Radar antenna based design method and system

Abstract

The present application relates to the technical field of simulation design, in particular to a design method and system based on a radar antenna, comprising the following steps: calculating phase error based on thermal deformation, analyzing dynamic sidelobe variance by combining displacement spectrum integration and covariance mapping, generating waveguide skeleton by using electromagnetic energy mapping fluid damping, extracting gain drop derivative according to measured difference, decoupling mixed components by using loss frequency response difference, and outputting medium loss correction data, in the present application, by introducing thermal phase error data, the influence of structure deformation on phase is accurately calculated, and by combining the calculation of dynamic group delay and group delay difference, the prediction of the influence of structure deformation on electrical performance is realized, the data fusion of multiple physical fields and the automatic optimization process are improved, the precision and efficiency of design are improved, the limitations of single simulation software are avoided, by accurately correcting factors such as material loss and gain evolution in the design process, the performance requirements of high-frequency radar are met, and the adaptability to complex environment is improved.

Description

Technical Field

[0001] This invention relates to the field of simulation design technology, and in particular to design methods and systems based on radar antennas. Background Technology

[0002] The field of simulation design technology involves the analysis, modeling, and prediction of multi-physics behaviors such as electromagnetic, structural, and thermodynamic fields using computational models. Specifically, it includes preliminary assessments of product structure, electrical performance, mechanical performance, and multi-field coupling characteristics through numerical simulation, as well as modeling, adjusting, and verifying parameters using computer-aided methods during the design process. This enables visualized deduction and parametric design of engineering structures and working mechanisms. It typically encompasses electromagnetic simulation calculations, structural stress simulation, multi-domain coupling modeling, parametric design processes, and quantitative evaluation of simulation results, forming a systematic technical framework from requirement modeling, model construction, simulation solving to result analysis. In contrast, the traditional design method for radar antennas typically involves engineers first setting the basic geometric dimensions and dielectric materials of the antenna based on experience when planning its radiation and structural performance. The design process involves considering material and electrical parameters, array element arrangement, and then using a single electromagnetic simulation software to calculate the electrical performance of the radiating elements, such as gain, beamwidth, and VSWR. Based on the simulation-derived radiation pattern and impedance characteristics, design parameters are manually adjusted. For the structural part, independent mechanical software is used to analyze the stress, thermal deformation, and mechanical stability of the radome, mounting structure, or array support components. Dimensions or thicknesses are manually corrected based on material mechanical parameters and environmental load conditions. In array design, to achieve feed path matching, a distributed feed network model is used to calculate the amplitude and phase distribution of the power divider structure. Matching is achieved by adjusting the power divider ratio, microstrip line length, and transition structure step by step. Parameter optimization relies on manually changing the array element position, element shape, or feed parameters. Through repeated simulations and comparisons of the electrical performance and structural stability of different schemes, a design scheme that meets the requirements of specific scenarios is obtained.

[0003] Current radar antenna design typically employs empirical methods to determine antenna geometry, materials, and array layout, relying on single electromagnetic simulation software for electrical performance calculations, combined with manual adjustments to design parameters. Structural analysis is performed using independent mechanical software, resulting in a disconnect between electromagnetic and structural simulations. This leads to low overall design efficiency and insufficient optimization for complex environments. Traditional design methods rely on manual experience and repeated simulations for parameter optimization and performance adjustment, lacking automated multi-physics collaborative optimization. This results in long design iteration cycles, difficulties in parameter adjustment, and inability to fully resolve structural-electrical performance coupling issues in high-precision designs, impacting design effectiveness and reliability. Summary of the Invention

[0004] To address the technical problems existing in the prior art, embodiments of the present invention provide a design method based on a radar antenna, including the following steps: To achieve the above objectives, the present invention adopts the following technical solution: a radar antenna design method, comprising the following steps: S1: Obtain thermodynamic simulation node displacement data, calculate microstrip thermal strain and cross-sectional deformation data, update characteristic impedance distribution, solve dynamic group time delay by combining path elongation and phase velocity change, calculate parallel branch differences and combine with center angular frequency to generate thermally induced phase error data. S2: Call the thermally induced phase error data, calculate the displacement response power spectrum of the radiation unit, derive the displacement correlation coefficient matrix by integrating the cross power spectral density, map and construct the phase error covariance matrix, analyze the far-field power distribution, and generate the dynamic sidelobe variance index. S3: Call the dynamic sidelobe variance index, configure the stiffness penalty coefficient, set the topology optimization target, compare the cavity cross section with the cutoff wavelength, apply the geometric expansion penalty, map the electromagnetic field energy density to the fluid damping coefficient, drive the fluid boundary to fill along the damping gradient, and generate a waveguide heterogeneous skeleton model. S4: Import the waveguide heterogeneous skeleton model, perform broadband frequency sweep simulation, collect measured gain curves, calculate differential data, construct gain drop function, perform derivative operation on the function, extract the tangent slope features of the center and sideband frequency points, and generate broadband gain evolution trend record; S5: Call the broadband gain evolution trend record, construct a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyze the physical difference between the linear change of dielectric loss and the square root change of conductor loss, and extract the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data.

[0005] As a further aspect of the present invention, the thermally induced phase error data includes the time delay difference component of the feed branch group, the equivalent phase offset value of path thermal elongation, and the additional phase shift due to impedance mismatch; the dynamic sidelobe variance index includes the sidelobe level probability density function, the confidence interval envelope of the far-field pattern, and the gain jitter amplitude caused by random vibration; the waveguide heterogeneous skeleton model includes the geometric topology information of the metal cavity, the adaptive fluid flow channel mesh, and the stiffened solid boundary; the broadband gain evolution trend record includes the first derivative characteristic curve of the gain drop function, the gain attenuation gradient value at the center frequency, and the gain roll-off rate parameter at the bandwidth edge; and the dielectric loss tangent correction data includes the true value of the substrate dielectric loss factor after decoupling, the imaginary part of the corrected material complex permittivity, and the frequency-dependent loss tangent fitting coefficient.

[0006] As a further aspect of the present invention, the step of obtaining the thermally induced phase error data specifically includes: S101: Obtain thermodynamic simulation node displacement data, calculate the thermal strain displacement vector of microstrip transmission line node by exporting the deformation data of mesh node, establish spatial deformation field, perform curve integration on the tangential physical elongation of signal transmission trajectory, accumulate the geometric increment of each micro-segment in the tangential direction, and generate the path thermal elongation accumulation. S102: Call the cumulative thermal elongation of the path, analyze the cross-sectional width deformation data of the microstrip line, update the characteristic impedance distribution along the path of the microstrip line, and combine the physical path increment and phase velocity change to calculate the propagation delay of the signal through each branch and generate a dynamic group delay value. S103: Based on the dynamic group delay value, calculate the delay difference between each parallel feed branch, extract the center angular frequency parameter of the radar system, combine the delay difference and angular frequency, perform phase domain conversion, quantify the relative phase shift of thermal deformation of each port, and generate thermally induced phase error data.

