interpolation or frequency-by-frequency solving, Chebyshev approximation has the advantages of high global approximation accuracy and outstanding computational efficiency, making it particularly suitable for wide-bandwidth analysis problems with high computational costs, such as electrically large platform-borne antennas. Continuing with the example in step S30 above, the 73 current coefficients at the 5 sampled frequency points are used as samples to construct the corresponding Chebyshev expansion and calculate the expansion coefficients of each order. Taking the current coefficient at the feed port of the helical antenna as an example, the average relative error between its Chebyshev series and the direct solution in the range of 350 MHz to 550 MHz is less than 1%, verifying the high accuracy of the approximation model.

[0028] S50: The surface current distribution corresponding to any sampling frequency point in the broadband frequency range is obtained by using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform in the broadband range.

[0029] In this embodiment, the electromagnetic characteristic analysis system utilizes a constructed Chebyshev series current reconstruction model to quickly obtain the surface current distribution of any frequency point within a broadband frequency range using the method of moments (MoM) without performing a frequency-by-frequency full-wave solution. Specifically, for any target frequency within the broadband frequency range, its wave value is first transformed to a standardized interval, and then substituted into the Chebyshev series formula to calculate approximate values ​​of each current coefficient, thereby obtaining a complete surface current vector. Based on this, according to the far-field integral formula or input impedance calculation formula in electromagnetic field theory, the broadband electromagnetic response parameters of the electrically large conductor carrier platform and antenna are calculated from the reconstructed surface current distribution, including characteristic parameters such as antenna radiation pattern, input impedance, gain, and radar cross section.

[0030] By directly applying the current reconstruction results to the calculation of electromagnetic response parameters required for engineering through the above process, a complete closed loop from sampling and solving to broadband characteristic acquisition can be achieved. Since repeatedly establishing and solving large matrix equations across the entire frequency band is avoided, the calculation time is significantly reduced, fully meeting the engineering requirements for rapid acquisition of broadband characteristic parameters of electrically large conductor platform antennas. Continuing with the example in step S40, using the Chebyshev series obtained in step S40, the surface current of the helical antenna at three frequency points of 400 MHz, 450 MHz, and 500 MHz is calculated, and then the input impedance at each frequency point is calculated respectively. The real parts of the input impedances are found to be 68 Ω, 72 Ω, and 66 Ω, and the imaginary parts are 15 Ω, 8 Ω, and 12 Ω, respectively. The error is small compared with the results obtained by solving the frequency point by frequency using the traditional FDM-PO method, while the total calculation time is significantly reduced.

[0031] Optionally, in this embodiment, a platform geometric model of the electrically large conductor carrier platform is obtained. The computational region of the platform geometric model is divided into a method of moments (MoM) region and a physical optics region. The surfaces of the MoM region and the physical optics region are discretized, including: geometrically modeling the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform to obtain the platform geometric model; on the platform geometric model, the region mapped to the antenna surface is taken as the MoM region, and the region mapped to the surface of the electrically large conductor carrier platform is taken as the physical optics region; the wavelength corresponding to the operating frequency is determined. ,Will Using the first partitioning dimension, the surface of the method of moments (MoM) region is divided into several MoM region triangles to complete the discrete partitioning of the MoM region. The side length of each of the several MoM region triangles does not exceed [a certain value]. Furthermore, any two triangles in the region measured by moments do not intersect or share a common edge; As the second partitioning dimension, the surface of the physical optical region is divided into several physical optical region triangles according to the second partitioning dimension to complete the discrete partitioning of the physical optical region. The side length of each of the several physical optical region triangles does not exceed [a certain value]. Furthermore, any two physical optical region triangles do not intersect or share a common side.

[0032] In this embodiment, after obtaining the platform geometric model of the electrically large conductor carrier platform, the electromagnetic characteristic analysis system divides the computational region into a method of moments (MoM) region and a physical optical region based on the structural electrical dimensional characteristics, and then discretizes them separately. The MoM region is used to refer to the MoM region, and the PO region is used to refer to the physical optical region. Specifically, the electromagnetic characteristic analysis system first performs accurate geometric modeling of the electrically large conductor carrier platform and the antenna structure loaded on it, obtaining a complete platform geometric model. In this platform geometric model, the region mapped by the antenna surface is taken as the MoM region, which includes the antenna and its surrounding fine structures, requiring a rigorous integral equation method for solution. The region mapped by the surface of the electrically large conductor carrier platform is taken as the physical optical region. The physical optical region has a relatively smooth surface and a large electrical size, allowing for physical optical approximation.

[0033] After the region is divided, the electromagnetic characteristic analysis system determines the wavelength corresponding to the operating frequency, denoted as λ. This wavelength is determined by typical frequencies within the analysis band, such as the center frequency. As the first partitioning dimension, the surface of the MoM region is divided into several triangles using the method of moments (MoM) method of times (MOM) region, with the side length of each MOM region triangle not exceeding [a certain value]. Furthermore, any two triangles in the method of moments region either do not intersect or share only one common edge, thus forming a surface mesh that meets the discretization requirements of the electromagnetic field integral equation. Simultaneously, with As the second partitioning dimension, the surface of the PO region is divided into several physical optical region triangles, with the side length of each physical optical region triangle not exceeding [a certain value]. Similarly, it ensures that the patches do not overlap or only share edges. This differentiated meshing strategy allows for the use of coarser meshes in the PO region while maintaining the computational accuracy of the MoM region, thereby effectively controlling the overall scale of unknowns.

[0034] Thus, by employing fine subdivision of the MoM region, accurate characterization of the antenna surface current can be ensured, while using coarser subdivision of the PO region can significantly reduce the number of triangular patches, thereby reducing the memory and computation time requirements of the PO region. Simultaneously, the explicit region division and subdivision rules provide a unified and standardized discretization foundation for subsequent acceleration of the Fast Dipole method and Chebyshev approximation. For example, see... Figure 2The platform geometry model shown represents a helical antenna system mounted on a simplified ship hull model. The ship hull model is 22.66 meters long, 4.4 meters wide, and 2.8 meters high. The helical antenna is located in the middle of the deck, with a helix diameter of 2.25 centimeters and a height of 2.25 centimeters. An ideal slot voltage source is placed at the center of the antenna as excitation. In the region partitioning, the entire surface of the helical antenna is mapped as a MoM region, i.e. Figure 2 The area marked in red maps the hull surface to the PO area, which is... Figure 2 The portion is marked in light gray. Next, assuming the operating frequency band is determined to be 350 MHz to 550 MHz, the wavelength corresponding to the center frequency of 450 MHz is taken. Therefore, the partitioning size of the MoM region is taken as follows: The surface of the helical antenna was discretized into 74 triangular patches using FEKO software, which are also known as the triangle regions using the method of moments; the partitioning dimensions of the PO region were taken as... The surface of the hull is discretized into 14,516 triangular patches, also known as physical optical region triangles. All patches meet the requirements that the side length does not exceed the corresponding subdivision size and that they do not overlap or only share sides.

[0035] Optionally, in this embodiment, a basis function is defined in the method of moments region to characterize the unknown surface current, and a current approximation model is established in the physical optics region. This includes defining RWG basis functions for each pair of triangular facets sharing a common edge in both the method of moments region and the physical optics region, to obtain a model containing... The set of basis functions in the method of moments region containing the basis functions of each basis function. The set of physical optical region basis functions of basis functions; define the integral operator shown in the following expression. ,

[0036] in, The imaginary unit, For wave number, For free space wave impedance, For gradient operators, For free space Green's function, The surface current density in the method of moments region. The surface current density in the physical optical region. The surface current density vector takes the value of the surface current density in the method of moments region. Or the surface current density of the physical optical region , For the conductor surface in the method of moments region or the physical optics region; combined with the integral operator Based on the boundary conditions of the conductor target, the following integral equation of electric field is established to characterize the unknown surface current.

[0037] in, Position vector The function, This represents the segmentation vector of the vector; by introducing the physical optics approximation and neglecting the mutual coupling between currents within the physical optics region, the Galerkin method is used, and RWG basis functions are selected as trial functions to test the electric field integral equation, resulting in the matrix equation shown in the following formula, thus completing the establishment of the current approximation model.

[0038] in, For the region of the method of moments The self-impedance matrix, For dimension is The vector of unknown current coefficients, where the elements are the unknown current coefficients in the region defined by the method of moments. For the region of the method of moments The mutual impedance matrix, For dimension is The activation vector, for The coupling matrix between the method of moments region and the physical optics region.

[0039] In this embodiment, after discretizing the MoM and physical optics regions, the electromagnetic characteristic analysis system defines corresponding basis functions for each pair of triangular facets in each region to establish a mathematical representation of the surface current. Specifically, the electromagnetic characteristic analysis system defines an RWG basis function for each pair of triangular facets sharing a common edge in both the MoM and PO regions, thereby obtaining the MoM region basis function set, the number of which is denoted as [missing information]. The set of basis functions for the PO region, denoted by the number of basis functions. .in, and The number of basis functions in the MoM region is determined by both the target surface size and the aforementioned partitioning dimensions. The number of basis functions in the MoM region corresponds to the total number of unknowns in the subsequent solution, while the basis functions in the PO region are only used to construct coupling terms and do not add any unknowns. Furthermore, the integral operator shown in the expression in Equation 1 below is defined. : Formula 1:

[0040] In Formula 1, The imaginary unit; For wave number, , The wavelength corresponding to the operating frequency; The free-space wave impedance is approximately 377 ohms. For gradient operators, This represents the divergence with respect to the source point coordinates. For free space Green's function, and These represent the surface current density vectors of the MoM region and the PO region, respectively. For the corresponding conductor surface.

