Millimeter wave antenna design optimization method based on dynamic hybrid feature modeling

Abstract

This invention relates to the field of computer-aided millimeter-wave antenna design optimization technology, and particularly to a millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling. The method involves obtaining the original design parameters of the millimeter-wave antenna and their corresponding electromagnetic simulation performance responses, constructing a full-parameter sample set; establishing a full-parameter Gaussian process regression model with automatic correlation determination characteristics for each antenna performance objective, determining parameter sensitivity based on dimensional length scale, forming a sensitive parameter set and an insensitive parameter set; performing principal component analysis on the insensitive parameters, combining the sensitive parameters with the principal components to form dynamic hybrid features, and establishing a hybrid feature Gaussian process regression model; using the model to perform multi-objective optimization, reconstructing the complete original design parameters in reverse, and updating the sample set after electromagnetic simulation verification; based on convergence conditions and the number of newly added verification samples, continuing to optimize or update the parameter hierarchy, dynamic hybrid feature mapping, and model, outputting the millimeter-wave antenna design parameters.

Description

Technical Field

[0001] This invention relates to the field of computer-aided millimeter-wave antenna design optimization technology, and in particular to a millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling. Background Technology

[0002] The electromagnetic performance of millimeter-wave antennas is typically influenced by multiple initial design parameters, which may include radiating element size, radiating element offset position, spacing between adjacent radiating elements, feed position, and matching structure position. These initial design parameters are coupled with each other; variations in their values ​​collectively affect the millimeter-wave antenna's reflection coefficient, operating bandwidth, gain, and radiation pattern. Therefore, in the design process of millimeter-wave antennas, a parametric model is usually established, selecting several parameter combinations within the value space of the initial design parameters, and then calculating the electromagnetic simulation performance response corresponding to each parameter combination through full-wave electromagnetic simulation.

[0003] Full-wave electromagnetic simulation requires mesh generation and numerical solution of the electromagnetic field for the parameterized model of the millimeter-wave antenna. When there are many original design parameters and multiple antenna performance targets need to be optimized simultaneously, repeatedly calling the electromagnetic simulation program directly by a multi-objective optimization algorithm will generate a large computational load. To reduce the number of times the electromagnetic simulation program is called, existing techniques typically use the original design parameters and their corresponding electromagnetic simulation performance responses to construct training samples. Based on these training samples, a surrogate model is established to predict the antenna performance targets, and the surrogate model is used to predict the performance responses corresponding to different candidate design parameters in order to search for candidate design parameters. After obtaining the candidate design parameters, the actual performance responses corresponding to the candidate design parameters are calculated through electromagnetic simulation, and the surrogate model is updated using newly added electromagnetic simulation data.

[0004] For example, the paper "Antenna optimization using machine learning with reduced-dimensionalitysurrogates" published by Koziel S., Pietrenko-Dabrowska A., and Leifsson L. in 2024 (Scientific Reports, 2024, 14: 21567) discloses a method for antenna optimization using a reduced-dimensionality surrogate model. The method described in this paper identifies the parameter directions that contribute significantly to antenna response changes in the original parameter space through rapid global sensitivity analysis. A Kriging surrogate model is then constructed within the low-dimensional parameter domain formed by these parameter directions, and a particle swarm optimization algorithm is used to search for candidate antenna design parameters. The searched parameters are then input into a full-wave electromagnetic simulation model, and the obtained electromagnetic simulation data is used to expand the surrogate model's training data. Local gradient optimization is then employed to adjust the candidate antenna design parameters.

[0005] When multiple antenna performance targets need to be optimized simultaneously, the degree to which different antenna performance targets are affected by the original design parameters may vary. If the dimensionality reduction parameter domain is determined based on the aggregated performance response or a fixed parameter orientation, the resulting dimensionality reduction parameter domain may not be able to fully represent the effective parameter information required for different antenna performance targets. If the loss of parameter information is reduced by increasing the retained dimensions, it will increase the input dimension of the surrogate model and the training burden under limited sample conditions.

[0006] Furthermore, as candidate design parameters are continuously verified through electromagnetic simulations and added to training samples, the distribution of training samples in the original design parameter space will change, and the influence relationship between each original design parameter and the antenna performance response may also change accordingly. If a fixed dimensionality reduction parameter domain or a fixed feature representation is continuously used in different optimization stages, the fit between the surrogate model input data and the current training samples may decrease, thereby affecting the prediction stability of the surrogate model in different optimization stages. Directly deleting original design parameters with low influence may also result in the loss of electromagnetic performance information carried by the joint changes of multiple original design parameters.

[0007] Therefore, the main technical problem that existing millimeter-wave antenna surrogate model optimization techniques need to solve is: under the condition of limited electromagnetic simulation samples, how to reduce the input dimension of the surrogate model for multiple antenna performance targets, while reducing the loss of effective parameter information during the dimensionality reduction process, and improving the prediction stability of the surrogate model at different optimization stages. Summary of the Invention

[0008] To address the aforementioned technical problem, the present invention aims to provide a millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling. This invention establishes a fully parameterized Gaussian process regression model with automatic correlation determination for each antenna performance target. It dynamically divides the sensitive parameter set into a sensitive parameter set and a non-sensitive parameter set based on dimensional length scales. The original parameter characteristics of the sensitive parameters are preserved, and principal component analysis is performed on the non-sensitive parameters to form dynamic hybrid features. Then, based on electromagnetic simulation verification samples of candidate design parameters, the parameter hierarchy, dynamic hybrid feature mapping, and surrogate model are periodically updated, thereby solving the aforementioned technical problem.

[0009] This invention discloses a millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling, executed by a computing device, comprising:

[0010] Obtain the original design parameters and electromagnetic simulation performance response of the millimeter-wave antenna, and construct a full parameter sample set;

[0011] For each antenna performance target, a full-parameter Gaussian process regression model with an automatically correlated kernel is constructed. The sensitivity index is determined according to the dimensional length scale. The target sensitive parameters are selected and their union is taken to form a sensitive parameter set. The remaining original design parameters form a non-sensitive parameter set.

[0012] Principal component analysis is performed on the sample submatrix of the non-sensitive parameter set. The parameter columns of the sensitive parameter set are combined with the obtained principal component columns to form the current dynamic hybrid feature. The current dynamic hybrid feature mapping is established, the full parameter sample set is transformed, and a Gaussian process regression model of the hybrid feature corresponding to the antenna performance target is constructed.

[0013] Multi-objective optimization is performed using the hybrid feature Gaussian process regression model to obtain candidate dynamic hybrid features. The complete original design parameters are reconstructed in reverse according to the current dynamic hybrid feature mapping. The electromagnetic simulation performance response is obtained through an electromagnetic simulation program. The complete original design parameters and the electromagnetic simulation performance response are combined to form a verification sample and added to the full parameter sample set. The number of newly added verification samples in the current round is recorded.

[0014] Determine whether the preset convergence condition is met; if it is met, output the millimeter-wave antenna design parameters; if it is not met, if the number of newly added verification samples in the current round is less than the preset update threshold, maintain the current dynamic hybrid feature mapping and continue multi-objective optimization; if the preset update threshold is reached, reconstruct the full-parameter Gaussian process regression model based on the updated full-parameter sample set, re-perform parameter stratification and principal component analysis, and update the current dynamic hybrid feature mapping and hybrid feature Gaussian process regression model.

[0015] Preferably, each original design parameter is dimensionless according to the lower limit and upper limit of each original design parameter. Each full-parameter Gaussian process regression model takes the dimensionless original design parameters as input and adopts the Matérn 5 / 2 kernel function with automatic correlation determination characteristics.

[0016] The number is determined according to the following formula. The antenna performance target corresponding to the first Sensitivity index of each original design parameter:

[0017]

[0018] in, Indicates the first The first antenna performance target corresponds to the first Sensitivity index of each original design parameter Indicates the first In the fully parameterized Gaussian process regression model, the first... The dimension length scale of each original design parameter , , Indicates the number of antenna performance targets. Indicates the number of original design parameters;

[0019] Arrange the sensitivity indices corresponding to the same antenna performance target from largest to smallest, and select the minimum number of parameters that satisfy the following formula. :

[0020]

[0021] in, Indicates the first The antenna performance targets, arranged in descending order, are the [number]th [number]th [number]. A sensitivity index, Indicates the first The number of target sensitive parameters corresponding to each antenna performance target Indicates the sensitivity contribution threshold, and ;

[0022] Before The original design parameters corresponding to the sensitivity index are determined as the first... The target sensitive parameters of the antenna performance target.

[0023] Preferably, when the current dynamic hybrid feature mapping is established for the first time and the number of newly added verification samples in the current round reaches the preset update threshold, the target sensitive parameters of each antenna performance target are determined according to each of the full-parameter Gaussian process regression models, and the union of each of the target sensitive parameters is taken to generate the current sensitive parameter index sequence.