[0007] As a further aspect of the present invention, the step of obtaining the dynamic sidelobe variance index specifically includes: S201: Call the thermally induced phase error data, set the initial phase reference by loading the reference phase state after thermal deformation, analyze the dynamic response characteristics of the structure under random load, evaluate the vibration amplitude response data of each unit at multiple frequency points, establish the spectrum set of the antenna array vibration state, and generate unit displacement response spectrum data. S202: Based on the unit displacement response spectrum data, perform full-band integral operation on the cross power spectral density to obtain the total energy value, derive the root mean square displacement statistics of each unit in physical space, analyze the synchronization characteristics of vibration between units, construct the displacement correlation coefficient matrix of the array surface motion coupling degree, determine the distribution pattern of mechanical vibration in the spatial domain, and generate spatial displacement related information. S203: Call the spatial displacement-related information, perform linear mapping operation on the displacement data using the free space wavenumber, construct the phase error covariance matrix, combine the array manifold vector to perform quadratic matrix operation on the covariance matrix, analyze the power variance distribution of the far-field radiation pattern in the full spatial scanning range, quantify the degree of electrical performance degradation, and generate a dynamic sidelobe variance index.

[0008] As a further aspect of the present invention, the steps for obtaining the waveguide heterogeneous skeleton model are as follows: S301: Call the dynamic sidelobe variance index, configure the local stiffness penalty coefficient of the structure, set the material property interpolation model parameters according to the variance distribution characteristics, initialize the three-dimensional voxel design domain of the antenna backplane and divide the finite element mesh, set the objectives of minimizing structural flexibility and minimizing electromagnetic transmission loss, and generate the initial configuration for multi-field topology optimization. S302: Based on the initial configuration of the multi-field topology optimization, extract the geometric width and height data of the material distribution cavity cross section, compare the cross section size with the preset working frequency band waveguide cutoff wavelength, calculate the geometric expansion penalty value and apply it to the design variable sensitivity field, perform size constraint calculation to correct the material distribution evolution direction, and generate geometric size constraint field data. S303: Call the geometric constraint field data, read the electromagnetic intrinsic mode field energy density scalar field, establish the mapping relationship between the energy density value and the fluid flow resistance, construct the virtual fluid damping coefficient matrix, drive the fluid boundary to fill along the damping gradient, and generate the waveguide heterogeneous skeleton model.

[0009] As a further aspect of the present invention, the process of configuring the local stiffness penalty coefficient of the structure is specifically as follows: Construct an adjoint equation for the far-field pattern power variance distribution data, solve the adjoint equation, calculate the partial derivative of the far-field pattern power variance distribution data with respect to the relative density of each finite element mesh element in the voxel domain, map the partial derivative to the voxel domain to construct a stiffness-sensitivity distribution field, and calculate the expected value and standard deviation of all stiffness-sensitivity values ​​in the stiffness-sensitivity distribution field. The preset reliability probability parameters of the antenna structure design are called to construct the inverse cumulative distribution function model of the standard normal distribution. The preset reliability probability parameters are substituted into the inverse cumulative distribution function model to perform mapping calculation, and the quantile values ​​of the corresponding standard normal distribution are analyzed. The quantile values ​​are set as the statistical confidence coefficient. The sum of the mathematical expectation value and the product of the statistical confidence coefficient and the standard deviation value is set as the stiffness sensitivity judgment threshold. The global basic penalty coefficient and stiffness enhancement adjustment factor of the topology optimization material interpolation model are set. All finite element mesh elements in the voxel domain are traversed, and the stiffness sensitivity value of each finite element mesh element is compared with the stiffness sensitivity judgment threshold. For finite element mesh elements whose stiffness sensitivity values ​​are greater than the stiffness sensitivity judgment threshold, the difference between the stiffness sensitivity value and the stiffness sensitivity judgment threshold is weighted using the stiffness enhancement adjustment factor. The weighted result is then superimposed on the global basic penalty coefficient to generate the local stiffness penalty coefficient of the corresponding finite element mesh element. For finite element mesh elements whose stiffness sensitivity values ​​are less than or equal to the stiffness sensitivity judgment threshold, the global basic penalty coefficient is directly assigned as the local stiffness penalty coefficient of the corresponding finite element mesh element. By summing the local stiffness penalty coefficients of all finite element mesh elements, a spatial distribution matrix of penalty coefficients is constructed to correct the material property interpolation model.

[0010] As a further aspect of the present invention, the steps for obtaining the broadband gain evolution trend record are specifically as follows: S401: Import the waveguide heterogeneous skeleton model, set the electromagnetic simulation boundary conditions and excitation source port, perform full-wave electromagnetic broadband frequency sweep operation, obtain frequency response data under ideal conditions, collect the measured broadband gain sweep curve of the physical prototype, calculate the difference data between the measured and simulated curves, and generate a gain response difference dataset. S402: Based on the gain response difference dataset, a gain drop function that continuously changes with frequency is constructed by performing a polynomial curve fitting operation, and the derivative of the gain drop function with frequency is calculated to generate a gain drop derivative distribution function. S403: Call the gain drop derivative distribution function to lock the center frequency point and edge frequency point coordinates of the radar operating frequency band, extract the tangent slope feature data at the corresponding frequency point, quantify the gain attenuation gradient dominated by dielectric loss and conductor loss in multiple frequency bands, and generate a broadband gain evolution trend record.