[0041] Integral Operator This describes the electric field generated in space by arbitrary surface current density. Combined with the boundary conditions of the conductor surface, the electric field integral equation shown in Equation 2 below can be established to characterize the unknown surface current: Formula 2:

[0042] in, The incident electric field or excitation electric field is specifically provided by an ideal slot voltage source at the antenna feed location; For position vectors, subscript This represents the tangential component of the vector. The equation shown in Formula 2 indicates that the sum of the total tangential electric field on the conductor surface, i.e., the incident field and the scattered field generated by the induced current, is zero.

[0043] To transform the above integral equation into a numerically solvable matrix form, this embodiment introduces a physical optics approximation, neglecting the mutual coupling between currents within the PO region. That is, it is assumed that the surface current in the PO region is determined solely by the incident magnetic field and does not require solving a matrix equation. Simultaneously, the Galerkin method is employed, selecting the RWG basis functions themselves as trial functions to test the electric field integral equation. Since the RWG basis functions only have tangential components, a set of linear equations is obtained after testing, which can be simplified to the matrix equation shown in Equation 3 below: Formula 3:

[0044] In formula 3, For the region of the method of moments The self-impedance matrix characterizes the electromagnetic interactions between the basis functions in the MoM region. dimension The unknown current coefficient vector, whose elements are the current coefficients corresponding to each RWG basis function in the MoM region, is the core unknown to be solved. For the region of the method of moments The mutual impedance matrix describes the electromagnetic coupling between the basis functions of the MoM region and the basis functions of the PO region; for The coupling matrix between the method of moments region and the physical optics region is introduced to maintain formal consistency with the standard method of moments equations. dimension The excitation vector is such that only the element corresponding to the feed position is non-zero (generated by an ideal gap voltage source). This matrix equation establishes a quantitative relationship between the unknown current coefficient in the MoM region and the excitation source, laying the foundation for subsequent solutions.

[0045] In the above process, by combining the rigorous method of moments description of the MoM region with the physical-optical approximation of the PO region, only the following needs to be considered: Solve for each unknown variable to avoid directly solving for all unknowns. The global matrix with one unknown can significantly reduce the computational scale; at the same time, the introduction of RWG basis functions can ensure the continuity of surface current at the edge of the triangular patch, improve the computational accuracy, and the clear definition of the integral operator and the electric field integral equation makes subsequent fast dipole acceleration and Chebyshev approximation possible.

[0046] Continue to combine Figure 2 The example of a ship-borne helical antenna is illustrated below. As mentioned earlier, the ship is 22.66 meters long, 4.4 meters wide, and 2.8 meters high. The diameter and height of the helical antenna are both 2.25 centimeters, and an ideal slot voltage source is placed at the center. Based on the partitioning results, the MoM region is discretized into 74 triangular patches. These patches form several internal edges, defining a total of 73 RWG basis functions, i.e. The value of is 73; the PO region is discretized into 14516 triangular patches, and 21782 RWG basis functions are defined, that is... The value is 21782, used only for calculating coupling, and does not generate unknowns. Wavenumber Determined by the operating frequency, for example, at a center frequency of 450 MHz, Approximately 9.42 rad / m, free-space wave impedance Approximately 377Ω, construct the self-impedance matrix The mutual impedance matrix is ​​73×73. The excitation vector is 73×21782. The matrix equation is non-zero only at the basis functions corresponding to the feed positions. This matrix equation is the core mathematical model for subsequent fast dipole method to accelerate the solution and Chebyshev approximation to perform broadband reconstruction.

[0047] Optionally, in this embodiment, a broadband frequency range to be analyzed is determined, several sampling frequency points are selected within the broadband frequency range, and a joint matrix equation is established at each sampling frequency point. The fast dipole method is then introduced to calculate the interactions within the method of moments region and the coupling interactions between the method of moments region and the physical optics region, obtaining the surface current solution at each sampling frequency point. This includes: assuming the wavenumber range corresponding to the broadband frequency range is... The following formula is used to calculate the number of sampling frequency points. Each sampling frequency point determines the corresponding wave value. ,

[0048] in, The value ranges from 1 to , The total number of sampling frequency points. To describe the wave value corresponding to the initial sampling frequency point among a number of sampling frequency points, To describe the wave value corresponding to the cutoff sampling frequency point among a number of sampling frequency points, For Chebyshev Gaussian nodes, Represents the cosine function. The method represents pi; combining the wave values ​​corresponding to several sampling frequency points, an octree structure is used to group the basis functions of the method of moments (MoM) region and the physical optics region, and according to the spatial interval between the basis functions, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks, respectively; the excitation vector corresponding to each sampling frequency point in the MoM region is calculated based on the electric field generated by the excitation source. , where the excitation vector The dimension is And the excitation vector Each element in is calculated using the following formula:

[0049] in, Excitation vector The Middle One element, For the first basis functions Let the electric field vector of the excitation source be denoted; the fast dipole method is introduced to construct an expression for calculating the physical optical current coefficient; combining the partitioned self-impedance matrix and mutual impedance matrix, and the excitation vector corresponding to each sampling frequency point in the method of moments region, we can further refine the expression. The expression for calculating the physical optical current coefficient is used to construct a joint matrix equation, and the joint matrix equation is solved to obtain the surface current solution at each sampling frequency point.

[0050] In this embodiment, after determining the broadband frequency range to be analyzed, the electromagnetic characteristic analysis system selects several sampling frequency points within this range for subsequent broadband reconstruction using Chebyshev approximation techniques. Specifically, let the wavenumber range corresponding to the broadband frequency range be... ,in The wavenumber corresponding to the starting frequency point. The wavenumber is the wavenumber corresponding to the cutoff frequency. , This represents the wavelength corresponding to the operating frequency. The total number of sampling points is selected. , The value of can be determined based on the bandwidth and required precision. For example, if the value is taken in the range of 5 to 10, then the ______ is... Wave value at each sampling frequency point Determined by the following formula 4: Formula 4:

[0051] in, These are called Chebyshev Gaussian nodes. It is a cosine function. This is pi. Formula 4 defines the standard interval. Chebyshev nodes on the curve are mapped to the actual wavenumber interval. This results in sampling points being more densely distributed at both ends of the interval and more sparsely distributed in the middle, which is beneficial to improving the accuracy of polynomial approximation.

[0052] For example, for Figure 2 The ship-borne helical antenna model shown is analyzed in the frequency band of 350 MHz to 550 MHz, corresponding to the wavenumber range. Approximately 7.33 rad / m (350 MHz) It is approximately equal to 11.52 rad / m (550 MHz). The value of is 5. Using the above formula 4, 5 sampling frequency points are calculated and the wave value corresponding to each sampling frequency point is determined.

[0053] Next, for each sampling frequency point, the joint matrix equation needs to be established and solved. Specifically, firstly, an octree structure is used to spatially group all RWG basis functions in the MoM and PO regions, that is, the entire computational domain is recursively divided into cubic units of equal size, and each group of basis functions is assigned to a leaf node according to its geometric center. Then, based on the spatial distance between basis function pairs, the self-impedance matrix and cross-impedance matrix are divided into near-field contributions and far-field contributions. The specific division principle is as follows: if the center distance between the cubic blocks to which two groups of basis functions belong is greater than the wavelength corresponding to the current sampling frequency point... If the elements of the mutual impedance matrix are true, then they belong to the far-field block; otherwise, they belong to the near-field block.

[0054] The self-impedance elements of each basis function are collectively grouped into near-field blocks. In this embodiment, the near-field blocks are directly calculated and stored using the traditional method of moments or the equivalent dipole moment method, while the far-field blocks utilize the fast dipole method for accelerated matrix-vector multiplication. The core idea of ​​the fast dipole method is to transform far-field interactions into three steps: aggregation, translation, and deaggregation, thereby reducing computational complexity. Simultaneously, it is also necessary to calculate the excitation vector at each sampling frequency point. Excitation vector The dimension is , its first Each element is calculated using the following formula 5: Formula 5:

[0055] In Formula 5, For the first A basis function is defined on a pair of triangular facets in the MoM region; Let be the electric field vector generated by the excitation source. Figure 2 The ideal slot voltage source shown has an excitation electric field that exists only at the feeding slot. Therefore, only the integral of the basis function at the corresponding feeding position is non-zero, while the rest are zero.