[0024] The original design parameter indices that are not included in the current sensitive parameter index sequence are used to form the current non-sensitive parameter index sequence;

[0025] According to the current sensitive parameter index sequence, extract the current sensitive parameter sample column from the full parameter sample set, and according to the current non-sensitive parameter index sequence, extract the current non-sensitive parameter sample sub-matrix from the full parameter sample set;

[0026] The current sensitive parameter sample column is used as the original parameter input in the current dynamic mixture feature, and the current non-sensitive parameter sample submatrix is ​​used as the input of the principal component analysis.

[0027] Preferably, the current mean vector of the current insensitive parameter sample submatrix is ​​calculated. According to the current mean vector The current non-sensitive parameter sample submatrix is ​​centered, the covariance matrix of the centered current non-sensitive parameter sample submatrix is ​​calculated, and the covariance matrix is ​​decomposed into eigenvalues.

[0028] Arrange the obtained eigenvalues ​​from largest to smallest, and select the minimum number of principal components that satisfy the following formula. :

[0029]

[0030] in, This indicates the number of the items arranged in descending order. 1 eigenvalue, This indicates the number of currently non-sensitive parameters. Indicates the number of principal components retained. This represents the principal component contribution threshold, and ;

[0031] Before The eigenvectors corresponding to the eigenvalues ​​form the current principal component loading matrix. The current insensitive parameter vector is then converted into a principal component score vector according to the following formula:

[0032]

[0033] in, This represents the principal component score vector. This represents the current insensitive parameter vector consisting of dimensionless parameter values. This represents the current mean vector. This represents the current principal component loading matrix;

[0034] The parameter values ​​are extracted according to the current sensitive parameter index sequence and the current sensitive parameter vector is formed. The current sensitive parameter vector is then arranged in the order of first arranging the current sensitive parameter vector and then arranging the principal component score vector to form the current dynamic hybrid feature.

[0035] The current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component load matrix, and the arrangement order are determined as the current dynamic hybrid feature map.

[0036] Preferably, after determining the current dynamic hybrid feature map each time, the corresponding current sensitive parameter vector is extracted from each sample of the full parameter sample set according to the current sensitive parameter index sequence, and the corresponding current non-sensitive parameter vector is extracted according to the current non-sensitive parameter index sequence.

[0037] Using the current mean vector and the current principal component loading matrix, each of the current insensitive parameter vectors is converted into a corresponding principal component score vector;

[0038] The current sensitive parameter vectors are combined with the corresponding principal component score vectors to form the current mixed feature sample set;

[0039] The current mixed feature sample set is used as the input data for each of the mixed feature Gaussian process regression models, and the electromagnetic simulation performance response corresponding to each antenna performance target in the full parameter sample set is used as the output data for the corresponding mixed feature Gaussian process regression model.

[0040] Preferably, the multi-objective optimization is performed using each of the aforementioned mixed-feature Gaussian process regression models, including:

[0041] An optimized population is generated in the feature space corresponding to the current dynamic hybrid feature mapping. The dynamic hybrid features corresponding to each optimized individual are input into the Gaussian process regression model of each hybrid feature to obtain multiple prediction performance values ​​corresponding to each optimized individual.

[0042] Based on the multiple predicted performance values, the optimized population is subjected to non-dominated sorting and crowding distance calculation, and selection, crossover and mutation are performed according to the non-dominated level and crowding distance to iteratively generate Pareto solution set;

[0043] Select a non-dominated solution from the Pareto solution set as a candidate solution, and determine the dynamic mixing feature corresponding to the candidate solution as the candidate dynamic mixing feature.

[0044] Preferably, reconstructing the complete original design parameters in reverse according to the current dynamic hybrid feature map includes:

[0045] From the candidate dynamic mixture features, extract the candidate sensitive parameter vector and the candidate principal component score vector, which are composed of dimensionless parameter values, and convert the candidate principal component score vector into a reconstructed dimensionless insensitive parameter vector according to the following formula:

[0046]

[0047] in, This represents the reconstructed dimensionless insensitive parameter vector. This represents the candidate principal component score vector. This represents the transpose of the current principal component loading matrix. This represents the current mean vector;

[0048] According to the current sensitive parameter index sequence, the parameter values ​​in the candidate sensitive parameter vector are written into the corresponding positions in the dimensionless original design parameter sequence, and according to the current non-sensitive parameter index sequence, the parameter values ​​in the reconstructed dimensionless non-sensitive parameter vector are written into the corresponding positions in the dimensionless original design parameter sequence, thus forming a complete dimensionless original design parameter vector.

[0049] Based on the lower and upper limits of each original design parameter, the complete dimensionless original design parameter vector is converted into the complete original design parameters.

[0050] Preferably, the complete original design parameters are written into the millimeter-wave antenna parameterized model, and the electromagnetic simulation program is called to calculate the verification electromagnetic simulation performance response of each antenna performance target corresponding to the complete original design parameters;

[0051] The electromagnetic simulation performance response of each of the above verification samples is used as the target response value of the verification sample. The complete original design parameters and each of the target response values ​​are associated and stored in the full parameter sample set according to the same verification sample identifier. The number of newly added verification samples in the current round is increased by one count unit.

[0052] Preferably, after each time the verification sample is added to the full parameter sample set, the current number of optimization iterations and the performance convergence index corresponding to the current Pareto solution set are obtained.

[0053] When the total number of samples in the full parameter sample set reaches the preset total number of samples, or when the performance convergence index meets the preset performance convergence threshold condition, it is determined that the preset convergence condition is met, and the millimeter-wave antenna design parameters are output.

[0054] If the preset convergence condition is not met and the number of newly added validation samples in the current round is less than the preset update threshold, the current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component loading matrix, the current dynamic mixed feature map, and each of the mixed feature Gaussian process regression models are maintained, and the multi-objective optimization continues to be performed.

[0055] If the preset convergence condition is not met and the number of newly added validation samples in the current round reaches the preset update threshold, the number of newly added validation samples in the current round is reset, and each of the full-parameter Gaussian process regression models is reconstructed in sequence, the sensitivity index of each original design parameter is redetermined, the sensitive parameter set and the non-sensitive parameter set are regenerated, principal component analysis is performed again, the current dynamic mixed feature map is reformed, and each of the mixed feature Gaussian process regression models is reconstructed.

[0056] Preferably, the millimeter-wave antenna is a substrate integrated waveguide slot array antenna, which includes an upper radiating layer, a lower feeding layer, and an adhesive layer located between the upper radiating layer and the lower feeding layer. The upper radiating layer is provided with 14 radiating slots, which are symmetrically distributed in pairs along the array centerline, and each radiating slot has the same slot width.

[0057] The original design parameters include the lengths of the first to seventh radial slots. to The offset distance of the first to seventh radiation slots relative to the center line of the array to Center-to-center distance between adjacent longitudinal radial gaps Distance between the central radiating slot and the feed port The distance between the short-circuit holes on both sides of the radiation cavity and the center of the radiation gap Distance between the center of the feed layer gap and the short-circuit end and the positional offset of the matching holes around the power supply gap. , , and ;

[0058] The target frequency band is set from 76 GHz to 81 GHz. The antenna performance targets include the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level in the target frequency band.

[0059] The millimeter-wave antenna design parameters output when the preset convergence condition is met are written into the parameterized model file of the substrate integrated waveguide slot array antenna.

[0060] Compared with existing technologies, the above technical solution has the following advantages:

[0061] 1. This invention constructs a full-parameter Gaussian process regression model with automatic correlation determination for each antenna performance target, determines the sensitivity of the original design parameters according to the dimensional length scale, and triggers the re-evaluation of parameter sensitivity by adding new electromagnetic simulation verification samples, so that the sensitive parameter set and the insensitive parameter set can be updated with the changes of the full parameter sample set and the optimization region, reducing the situation where the fixed parameter layering is not compatible with the subsequent sample distribution.

[0062] 2. This invention retains the independent parameter dimension of sensitive parameters, performs principal component analysis only on the set of insensitive parameters, and combines sensitive parameters with principal components to form dynamic mixed features. While reducing the input dimension of the surrogate model, it retains the physical meaning of sensitive parameters and the joint change information between insensitive parameters, reducing the loss of effective information caused by directly deleting low-sensitivity parameters.

[0063] 3. This invention utilizes dynamic hybrid features to construct hybrid feature Gaussian process regression models corresponding to various antenna performance targets, reducing the impact of redundant input dimensions and parameter collinearity on model training under limited sample conditions. Experimental results show that, under 100 to 600 sets of samples, the input dimension of the dynamic hybrid features is reduced from the original 22 dimensions to 14 to 19 dimensions; with 600 sets of samples, the prediction errors for the two antenna performance targets are 0.06 and 0.04, respectively, which are lower than the 0.13 and 0.11 corresponding to the full-parameter Gaussian process regression model.