[0011] As a further aspect of the present invention, the step of obtaining the dielectric loss angle tangent correction data specifically includes: S501: Call the broadband gain evolution trend record, set the parameter scanning range, construct a bivariate parameterized scanning space based on the dielectric loss tangent and conductor roughness, calculate the simulation gain frequency response curves corresponding to various discrete parameter combinations, perform differential operations on the curves, extract the gain drop derivative features, and generate the simulation gain drop derivative matrix. S502: Based on the simulated gain drop derivative matrix, the global optimal matching parameter set is searched by iterative fitting operation of the deviation between measured features and simulated data, the independent weight of each component in the mixed loss is analyzed, and the loss component deviation fitting solution is generated. S503: For the fitting solution of the loss component deviation, extract the dielectric loss value under the optimal matching state, perform separation operation, remove the interference of surface impedance loss due to rough conductor, output dielectric loss factor, and generate dielectric loss tangent correction data. The design system based on radar antennas includes: The thermal response analysis module acquires thermodynamic simulation node displacement data, calculates microstrip thermal strain and cross-sectional deformation data, updates characteristic impedance distribution, solves dynamic group time delay by combining path elongation and phase velocity changes, calculates parallel branch differences and combines them with center angular frequency to generate thermally induced phase error data. The radiation unit response module calls the thermally induced phase error data, calculates the displacement response power spectrum of the radiation unit, derives the displacement correlation coefficient matrix by integrating the cross power spectral density, maps and constructs the phase error covariance matrix, analyzes the far-field power distribution, and generates a dynamic sidelobe variance index. The waveguide structure optimization module calls the dynamic sidelobe variance index, configures the stiffness penalty coefficient, sets the topology optimization target, compares the cavity cross section with the cutoff wavelength, applies a geometric expansion penalty, maps the electromagnetic field energy density to the fluid damping coefficient, drives the fluid boundary to fill along the damping gradient, and generates a waveguide heterogeneous skeleton model. The gain evolution analysis module imports the waveguide heterogeneous skeleton model, performs broadband frequency sweep simulation, collects measured gain curves, calculates differential data, constructs a gain drop function, performs derivative operations on the function, extracts the tangent slope features of the center and sideband frequency points, and generates a broadband gain evolution trend record. The dielectric loss correction module calls the broadband gain evolution trend record, constructs a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyzes the physical differences between the linear change of dielectric loss and the square root change of conductor loss, and extracts the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data.

[0012] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, by introducing thermally induced phase error data, the influence of structural deformation on the phase is accurately calculated. At the same time, by combining the calculation of dynamic group delay and group delay difference, the influence of structural deformation on electrical performance is predicted. The data fusion of multiple physics fields and the automated optimization process improve the accuracy and efficiency of the design, avoid the limitations of single simulation software, and meet the performance requirements of high-frequency radar by accurately correcting factors such as material loss and gain evolution during the design process, thereby improving the adaptability to complex environments. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of the steps of the present invention; Figure 2 This is a detailed schematic diagram of S1 of the present invention; Figure 3 This is a detailed schematic diagram of S2 of the present invention; Figure 4 This is a detailed schematic diagram of S3 of the present invention; Figure 5 This is a detailed schematic diagram of S4 of the present invention; Figure 6 This is a detailed schematic diagram of S5 of the present invention; Figure 7 This is a system module diagram of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0016] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0017] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0018] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0019] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0020] Please see Figure 1 This invention provides a design method based on a radar antenna, including the following steps: S1: Obtain thermodynamic simulation node displacement data, calculate microstrip thermal strain and cross-sectional deformation data, update characteristic impedance distribution, solve dynamic group time delay by combining path elongation and phase velocity change, calculate parallel branch differences and combine with center angular frequency to generate thermally induced phase error data. S2: Call thermally induced phase error data, calculate the displacement response power spectrum of the radiating unit, derive the displacement correlation coefficient matrix by integrating the cross power spectral density, map and construct the phase error covariance matrix, analyze the far-field power distribution, and generate the dynamic sidelobe variance index. S3: Call the dynamic sidelobe variance index, configure the stiffness penalty coefficient, set the topology optimization target, compare the cavity cross section with the cutoff wavelength, apply the geometric expansion penalty, map the electromagnetic field energy density to the fluid damping coefficient, drive the fluid boundary to fill along the damping gradient, and generate a waveguide heterogeneous skeleton model. S4: Import the waveguide heterogeneous skeleton model, perform broadband frequency sweep simulation, collect measured gain curves, calculate differential data, construct the gain drop function, perform derivative operations on the function, extract the tangent slope features of the center and sideband frequency points, and generate a record of broadband gain evolution trend. S5: Call the broadband gain evolution trend record, construct a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyze the physical difference between the linear change of dielectric loss and the square root change of conductor loss, and extract the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data.

[0021] Thermally induced phase error data includes the time delay difference component of the feed branch group, the equivalent phase shift value of path thermal elongation, and the additional phase shift due to impedance mismatch. Dynamic sidelobe variance indices include the sidelobe level probability density function, the confidence interval envelope of the far-field pattern, and the gain jitter amplitude caused by random vibration. The waveguide heterogeneous skeleton model includes the geometric topology information of the metal cavity, the adaptive fluid flow channel mesh, and the stiffened solid boundary. The broadband gain evolution trend record includes the first derivative characteristic curve of the gain drop function, the gain attenuation gradient value at the center frequency, and the gain roll-off rate parameter at the bandwidth edge. The dielectric loss tangent correction data includes the true value of the substrate dielectric loss factor after decoupling, the imaginary part of the material complex permittivity after correction, and the frequency-dependent loss tangent fitting coefficient.

[0022] Please see Figure 2 The specific steps for obtaining thermally induced phase error data are as follows: S101: Obtain thermodynamic simulation node displacement data, calculate the thermal strain displacement vector of microstrip transmission line node by exporting the deformation data of mesh node, establish spatial deformation field, perform curve integration on the tangential physical elongation of signal transmission trajectory, accumulate the geometric increment of each micro-segment in the tangential direction, and generate the path thermal elongation accumulation. During the thermal deformation analysis of the microstrip transmission line, the coordinate data of the entire array mesh nodes exported from the finite element thermodynamic simulation software were first read through the data interface. This data covers the deformation state of the antenna array under high-temperature conditions (e.g., 120 degrees Celsius) during on-orbit operation. For the structural layer containing the microstrip feed network, the displacement vectors of all discrete nodes were extracted. Select a specific signal transmission path, such as from the feed port to the... The microstrip line trajectory of each radiating unit is discretized into... Each micro-segment has a length of 0.1 mm. For each micro-segment, the displacement vectors of its two end nodes are used to calculate the spatial Euclidean distance of the micro-segment after thermal deformation. This distance is then projected onto the original tangential direction to obtain the tangential tensile amount. Based on the material's mechanical properties, the coefficient of thermal expansion of the substrate material (e.g., Rogers RO4350B) is set to... However, under complex structural constraints, actual deformation needs to be calculated based on nodal displacements. An accumulation operation is performed on the tangential geometric increments of all infinitesimal segments along the path, i.e. ,in The coordinates are after deformation. This process precisely quantifies the length change of the physical path of signal transmission due to thermal expansion. Subsequently, a spatial deformation field mapping of the path is established, associating the deformation data with specific circuit trace IDs. After calculating each of the 1024 channels of the entire array, the cumulative thermal elongation of the path, containing the physical length changes of all feeder branches, is generated as the geometric basis for subsequent electrical parameter corrections.