[0056] After completing the above preparations, the fast dipole method is introduced to further construct an expression for calculating the current coefficient in the physically optical region. Under the physically optical approximation, the surface current density in the PO region is directly determined by the incident magnetic field. Finally, combining the matrix portion directly filled by the near-field block, the matrix-vector product accelerated by FDM in the far-field block, and the excitation vector, a complete joint matrix equation is constructed. Iterative solvers such as the stable biconjugate gradient method are used to solve the joint matrix equation, obtaining the surface current solution at each sampling frequency point. For example, in Figure 2 In this example, for the five sampling frequency points, each sampling point requires solving the joint equations based on the unknowns in the MoM region, combining the MoM-PO coupling effect and the matrix-vector product accelerated by FDM. After acceleration using FDM, the solution time for each point is only a few dozen iterations, far less than direct solution. Thus, by employing the Chebyshev sampling strategy, full-wave solutions are only needed at a small number of frequency points, avoiding the dozens or even hundreds of solutions required by traditional frequency-by-frequency sweeping methods. Simultaneously, the octree grouping and fast dipole method significantly accelerate the matrix-vector product operation in each iteration, significantly shortening the computation time for each sampling frequency point. Furthermore, the reasonable division of the near and far fields ensures computational accuracy while controlling memory overhead. Finally, the surface current solutions at each sampling frequency point serve as sample data, providing accurate and reliable input for subsequent Chebyshev approximation to construct a broadband current reconstruction model.

[0057] Optionally, in this embodiment, the basis functions of the method of moments region and the physical optics region are grouped using an octree structure, based on the wave values ​​corresponding to several sampling frequency points. Furthermore, according to the spatial interval between the basis functions, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks, respectively. This includes: for the wave value corresponding to each of the several sampling frequency points... An octree structure is used to spatially group all basis functions in the method of moments and physical optics regions, resulting in multiple basis function data sets. Each basis function data set belongs to a cube cell. The distance between the centers of the cube cells to which any two basis function data sets belong and the wave value are then used as the basis function data sets. Corresponding wavelength Based on the magnitude relationship, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks, respectively. During partitioning, if the distance between the centers of the cube cells belonging to two basis function data sets is greater than... If the two basis function data sets are true, they are classified as far-field contribution blocks; otherwise, they are classified as near-field contribution blocks. The matrix elements in the near-field contribution blocks of the self-impedance matrix are calculated using the equivalent dipole moment method shown in the following formula.

[0058] in, The first in the self-impedance matrix Line number Column matrix elements, For free space wave impedance, The imaginary unit, The first in the self-impedance matrix Each sampling frequency point determines the corresponding wave value. To extract the first from the self-impedance matrix The center of the basis function points to the first... Vectors centered on basis functions The length of the mold, The first in the self-impedance matrix The equivalent dipole moment vector of each basis function The first in the self-impedance matrix The equivalent dipole moment vector of each basis function , Let be the free-space wavenumber of the self-impedance matrix; where the matrix elements in the near-field contribution block of the mutual impedance matrix are calculated using the following formula.

[0059] in, For the first in the physical optics region The basis functions have a moment method region for the _ _ basis functions Electromagnetic coupling contribution of each basis function Used to account for the shadowing effect of the incident wave at the observation point in the mutual impedance matrix. Representing the first in the physical optics region Two tangential unit vectors are defined at the center of the common edge related to the basis functions, and their directions point to the outside of the two adjacent triangles respectively. Indicates the physical optics region and the first The unit normal vector of the triangle associated with each basis function. For the first from the physical optics region The center of the basis function points to the region of the moment method. Vectors centered on basis functions The length of the mold, It is the imaginary unit.

[0060] Optionally, after selecting the Chebyshev sampling frequency points, the electromagnetic characteristic analysis system will analyze the wavenumber corresponding to each sampling frequency point. This study utilizes an octree structure to spatially group all RWG basis functions in the Method of Moments (MoM) and Physical Optics (PIO) regions. The octree is a recursive spatial partitioning data structure. First, the entire computational domain is enclosed within a cube root node. Then, it is uniformly divided into eight sub-cubes. This process is repeated for each non-empty sub-cube until the number of basis functions contained in each sub-cube cell does not exceed a preset threshold. Each group of basis functions is assigned to a leaf cube cell based on its geometric center. This grouping allows for the rapid determination of the spatial distance between any two groups of basis functions; specifically, it suffices to calculate the distance between the centers of their respective cube cells. ,in For from the first The center of the basis function points to the first... The vector centered on each basis function Its modulus. Based on this distance and the wavelength corresponding to the current sampling frequency point. Based on the magnitude relationship, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks. That is, if the distance between the centers of two cubic elements is greater than... The corresponding basis function pairs are classified as far-field contribution blocks, and the fast dipole method is used in the iterative solution to accelerate the calculation in a aggregation-translation-deaggregation form; if the distance is less than or equal to If the result is a near-field contribution block, the matrix elements are calculated and stored precisely using a direct method.

[0061] For the self-impedance matrix elements in the near-field contribution block, the electromagnetic property analysis system uses the equivalent dipole moment method for calculation. Each RWG basis function is equivalent to a dipole located at the center of its common edge, possessing an equivalent dipole moment vector. and , respectively corresponding to the first The and the first The basis function. The first basis function in the impedance matrix. Line number Column elements It is calculated using the following formula 6: Formula 6:

[0062] in, The free-space wave impedance is approximately 377 ohms. The imaginary unit, The wavenumber at the current sampling frequency point. To extract the first from the self-impedance matrix The center of the basis function points to the first... Vectors centered on basis functions The length of the mold, , Let be the free-space wavenumber of the self-impedance matrix. Equation 6 approximates the impedance between the original RWG basis function pairs by means of the electromagnetic field interaction between equivalent dipoles, which significantly reduces the computational cost of near-field matrix filling while maintaining accuracy.

[0063] For the near-field contribution block between the MoM region and the PO region in the mutual impedance matrix, its matrix elements Indicates the PO region number The basis functions for the MoM region are... The electromagnetic coupling contribution of each basis function is calculated using the following formula 7: Formula 7:

[0064] In Formula 7, This is the shading factor, used to account for the shading effect of the incident wave at the observation point in the PO region. If the point is in the shadow region, then... The value is 0 if it is not 1 otherwise; and Representing the first and second regions of PO respectively Two tangential unit vectors are defined at the center of the common edge related to the basis functions, and their directions point to the outside of the two triangles adjacent to the common edge, respectively. Let be the unit normal vector of the triangular facet in the PO region that is associated with the basis function; For the MoM region The equivalent dipole moment vector of each basis function; For the first from the physical optics region The center of the basis function points to the region of the moment method. Vectors centered on basis functions The modulus length; Equation 7 transforms the influence of the surface induced current in the PO region on the MoM region into the coupling of the equivalent dipole field, which has a clear physical meaning.

[0065] In the above process, the near-field and far-field adaptive partitioning of the impedance matrix was achieved by using octree spatial grouping and wavelength-based distance criteria. The near-field was accurately filled using the equivalent dipole moment method, while the far-field was accelerated using the fast dipole method, which reduced the computational complexity of matrix-vector multiplication in each iteration. At the same time, the introduction of the shading factor takes into account the actual lighting conditions of the PO region, only considering the coupling of the illuminated PO region to the MoM region, which greatly reduces the computational load.

[0066] Optionally, in this embodiment, a fast dipole method is introduced to construct an expression for calculating the physical optical current coefficient, including: constructing the following formula for calculating the physical optical current coefficient based on the fast dipole method. The expression,

[0067] in, For the physical optics region The basis functions and the method of moments region of the first Elements of the mutual impedance matrix between basis functions In the first The moment method region at the sampling frequency point. Current coefficients of each basis function For the first Each sampling frequency point determines the corresponding wave value. Used for belonging to the observation group Near-field group set All source groups Summation, Used for source groups The first Summation of basis functions in a region using the method of moments Used for belonging to the observation group Far-field group set All source groups Summation, For the first The de-clusters corresponding to the basis functions of each physical optical region depend on the source group. Center to observation group The center vector and wave number , To obtain the source set from the method of moments region Center to Physical Optics Area Observation Group The translation function of the center, For the source group Center-pointing physical optics region observation group The center vector, For observation group from the physical optics region Center points to source group The center vector, For the region of the method of moments An aggregate function of basis functions.