[0064] 4. This invention utilizes multiple hybrid feature Gaussian process regression models to predict different antenna performance targets, and obtains Pareto solutions through a non-dominated sorting genetic algorithm. This allows for the coordination of multiple antenna performance targets, such as the reflection coefficient amplitude in decibels and the E-plane sidelobe level, in the same optimization process, reducing the impact of subsequent target adjustments on previous targets when performing single-target optimization sequentially.

[0065] 5. This invention reversely reconstructs candidate dynamic hybrid features into complete original design parameters, and uses an electromagnetic simulation program to obtain a verification electromagnetic simulation performance response. Then, the complete original design parameters and the corresponding verification electromagnetic simulation performance response are added to the full parameter sample set, so that the target output data used for subsequent model updates comes from the electromagnetic simulation results, forming a closed-loop optimization process of surrogate prediction, candidate screening, parameter reverse reconstruction, electromagnetic simulation verification, and sample update.

[0066] 6. This invention controls the update frequency of the full-parameter Gaussian process regression model, parameter stratification results, principal component loading matrix, dynamic mixture feature map, and mixture feature Gaussian process regression model by setting a preset update threshold. While the current dynamic mixture feature map can be adjusted with the addition of new samples, it reduces the computational overhead caused by re-executing sensitivity analysis and principal component analysis for each additional sample.

[0067] 7. When this invention is applied to the design of substrate integrated waveguide slot array antennas in the 76GHz to 81GHz range, the optimized reflection coefficient amplitude decibel curve is lower than [value missing] in the target frequency band. The reference line ensures that the main lobe direction of the E-plane radiation pattern at six frequency points (76GHz, 77GHz, 78GHz, 79GHz, 80GHz, and 81GHz) remains stable, providing a design basis for the target band impedance matching performance and radiation pattern performance of the corresponding millimeter-wave antenna. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling of the present invention.

[0069] Figure 2 This is a schematic diagram of the structural parameters of the substrate-integrated waveguide slot array antenna in an embodiment of the present invention, wherein, Figure 2 (a) is a schematic diagram of the structural parameters of the upper radiation layer. Figure 2 (b) is a schematic diagram of the structural parameters of the lower feed layer;

[0070] Figure 3 The above are the S-parameter simulation curves of the initial and optimized designs of the substrate integrated waveguide slot array antenna in this embodiment of the invention.

[0071] Figure 4 The image shows the E-plane normalized gain patterns of the optimized substrate-integrated waveguide slot array antenna at 76 GHz, 77 GHz, 78 GHz, 79 GHz, 80 GHz, and 81 GHz in this embodiment of the invention. Figure 4 (a) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 76 GHz in this embodiment of the invention; Figure 4 (b) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 77 GHz in this embodiment of the invention; Figure 4 (c) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 78 GHz in this embodiment of the invention; Figure 4 (d) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 79 GHz in this embodiment of the invention; Figure 4(e) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 80 GHz in this embodiment of the invention; Figure 4 (f) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 81 GHz in this embodiment of the invention. Detailed Implementation

[0072] The following is combined Figures 1 to 4 This paper details a millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling. This embodiment uses a substrate-integrated waveguide slot array antenna operating in the 76GHz to 81GHz frequency band as the design object. The process involves a computing device performing the following steps: calling the millimeter-wave antenna parameterized model, reading electromagnetic simulation data, training the full-parameter Gaussian process regression model, performing sensitivity analysis of the original design parameters, principal component analysis, multi-objective optimization, inverse reconstruction of candidate parameters, and dynamic model updating.

[0073] Figure 1 The overall process of the millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling is shown, including initial sample acquisition and simulation, full-parameter Gaussian process regression modeling, sensitivity analysis and parameter hierarchical analysis, principal component analysis and dynamic hybrid feature construction, hybrid feature Gaussian process regression modeling, multi-objective optimization, candidate parameter reverse reconstruction and electromagnetic simulation verification, full-parameter sample set update, preset convergence condition judgment and preset update threshold judgment. Figure 2 The top view of the upper radiating layer and lower feed layer of the substrate integrated waveguide slot array antenna is shown. Figure 3 The simulation curves of the S-parameters of the initial and optimized designs are shown. Figure 4 The optimized substrate-integrated waveguide slot array antenna exhibits E-plane radiation patterns at six frequency points: 76 GHz, 77 GHz, 78 GHz, 79 GHz, 80 GHz, and 81 GHz. Figure 4 (a) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 76 GHz in this embodiment of the invention; Figure 4 (b) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 77 GHz in this embodiment of the invention; Figure 4 (c) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 78 GHz in this embodiment of the invention; Figure 4 (d) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 79 GHz in this embodiment of the invention; Figure 4 (e) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 80 GHz in this embodiment of the invention; Figure 4(f) is the E-plane normalized gain pattern of the optimized substrate integrated waveguide slot array antenna at 81 GHz in this embodiment of the invention.

[0074] In this embodiment, the term "computing device" refers to a computer, workstation, or server capable of running parametric modeling programs, machine learning programs, multi-objective optimization programs, and electromagnetic simulation program call scripts. The millimeter-wave antenna parametric model, electromagnetic simulation program, full-parameter Gaussian process regression model, and mixture feature Gaussian process regression model can run on the same computing device, or the computing device can call an electromagnetic simulation program set up on another computing device via a data interface. The data processed by the computing device includes original design parameters, electromagnetic simulation performance response, model training parameters, sensitivity index, principal component data, dynamic mixture features, and candidate design parameters.

[0075] In this embodiment, the original design parameters refer to parameters that can be directly written into the parameterized model of the millimeter-wave antenna and used to determine the geometry of the millimeter-wave antenna. Each original design parameter is arranged in a preset order as an original design parameter vector, and associated with its name, value, unit, lower limit, and upper limit. This preset order remains consistent throughout the initial sample acquisition, electromagnetic simulation, model training, parameter hierarchical analysis, principal component analysis, and candidate parameter reverse reconstruction processes.

[0076] The millimeter-wave antenna parameterized model referred to in this embodiment is a pre-established geometric model of the millimeter-wave antenna in the electromagnetic simulation program. Each adjustable geometric dimension in the model is associated with an original design parameter. After a complete set of original design parameters is written into the millimeter-wave antenna parameterized model, the electromagnetic simulation program regenerates the antenna geometry based on the written complete original design parameters and performs electromagnetic field numerical calculations according to the pre-set port, boundary conditions, material parameters, frequency range, and mesh conditions. Except for the 22 original design parameters, non-optimized parameters such as substrate material, substrate thickness, metal layer parameters, substrate integrated waveguide width, short-circuit hole diameter, and radiating slot width remain unchanged in the same set of experiments.

[0077] In this embodiment, the electromagnetic simulation performance response refers to the antenna performance data output by the electromagnetic simulation program for a complete set of original design parameters, including S-parameter data and E-plane radiation pattern data. Each complete set of original design parameters is associated with a corresponding electromagnetic simulation performance response through the same sample identifier.

[0078] The substrate-integrated waveguide slot array antenna in this embodiment includes an upper radiating layer, a lower feed layer, and an adhesive layer disposed between the upper radiating layer and the lower feed layer. The upper radiating layer has 14 radiating slots, which are divided into two groups, left and right, and are symmetrically distributed in pairs along the array centerline. Each radiating slot has the same slot width. The lower feed layer has feed slots, short-circuit terminals, and matching holes located around the feed slots. Figure 2 (a) shows the radiation gaps, short-circuit holes, and corresponding structural parameters of the upper radiation layer. Figure 2 (b) shows the location of the feed gap, short-circuit terminal and matching hole of the lower feed layer.

[0079] In this embodiment, 22 geometric parameters of the substrate-integrated waveguide slot array antenna are determined as the original design parameters. These 22 original design parameters include the lengths of the first to seventh radiating slots. to Offset distance of the first to seventh radiation slots relative to the array centerline to Center-to-center distance between adjacent longitudinal radial gaps Distance between the central radiating slot and the feed port The distance between the short-circuit holes on both sides of the radiation cavity and the center of the radiation gap Distance between the center of the feed layer gap and the short-circuit end and the positional offset of the matching holes around the power supply gap , , and All geometric dimensions are uniformly expressed in millimeters as the unit of length.

[0080] The first to seventh radial slots correspond to the seven radial slots on one side of the array's center line, while the seven radial slots on the other side of the array's center line are arranged in a paired symmetrical relationship. The length of the radial slots... to Used to determine the longitudinal dimension of the corresponding radial slit; offset distance to Used to determine the lateral position of the center of the corresponding radial slot relative to the array centerline; the center-to-center distance between adjacent longitudinal radial slots. Used to determine the spacing between adjacent radiating slots along the array extension direction; the distance between the central radiating slot and the feed port. Used to determine the position of the central radiating slot relative to the feed structure; distance between the short-circuit holes on both sides of the radiating cavity and the center of the radiating slot. Used to determine the positional relationship between the radiation cavity boundary and the radiation slot; distance between the center of the feed layer slot and the short-circuit end. Used to determine the position of the feed slot in the feed waveguide; position offset , , and Used to determine the positions of different matching holes around the power supply gap in two mutually orthogonal directions.