[0023] S102: Call the cumulative thermal elongation of the path, analyze the cross-sectional width deformation data of the microstrip line, update the characteristic impedance distribution along the path of the microstrip line, combine the physical path increment and phase velocity change, calculate the propagation delay of the signal through each branch, and generate the dynamic group delay value. By invoking the aforementioned cumulative thermal elongation along the path and combining it with the lateral displacement data of the nodes in the microstrip line cross-section, the variation in the conductor width is analyzed. Taking the first... Taking the microstrip line as an example, its initial design width The thickness is 1.2mm. After heating, the edge nodes of the cross-section expand outward, causing the actual width to become... Based on the characteristic impedance calculation logic of microstrip lines, and utilizing the width... Dielectric substrate thickness (Also obtained from the difference in Z-direction displacement at the nodes) and the relative permittivity Recalculate the characteristic impedance at that location. and effective dielectric constant In the specific calculation, if Then, the effective dielectric constant is calculated using the corresponding closed-form analytical expression. Subsequently, the formula is used... Update the phase velocity of the signal in the deformed microstrip line, where The speed is the speed of light. Since thermal deformation is non-uniformly distributed along the path, the phase velocity along the path needs to be integrated piecewise. The entire path length is divided into multiple segments with uniform impedance, and the signal transmission time through each segment is calculated separately. Then, the delays of all segments are summed to obtain the total propagation delay of the signal through the complete branch. Table 1 shows the changes in time delay parameters of some key branches before and after thermal deformation. This calculation process maps geometric deformation and material parameter changes into time-domain signal delay values, generating dynamic group delay values ​​that accurately reflect the dual impact of the physical environment on the speed and path of electrical signal transmission.

[0024] Table 1 Monitoring Table of Thermal Parameter Changes in Critical Feed Branches

[0025] As shown in Table 1, branches of different lengths and locations are affected by heat to varying degrees, resulting in nonlinear characteristics in the dynamic group time delay.

[0026] S103: Based on the dynamic group delay value, calculate the delay difference between each parallel feed branch, extract the center angular frequency parameter of the radar system, combine the delay difference and angular frequency, perform phase domain conversion, quantify the relative phase shift of thermal deformation of each port, and generate thermally induced phase error data. Based on the dynamic group delay values ​​obtained in Table 1, phase consistency analysis between channels is performed. The feed channel at the center of the array is selected as the reference, and its dynamic group delay is denoted as... Calculate the remaining channels latency difference For the center operating frequency of the radar system (e.g.) Extract its corresponding center angular frequency. Using the linear relationship between phase and time delay This converts picosecond-level time delay differences into phase deviations in angle units. For example, for the Ch-024 branch, if its time delay difference relative to the reference channel is 1.5 ps, the calculated phase deviation is approximately... Degree. Perform this operation on all elements of the entire array to construct a dimension of... The phase error matrix (assuming a 1024-element array) is calculated. In this process, additional phase terms caused by the thermal drift of the T / R components themselves must also be considered, and these are linearly superimposed with the phase terms caused by the microstrip line delay. Finally, the degree of phase deviation relative to the ideal wavefront caused by structural thermal deformation at each radiating port is quantified, generating thermally induced phase error data. This data directly characterizes the phase distortion effect of the thermal environment on the antenna's electrical interface.

[0027] Please see Figure 3 The specific steps for obtaining the dynamic sidelobe variance index are as follows: S201: Call thermally induced phase error data, set the initial phase reference by loading the reference phase state after thermal deformation, analyze the dynamic response characteristics of the structure under random load, evaluate the vibration amplitude response data of each unit at multiple frequency points, establish the spectrum set of the antenna array vibration state, and generate unit displacement response spectrum data. The generated thermally induced phase error data is used as a static reference and loaded into the electromagnetic model of the antenna array to set the initial phase state. Subsequently, the random vibration environmental load spectrum (accelerated spectral density ASD curve) from the spacecraft launch phase is imported. This curve defines the vibration energy input in the 20Hz to 2000Hz frequency band; for example, the spectral density at the main resonance frequency of 150Hz is... The load spectrum is used as the excitation input to the dynamic equations of the antenna structure. In this study, the modal superposition method was used to perform frequency response analysis on the structure. The displacement response transfer function of the geometric center node of each radiating element on the antenna array surface was extracted. Combined with input spectral density Calculate the displacement response power spectral density of each node in the Z-direction (perpendicular to the frontal plane). Within the frequency domain, the vibration energy distribution characteristics at each frequency point (frequency resolution set to 5Hz) are scanned, with a focus on the peak response regions corresponding to the first-order bending mode and the second-order torsional mode. The root-mean-square displacement response amplitude of each element at different frequency points is established, constructing a spectral set describing the dynamic deformation state of the antenna array under random vibration conditions. For example, for edge element nodes, the peak value of the displacement response spectrum at the resonant frequency may reach... Finally, the unit displacement response spectrum data is generated, which covers the dynamic vibration properties of all radiating nodes across the entire frequency band.

[0028] S202: Based on the unit displacement response spectrum data, the cross power spectral density is integrated across the entire frequency band to obtain the total energy value, the root mean square displacement statistics of each unit in physical space are derived, the synchronization characteristics of vibration between units are analyzed, the displacement correlation coefficient matrix of the array surface motion coupling degree is constructed, the distribution pattern of mechanical vibration in the spatial domain is determined, and spatial displacement related information is generated. Spatial correlation analysis is performed based on element displacement response spectrum data. Any two radiating element nodes on the array surface are selected. and Extract its cross-power spectral density function The cross-power spectral density function is then subjected to a full-band definite integral operation within the analysis frequency band (20Hz-2000Hz), i.e. The integral result represents the covariance of the displacements of the two nodes. Specifically, when... When the integral result is the root mean square displacement variance of that node, the result is obtained. Based on this, computing nodes and nodes Spatial correlation coefficient between The coefficient ranges from -1 to 1. A value close to 1 indicates that the vibrations at two points are highly synchronized (e.g., located on the same rigid plate), while a value close to 0 indicates that the vibrations are uncorrelated. The construction dimension is... The displacement correlation coefficient matrix fully records the coupling degree of motion between any two points on the array surface. By analyzing the matrix eigenvalues, the main deformation modes of the array surface (such as "bowl-shaped" or "saddle-shaped" deformations) can be identified. This process transforms the random vibration signal in the time domain into statistical laws in the spatial domain, establishes the distribution pattern of mechanical vibration on the antenna aperture, and generates spatial displacement-related information, providing a statistical basis for subsequent coupling calculations from the mechanical domain to the electromagnetic domain.