[0068] In this embodiment, after constructing the joint matrix equations and dividing the near and far fields, the electromagnetic property analysis system introduces the fast dipole method to efficiently calculate the current coefficients in the physical optics region. The current in the PO region is not obtained by solving the matrix equations, but is directly determined by the incident magnetic field. The incident magnetic field The calculation involves the field radiated from the MoM region and the scattered field generated by the current in the MoM region. Directly calculating the current coefficient corresponding to each basis function in the PO region requires traversing the contributions of all basis functions in the MoM region, resulting in a computational complexity of O(n log n). When the number of basis functions in the PO region For large datasets, such as the 21,782 basis functions in a ship hull model, this computation becomes extremely time-consuming. The Fast Dipole method reduces the complexity by grouping the MoM region basis functions, transforming the far-field contribution into a aggregation-translation-deaggregation form. Specifically, in the first The sampling frequency point, the PO region's sampling frequency point. Current coefficients of each basis function It is calculated using the following formula 8: Formula 8:

[0069] In Formula 8, the first summation represents the near-field contribution: For the observation group (i.e., PO area number) The near-field combination set of the cubic units to which each basis function belongs, containing all those related to... Distance less than or equal to wavelength The source group; For the PO region The basis functions and the MoM region of the first The elements of the mutual impedance matrix between the basis functions are directly calculated using the aforementioned equivalent dipole moment method. For the first At the sampling frequency point, the MoM region is at the th sampling frequency point. The current coefficients of the basis functions are obtained by solving the matrix equations from the previous stage. The second summation represents the far-field contribution: For the observation group The far-field combination set, containing all of the above. Distance greater than The source group; For the PO region The ungrouping function of the basis functions depends on the source set. Center-pointing observation group The center vector and wave number ; For the PO region The unit normal vector of the triangular facet containing the basis functions; For source groups from MoM region Center to PO area observation group The translation function at the center describes the transmission of far-field interactions between groups; For the region of the method of moments, the first Aggregate functions of basis functions For observation group from the physical optical region Center points to source group The vector at the center. As can be seen from Equation 8, the entire far-field calculation process is divided into three steps: aggregation, which is to calculate the aggregation amount of each source group; translation, which is to multiply the aggregation amount by the translation function and pass it to the observation group; and deaggregation, which is to distribute the translation result to each PO basis function within the observation group.

[0070] In the above process, the far-field part of the PO current coefficient calculation is transformed from direct accumulation to aggregation-translation-deaggregation by using the fast dipole method, which can significantly reduce the amount of calculation. At the same time, the near-field part still maintains accurate calculation, ensuring overall accuracy. This makes the iterative solution process of the entire sampling frequency point complete efficiently, providing accurate current samples for subsequent Chebyshev approximation.

[0071] In this embodiment, optionally, the self-impedance matrix and mutual impedance matrix after partitioning are combined, along with the excitation vector corresponding to each sampling frequency point in the method of moments region. Based on the expression for calculating the physical optical current coefficient, a joint matrix equation is constructed, and the joint matrix equation is solved to obtain the surface current solution at each sampling frequency point. This solution includes: combining the partitioned self-impedance matrix and mutual impedance matrix, and combining the excitation vector corresponding to the method of moments region at each sampling frequency point. Based on the expression for calculating the physical optics current coefficient, construct the joint matrix equation shown in the following formula.

[0072] in, For the first The moment method region at the sampling frequency point The basis functions for the th basis function The elements of the self-impedance matrix of the basis functions, For the de-aggregation function, For the first A group of regional observations using the method of moments. For the source group, For physical optics region group; and Observation group The near-field set and the far-field set; For the source group Center to observation group The center vector, To source groups from physical optical regions Center to Method of Moments Regional Observation Group The vector at the center; For the region of the method of moments The basis functions and the first in the physical optics region Elements of the mutual impedance matrix between basis functions; For aggregate functions, Let be the translation function that acts self-acting in the region according to the method of moments. It is the translation function of the coupling effect between the method of moments region and the physical optics region; For the first The excitation vector of the method of moments region at each sampling frequency point; the joint matrix equation is solved using the stable double conjugate gradient method to obtain the current coefficient vector of the method of moments region. Furthermore, the vector of the physical optical region current coefficient is obtained through the expression for the physical optical current coefficient. To determine the surface current solution at each sampling frequency point.

[0073] In this embodiment, after completing the near-field and far-field partitioning of the self-impedance matrix and mutual impedance matrix, and obtaining the excitation vector corresponding to each sampling frequency point, the electromagnetic characteristic analysis system will unify all the above parts into a complete joint matrix equation and solve it. The joint matrix equation describes the quantitative relationship between the unknown current coefficients in the method of moments region and the excitation source, while incorporating far-field interactions into the equation in a aggregation-translation-deaggregation form using the fast dipole method. Specifically, in the first... For each sampling frequency point, the joint matrix equation can be written as the following formula: Formula 9:

[0074] In the joint matrix equation shown in Equation 9, the first row corresponds to the self-interactions of the MoM region: For the first A MoM region observation group, that is, the basis function group where the current coefficient to be determined is located; and Observation group The near-field combinatorial set and the far-field combinatorial set; For the first The moment method region at the sampling frequency point The basis functions for the th basis function The self-impedance matrix elements of each basis function are obtained by direct calculation for the matrix elements in the near-field contribution block, where the equivalent dipole moment method can be used to accelerate the calculation for those satisfying the approximation conditions; for the far-field group ( The fast dipole method is used to transform it into an aggregation function. Translation function Sum and decomposition functions The product form, where For the source group Center-pointing observation group The vector at the center. The second row corresponds to the coupling interaction between the MoM region and the PO region: This is a source group for the PO region, i.e., a grouping of PO basis functions; and Observation group Relative to the near-field and far-field sets of the PO source group; For the MoM region The basis functions and the PO region of the first basis function The elements of the mutual impedance matrix between the basis functions are also calculated directly in the near field and accelerated by FDM in the far field. For aggregate functions, It is a translation function. To source groups from physical optical regions Center to Method of Moments Regional Observation Group The vector at the center; For the PO region The current coefficients of each basis function are given by the physical optical current expression shown in Equation 8 above, but during the iteration process, it is necessary to adjust them according to the current MoM current coefficients. Update. Right-hand side of the equation. For the first The excitation vector of the MoM region at each sampling frequency point is non-zero only at the basis function corresponding to the antenna feed position.

[0075] Next, the stable double conjugate gradient method is used to iteratively solve the above joint matrix equation. In each iteration, the product of the left-hand side matrix and the currently guessed solution vector needs to be calculated. Specifically, for the near-field part, the stored impedance matrix elements are directly used for multiplication; for the far-field part, the aggregation-translation-deaggregation process is quickly completed using FDM, without the need to explicitly store the far-field matrix elements. After the iteration converges, the current coefficient vector of the MoM region is obtained. That is, the surface current solution at each sampling frequency point. Simultaneously, the converged solution... Substituting into the physical optics current coefficient expression, we can further obtain the current coefficients of each basis function in the PO region. This allows us to obtain a complete surface current distribution.

[0076] Thus, through the above process, the self-action of MoM and the coupling effect of MoM-PO are unified into the joint matrix equation, and through near-field / far-field partitioning and FDM acceleration, the solution complexity of each sampling frequency point and the unknowns in the MoM region are reduced. Approximately linear correlation, and related to the number of basis functions in the PO region. Almost irrelevant; at the same time, the BiCGSTAB iterative method, combined with the rapid update of physical optical current, can ensure the stability and convergence speed of the equation solution. The surface current solutions obtained at each sampling frequency point are used as accurate samples to provide high-fidelity training data for subsequent Chebyshev approximation, ensuring the accuracy of the broadband reconstruction model.

[0077] Optionally, in this embodiment, the Chebyshev approximation method is used to approximate the frequency response of the surface current solution at each sampling frequency point to construct a current reconstruction model over a wide frequency range, including: defining the Chebyshev polynomial through the recursive relationship shown in the following formula. ,

[0078] By utilizing the discrete orthogonality of Chebyshev polynomials, the Chebyshev expansion coefficients of each order can be calculated using the following formula. ,

[0079] in, In the first The moment method region obtained by solving the joint matrix equation at the nth sampling frequency point. Vector of region current coefficients of each basis function using the method of moments. This represents the total number of Chebyshev sampling points; For any wave value within the broadband frequency range The current coefficient of each basis function is calculated using the following formula. The surface current distribution in the method of moments region at any frequency point is obtained.

[0080] in, For the first Current coefficient at each sampling frequency point For the corresponding to the first Standardized wave values ​​at each sampling frequency point The coefficients are the first-order Chebyshev expansion coefficients; based on the current coefficients in the method of moments region, a current reconstruction model covering the entire broadband frequency range is constructed.

[0081] In this embodiment, after obtaining the surface current solution at each sampling frequency point, the electromagnetic characteristic analysis system uses Chebyshev approximation technology to globally model the frequency response of the current, thereby constructing a current reconstruction model covering the entire broadband frequency range. First, it is necessary to define a first-kind Chebyshev polynomial. The recursive relationship is shown in Formula 10 below: Formula 10:

[0082] in, Furthermore, these are standardized variables. The polynomial system shown in Equation 10 exhibits uniform oscillation characteristics at the endpoints of the interval, which allows for exponential convergence when used for function approximation. For the th... The method of moments provides a basis function for the region, which in... The current coefficients obtained by solving the joint matrix equation at each Chebyshev sampling frequency point are denoted as follows: , The value ranges from 0 to By utilizing the discrete orthogonality of Chebyshev polynomials, the expansion coefficients of each order can be calculated using the following formula 11. : Formula 11:

[0083] In Formula 11, The summation index represents the total number of Chebyshev sampling points, i.e., the number of sampling frequency points selected previously. Iterate through all sampling points. Indicates the first The basis function corresponding to the th basis function Chebyshev expansion coefficients. Formula 11 uses a weighted sum of function values ​​at Chebyshev nodes to approximate the projection of a continuous function into polynomial space. For any wave value within a wide frequency range... , No. The current coefficients of each basis function can be reconstructed using truncated Chebyshev series, as detailed in Equation 12 below: Formula 12:

[0084] In formula 12, For the first The expansion coefficients are omitted, and the subscripts of the basis functions are omitted. To simplify the expression; For the corresponding to the first Standardized wave values ​​at each sampling frequency point For the first Chebyshev polynomials in The value at that location, The correction term before the first-order coefficients and originates from the discrete orthogonal formula. Special handling for items. This level only needs to be stored. With a single expansion coefficient, the current value can be quickly calculated at any frequency point without resolving the matrix equation.