[0081] Each original design parameter has a pre-defined allowable value range. This allowable range is determined based on the cutoff condition of the substrate-integrated waveguide, the structural spacing between radiating slots, the distance between radiating slots and short-circuit holes, the non-overlap condition between feed slots and matching holes, fabrication accuracy, and the structural boundaries of the millimeter-wave antenna parameterized model. The lower and upper limits of the original design parameters are stored along with the millimeter-wave antenna parameterized model and are used during initial sample acquisition, model input preprocessing, multi-objective optimization, and candidate parameter reverse reconstruction.

[0082] The antenna performance target referred to in this embodiment is the performance index calculated based on the electromagnetic simulation performance response corresponding to a complete set of original design parameters, and used as the output data of the Gaussian process regression model and the multi-objective optimization evaluation data. In this embodiment, 76GHz to 81GHz is determined as the target frequency band, and the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level within the target frequency band are respectively used as two antenna performance targets.

[0083] At simulation frequency At this location, the reflection coefficient amplitude in decibels is calculated according to formula (1):

[0084] (1)

[0085] In the formula, Indicates the simulation frequency The reflection coefficient amplitude in decibels at the location, in dB. Indicates the simulation frequency The input reflection coefficient at that location.

[0086] The first antenna performance target is determined according to equation (2):

[0087] (2)

[0088] In the formula, This represents the maximum value of the reflection coefficient amplitude in decibels within the target frequency band, expressed in dB. Since the reflection coefficient amplitude in decibels is typically negative, the first antenna performance target is optimized in the direction of decreasing value, thereby reducing the reflection coefficient amplitude in decibels corresponding to the worst frequency point within the target frequency band.

[0089] The E-plane sidelobe level is used to characterize the magnitude of local peaks other than the main lobe in the E-plane radiation pattern relative to the main lobe peak. For each simulation frequency, the E-plane radiation pattern is first normalized relative to the main lobe peak, then the main lobe region is determined, and the maximum normalized gain outside the main lobe region is extracted as the E-plane sidelobe level for the corresponding simulation frequency. The main lobe region can be determined based on the first nulls on both sides of the main lobe; when the first nulls in the radiation pattern cannot be stably identified, a pre-set main lobe exclusion angle interval can be used to determine the main lobe region. The same main lobe region determination rule is used for all samples in the same set of experiments.

[0090] The second antenna performance target is determined according to equation (3):

[0091] (3)

[0092] In the formula, This represents the maximum E-plane sidelobe level within the target frequency band, in dB. Indicates the simulation frequency The E-plane sidelobe level at that location. The second antenna performance target is also optimized in the direction of decreasing value.

[0093] like Figure 1 As shown, the millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling first performs initial sample acquisition and simulation. In this embodiment, 60 initial parameter samples are generated in the 22-dimensional original design parameter space using Latin hypercube sampling. For any original design parameter, the allowable value range of the original design parameter is divided into 60 equally probable sub-intervals, and a parameter value is selected in each equally probable sub-interval. The parameter values ​​corresponding to different original design parameters are randomly paired, so that each equally probable sub-interval of each original design parameter is used once in the 60 initial parameter samples, thereby forming 60 sets of initial parameter samples.

[0094] The computing device writes each set of initial parameter samples into the parameterized model file of the substrate integrated waveguide slot array antenna and calls the electromagnetic simulation program to perform frequency scanning from 76 GHz to 81 GHz and E-plane radiation pattern calculation. For each set of initial parameter samples, the electromagnetic simulation program outputs the corresponding S-parameter data and E-plane radiation pattern data. The computing device extracts the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level in the target frequency band according to equations (2) and (3), respectively, and stores the 22 original design parameters, the maximum value of the reflection coefficient amplitude in decibels, and the maximum value of the E-plane sidelobe level in association with the same initial sample identifier to construct a full parameter sample set.

[0095] The full parameter sample set is represented by equation (4):

[0096] (4)

[0097] In the formula, Represents a fully parameterized sample set; Indicates the first The original design parameter vector for each sample; Indicates the first The maximum value of the reflectance coefficient amplitude in decibels for each sample; Indicates the first The maximum E-plane sidelobe level of each sample; This indicates the number of samples in the full parameter sample set.

[0098] The full-parameter sample set preserves complete original design parameters and corresponding electromagnetic simulation performance responses. Subsequently generated dynamic hybrid features are derived data based on the complete original design parameters and do not replace the complete original design parameters in the full-parameter sample set.

[0099] Since the units and allowable ranges of different original design parameters may differ, before constructing the full-parameter Gaussian process regression model, the computing device performs dimensionless processing on the original design parameters based on the lower and upper limits of each parameter. The original design parameters are dimensionless according to equation (5):

[0100] (5)

[0101] In the formula, Indicates the first Dimensionless parameter values ​​of the original design parameters; Indicates the first The actual parameter values ​​of each original design parameter; Indicates the first The lower limit of each original design parameter; Indicates the first The upper limit of each original design parameter is determined. After dimensionless processing, the value range of each original design parameter is converted to [0,1]. The dimensionality scale and subsequent parameter sensitivity index of the full-parameter Gaussian process regression model are both determined based on the dimensionless original design parameters.

[0102] After initial sample acquisition and dimensionless processing, the computing device constructs a full-parameter Gaussian process regression model for the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level, respectively. The full-parameter Gaussian process regression model uses all 22 dimensionless original design parameters as input and an antenna performance target as output. Both full-parameter Gaussian process regression models use the same input samples, but use the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level, respectively, as output data.

[0103] Both fully parameter Gaussian process regression models employ the Matérn 5 / 2 kernel function, which features automatic correlation determination. Automatic correlation determination refers to setting a dimension length scale for each input dimension, ensuring that different original design parameters have independent response change scales.

[0104] No. The Matérn 5 / 2 kernel function corresponding to each antenna performance target is determined according to equation (6):

[0105] (6)

[0106] In the formula, Indicates the first The kernel function value between two dimensionless original design parameter vectors corresponding to each antenna performance target; and Represents two sets of dimensionless original design parameter vectors; Indicates the first Signal variance of a fully parameterized Gaussian process regression model; This represents the distance between parameter vectors after normalization by length scales in each dimension.

[0107] The distance between parameter vectors after normalization of length scales in each dimension is calculated according to equation (7):

[0108] (7)

[0109] In the formula, and These represent the dimensionless original design parameter vectors, respectively. and dimensionless original design parameter vector The first in A dimensionless original design parameter; Indicates the first In the fully parameterized Gaussian process regression model, the first... The dimensional length scale of each original design parameter; This indicates the number of original design parameters. In this embodiment, The number of antenna performance targets is 2.

[0110] For the For a fully parameterized Gaussian process regression model, the covariance matrix of the training samples is determined according to equation (8):

[0111] (8)

[0112] In the formula, Indicates the first The covariance matrix of the training samples of a fully parameterized Gaussian process regression model; This represents the kernel function matrix calculated according to equation (6); Indicates the first Noise variance of a fully parameterized Gaussian process regression model; This represents the identity matrix with the same dimension as the kernel function matrix.

[0113] The computing device determines the signal variance by maximizing the log-marginal likelihood of each fully parameterized Gaussian process regression model. Length scale of each dimension and noise variance The smaller the dimensional length scale, the smaller the parameter change required for the model output to change by the same magnitude along the corresponding original design parameter dimension.

[0114] Based on the aforementioned dimension length scale, the first The first antenna performance target corresponds to the first The sensitivity index of each original design parameter is calculated according to equation (9):

[0115] (9)

[0116] In the formula, Indicates the first The first antenna performance target corresponds to the first Sensitivity index of each original design parameter; Indicates the first In the fully parameterized Gaussian process regression model, the first... The sensitivity index is the dimensional length scale of each original design parameter. A larger sensitivity index indicates a greater impact of the corresponding original design parameter on the corresponding antenna performance objective. The sensitivity index is used for parameter hierarchical analysis and is not considered as an antenna performance objective in multi-objective optimization.

[0117] For each antenna performance target, the computing device arranges the 22 sensitivity indices in descending order and selects the minimum number of parameters that satisfy equation (10). :

[0118] (10)

[0119] In the formula, Indicates the first The antenna performance targets, arranged in descending order, are the [number]th [number]th [number]. One sensitivity index; Indicates the first The number of target sensitive parameters corresponding to each antenna performance target; This represents the sensitivity contribution threshold. In this embodiment, the sensitivity contribution threshold... Take 0.9.

[0120] Target sensitivity parameters refer to the minimum number of original design parameters, arranged in descending order of sensitivity index, that contribute a cumulative sensitivity rate no less than the sensitivity contribution threshold for a given antenna performance target. Since two antenna performance targets can be modeled using fully parameterized Gaussian regression models, they can correspond to different target sensitivity parameters.