[0029] S203: Call spatial displacement-related information, perform linear mapping operation on displacement data using free space wavenumber, construct phase error covariance matrix, combine array manifold vector to perform quadratic matrix operation on covariance matrix, analyze power variance distribution of far-field radiation pattern in full spatial scanning range, quantify the degree of electrical performance degradation, and generate dynamic sidelobe variance index. Calling spatial displacement-related information and introducing free space wavenumber parameters (14GHz corresponds to approximately the wavenumber) By utilizing a linear mapping relationship, the statistical characteristics of mechanical displacement are transformed into statistical characteristics of phase error. Specifically, for displacement deviations perpendicular to the phase plane... The phase error it introduces is (Considering the effects of reflection or two-way path). Construct the phase error covariance matrix. Its elements The far-field radiation pattern calculation formula is combined with a preset array weighting vector. and guide vector Quadratic matrix operations are performed to resolve the power variance. Specifically, the radiation pattern is calculated at a given observation angle. power variance at (This is a simplified description; the actual process involves fourth-order moments or approximate expansions.) Within the full spatial scanning range (e.g., azimuth -60 degrees to +60 degrees), calculate the variance of the pattern power fluctuation at each angle. Superimpose the static thermal deformation effects from step S1 and calculate the confidence interval (e.g., ...). The maximum sidelobe level rise within the specified principle. If the calculated power variance of the first sidelobe region causes the upper limit of level fluctuation to reach -20dB (the design specification is -25dB), it indicates a significant deterioration in electrical performance. Finally, the quantized electrical performance degradation index is output, generating a dynamic sidelobe variance index.

[0030] Please see Figure 4 The specific steps for obtaining the waveguide heterogeneous skeleton model are as follows: S301: Call the dynamic sidelobe variance index, configure the local stiffness penalty coefficient of the structure, set the material property interpolation model parameters according to the variance distribution characteristics, initialize the three-dimensional voxel design domain of the antenna backplane and divide the finite element mesh, set the objectives of minimizing structural flexibility and minimizing electromagnetic transmission loss, and generate the initial configuration for multi-field topology optimization. The dynamic sidelobe variance index is invoked, and the local stiffness penalty coefficient of the structure is configured based on the distribution of variance across the array surface (the edge regions typically have a greater impact on or displacement of the sidelobes). The three-dimensional voxel design domain of the antenna backplane is defined and divided into... The hexahedral mesh elements are used. Based on the variance distribution characteristics, mesh elements located at the edge of the frontal plane or in areas with weak stiffness are assigned higher initial stiffness importance weights. The optimization objective function is set as follows: ,in For structural compliance. For electromagnetic transmission loss, These are weighting coefficients (e.g., initially set to 0.6 and 0.4). A solid isotropic material penalty model (SIMP) is used, and the penalty exponent for the material property interpolation model is set. The design variables (relative density) are initialized to a uniform distribution of 0.5. At this stage, instead of direct iteration, all optimization prerequisites are configured, including defining the fixed boundary conditions for the base mounting surface and applying equivalent mass loads at the radiating element mounting points. The sensitivity calculation link between the design variables (density of each element) and the objective functions (compliance and loss) is established. This process establishes the basic environment for multiphysics coupled optimization, generates the initial configuration for multiphysics topology optimization, and provides a definite mathematical framework for the subsequent evolution of material distribution.

[0031] S302: Based on the initial configuration of multi-field topology optimization, extract the geometric width and height data of the material distribution cavity cross section, compare the cross section size with the preset working frequency band waveguide cutoff wavelength, calculate the geometric expansion penalty value and apply it to the design variable sensitivity field, perform size constraint calculation to correct the material distribution evolution direction, and generate geometric size constraint field data; Based on the initial configuration of multi-field topology optimization, the process proceeds to the geometric constraint processing stage. In each topology evolution iteration, cross-sectional data of the cavity structure (i.e., waveguide cavity) formed by the current material distribution is extracted. For the operating frequency band of 12GHz-16GHz, the cutoff wavelength limit of the standard rectangular waveguide is calculated. For example, for the TE10 mode, the cutoff wavelength... To ensure effective transmission of 12GHz signals, the wide side of the waveguide... Must be greater than The cavity region identified by scanning on the cross-section of the design domain, if the cavity width at a certain point... If the difference is less than 12.5mm, it is considered a dimensional violation. Calculate the geometric expansion penalty value, which is related to the dimensional violation amount. Proportional, for example, using an exponential penalty function. This penalty value is applied to the sensitivity field of the corresponding region's design variables, artificially reducing the sensitivity of the solid material in that region. This forces the optimization algorithm to "erode" the surrounding material in the next iteration, thereby increasing the cavity size. Through this forced geometric constraint calculation, the evolution direction of the material distribution is corrected, preventing the formation of narrow channels that cannot transmit electromagnetic waves. Simultaneously, regarding the height direction... Similar constraints are applied to prevent breakdown risk. Geometric constraint field data is generated, which exists in the form of a sensitivity correction matrix, ensuring that the topology always meets the cutoff frequency requirement for electromagnetic wave propagation.

[0032] Table 2 Geometric Constraint Parameter Configuration Table

[0033] As shown in Table 2, when the identified cavity width is lower than the set constraint threshold of 15.00 mm, the intensity of the applied penalty factor increases significantly, forcing the geometric boundary to expand outward.

[0034] S303: Call the geometric constraint field data, read the electromagnetic intrinsic mode field energy density scalar field, establish the mapping relationship between the energy density value and the fluid flow resistance, construct the virtual fluid damping coefficient matrix, drive the fluid boundary to fill along the damping gradient, and generate the waveguide heterogeneous skeleton model. The system retrieves geometric constraint field data and reads the electromagnetic eigenmode field simulation results under the current configuration, extracting the energy density scalar field. Establish the relationship between energy density and virtual fluid flow resistance coefficient. The inverse mapping relationship between them, that is ,in This is a constant. This means that in regions with high electromagnetic energy (i.e., inside the waveguide), the fluid flow resistance is minimal; while in regions with low energy (i.e., waveguide walls or dead zones), the resistance is extremely high. A virtual fluid damping coefficient matrix covering the entire design domain is constructed. A virtual fluid source is placed at the inlet boundary of the design domain to drive the fluid in the damped field, simulating Darcy flow. The fluid velocity vector field is calculated. The fluid will naturally flow along the path of least resistance (i.e., strongest electromagnetic energy), thus outlining the optimal waveguide channel shape. The material distribution is reconstructed using fluid-filled regions (e.g., regions with fluid saturation greater than 0.9), defining fluid-occupied voxels as cavities and unoccupied regions as the metal skeleton. Through this physical metaphor, a well-connected and smooth heterogeneous waveguide skeleton model is generated. This model satisfies both mechanical stiffness requirements (guaranteed by a topology-optimized substrate) and perfectly fits the electromagnetic wave transmission path (guaranteed by fluid filling), achieving a deep integration of structure and electromagnetic function.