[0085] Finally, based on the current coefficients in the method of moments region, a current reconstruction model covering the entire broadband frequency range is constructed, thus forming a complete broadband current reconstruction model that covers the entire analysis frequency band.

[0086] Thus, through the above process, utilizing the exponential convergence property of Chebyshev polynomials, the current response can be reconstructed with engineering-acceptable accuracy across the entire frequency band using only a small number of sampling points, avoiding the dozens or even hundreds of full-wave solutions required by traditional frequency-point sweeping methods; the computational complexity of the reconstruction model is significantly reduced compared to the number of sampling points. Proportional to, and with the scale of the unknown quantity The results show a linear relationship, reducing the overall computation time by more than 85%, with the total CPU time decreasing from 901 seconds to 77 seconds. At the same time, by constructing a current reconstruction model, the consistency and integrity of the hybrid model in broadband analysis are ensured, providing a reliable foundation for the rapid calculation of subsequent electromagnetic response parameters.

[0087] In this embodiment of the application, optionally, the surface current distribution corresponding to any sampling frequency point within the broadband frequency range is obtained using a current reconstruction model, in order to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband frequency range, including: for any wave value within the broadband frequency range The surface current density distribution in the method of moments region was calculated using the current reconstruction model. Based on surface current density distribution The far-field radiated electric field is calculated using the following formula. ,

[0088] in, The position vector of the field point. The position vector of the source point. The imaginary unit, Angular frequency, Permeability in free space And it is a unit vector in the direction of the field point. The total conductor surface in the method of moments region and the physical optics region. As the source Surface current density distribution in the method of moments region , For wave number, As the source Arrival Point The distance; based on the far-field radiated electric field Extracting antenna waveform values The electromagnetic response parameters at the corresponding target frequency are calculated, and the far-field radiated electric field and electromagnetic response parameters are extracted for other sampling frequency points in the broadband frequency range until all sampling frequency points in the broadband frequency range are traversed to obtain the electromagnetic response parameters for the entire broadband range. The electromagnetic response parameters include one or more of the following: radiation pattern, gain, and input impedance.

[0089] In this embodiment, after constructing the broadband current reconstruction model, the surface current distribution at any frequency point can be quickly obtained using this model, and then the electromagnetic response parameters of the electrically large conductor carrier platform and its antenna can be calculated. For any wave value within the broadband frequency range... First, the current coefficients of each basis function in the method of moments region are obtained through Chebyshev series reconstruction, and then the surface current density distribution of the MoM region is synthesized. ,in This represents the source point location vector. Based on electromagnetic field theory and the surface current density distribution... The far-field radiated electric field is calculated using the following formula 13. : Formula 13:

[0090] in, The position vector of the field point. This is the position vector of the source point (the point where the surface current is located). And it is a unit vector in the direction of the field point; The imaginary unit; Angular frequency; Permeability in free space; The free space dielectric constant; Wave number; The distance from the source point to the field point; the integration region. The total conductor surface area of ​​the MoM region. In Equation 13 As the source Surface current density distribution in the method of moments region The physical meaning of Formula 13 is: the surface current density distribution in the method of moments region. Generate a vector potential in space electric field in the far field region and The horizontal component is proportional to it.

[0091] Based on the calculated far-field radiated electric field The antenna can be extracted at the wavenumber. The corresponding electromagnetic response parameters at the target frequency can include one or more of the following: radiation pattern, gain, input impedance, and radar cross section. The radiation pattern indicates... Depending on the angle , The change in gain is the product of the directivity coefficient and the efficiency; the input impedance is derived from the ratio of voltage to current at the feed port, where the current has been obtained through the reconstruction model. Subsequently, the above process is repeated for other sampling frequency points or any desired frequency points within the broadband frequency range, using the same set of Chebyshev expansion coefficients to quickly reconstruct the surface current at that frequency, calculate the far-field electric field and extract parameters, until the entire frequency band is traversed, finally obtaining the electromagnetic response characteristic curve covering the entire frequency band.

[0092] In this way, by connecting the Chebyshev reconstruction model with the far-field integral formula through the above process, a fast full-band calculation from current to radiation parameters can be achieved. Since the current reconstruction model has exponential convergence characteristics, it only requires a small number of sampling points to maintain high accuracy across the entire band. It fully considers the reflection and diffraction effects of the electrically large platform on antenna radiation, ensuring the accuracy of electromagnetic response parameters. It is especially suitable for engineering scenarios that require frequent evaluation of broadband antenna performance, such as antenna optimization and electromagnetic compatibility analysis. It can significantly reduce computational overhead and improve design iteration efficiency.

[0093] In summary, the logical process of the technical solution proposed in this application is summarized as follows: See Figure 3 For the antenna array near the carrier, the computational region is first divided into a Moment of Moments (MoM) region and a Physical Optics (PO) region. The MoM region includes the antenna and its surrounding area, while the PO region is the carrier platform area. Then, the MoM-PO hybrid system is solved at Q+1 sampling points. The BiCGSTAB (Stable Bijugate Gradient Method) is used to iteratively solve the equations, and FDM is used to accelerate all matrix-vector multiplications. After solving the equations, the current coefficients of the MoM region are obtained, and then the current coefficients of the PO region are solved. Subsequently, Chebyshev polynomial expansion is used to fit the broadband current response, and Maehly approximation is used to further improve the fitting accuracy. Finally, the broadband radiation characteristics of the antenna on the carrier platform are obtained.

[0094] Thus, the technical solution of this application, by establishing and solving the hybrid matrix equations of the method of moments (MoM) and physical optics only at a small number of representative Chebyshev sampling points after determining the broadband frequency range, and using the fast dipole method to accelerate the calculation of the coupling interaction within the MoM region and between it and the physical optics region, and using the surface current at the sampling point as the broadband reconstruction sample, avoids the frequency-by-frequency full-wave solution across the entire frequency band, significantly reducing the number of solutions and the overall calculation time, and improving the efficiency of broadband analysis; at the same time, within the MoM-physical optics hybrid modeling framework, the self-interaction of the MoM region and the coupling interaction with the physical optics region are uniformly processed, and the surface current at the sampling frequency point is used as the sample. Accelerated solution is achieved, allowing the broadband approximation process to be directly built upon the hybrid model solution results, forming a clear and unified technical process. This avoids the problem of frequency approximation and hybrid modeling being disconnected, and enhances the applicability of the method in complex electrically large platform antenna problems. In addition, by performing Chebyshev approximation modeling on the frequency response of the surface current in the method of moments region, broadband reconstruction is directly applied to the level of the most electromagnetically coupled unknown current. This achieves rapid reconstruction of the broadband electromagnetic response while maintaining an accurate description of the coupling relationship, without increasing the model complexity, and improves the stability and consistency of the analysis results. It is particularly suitable for engineering analysis needs in scenarios with strong coupling between electrically large platforms and local antenna structures.

[0095] The method provided in this application divides the antenna and local fine structures into a method of moments (MoM) region and the electrically large platform body into a physical optics region. It introduces the fast dipole method to accelerate the coupling calculation within the MoM region and between the MoM region and the physical optics region, effectively controlling the scale of unknowns and solving the problem of excessively large unknowns in existing methods when dealing with local fine structures. Secondly, it uses the Chebyshev approximation method to perform broadband reconstruction of the surface current at sampling frequency points. This only requires establishing and solving the joint matrix equation at a small number of sampling points, avoiding frequency-by-frequency full-wave solutions over a wide bandwidth. This significantly reduces computation time and storage resource consumption, overcoming the shortcomings of existing broadband analyses that still require solving multiple representative frequency points and involve large computational loads. Simultaneously, the broadband reconstruction process is directly established on a unified solution framework of the MoM and physical optics hybrid model, closely linking frequency approximation and hybrid modeling. This improves the overall efficiency of broadband response reconstruction, thereby meeting the engineering requirements for rapid acquisition of broadband characteristic parameters of electrically large conductor platform antennas.

[0096] Furthermore, as Figure 1 In a specific implementation of the method, this application provides a device for acquiring broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, such as... Figure 4 As shown, the device includes: a partitioning module 401, a definition module 402, a solution module 403, a construction module 404, and an acquisition module 405.