[0121] In a parameter stratification process, the sum of the 22 sensitivity indices corresponding to the first antenna performance target is 12.0. The sum of the first 8 sensitivity indices, arranged in descending order, is 10.7. Therefore, the cumulative sensitivity contribution rate of the first 8 sensitivity indices is... The value is less than the sensitivity contribution threshold of 0.9; after adding the 9th sensitivity index, the sum of the first 9 sensitivity indices is 11.4, and the corresponding cumulative sensitivity contribution rate is... The number of target sensitive parameters corresponding to the first antenna performance target reaches the sensitivity contribution threshold. It is 9.

[0122] The computing device uses the same method to determine the target sensitive parameters corresponding to the second antenna performance target, and then takes the union of the target sensitive parameters corresponding to the two antenna performance targets to form a sensitive parameter set. Taking the union means including all target sensitive parameters belonging to at least one antenna performance target in the sensitive parameter set, and retaining only once the original design parameters belonging to both antenna performance targets. The remaining original design parameters not included in the sensitive parameter set form a non-sensitive parameter set.

[0123] The non-sensitive parameters in this embodiment do not mean that the corresponding original design parameters have no impact on the antenna performance target. Rather, they mean that under the current full parameter sample set, the current full parameter Gaussian process regression model, and the current sensitivity contribution threshold, the corresponding original design parameters are not included in the target sensitive parameters of any antenna performance target.

[0124] The computing device arranges the original design parameters in the sensitive parameter set according to their positions in the 22-dimensional original design parameter vector, forming the current sensitive parameter index sequence; the indices of the remaining original design parameters form the current non-sensitive parameter index sequence. The parameter index represents the position number of the corresponding original design parameter in the preset 22-dimensional original design parameter vector.

[0125] The computing device extracts the current sensitive parameter sample column from the full parameter sample set according to the current sensitive parameter index sequence; it also extracts the current non-sensitive parameter sample column from the full parameter sample set according to the current non-sensitive parameter index sequence, and combines all the current non-sensitive parameter sample columns into a current non-sensitive parameter sample sub-matrix. The data in the current non-sensitive parameter sample sub-matrix uses the dimensionless parameter values ​​obtained by equation (5).

[0126] The current sensitive parameter sample column serves as the original parameter input in the current dynamic mixing feature. The current non-sensitive parameter sample submatrix serves as the input for principal component analysis. By maintaining a separate parameter dimension for the current sensitive parameters, the corresponding dynamic mixing feature dimension can continue to correspond to the specific antenna structure size; by performing principal component analysis on the current non-sensitive parameters, the common changes among multiple current non-sensitive parameters can be compressed into a smaller number of principal components without directly deleting the current non-sensitive parameters.

[0127] For the current non-sensitive parameter sample submatrix, the computing device first calculates the mean of each parameter sample column to form the current mean vector. Then use the current mean vector The current non-sensitive parameter sample submatrix is ​​centered. Centering means subtracting the mean of the corresponding parameter sample column from each current non-sensitive parameter sample value.

[0128] The computing device calculates the covariance matrix based on the centered current insensitive parameter sample submatrix, and performs eigenvalue decomposition on the covariance matrix to obtain corresponding eigenvalues ​​and eigenvectors. Eigenvalues ​​characterize the sample variance along the corresponding eigenvector direction, and eigenvectors determine the linear combination coefficients of the current insensitive parameter when transformed from the original parameter coordinates to the principal component coordinates.

[0129] The computing device arranges the obtained eigenvalues ​​in descending order and selects the minimum number of principal components that satisfy equation (11). :

[0130] (11)

[0131] In the formula, This indicates the number of the items arranged in descending order. One eigenvalue; Indicates the number of currently non-sensitive parameters; Indicates the number of principal components retained; This represents the principal component contribution threshold. In this embodiment, the principal component contribution threshold... Take 0.9.

[0132] Sensitivity contribution threshold Used to determine sensitive parameters, principal component contribution threshold. The two terms, used to determine the number of principal components to be retained, have different technical implications.

[0133] When the full parameter sample set contains 100 samples, the sensitive parameter set contains 13 original design parameters, and the number of currently insensitive parameters is... The value is 9. Assume the nine eigenvalues ​​are 3.4, 2.2, 1.4, 1.0, 0.8, 0.4, 0.3, 0.3, and 0.2, respectively, with a sum of 10.0. The sum of the first five eigenvalues ​​is 8.8, corresponding to a cumulative variance contribution rate of 0.88, which does not reach the principal component contribution threshold of 0.9. After adding the sixth eigenvalue, the sum of the first six eigenvalues ​​becomes 9.2, corresponding to a cumulative variance contribution rate of 0.92. Therefore, the number of principal components retained is [not specified]. It is 6.

[0134] computing devices will be front The eigenvectors corresponding to the eigenvalues ​​are arranged in the column direction to form the current principal component loading matrix. If the current number of non-sensitive parameters is The number of principal components retained is Then the current principal component loading matrix The matrix size is .

[0135] The computing device converts the current insensitive parameter vector into a principal component score vector according to equation (12):

[0136] (12)

[0137] In the formula, Represents the principal component score vector; This represents the current insensitive parameter vector consisting of dimensionless parameter values; Represents the current mean vector; This represents the current principal component loading matrix.

[0138] The computing device extracts sensitive parameter values ​​according to the current sensitive parameter index sequence and forms a current sensitive parameter vector. Then, it combines the current sensitive parameter vectors first and the principal component score vectors second to form the current dynamic mixed features.

[0139] The current dynamic hybrid feature map refers to the data transformation relationship that converts the complete original design parameter vector into a hybrid feature vector composed of the current sensitive parameter vector and the principal component score vector. The current dynamic hybrid feature map includes the current sensitive parameter index sequence, the current non-sensitive parameter index sequence, and the current mean vector. Current principal component loading matrix The order of mixed features.

[0140] If the number of sensitive parameters is The number of principal components retained is Then the dimension of the current dynamic mixture feature is The sensitive parameter dimension in the current dynamic hybrid feature is the corresponding dimensionless original design parameter, and the principal component dimension is the score of the current insensitive parameter in the corresponding principal component direction.

[0141] In the current dynamic hybrid feature mapping, "dynamic" means that at least one of the following can change as the full parameter sample set is updated: the current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component loading matrix, and the number of principal components. "Hybrid features" means that the same model input simultaneously includes sensitive parameter features that maintain individual parameter dimensions and principal component features obtained by combining multiple non-sensitive parameters.

[0142] In this embodiment, the "current round" refers to the processing stage from the completion of the establishment or update of a current dynamic mixed feature map to the triggering of the next current dynamic mixed feature map update. All mixed feature data in the same current round use the same current sensitive parameter index sequence, current non-sensitive parameter index sequence, current mean vector, and current principal component loading matrix.

[0143] After each determination or update of the current dynamic blending feature map, the computing device reprocesses all samples in the full parameter sample set according to the current dynamic blending feature map. For any sample in the full parameter sample set, the computing device extracts the current sensitive parameter vector according to the current sensitive parameter index sequence, extracts the current non-sensitive parameter vector according to the current non-sensitive parameter index sequence, calculates the principal component score vector using the current mean vector and the current principal component loading matrix, and then combines the current sensitive parameter vector with the principal component score vector.

[0144] After transforming all samples in the full-parameter sample set, the current hybrid feature sample set is formed. The electromagnetic simulation performance response of the current hybrid feature sample set and the full-parameter sample set maintains the correspondence according to the original sample identifiers.

[0145] The current mixed feature sample set is generated using the current dynamic mixed feature mapping of the current round. The mixed feature data corresponding to the previous round's dynamic mixed feature mapping is not directly mixed with the current mixed feature sample set. Instead, it is regenerated using the complete original design parameters from the full parameter sample set as a unified data source, according to the current dynamic mixed feature mapping. Thus, all training samples of the same mixed feature Gaussian process regression model use the same feature definition and principal component coordinate system.

[0146] The computing device uses the current mixed feature sample set as the common input data for two mixed feature Gaussian process regression models, and uses the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level corresponding to each sample in the full parameter sample set as the output data of the two mixed feature Gaussian process regression models.

[0147] A hybrid feature Gaussian process regression model is a Gaussian process regression model that takes the current dynamic hybrid features as input and an antenna performance target as output, and is used to predict the performance response corresponding to candidate dynamic hybrid features in multi-objective optimization. A full-parameter Gaussian process regression model takes all original design parameters as input and is mainly used for parameter sensitivity analysis; a hybrid feature Gaussian process regression model takes the current dynamic hybrid features as input and is mainly used for performance prediction in multi-objective optimization.

[0148] Both mixed-feature Gaussian process regression models employ the Matérn 5 / 2 kernel function, which has automatic correlation determination properties. The corresponding kernel function has the same form as Equation (6), and the kernel function input is replaced by the dimensionless original design parameter vector with the current dynamic mixed feature vector. The signal variance, dimensionality scale of each input dimension, and noise variance of each mixed-feature Gaussian process regression model are determined using the same log-marginal likelihood maximization method as the full-parameter Gaussian process regression model. Each time the mixed-feature Gaussian process regression model is reconstructed, the model hyperparameters are re-determined based on the updated current mixed feature sample set.