[0035] Please see Figure 5 The specific steps for obtaining the broadband gain evolution trend record are as follows: S401: Import the waveguide heterogeneous skeleton model, set the electromagnetic simulation boundary conditions and excitation source port, perform full-wave electromagnetic broadband frequency sweep operation, obtain frequency response data under ideal conditions, collect the measured broadband gain sweep curve of the physical prototype, calculate the difference data between the measured and simulated curves, and generate the gain response difference dataset. Import the generated waveguide heterogeneous skeleton model into full-wave electromagnetic simulation software (such as HFSS). Set the perfect matching layer (PML) boundary conditions and waveguide port excitation, and perform a broadband frequency sweep operation from 12 GHz to 16 GHz with a step size of 0.1 GHz. Obtain the simulated ideal gain frequency response curve. This curve is typically quite smooth, with a lossless gain of approximately 25 dBi. Simultaneously, measurements were performed on the fabricated physical prototype in a microwave anechoic chamber, acquiring broadband gain scan curves at the same frequency band. Due to dielectric loss and machining roughness, the measured curve will decrease. Calculate the difference vector between the measured and simulated data. For example, at 14 GHz, the simulated gain is 25.1 dBi, and the measured gain is 23.5 dBi, a difference of 1.6 dB. A gain response differential dataset containing 41 frequency points (hypothetically) was constructed. This dataset eliminates the influence of the structural form itself (such as aperture efficiency and mismatch) on the gain, and simply reflects the gain drop caused by material and process losses.

[0036] S402: Based on the gain response difference dataset, a gain drop function that continuously changes with frequency is constructed by performing polynomial curve fitting operation, and the derivative of the gain drop function with frequency is calculated to generate the gain drop derivative distribution function. Based on the gain response difference dataset, a gain drop function is constructed by performing cubic polynomial curve fitting using the least squares method. This function describes the continuous variation of gain decrease caused by losses with frequency. Regarding this function with respect to frequency... Taking the first derivative, we get This derivative physically represents the rate of gain decay (dB / GHz) with frequency. The gain drop derivative distribution function is calculated and generated. The purpose of this step is to separate loss mechanisms using the "rate of change" rather than the absolute value, because different loss mechanisms (dielectric loss and conductor loss) have different sensitivities to frequency and their slope characteristics in the frequency domain differ significantly. By calculating the derivative, this difference in frequency response characteristics is amplified, providing a highly sensitive characteristic fingerprint for subsequent parameter decoupling.

[0037] S403: Call the gain drop derivative distribution function to lock the center frequency point and edge frequency point coordinates of the radar operating frequency band, extract the tangent slope feature data at the corresponding frequency point, quantify the gain attenuation gradient dominated by dielectric loss and conductor loss in multiple frequency bands, and generate a broadband gain evolution trend record. By applying the gain drop derivative distribution function, the center frequency (14GHz) and edge frequencies (12GHz and 16GHz) of the radar's operating band are locked. Tangent slope characteristic data at these specific frequencies are extracted. For example, the slope at 12GHz is calculated as follows: At 14GHz At 16GHz These slope values ​​constitute the feature vector. This quantizes the gain attenuation gradient dominated by dielectric loss and conductor loss at different frequency bands. Theoretically, dielectric loss is proportional to frequency. (Linear growth) should result in a gain drop slope that is approximately constant; while conductor losses are proportional to... The resulting gain drop slope decreases with frequency. By extracting the slope combinations of these key frequency points, a broadband gain evolution trend record is generated, which serves as an observation vector for inverting the microscopic parameters of the material.

[0038] Please see Figure 6 The specific steps for obtaining the dielectric loss angle tangent correction data are as follows: S501: Call the broadband gain evolution trend record, set the parameter scan range, construct a bivariate parameterized scan space based on the dielectric loss tangent and conductor roughness, calculate the simulation gain frequency response curves corresponding to various discrete parameter combinations, perform differential operations on the curves, extract the gain drop derivative features, and generate the simulation gain drop derivative matrix. Access the broadband gain evolution trend record and set the scan range for parameter inversion. For the Rogers RO4350B substrate, set the dielectric loss tangent. The scanning range is 0.0030 to 0.0060, with a step size of 0.0005; the surface roughness of the copper foil is set. The scanning range is 0.5µm to 3.0µm, with a step size of 0.5µm. A [database name] is constructed. A bivariate parameterized scan space. For each... Combine the results, update the material properties in the simulation software, and rerun the broadband frequency sweep (or use a reduced-order model for rapid prediction). Calculate the gain frequency response for each combination and process it in the same way as in S402 to obtain the corresponding simulated gain drop derivative eigenvector. For example, when When, the calculated eigenvector is A theoretical attenuation gradient set covering 42 different material property combinations was established, and the simulation gain drop derivative matrix was generated, as shown in Table 3.

[0039] Table 3 Simulation gain drop derivative matrix (partial data)

[0040] As shown in Table 3, with the increase of loss parameters, the gain drop slope at each frequency point shows an upward trend, but different parameters have different contribution weights to the slope increase.

[0041] S502: Based on the simulated gain drop derivative matrix, the global optimal matching parameter set is searched by iterative fitting calculation of the deviation between measured features and simulated data, the independent weight of each component in the mixed loss is analyzed, and the loss component deviation fitting solution is generated. Based on the simulated gain drop derivative matrix, and using measured eigenvectors Construct a weighted least squares objective function By traversing all elements of the matrix, the search yields an error. Minimum index To further improve accuracy, interpolation fitting can be performed near the optimal grid points. This process utilizes physical differences: dielectric loss varies linearly with frequency ( ), while conductor loss varies with the square root of frequency ( This orthogonality of frequency response patterns ensures that in the broadband slope characteristic space, each pair Each corresponds to a unique eigenvector. Through iterative fitting of the deviation, the position of the measured data in the parameter space can be uniquely determined, thereby analyzing the independent weight of each component in the mixed loss and generating a deviation fitting solution for the loss component, that is, finding the parameter combination that best matches the physical measurements.

[0042] S503: For the fitting solution of the loss component deviation, extract the dielectric loss value under the optimal matching state, perform separation operation, remove the interference of surface impedance loss of the conductor roughness, output the dielectric loss factor, and generate dielectric loss tangent correction data. For the fitting solution of the loss component deviation, the dielectric loss value under the optimal matching state is extracted. Assume the matching result is... Perform a split operation on the [object / component]. The numerical value was locked and confirmed to be the true dielectric loss property of the substrate material after actual processing. This eliminated [materials / products]. The resulting surface impedance loss is due to surface roughness being a manufacturing process error, not an intrinsic material property. The obtained... Defined as the corrected dielectric loss factor, the corrected dielectric loss tangent data is output. The results show that, compared to the nominal value of 0.0037, the actual material loss is higher in specific batches and environments. This corrected data will be fed back into the electromagnetic model from the previous steps for the next round of high-precision performance prediction, forming a closed-loop optimization. This step enables the inversion of internal material properties based solely on the far-field gain data of the finished antenna without destructive slicing tests, providing crucial data support for the precise modeling of high-frequency antennas.