[0097] The partitioning module 401 is used to obtain the platform geometric model of the electrically large conductor carrier platform, divide the calculation area of ​​the platform geometric model into a moment method region and a physical optical region, and discretize the surfaces of the moment method region and the physical optical region respectively. The platform geometric model is used to characterize the platform structure of the electrically large conductor carrier platform and the antenna structure of the antenna loaded on the electrically large conductor carrier platform. Definition module 402 is used to define basis functions in the method of moments region to characterize the unknown surface current and to establish an approximate current model in the physical optics region. The solver module 403 is used to determine the broadband frequency range to be analyzed, select several sampling frequency points in the broadband frequency range, establish a joint matrix equation at each sampling frequency point, and introduce the fast dipole method to calculate the interaction within the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point. Module 404 is used to construct the current reconstruction model in the broadband frequency range by approximating the frequency response of the surface current solution at each sampling frequency point using the Chebyshev approximation method. The acquisition module 405 is used to obtain the surface current distribution corresponding to any sampling frequency point in the broadband frequency range using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform in the broadband range.

[0098] In a specific application scenario, the partitioning module 401 is used to perform geometric modeling on the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform to obtain the platform geometric model; on the platform geometric model, the area mapped to the antenna surface is taken as the method of moments region, and the area mapped to the surface of the electrically large conductor carrier platform is taken as the physical optical region; the wavelength corresponding to the operating frequency is determined. ,Will Using the first partitioning size, the surface of the method of moments region is divided into several method of moments region triangles to complete the discrete partitioning of the method of moments region. The side length of each of the several method of moments region triangles does not exceed [a certain value]. Furthermore, any two triangles in the region measured by moments do not intersect or share a common edge; As a second partitioning dimension, the surface of the physical optical region is divided into several physical optical region triangles according to the second partitioning dimension to complete the discrete partitioning of the physical optical region. The side length of each of the several physical optical region triangles does not exceed [a certain value]. Furthermore, any two physical optical region triangles do not intersect or share a common side.

[0099] In specific application scenarios, the definition module 402 is used to define RWG basis functions for each pair of triangular patches sharing a common edge in the method of moments region and the physical optics region, respectively, to obtain a set of RWG basis functions. The set of basis functions in the method of moments region containing the basis functions of each basis function. The set of physical optical region basis functions of basis functions; define the integral operator shown in the following expression. ,

[0100] in, The imaginary unit, For wave number, For free space wave impedance, For gradient operators, For free space Green's function, Let be the surface current density of the region defined by the method of moments. The surface current density of the physical optical region. The surface current density vector is defined as the surface current density of the region defined by the method of moments. Or the surface current density of the physical optical region , The conductor surface of the method of moments region or the physical optical region; combined with the integral operator Based on the boundary conditions of the conductor target, the following integral equation of electric field is established to characterize the unknown surface current.

[0101] in, Position vector The function, This represents the segmentation vector of the vector; by introducing the physical optics approximation and ignoring the mutual coupling between currents within the physical optics region, the Galerkin method is used, and RWG basis functions are selected as trial functions to test the electric field integral equation, resulting in the matrix equation shown in the following formula, thus completing the establishment of the current approximation model.

[0102] in, The region of the method of moments The self-impedance matrix, For dimension is The vector of unknown current coefficients, with elements representing the unknown current coefficients of the region defined by the method of moments. The region of the method of moments The mutual impedance matrix, For dimension is The activation vector, for The coupling matrix between the method of moments region and the physical optics region.

[0103] In specific application scenarios, the solution module 403 is used to determine the broadband frequency range to be analyzed, select several sampling frequency points within the broadband frequency range, establish a joint matrix equation at each sampling frequency point, and introduce the fast dipole method to calculate the internal interactions of the method of moments region and the coupling interactions between the method of moments region and the physical optics region, obtaining the surface current solution at each sampling frequency point, including: assuming the wavenumber range corresponding to the broadband frequency range is... The following formula is used to determine the number of sampling frequency points. Each sampling frequency point determines the corresponding wave value. ,

[0104] in, The value ranges from 1 to , The total number of the aforementioned sampling frequency points. To describe the wave value corresponding to the initial sampling frequency point among a number of sampling frequency points, To describe the wave value corresponding to the cutoff sampling frequency point among a number of sampling frequency points, For Chebyshev Gaussian nodes, Represents the cosine function. The value of pi is represented; combining the wave values ​​corresponding to the several sampling frequency points, an octree structure is used to group the basis functions of the method of moments region and the physical optics region, and according to the spatial interval between the basis functions, the self-impedance matrix and the mutual impedance matrix are respectively divided into near-field contribution blocks and far-field contribution blocks; the excitation vector of the method of moments region at each sampling frequency point is calculated based on the electric field generated by the excitation source. , wherein the excitation vector The dimension is And the excitation vector Each element in is calculated using the following formula:

[0105] in, The excitation vector The Middle One element, For the first basis functions Let the electric field vector of the excitation source be denoted; the fast dipole method is introduced to construct an expression for calculating the physical optical current coefficient; combining the partitioned self-impedance matrix and the mutual impedance matrix, and combining the excitation vector corresponding to each sampling frequency point in the method of moments region. The expression for calculating the physical optical current coefficient is used to construct the joint matrix equation, and the joint matrix equation is solved to obtain the surface current solution at each sampling frequency point.

[0106] In specific application scenarios, the solving module 403 is used to calculate the wave value corresponding to each of the plurality of sampling frequency points. The octree structure is used to spatially group all basis functions in the method of moments region and the physical optics region to obtain multiple basis function data sets, where each basis function data set belongs to a cube cell. The distance between the centers of the cube cells to which any two basis function data sets belong and the wave value are then used as the basis function data sets. Corresponding wavelength Based on the size relationship, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks, respectively. During partitioning, if the distance between the centers of the cube cells belonging to two basis function data sets is greater than... If the two basis function data sets are true, they are classified as a far-field contribution block; otherwise, they are classified as a near-field contribution block. The matrix elements in the near-field contribution block of the self-impedance matrix are calculated using the equivalent dipole moment method shown in the following formula.

[0107] in, The first in the self-impedance matrix Line number Column matrix elements, For free space wave impedance, The imaginary unit, The first in the self-impedance matrix Each sampling frequency point determines the corresponding wave value. To extract the first from the self-impedance matrix The center of the basis function points to the first... Vectors centered on basis functions The length of the mold, The first in the self-impedance matrix The equivalent dipole moment vector of each basis function The first in the self-impedance matrix The equivalent dipole moment vector of each basis function , Let be the free-space wavenumber of the self-impedance matrix; wherein, the matrix elements in the near-field contribution block of the mutual impedance matrix are calculated using the following formula.

[0108] in, For the physical optical region, the first The basis functions have the same effect on the region of moments. Electromagnetic coupling contribution of each basis function Used to account for the shadowing effect of the incident wave at the observation point in the mutual impedance matrix. and Representing the first in the physical optical region respectively Two tangential unit vectors are defined at the center of the common edge related to the basis functions, and their directions point to the outside of the two adjacent triangles respectively. Indicates the physical optical region and the first The unit normal vector of the triangle associated with each basis function. For the first physical optical region The center of the basis function points to the region of the moment method. Vectors centered on basis functions The length of the mold, It is the imaginary unit.

[0109] In specific application scenarios, the solution module 403 is used to construct the following formula for calculating the physical optics current coefficient based on the fast dipole method. The expression,

[0110] in, For the physical optical region number 1 The basis functions and the moment method region Elements of the mutual impedance matrix between basis functions In the first The moment method region at the sampling frequency point is the Current coefficients of each basis function For the first Each sampling frequency point determines the corresponding wave value. Used for belonging to the observation group Near-field group set All source groups Summation, Used for source groups The first Summing the basis functions of the method of moments in the specified region. Used for belonging to the observation group Far-field group set All source groups Summation, For the first The de-clusters corresponding to the basis functions of the physical optical regions and depend on the source group Center to observation group The center vector and wave number , For the source set from the method of moments region Center to the physical optical region observation group The translation function of the center, For the source group The center points to the physical optical region observation group The center vector, For observation group from the physical optical region Center points to source group The center vector, For the region of the method of moments, the first An aggregate function of basis functions.

[0111] In specific application scenarios, the solution module 403 is used to combine the partitioned self-impedance matrix and the mutual impedance matrix, as well as the excitation vector corresponding to each sampling frequency point of the method of moments region. And, based on the expression for calculating the physical optical current coefficient, construct the joint matrix equation shown in the following formula.

[0112] in, For the first The moment method region at the nth sampling frequency point The basis functions for the th basis function The elements of the self-impedance matrix of the basis functions, For the de-aggregation function, For the first A group of regional observations using the method of moments. For the source group, For physical optics region group; and Observation group The near-field set and the far-field set; For the source group Center to observation group The center vector, To source groups from physical optical regions Center to Method of Moments Regional Observation Group The vector at the center; For the region of the method of moments, the first The basis function and the first in the physical optics region Elements of the mutual impedance matrix between basis functions; For aggregate functions, Let be the translation function that acts on the self-actualizing region of the method of moments. The translation function is the coupling effect between the method of moments region and the physical optics region. For the first The excitation vector of the method of moments region at each sampling frequency point; the joint matrix equation is solved using the stable double conjugate gradient method to obtain the current coefficient vector of the method of moments region. And by using the expression for the physical optical current coefficient, the vector of the physical optical region current coefficient is obtained. To determine the surface current solution at each sampling frequency point.