[0149] After training the Gaussian process regression model with mixed features, the computing device performs multi-objective optimization within the feature space corresponding to the current dynamic mixed feature map. In this embodiment, the non-dominated sorting genetic algorithm NSGA-II is used to generate the optimization population.

[0150] In the current dynamic hybrid feature space, the value range of the sensitive parameter dimension is [0,1]. For the th The lower and upper bounds of the principal component dimensions are respectively determined based on the current mixed feature sample set. The minimum and maximum values ​​of the principal component scores are determined. Candidate dynamic mixture features generated during the multi-objective optimization process are restricted to the range of these feature values.

[0151] An optimized population refers to a set of candidate solutions composed of multiple sets of candidate dynamic mixture features, with each optimized individual corresponding to a set of current dynamic mixture features. For any optimized individual, the computing device inputs the corresponding dynamic mixture features into two mixture feature Gaussian process regression models to obtain the prediction results of the maximum value of the reflection coefficient amplitude in decibels and the prediction results of the maximum value of the E-plane sidelobe level.

[0152] The computing device performs a non-dominated ranking of the optimization population based on two predicted performance values. For two candidate solutions, if the first candidate solution is not inferior to the second candidate solution on all antenna performance objectives and is superior to the second candidate solution on at least one antenna performance objective, then the first candidate solution dominates the second candidate solution, provided that all antenna performance objectives are evaluated according to the minimization direction.

[0153] Candidate solutions that are not dominated by other candidate solutions in the optimized population constitute the first non-dominated level; after removing the first non-dominated level, candidate solutions that are not dominated among the remaining candidate solutions constitute the second non-dominated level, and so on, forming each non-dominated level.

[0154] For candidate solutions within the same non-dominated class, the computing device calculates the crowding distance. The crowding distance is the sum of the normalized spacing between a candidate solution and its neighboring candidate solutions in each antenna performance target direction. When the non-dominated class is the same, candidate solutions with larger crowding distances are preferentially retained. The computing device performs selection, crossover, and mutation based on the non-dominated class and crowding distance, iteratively generating a Pareto solution set.

[0155] The Pareto solution set refers to the set of candidate dynamic mixture features obtained in the current multi-objective optimization stage, which do not have a dominant relationship with each other. The corresponding boundary of the Pareto solution set in the antenna performance target space is the Pareto front.

[0156] When determining candidate solutions for electromagnetic simulation verification from the Pareto solution set, the computing device first converts the predicted performance values ​​of the two antenna performance targets into normalized predicted performance values ​​in the same direction. The first non-dominated solution corresponds to the th Each normalized prediction performance value is calculated according to equation (13):

[0157] (13)

[0158] In the formula, Indicates the first The first non-dominated solution corresponds to the th One normalized prediction performance value; Indicates the first The first non-dominated solution corresponds to the th One predicted performance value; Indicates the current Pareto solution set. The minimum value of each predicted performance value; Indicates the current Pareto solution set. The maximum value of the predicted performance values.

[0159] when In this embodiment, the normalized predicted performance value of the corresponding antenna performance target in each non-dominated solution is uniformly set to zero, so that the corresponding antenna performance target does not affect the distance ranking between candidate solutions in this round.

[0160] No. The distance between each non-dominated solution and the ideal point in the normalized objective space is calculated according to equation (14):

[0161] (14)

[0162] In the formula, Indicates the first The distance between a non-dominated solution and an ideal point in the normalized objective space; Indicates the first The first non-dominated solution corresponds to the th One normalized prediction performance value; This represents the number of antenna performance targets. In this embodiment, both coordinates of the ideal point in the normalized target space are zero.

[0163] The computing device will distance The smallest nondominated solution is identified as a candidate solution, and the dynamic mixing characteristics corresponding to the candidate solution are identified as candidate dynamic mixing characteristics. By normalizing the performance targets of the two antennas in the same direction before calculating the distance, the directional ambiguity caused by directly using negative decibel values ​​to calculate the distance to the origin of the target space is avoided.

[0164] The normalized prediction performance values ​​corresponding to the three non-dominated solutions in the Pareto solution set are as follows: , and The distances calculated according to equation (14) are approximately 0.277, 0.228 and 0.215 respectively, so the third non-dominated solution is determined as a candidate solution.

[0165] The computing device reconstructs the candidate dynamic blending features into complete original design parameters according to the current dynamic blending feature mapping. Reverse reconstruction means writing the sensitive parameter parts in the candidate dynamic blending features back to their corresponding original design parameter positions, and restoring the candidate principal component score vectors to approximate values ​​of non-sensitive parameters through inverse principal component transformation.

[0166] Extract candidate sensitive parameter vectors and candidate principal component score vectors from the candidate dynamic mixture features, and convert the candidate principal component score vectors into reconstructed dimensionless insensitive parameter vectors according to equation (15):

[0167] (15)

[0168] In the formula, This represents a reconstructed dimensionless insensitive parameter vector composed of dimensionless parameter values; Represents the candidate principal component score vector; This represents the transpose of the current principal component loading matrix; This represents the current mean vector.

[0169] The computing device writes the parameter values ​​from the candidate sensitive parameter vector into the corresponding positions in the 22-dimensional dimensionless original design parameter vector according to the current sensitive parameter index sequence; and writes the parameter values ​​from the reconstructed dimensionless non-sensitive parameter vector into the remaining positions according to the current non-sensitive parameter index sequence, forming a complete dimensionless original design parameter vector.

[0170] For the first element in the complete dimensionless original design parameter vector The parameters are converted into actual original design parameters according to equation (16):

[0171] (16)

[0172] In the formula, Indicates the first One actual original design parameter; Indicates the first One dimensionless original design parameter; and They represent the first The lower limit and upper limit of each original design parameter.

[0173] Taking a 100-sample stage as an example, if the current sensitive parameter set contains 13 original design parameters and retains 6 principal components, then the candidate dynamic hybrid feature is 19-dimensional, of which 13 dimensions are candidate sensitive parameters and 6 dimensions are candidate principal component scores. The 6-dimensional candidate principal component scores are converted into 9-dimensional reconstructed dimensionless insensitive parameters by Equation (15), and then merged with the 13-dimensional candidate sensitive parameters according to the parameter index to form a 22-dimensional complete dimensionless original design parameter vector. Subsequently, it is converted into 22-dimensional complete original design parameters by Equation (16).

[0174] After reverse reconstruction, the computing device performs boundary checks on the complete dimensionless original design parameter vector. Parameter values ​​less than zero are set to zero, and parameter values ​​greater than one are set to one. The complete dimensionless original design parameter vector after boundary processing is converted into complete original design parameters according to equation (16). Subsequent electromagnetic simulations are based on the complete original design parameters after boundary processing, and the predicted performance values ​​output by the mixed characteristic Gaussian process regression model are only used for candidate solution screening.

[0175] After obtaining the complete original design parameters, the computing device writes the complete original design parameters into the parameterized model file of the substrate integrated waveguide slot array antenna, and calls the electromagnetic simulation program to re-execute the frequency scan from 76 GHz to 81 GHz and the E-plane radiation pattern simulation. The computing device extracts the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level corresponding to the complete original design parameters from the simulation results according to equations (2) and (3), as verification of the electromagnetic simulation performance response.

[0176] Verifying the electromagnetic simulation performance response refers to recalculating the true values ​​of the two antenna performance targets using an electromagnetic simulation program after reconstructing the candidate dynamic hybrid features generated by multi-objective optimization and completing the reverse reconstruction of the original design parameters.

[0177] The computing device assigns the same verification sample identifier to all complete original design parameters and the corresponding verification electromagnetic simulation performance response. The verification sample is composed of the 22-dimensional complete original design parameters, the maximum value of the reflection coefficient amplitude in decibels, and the maximum value of the E-plane sidelobe level. This verification sample is then added to the full parameter sample set. The performance response in the verification sample is the verification electromagnetic simulation performance response output by the electromagnetic simulation program.

[0178] In this embodiment, each completion of candidate dynamic hybrid feature determination, reverse reconstruction of complete original design parameters, and electromagnetic simulation verification is counted as one outer-layer optimization iteration. The genetic generations used within NSGA-II to generate the Pareto solution set are not included in the outer-layer optimization iteration count. The number of newly added verification samples in the current round refers to the cumulative number of verification samples added to the full-parameter sample set since the most recent establishment or update of the current dynamic hybrid feature map.

[0179] Each time a validation sample is added to the full parameter sample set, the computing device first determines whether the preset convergence conditions are met. The preset convergence conditions include the total number of samples in the full parameter sample set reaching the preset total number of samples, or the performance convergence index meeting the preset performance convergence threshold condition.