[0043] Please see Figure 7 The design system based on radar antennas includes: The thermal response analysis module acquires thermodynamic simulation node displacement data, calculates microstrip thermal strain and cross-sectional deformation data, updates characteristic impedance distribution, solves dynamic group time delay by combining path elongation and phase velocity changes, calculates parallel branch differences and combines them with center angular frequency to generate thermally induced phase error data. The radiation unit response module calls thermally induced phase error data, calculates the displacement response power spectrum of the radiation unit, derives the displacement correlation coefficient matrix by integrating the cross power spectral density, maps and constructs the phase error covariance matrix, analyzes the far-field power distribution, and generates a dynamic sidelobe variance index. The waveguide structure optimization module calls the dynamic sidelobe variance index, configures the stiffness penalty coefficient, sets the topology optimization target, compares the cavity cross section with the cutoff wavelength, applies geometric expansion penalty, maps the electromagnetic field energy density to the fluid damping coefficient, drives the fluid boundary to fill along the damping gradient, and generates a waveguide heterogeneous skeleton model. The gain evolution analysis module imports a waveguide heterogeneous skeleton model, performs broadband frequency sweep simulation, collects measured gain curves, calculates differential data, constructs a gain drop function, performs derivative operations on the function, extracts the tangent slope features of the center and sideband frequency points, and generates a broadband gain evolution trend record. The dielectric loss correction module calls the broadband gain evolution trend record, constructs a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyzes the physical differences between the linear change of dielectric loss and the square root change of conductor loss, and extracts the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data.

[0044] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A design method based on radar antennas, characterized in that, Includes the following steps: S1: Obtain thermodynamic simulation node displacement data, calculate microstrip thermal strain and cross-sectional deformation data, update characteristic impedance distribution, solve dynamic group time delay by combining path elongation and phase velocity change, calculate parallel branch differences and combine with center angular frequency to generate thermally induced phase error data. S2: Call the thermally induced phase error data, calculate the displacement response power spectrum of the radiation unit, derive the displacement correlation coefficient matrix by integrating the cross power spectral density, map and construct the phase error covariance matrix, analyze the far-field power distribution, and generate the dynamic sidelobe variance index. S3: Call the dynamic sidelobe variance index, configure the stiffness penalty coefficient, set the topology optimization target, compare the cavity cross section with the cutoff wavelength, apply the geometric expansion penalty, map the electromagnetic field energy density to the fluid damping coefficient, drive the fluid boundary to fill along the damping gradient, and generate a waveguide heterogeneous skeleton model. S4: Import the waveguide heterogeneous skeleton model, perform broadband frequency sweep simulation, collect measured gain curves, calculate differential data, construct gain drop function, perform derivative operation on the function, extract the tangent slope features of the center and sideband frequency points, and generate broadband gain evolution trend record; S5: Call the broadband gain evolution trend record, construct a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyze the physical difference between the linear change of dielectric loss and the square root change of conductor loss, and extract the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data. The dielectric loss tangent correction data includes the true value of the substrate dielectric loss factor after decoupling, the imaginary part of the material complex dielectric constant after correction, and the frequency-dependent loss tangent fitting coefficient. The thermally induced phase error data includes the time delay difference component of the feed branch group, the equivalent phase offset value of path thermal elongation, and the additional phase shift due to impedance mismatch. The dynamic sidelobe variance index includes the sidelobe level probability density function, the confidence interval envelope of the far-field pattern, and the gain jitter amplitude caused by random vibration. The waveguide heterogeneous skeleton model includes the geometric topology information of the metal cavity, the adaptive fluid flow channel mesh, and the stiffened solid boundary. The broadband gain evolution trend record includes the first derivative characteristic curve of the gain drop function, the gain attenuation gradient value at the center frequency, and the gain roll-off rate parameter at the bandwidth edge.

2. The design method based on radar antenna according to claim 1, characterized in that, The specific steps for obtaining the thermally induced phase error data are as follows: S101: Obtain thermodynamic simulation node displacement data, calculate the thermal strain displacement vector of microstrip transmission line node by exporting the deformation data of mesh node, establish spatial deformation field, perform curve integration on the tangential physical elongation of signal transmission trajectory, accumulate the geometric increment of each micro-segment in the tangential direction, and generate the path thermal elongation accumulation. S102: Call the cumulative thermal elongation of the path, analyze the cross-sectional width deformation data of the microstrip line, update the characteristic impedance distribution along the path of the microstrip line, and combine the physical path increment and phase velocity change to calculate the propagation delay of the signal through each branch and generate a dynamic group delay value. S103: Based on the dynamic group delay value, calculate the delay difference between each parallel feed branch, extract the center angular frequency parameter of the radar system, combine the delay difference and angular frequency, perform phase domain conversion, quantify the relative phase shift of thermal deformation of each port, and generate thermally induced phase error data.

3. The design method based on radar antenna according to claim 2, characterized in that, The specific steps for obtaining the dynamic sidelobe variance index are as follows: S201: Call the thermally induced phase error data, set the initial phase reference by loading the reference phase state after thermal deformation, analyze the dynamic response characteristics of the structure under random load, evaluate the vibration amplitude response data of each unit at multiple frequency points, establish the spectrum set of the antenna array vibration state, and generate unit displacement response spectrum data. S202: Based on the unit displacement response spectrum data, perform full-band integral operation on the cross power spectral density to obtain the total energy value, derive the root mean square displacement statistics of each unit in physical space, analyze the synchronization characteristics of vibration between units, construct the displacement correlation coefficient matrix of the array surface motion coupling degree, determine the distribution pattern of mechanical vibration in the spatial domain, and generate spatial displacement related information. S203: Call the spatial displacement-related information, perform linear mapping operation on the displacement data using the free space wavenumber, construct the phase error covariance matrix, combine the array manifold vector to perform quadratic matrix operation on the covariance matrix, analyze the power variance distribution of the far-field radiation pattern in the full spatial scanning range, quantify the degree of electrical performance degradation, and generate a dynamic sidelobe variance index.