[0113] In specific application scenarios, the construction module 404 is used to define Chebyshev polynomials through the recursive relationship shown in the following formula. ,

[0114] Based on the discrete orthogonality of the Chebyshev polynomials, the Chebyshev expansion coefficients of each order are calculated using the following formula. ,

[0115] in, In the first The moment method region obtained by solving the joint matrix equation at the nth sampling frequency point is the nth sampling frequency point. Vector of region current coefficients of each basis function using the method of moments. The total number of Chebyshev sampling points; for any wave value within the broadband frequency range. The current coefficient of each basis function is calculated using the following formula. The surface current distribution of the method of moments region at any frequency point is obtained.

[0116] in, For the first Current coefficient at each sampling frequency point For the corresponding to the first Standardized wave values ​​at each sampling frequency point The coefficients are the first-order Chebyshev expansion coefficients; based on the current coefficients in the method of moments region, the current reconstruction model covering the entire broadband frequency range is constructed.

[0117] In specific application scenarios, the acquisition module 405 is used to obtain any wave value within the broadband frequency range. Using the current reconstruction model, the surface current density distribution in the method of moments region is calculated. Based on the surface current density distribution The far-field radiated electric field is calculated using the following formula. ,

[0118] in, The position vector of the field point. The position vector of the source point. The imaginary unit, Angular frequency, Permeability in free space And it is a unit vector in the direction of the field point. The total conductor surface of the method of moments region and the physical optics region. As the source Surface current density distribution in the method of moments region , For wave number, As the source Arrival Point The distance; according to the far-field radiated electric field Extracting antenna waveform values The electromagnetic response parameters at the corresponding target frequency are calculated, and the far-field radiated electric field and electromagnetic response parameters are extracted for other sampling frequency points within the broadband frequency range until all sampling frequency points within the broadband frequency range are traversed to obtain the electromagnetic response parameters for the entire broadband range. The electromagnetic response parameters include one or more of the following: radiation pattern, gain, input impedance, and radar cross section.

[0119] The apparatus provided in this application divides the antenna and local fine structures into a method of moments (MoM) region and the electrically large platform body into a physical optics region. It introduces the fast dipole method to accelerate the coupling calculation within the MoM region and between the MoM region and the physical optics region, effectively controlling the scale of unknowns and solving the problem of excessively large unknowns when processing local fine structures in existing methods. Secondly, it uses the Chebyshev approximation method to perform broadband reconstruction of the surface current at sampling frequency points. This only requires establishing and solving the joint matrix equation at a small number of sampling points, avoiding frequency-by-frequency full-wave solutions over a wide bandwidth. This significantly reduces computation time and storage resource consumption, overcoming the shortcomings of existing broadband analysis methods that still require solving multiple representative frequency points and have a large computational load. Simultaneously, the broadband reconstruction process is directly established on a unified solution framework of the MoM and physical optics hybrid model, closely linking frequency approximation and hybrid modeling. This improves the overall efficiency of broadband response reconstruction, thereby meeting the engineering requirement of rapidly acquiring broadband characteristic parameters of the electrically large conductor platform antenna.

[0120] It should be noted that for other corresponding descriptions of the functional units involved in the wideband characteristic parameter acquisition device for electrically large conductor platform antennas based on FDM-PO and CAT provided in the embodiments of this application, please refer to... Figures 1 to 3 The corresponding description in [the document] will not be repeated here.

[0121] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0122] The above embodiments and the technical features in the embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0123] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

[0124] In an exemplary embodiment, see Figure 5Furthermore, a computer device is provided, comprising a bus, a processor, a memory, and a communication interface. It may also include an input / output interface and a display device, wherein the various functional units can communicate with each other via the bus. The memory stores a computer program, and the processor executes the program stored in the memory, performing the method for obtaining broadband characteristic parameters of electrically large conductor platform antennas based on FDM-PO and CAT as described in the above embodiments.

[0125] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT.

[0126] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented in hardware or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0127] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application.

[0128] Those skilled in the art will understand that the modules in the apparatus of the implementation scenario can be distributed within the apparatus of the implementation scenario as described, or they can be located in one or more apparatuses different from this implementation scenario, with corresponding changes. The modules of the above-described implementation scenario can be combined into one module, or they can be further divided into multiple sub-modules.

[0129] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of the implementation scenario.

[0130] The above disclosures are only a few specific implementation scenarios of this application. However, this application is not limited to these. Any variations that can be conceived by those skilled in the art should fall within the protection scope of this application.

Claims

1. A method for obtaining broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, characterized in that, include: A platform geometric model of an electrically large conductor carrier platform is obtained. The computational region of the platform geometric model is divided into a method of moments region and a physical optical region. The surfaces of the method of moments region and the physical optical region are discretized respectively. The platform geometric model is used to characterize the platform structure of the electrically large conductor carrier platform and the antenna structure of the antenna loaded on the electrically large conductor carrier platform. A basis function is defined in the method of moments region to characterize the unknown surface current, and an approximate current model is established in the physical optics region. The broadband frequency range to be analyzed is determined, several sampling frequency points are selected in the broadband frequency range, and a joint matrix equation is established at each sampling frequency point. The fast dipole method is introduced to calculate the interaction within the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point. The Chebyshev approximation method is used to approximate the frequency response of the surface current solution at each sampling frequency point to construct the current reconstruction model in the broadband frequency range. The surface current distribution corresponding to any sampling frequency point within the broadband frequency range is obtained using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband range.

2. The method according to claim 1, characterized in that, The process of obtaining the platform geometric model of the electrically large conductor carrier platform involves dividing the computational region of the platform geometric model into a method of moments (MoM) region and a physical optical region, and then discretizing the surfaces of the MoM region and the physical optical region respectively, including: Geometric modeling is performed on the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform to obtain the geometric model of the platform; On the platform geometric model, the area mapped to the antenna surface is taken as the method of moments region, and the area mapped to the surface of the electrically large conductor carrier platform is taken as the physical optical region; Determine the wavelength corresponding to the operating frequency ,Will Using the first partitioning size, the surface of the method of moments region is divided into several method of moments region triangles to complete the discrete partitioning of the method of moments region. The side length of each of the several method of moments region triangles does not exceed [a certain value]. Furthermore, any two triangles in the method of moments do not intersect or share a common edge; Will As a second partitioning dimension, the surface of the physical optical region is divided into several physical optical region triangles according to the second partitioning dimension to complete the discrete partitioning of the physical optical region. The side length of each of the several physical optical region triangles does not exceed [a certain value]. Furthermore, any two physical optical region triangles do not intersect or share a common side.

3. The method according to claim 1, characterized in that, The process of defining basis functions in the method of moments region to characterize the unknown surface current and establishing an approximate current model in the physical optics region includes: For each pair of triangular faces sharing a common edge in the method of moments region and the physical optics region, RWG basis functions are defined to obtain the following: The set of basis functions in the method of moments region containing the basis functions of each basis function. The set of physical optical region basis functions of basis functions; Define the integral operator shown in the following expression. , in, The imaginary unit, For wave number, For free space wave impedance, For gradient operators, For free space Green's function, Let be the surface current density of the region defined by the method of moments. The surface current density of the physical optical region. The surface current density vector is defined as the surface current density of the region defined by the method of moments. Or the surface current density of the physical optical region , The conductor surface of the method of moments region or the physical optical region; Combined with the aforementioned integral operator Based on the boundary conditions of the conductor target, the following integral equation of electric field is established to characterize the unknown surface current. in, Position vector The function, This represents the segmentation vector of the vector; By introducing a physical optics approximation and neglecting the mutual coupling between currents within the physical optics region, the Galerkin method is employed, and RWG basis functions are selected as trial functions to test the electric field integral equation. This yields the matrix equation shown in the following formula, thus completing the establishment of the current approximation model. in, The region of the method of moments The self-impedance matrix, For dimension is The vector of unknown current coefficients, with elements representing the unknown current coefficients of the region defined by the method of moments. The region of the method of moments The mutual impedance matrix, For dimension is The activation vector, for The coupling matrix between the method of moments region and the physical optics region.

4. The method according to claim 3, characterized in that, The process involves determining the broadband frequency range to be analyzed, selecting several sampling frequency points within the broadband frequency range, establishing a joint matrix equation at each sampling frequency point, and introducing the fast dipole method to calculate the interactions within the method of moments region and the coupling interactions between the method of moments region and the physical optics region, thereby obtaining the surface current solution at each sampling frequency point, including: Let the wavenumber range corresponding to the broadband frequency range be . The following formula is used to determine the number of sampling frequency points. Each sampling frequency point determines the corresponding wave value. , in, The value ranges from 1 to , The total number of the aforementioned sampling frequency points. To describe the wave value corresponding to the initial sampling frequency point among a number of sampling frequency points, To describe the wave value corresponding to the cutoff sampling frequency point among a number of sampling frequency points, For Chebyshev Gaussian nodes, Represents the cosine function. Represents pi; Combining the wave values ​​corresponding to the several sampling frequency points, the basis functions of the method of moments region and the physical optics region are grouped using an octree structure, and the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks according to the spatial interval between the basis functions. Calculate the excitation vector at each sampling frequency point in the method of moments region based on the electric field generated by the excitation source. , wherein the excitation vector The dimension is And the excitation vector Each element in is calculated using the following formula: in, The excitation vector The Middle One element, For the first basis functions Let be the electric field vector of the excitation source; By introducing the fast dipole method, an expression for calculating the physical optics current coefficient is constructed; Combining the partitioned self-impedance matrix and the mutual impedance matrix, and combining the excitation vector corresponding to each sampling frequency point in the method of moments region. The expression for calculating the physical optical current coefficient is used to construct the joint matrix equation, and the joint matrix equation is solved to obtain the surface current solution at each sampling frequency point.