[0180] As a performance convergence metric, the computing device records the first... Distance of the normalized objective space ideal point corresponding to the candidate solution in the next outermost optimization iteration And record the first Distance of the normalized objective space ideal point corresponding to the candidate solution in the next outermost optimization iteration .in, Indicates the first The distance between the candidate solutions and the ideal points in the normalized objective space during the next outermost optimization iteration. Indicates the first The distance between the candidate solutions and the ideal points in the normalized objective space during the next outermost optimization iteration. This represents the outer optimization iteration number, and In some embodiments, to ensure the comparability of the normalized target space ideal point distances in adjacent outer layer optimization iterations, the same target normalization lower bound and target normalization upper bound are used for calculation within a preset comparison window. and The target normalization lower limit and the target normalization upper limit remain unchanged within the preset comparison window.

[0181] The computing device calculates the distance change rate between two adjacent outer-layer optimization iterations according to equation (17):

[0182] (17)

[0183] In the formula, Indicates the first The rate of change of distance corresponding to the next outermost optimization iteration; Indicates the first The distance between the normalized target space ideal points corresponding to the candidate solutions in the next outermost optimization iteration; Indicates the first The distance between the normalized target space ideal points corresponding to the candidate solutions in the next outermost optimization iteration; This indicates a preset positive number to prevent the denominator from being zero.

[0184] When the rate of change of distance If the number of consecutive attempts does not exceed the preset performance convergence threshold, the performance convergence index is determined to meet the preset performance convergence threshold condition. The preset performance convergence threshold, the number of consecutive attempts, and the preset positive number are used as parameters. The settings are pre-defined based on the required optimization accuracy and remain unchanged throughout a complete optimization process.

[0185] In this embodiment, the termination condition is that the total number of samples in the full parameter sample set reaches 600. Based on the initial 60 parameter samples, after 540 outer layer optimization iterations and obtaining 540 validation samples, the total number of samples in the full parameter sample set reaches 600.

[0186] When the preset convergence condition is met, the computing device extracts all samples that have completed electromagnetic simulation verification from the full parameter sample set, forms a Pareto solution set of verification samples based on the actual performance response of the two antenna performance targets, calculates the distance between each verification sample and the ideal point in the normalized target space according to equations (13) and (14), determines the complete original design parameters corresponding to the verification sample with the smallest distance as the output millimeter-wave antenna design parameters, and writes the millimeter-wave antenna design parameters into the parameterized model file of the substrate integrated waveguide slot array antenna.

[0187] If the preset convergence condition is not met, the computing device determines whether the number of newly added verification samples in the current round has reached the preset update threshold. In this embodiment, the preset update threshold is set to 40, that is, since the last establishment or update of the current dynamic hybrid feature map, a dynamic update is triggered every time 40 verification samples are added.

[0188] If the number of new validation samples added in the current round is less than 40, then retain the current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component loading matrix, the current dynamic mixed feature map, and the two mixed feature Gaussian process regression models, and return to the multi-objective optimization process to continue generating candidate dynamic mixed features.

[0189] If the number of newly added validation samples in the current round reaches 40, the number of newly added validation samples in the current round is reset, and the two fully parameter Gaussian process regression models are retrained using the updated fully parameter sample set. The computing device recalculates the sensitivity index of each original design parameter based on the dimensional length scale obtained from the retraining, redetermines the target sensitivity parameters of the two antenna performance targets, regenerates the sensitive parameter set and the insensitive parameter set, and updates the current sensitive parameter index sequence and the current insensitive parameter index sequence.

[0190] When an original design parameter is transferred from the set of insensitive parameters to the set of sensitive parameters, the computing device removes the parameter sample column corresponding to the original design parameter from the current insensitive parameter sample submatrix and uses the parameter sample column as the current sensitive parameter sample column; when an original design parameter is transferred from the set of sensitive parameters to the set of insensitive parameters, the computing device adds the parameter sample column corresponding to the original design parameter to the current insensitive parameter sample submatrix.

[0191] After the parameter set changes, the computing device recalculates the current mean vector, covariance matrix, eigenvalues, eigenvectors, and current principal component loading matrix, and redetermines the number of principal components to retain. Subsequently, the computing device uses the updated current dynamic mixture feature map to retransform all samples in the full parameter sample set, forming an updated current mixture feature sample set, and reconstructs two mixture feature Gaussian process regression models.

[0192] Therefore, each dynamic update not only increases the training samples of the Gaussian process regression model, but also synchronously updates the hierarchical results of the original design parameters, the principal component coordinate system, the dynamic mixed feature dimension, and the input definition of the mixed feature Gaussian process regression model.

[0193] In this embodiment, 540 verification samples are added to the initial 60 sets of parameter samples, with a preset update threshold of 40. During the process of adding the 540 verification samples, a total of 13 complete dynamic updates triggered by 40 new verification samples are completed. The remaining fewer than 40 new verification samples are used for the final design parameter selection.

[0194] To verify the model structure changes and prediction performance of the millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling, the number of sensitive parameters, the number of retained principal components, the number of dynamic hybrid feature input parameters, and the prediction errors of the two antenna performance targets were recorded when the full parameter sample set contained 100, 200, 300, 400, 500, and 600 samples, respectively. The results are shown in Table 1. In some embodiments, the sample size node is used to record and compare the model structure and prediction performance corresponding to different sample sizes, without changing the control rule that triggers an online dynamic update every 40 newly added validation samples.

[0195] Table 1. Changes in model structure and prediction error under different sample sizes.

[0196]

[0197] In Table 1, Target 1 represents the maximum value of the reflection coefficient amplitude in decibels within the target frequency band, and Target 2 represents the maximum value of the E-plane sidelobe level within the target frequency band. The number of input parameters is the sum of the number of sensitive parameters and the number of principal components. The prediction errors for Target 1 and Target 2 are measured in the same dimensions as the corresponding antenna performance targets.

[0198] The prediction error was obtained using the same test conditions. For the same sample size, the dynamic mixture feature Gaussian process regression model and the full parameter Gaussian process regression model used the same target output data and the same test sample. The root mean square prediction error of each antenna performance target is calculated according to equation (18):

[0199] (18)

[0200] In the formula, Indicates the first The prediction error of individual antenna performance targets; Indicates the number of test samples; Indicates the first The prediction performance values ​​corresponding to each test sample; Indicates the first The electromagnetic simulation performance value corresponding to each test sample.

[0201] As shown in Table 1, the number of sensitive parameters varies between 11 and 13, the number of retained principal components varies between 2 and 6, and the number of dynamic blending feature input parameters varies between 14 and 19 dimensions. Compared to the original 22-dimensional full-parameter input, the dynamic blending feature input reduces 3 to 8 dimensions.

[0202] Controlled Experiment 1

[0203] For comparison, a fully parameterized Gaussian process regression model was directly trained using 22 dimensionless original design parameters with the same sample size, and the prediction errors of the two antenna performance targets were recorded. The results are shown in Table 2. Except for the different input feature forms, the kernel function type, model training method, target output data, and test samples in control experiment 1 were consistent with the dynamic mixed feature Gaussian process regression model.

[0204] Table 2. Prediction Errors of Full-Parameter Gaussian Process Regression Models for Different Sample Sizes

[0205]

[0206] With 600 samples, the target prediction error of the dynamic mixed-feature Gaussian process regression model is 0.06, and the target prediction error of the full-parameter Gaussian process regression model is 0.13; the target prediction error of the dynamic mixed-feature Gaussian process regression model is 0.04, and the target prediction error of the full-parameter Gaussian process regression model is 0.11.

[0207] Figure 3 The simulation curves of S-parameters for the initial and optimized designs of the substrate integrated waveguide slot array antenna are shown in the range of 76 GHz to 81 GHz. Figure 3 The dashed lines represent the initial design, the solid lines represent the optimized design, and the horizontal reference lines represent... Reference line. The optimized design's reflection coefficient amplitude decibel curve is lower than [value missing] in the 76GHz to 81GHz range. A reference line is established, and low-reflection zones are formed near 77GHz, 78GHz, and 80GHz, so that the impedance bandwidth covers the target frequency band.

[0208] Figure 4 The optimized substrate-integrated waveguide slot array antenna exhibits E-plane normalized gain patterns at six frequency points: 76 GHz, 77 GHz, 78 GHz, 79 GHz, 80 GHz, and 81 GHz. The main lobe directions at all six frequency points are located close to... The direction of the main lobe changes accordingly with frequency, while the position of the side lobes and the null position remain stable overall.

[0209] As shown in Tables 1 and 2, the millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling retains the original design parameters that have a major impact on at least one antenna performance objective, and performs principal component compression on the joint variation information of the remaining original design parameters. As the full-parameter sample set increases, the full-parameter Gaussian process regression model is retrained and the parameter hierarchical results are updated, allowing the original design parameters to be adjusted between the sensitive parameter set and the insensitive parameter set. Simultaneously, the current principal component load matrix is ​​recalculated, and all samples in the full-parameter sample set are transformed according to the updated current dynamic hybrid feature mapping.