4. The design method based on radar antenna according to claim 3, characterized in that, The specific steps for obtaining the waveguide heterogeneous skeleton model are as follows: S301: Call the dynamic sidelobe variance index, configure the local stiffness penalty coefficient of the structure, set the material property interpolation model parameters according to the variance distribution characteristics, initialize the three-dimensional voxel design domain of the antenna backplane and divide the finite element mesh, set the objectives of minimizing structural flexibility and minimizing electromagnetic transmission loss, and generate the initial configuration for multi-field topology optimization. S302: Based on the initial configuration of the multi-field topology optimization, extract the geometric width and height data of the material distribution cavity cross section, compare the cross section size with the preset working frequency band waveguide cutoff wavelength, calculate the geometric expansion penalty value and apply it to the design variable sensitivity field, perform size constraint calculation to correct the material distribution evolution direction, and generate geometric size constraint field data. S303: Call the geometric constraint field data, read the electromagnetic intrinsic mode field energy density scalar field, establish the mapping relationship between the energy density value and the fluid flow resistance, construct the virtual fluid damping coefficient matrix, drive the fluid boundary to fill along the damping gradient, and generate the waveguide heterogeneous skeleton model.

5. The design method based on radar antenna according to claim 4, characterized in that, The process of configuring the local stiffness penalty coefficient of the structure is as follows: Construct an adjoint equation for the far-field pattern power variance distribution data, solve the adjoint equation, calculate the partial derivative of the far-field pattern power variance distribution data with respect to the relative density of each finite element mesh element in the voxel domain, map the partial derivative to the voxel domain to construct a stiffness-sensitivity distribution field, and calculate the expected value and standard deviation of all stiffness-sensitivity values ​​in the stiffness-sensitivity distribution field. The preset reliability probability parameters of the antenna structure design are called to construct the inverse cumulative distribution function model of the standard normal distribution. The preset reliability probability parameters are substituted into the inverse cumulative distribution function model to perform mapping calculation, and the quantile values ​​of the corresponding standard normal distribution are analyzed. The quantile values ​​are set as statistical confidence coefficients. The sum of the mathematical expectation value and the product of the statistical confidence coefficient and the standard deviation value is set as the stiffness sensitivity judgment threshold. The global basic penalty coefficient and stiffness enhancement adjustment factor of the topology optimization material interpolation model are set. All finite element mesh elements in the voxel domain are traversed. The stiffness sensitivity value of each finite element mesh element is compared with the stiffness sensitivity judgment threshold. For finite element mesh elements whose stiffness sensitivity values ​​are greater than the stiffness sensitivity judgment threshold, the difference between the stiffness sensitivity value and the stiffness sensitivity judgment threshold is weighted using the stiffness enhancement adjustment factor. The weighted result is then superimposed on the global basic penalty coefficient to generate the local stiffness penalty coefficient of the corresponding finite element mesh element. For finite element mesh elements whose stiffness sensitivity values ​​are less than or equal to the stiffness sensitivity judgment threshold, the global basic penalty coefficient is directly assigned as the local stiffness penalty coefficient of the corresponding finite element mesh element. By summing the local stiffness penalty coefficients of all finite element mesh elements, a spatial distribution matrix of penalty coefficients is constructed to correct the material property interpolation model.

6. The design method based on radar antenna according to claim 5, characterized in that, The specific steps for obtaining the broadband gain evolution trend record are as follows: S401: Import the waveguide heterogeneous skeleton model, set the electromagnetic simulation boundary conditions and excitation source port, perform full-wave electromagnetic broadband frequency sweep operation, obtain frequency response data under ideal conditions, collect the measured broadband gain sweep curve of the physical prototype, calculate the difference data between the measured and simulated curves, and generate a gain response difference dataset. S402: Based on the gain response difference dataset, a gain drop function that continuously changes with frequency is constructed by performing a polynomial curve fitting operation, and the derivative of the gain drop function with frequency is calculated to generate a gain drop derivative distribution function. S403: Call the gain drop derivative distribution function to lock the center frequency point and edge frequency point coordinates of the radar operating frequency band, extract the tangent slope feature data at the corresponding frequency point, quantify the gain attenuation gradient dominated by dielectric loss and conductor loss in multiple frequency bands, and generate a broadband gain evolution trend record.

7. The design method based on radar antenna according to claim 6, characterized in that, The specific steps for obtaining the dielectric loss angle tangent correction data are as follows: S501: Call the broadband gain evolution trend record, set the parameter scanning range, construct a bivariate parameterized scanning space based on the dielectric loss tangent and conductor roughness, calculate the simulation gain frequency response curves corresponding to various discrete parameter combinations, perform differential operations on the curves, extract the gain drop derivative features, and generate the simulation gain drop derivative matrix. S502: Based on the simulated gain drop derivative matrix, the global optimal matching parameter set is searched by iterative fitting operation of the deviation between measured features and simulated data, the independent weight of each component in the mixed loss is analyzed, and the loss component deviation fitting solution is generated. S503: For the fitting solution of the loss component deviation, extract the dielectric loss value under the optimal matching state, perform separation operation, eliminate the interference of surface impedance loss due to rough conductor, output dielectric loss factor, and generate dielectric loss tangent correction data.

8. A radar antenna-based design system, characterized in that, The system is used to implement the radar antenna-based design method according to any one of claims 1-7, and the system comprises: The thermal response analysis module acquires thermodynamic simulation node displacement data, calculates microstrip thermal strain and cross-sectional deformation data, updates characteristic impedance distribution, solves dynamic group time delay by combining path elongation and phase velocity changes, calculates parallel branch differences and combines them with center angular frequency to generate thermally induced phase error data. The radiation unit response module calls the thermally induced phase error data, calculates the displacement response power spectrum of the radiation unit, derives the displacement correlation coefficient matrix by integrating the cross power spectral density, maps and constructs the phase error covariance matrix, analyzes the far-field power distribution, and generates a dynamic sidelobe variance index. The waveguide structure optimization module calls the dynamic sidelobe variance index, configures the stiffness penalty coefficient, sets the topology optimization target, compares the cavity cross section with the cutoff wavelength, applies a geometric expansion penalty, maps the electromagnetic field energy density to the fluid damping coefficient, drives the fluid boundary to fill along the damping gradient, and generates a waveguide heterogeneous skeleton model. The gain evolution analysis module imports the waveguide heterogeneous skeleton model, performs broadband frequency sweep simulation, collects measured gain curves, calculates differential data, constructs a gain drop function, performs derivative operations on the function, extracts the tangent slope features of the center and sideband frequency points, and generates a broadband gain evolution trend record. The dielectric loss correction module calls the broadband gain evolution trend record, constructs a bivariate matrix of dielectric loss tangent and conductor roughness through parametric scanning, analyzes the physical differences between the linear change of dielectric loss and the square root change of conductor loss, and extracts the dielectric loss component from the mixed loss through deviation fitting to generate dielectric loss tangent correction data.

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