5. The method according to claim 4, characterized in that, The method combines the wave values ​​corresponding to the plurality of sampling frequency points, uses an octree structure to group the basis functions of the method of moments region and the physical optics region, and divides the self-impedance matrix and the mutual impedance matrix into near-field contribution blocks and far-field contribution blocks respectively according to the spatial interval between the basis functions, including: For the wave value corresponding to each of the plurality of sampling frequency points The octree structure is used to spatially group all basis functions in the method of moments region and the physical optics region to obtain multiple basis function data groups, wherein each basis function data group belongs to a cube cell. Based on the distance between the centers of the cube cells belonging to any two basis function data sets and the wave value Corresponding wavelength Based on the size relationship, the self-impedance matrix and the mutual impedance matrix are divided into near-field contribution blocks and far-field contribution blocks, respectively. During partitioning, if the distance between the centers of the cube cells belonging to two basis function data sets is greater than... If the two basis function data sets are true, they are classified as a far-field contribution block; otherwise, they are classified as a near-field contribution block. The matrix elements in the near-field contribution block of the self-impedance matrix are calculated using the equivalent dipole moment method shown in the following formula. in, The first in the self-impedance matrix Line 1 Column matrix elements, For free space wave impedance, The imaginary unit, The first in the self-impedance matrix Each sampling frequency point determines the corresponding wave value. To extract the first from the self-impedance matrix The center of the basis function points to the first... Vectors centered on basis functions The length of the mold, The first in the self-impedance matrix The equivalent dipole moment vector of each basis function The first in the self-impedance matrix The equivalent dipole moment vector of each basis function , Let be the free space wavenumber of the self-impedance matrix; The matrix elements in the near-field contribution block of the mutual impedance matrix are calculated using the following formula. in, For the physical optical region, the first The basis functions have the same effect on the region of moments. Electromagnetic coupling contribution of each basis function Used to account for the shadowing effect of the incident wave at the observation point in the mutual impedance matrix. and Representing the first in the physical optical region respectively Two tangential unit vectors are defined at the center of the common edge related to the basis functions, and their directions point to the outside of the two adjacent triangles respectively. Indicates the physical optical region and the first The unit normal vector of the triangle associated with each basis function. For the first physical optical region The center of the basis function points to the region of the moment method. Vectors centered on basis functions The length of the mold, It is the imaginary unit.

6. The method according to claim 4, characterized in that, The introduction of the fast dipole method to construct an expression for calculating the physical optics current coefficient includes: Based on the fast dipole method, the following formula is constructed for calculating the physical optics current coefficient. The expression, in, For the physical optical region number 1 The basis functions and the moment method region Elements of the mutual impedance matrix between basis functions In the first The moment method region at the sampling frequency point is the Current coefficients of each basis function For the first Each sampling frequency point determines the corresponding wave value. Used for belonging to the observation group Near-field group set All source groups Summation, Used for source groups The first Summing the basis functions of the method of moments in the specified region. Used for belonging to the observation group Far-field group set All source groups Summation, For the first The de-clusters corresponding to the basis functions of the physical optical regions and depend on the source group Center to observation group The center vector and wave number , For the source set from the method of moments region Center to the physical optical region observation group The translation function of the center, For the source group The center points to the physical optical region observation group The vector at the center, For observation group from the physical optical region Center points to source group The vector at the center, For the region of the method of moments, the first An aggregate function of basis functions.

7. The method according to claim 4, characterized in that, The combination of the self-impedance matrix and the mutual impedance matrix after partitioning, and the excitation vector corresponding to each sampling frequency point in the method of moments region. The expression for calculating the physical optical current coefficient is used to construct the joint matrix equation, and the joint matrix equation is solved to obtain the surface current solution at each sampling frequency point, including: Combining the partitioned self-impedance matrix and the mutual impedance matrix, and combining the excitation vector corresponding to each sampling frequency point in the method of moments region. And, based on the expression for calculating the physical optics current coefficient, construct the joint matrix equation shown in the following formula. in, For the first The moment method region at the nth sampling frequency point The basis functions for the th basis function The elements of the self-impedance matrix of the basis functions, For the de-aggregation function, For the first A group of regional observations using the method of moments. For the source group, For physical optics region group; and Observation group The near-field set and the far-field set; For the source group Center to observation group The vector at the center, To source groups from physical optical regions Center to Method of Moments Regional Observation Group The vector at the center; For the region of the method of moments, the first The basis function and the first in the physical optics region Elements of the mutual impedance matrix between basis functions; It is an aggregate function. Let be the translation function that acts on the self-actualizing region of the method of moments. The translation function is the coupling effect between the method of moments region and the physical optics region. For the first The excitation vector of the method of moments region at each sampling frequency point; The joint matrix equation is solved using the stable double conjugate gradient method to obtain the region current coefficient vector of the method of moments. And by using the expression for the physical optical current coefficient, the vector of the physical optical region current coefficient is obtained. To determine the surface current solution at each sampling frequency point.

8. The method according to claim 1, characterized in that, The Chebyshev approximation method is used to approximate the frequency response of the surface current solution at each sampling frequency point, constructing a current reconstruction model within the broadband frequency range, including: The Chebyshev polynomial is defined by the recurrence relation shown in the following formula. , Based on the discrete orthogonality of the Chebyshev polynomials, the Chebyshev expansion coefficients of each order are calculated using the following formula. , in, In the first The moment method region obtained by solving the joint matrix equation at the nth sampling frequency point is the nth sampling frequency point. Vector of region current coefficients of each basis function using the method of moments. This represents the total number of Chebyshev sampling points; For any wave value within the broadband frequency range The current coefficient of each basis function is calculated using the following formula. The surface current distribution of the method of moments region at any frequency point is obtained. in, For the first Current coefficient at each sampling frequency point For the corresponding to the first Standardized wave values ​​at each sampling frequency point These are the first-order Chebyshev expansion coefficients; Based on the current coefficients in the method of moments region, a current reconstruction model covering the entire broadband frequency range is constructed.

9. The method according to claim 1, characterized in that, The process of obtaining the surface current distribution corresponding to any sampling frequency point within the broadband frequency range using the current reconstruction model, and calculating the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband frequency range, includes: For any wave value within the broadband frequency range Using the current reconstruction model, the surface current density distribution in the method of moments region is calculated. ; Based on the surface current density distribution The far-field radiated electric field is calculated using the following formula. , in, The position vector of the field point. The position vector of the source point. The imaginary unit, Angular frequency, Permeability in free space And it is a unit vector in the direction of the field point. The total conductor surface of the method of moments region and the physical optics region. As the source Surface current density distribution in the method of moments region , For wave number, As the source Arrival Point The distance; According to the far-field radiated electric field Extracting antenna waveform values The electromagnetic response parameters at the corresponding target frequency are calculated, and the far-field radiated electric field and electromagnetic response parameters are extracted for other sampling frequency points within the broadband frequency range until all sampling frequency points within the broadband frequency range are traversed to obtain the electromagnetic response parameters for the entire broadband range. The electromagnetic response parameters include one or more of the following: radiation pattern, gain, input impedance, and radar cross section.

10. A device for acquiring broadband characteristic parameters of an electrically large conductor platform antenna based on FDM-PO and CAT, characterized in that, include: A partitioning module is used to obtain the platform geometric model of the electrically large conductor carrier platform, divide the computational region of the platform geometric model into a method of moments region and a physical optical region, and discretize the surfaces of the method of moments region and the physical optical region respectively. The platform geometric model is used to characterize the platform structure of the electrically large conductor carrier platform and the antenna structure of the antenna loaded on the electrically large conductor carrier platform. A definition module is used to define basis functions in the method of moments region to characterize the unknown surface current and to establish an approximate current model in the physical optics region. The solution module is used to determine the broadband frequency range to be analyzed, select several sampling frequency points in the broadband frequency range, establish a joint matrix equation at each sampling frequency point, and introduce the fast dipole method to calculate the interaction within the method of moments region and the coupling interaction between the method of moments region and the physical optics region, so as to obtain the surface current solution at each sampling frequency point. The module is used to approximate the frequency response of the surface current solution at each sampling frequency point using the Chebyshev approximation method, and to construct the current reconstruction model in the broadband frequency range. The acquisition module is used to obtain the surface current distribution corresponding to any sampling frequency point within the broadband frequency range using the current reconstruction model, so as to calculate the electromagnetic response parameters of the electrically large conductor carrier platform and the antenna structure loaded on the electrically large conductor carrier platform within the broadband frequency range.

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