[0210] Through this processing, under limited electromagnetic simulation sample conditions, the input dimension of the hybrid feature Gaussian process regression model is lower than the number of original design parameters, while retaining the independent parameter dimensions of sensitive parameters and the joint variation information between insensitive parameters. By verifying candidate design parameters through electromagnetic simulation and adding the verification samples to the full parameter sample set, the target output data used for subsequent model updates is derived from the electromagnetic simulation performance response. By controlling the re-execution frequency of parameter sensitivity analysis and principal component analysis through a preset update threshold, the current dynamic hybrid feature mapping can be updated as the full parameter sample set changes.

[0211] The substrate-integrated waveguide slot array antenna optimized in this embodiment can be placed at the radio frequency front end of a 76GHz to 81GHz millimeter-wave radar to transmit millimeter-wave signals and receive micro-motion echoes from the human chest cavity. When used for heart rate and respiration monitoring, the impedance matching performance and E-plane sidelobe performance within the target frequency band provide the corresponding antenna performance conditions for acquiring micro-motion echoes from the human chest cavity.

[0212] It should be noted that the embodiments of the present invention have better implementability and are not intended to limit the present invention in any way. Any person skilled in the art may use the above-disclosed technical content to change or modify it into equivalent effective embodiments. However, any modifications or equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling, executed by a computing device, characterized in that, include: Obtain the original design parameters and electromagnetic simulation performance response of the millimeter-wave antenna, and construct a full parameter sample set; For each antenna performance target, a full-parameter Gaussian process regression model with an automatically correlated kernel is constructed. The sensitivity index is determined according to the dimensional length scale. The target sensitive parameters are selected and their union is taken to form a sensitive parameter set. The remaining original design parameters form a non-sensitive parameter set. Principal component analysis is performed on the sample submatrix of the non-sensitive parameter set. The parameter columns of the sensitive parameter set are combined with the obtained principal component columns to form the current dynamic hybrid feature. The current dynamic hybrid feature mapping is established, the full parameter sample set is transformed, and a Gaussian process regression model of the hybrid feature corresponding to the antenna performance target is constructed. Multi-objective optimization is performed using the hybrid feature Gaussian process regression model to obtain candidate dynamic hybrid features. The complete original design parameters are reconstructed in reverse according to the current dynamic hybrid feature mapping. The electromagnetic simulation performance response is obtained through an electromagnetic simulation program. The complete original design parameters and the electromagnetic simulation performance response are combined to form a verification sample and added to the full parameter sample set. The number of newly added verification samples in the current round is recorded. Determine whether the preset convergence condition is met; if it is met, output the millimeter-wave antenna design parameters; if it is not met, and the number of newly added verification samples in the current round is less than the preset update threshold, maintain the current dynamic hybrid feature mapping and continue multi-objective optimization. If the preset update threshold is reached, the full-parameter Gaussian process regression model is reconstructed based on the updated full-parameter sample set, and parameter stratification and principal component analysis are performed again to update the current dynamic mixed feature mapping and mixed feature Gaussian process regression model.

2. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 1, characterized in that, The original design parameters are dimensionless based on their lower and upper limits. The full-parameter Gaussian process regression models use the dimensionless original design parameters as input and employ the Matérn 5 / 2 kernel function, which has automatic correlation determination properties. The number is determined according to the following formula. The first antenna performance target corresponds to the first Sensitivity index of each original design parameter: ； in, Indicates the first The first antenna performance target corresponds to the first Sensitivity index of each original design parameter Indicates the first In the fully parameterized Gaussian process regression model, the first... The dimension length scale of each original design parameter , , Indicates the number of antenna performance targets. Indicates the number of original design parameters; Arrange the sensitivity indices corresponding to the same antenna performance target from largest to smallest, and select the minimum number of parameters that satisfy the following formula. : ； in, Indicates the first The antenna performance targets, arranged in descending order, are the [number]th [number]th [number]. A sensitivity index, Indicates the first The number of target sensitive parameters corresponding to each antenna performance target Indicates the sensitivity contribution threshold, and ; Before The original design parameters corresponding to the sensitivity index are determined as the first... The target sensitive parameters of the antenna performance target.

3. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 2, characterized in that, When the current dynamic hybrid feature mapping is established for the first time and the number of newly added verification samples in the current round reaches the preset update threshold, the target sensitive parameters of each antenna performance target are determined according to each full-parameter Gaussian process regression model, and the union of each target sensitive parameter is taken to generate the current sensitive parameter index sequence. The original design parameter indices that are not included in the current sensitive parameter index sequence are used to form the current non-sensitive parameter index sequence; According to the current sensitive parameter index sequence, extract the current sensitive parameter sample column from the full parameter sample set, and according to the current non-sensitive parameter index sequence, extract the current non-sensitive parameter sample sub-matrix from the full parameter sample set; The current sensitive parameter sample column is used as the original parameter input in the current dynamic mixture feature, and the current non-sensitive parameter sample submatrix is ​​used as the input of the principal component analysis.

4. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 3, characterized in that, Calculate the current mean vector of the current insensitive parameter sample submatrix. According to the current mean vector The current non-sensitive parameter sample submatrix is ​​centered, the covariance matrix of the centered current non-sensitive parameter sample submatrix is ​​calculated, and the covariance matrix is ​​decomposed into eigenvalues. Arrange the obtained eigenvalues ​​from largest to smallest, and select the minimum number of principal components that satisfy the following formula. : ； in, This indicates the number of the items arranged in descending order. 1 eigenvalue, This indicates the number of currently non-sensitive parameters. Indicates the number of principal components retained. This represents the principal component contribution threshold, and ; Before The eigenvectors corresponding to the eigenvalues ​​form the current principal component loading matrix. The current insensitive parameter vector is then converted into a principal component score vector according to the following formula: ； in, This represents the principal component score vector. This represents the current insensitive parameter vector consisting of dimensionless parameter values. This represents the current mean vector. This represents the current principal component loading matrix; Parameter values ​​are extracted according to the current sensitive parameter index sequence and the current sensitive parameter vector is formed. The current dynamic mixed features are then combined according to the mixed feature arrangement order of first arranging the current sensitive parameter vector and then arranging the principal component score vector. The current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component load matrix, and the arrangement order of the mixed features are determined as the current dynamic mixed feature map.

5. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 4, characterized in that, After determining the current dynamic hybrid feature map each time, the corresponding current sensitive parameter vector is extracted from each sample of the full parameter sample set according to the current sensitive parameter index sequence, and the corresponding current non-sensitive parameter vector is extracted according to the current non-sensitive parameter index sequence. Using the current mean vector and the current principal component loading matrix, each of the current insensitive parameter vectors is converted into a corresponding principal component score vector; The current sensitive parameter vectors are combined with the corresponding principal component score vectors to form the current mixed feature sample set; The current mixed feature sample set is used as the input data for each of the mixed feature Gaussian process regression models, and the electromagnetic simulation performance response corresponding to each antenna performance target in the full parameter sample set is used as the output data for the corresponding mixed feature Gaussian process regression model.

6. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 5, characterized in that, Performing the multi-objective optimization using the aforementioned mixed-feature Gaussian process regression models includes: An optimized population is generated in the feature space corresponding to the current dynamic hybrid feature mapping. The dynamic hybrid features corresponding to each optimized individual are input into the Gaussian process regression model of each hybrid feature to obtain multiple prediction performance values ​​corresponding to each optimized individual. Based on the multiple predicted performance values, the optimized population is subjected to non-dominated sorting and crowding distance calculation, and selection, crossover and mutation are performed according to the non-dominated level and crowding distance to iteratively generate Pareto solution set; Select a non-dominated solution from the Pareto solution set as a candidate solution, and determine the dynamic mixing feature corresponding to the candidate solution as the candidate dynamic mixing feature.

7. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 6, characterized in that, The complete original design parameters are reconstructed in reverse according to the current dynamic hybrid feature map, including: From the candidate dynamic mixture features, extract the candidate sensitive parameter vector and the candidate principal component score vector, which are composed of dimensionless parameter values, and convert the candidate principal component score vector into a reconstructed dimensionless insensitive parameter vector according to the following formula: ； in, This represents the reconstructed dimensionless insensitive parameter vector. This represents the candidate principal component score vector. This represents the transpose of the current principal component loading matrix. This represents the current mean vector; According to the current sensitive parameter index sequence, the parameter values ​​in the candidate sensitive parameter vector are written into the corresponding positions in the dimensionless original design parameter sequence, and according to the current non-sensitive parameter index sequence, the parameter values ​​in the reconstructed dimensionless non-sensitive parameter vector are written into the corresponding positions in the dimensionless original design parameter sequence, thus forming a complete dimensionless original design parameter vector. Based on the lower and upper limits of each original design parameter, the complete dimensionless original design parameter vector is converted into the complete original design parameters.

8. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 7, characterized in that, The complete original design parameters are written into the millimeter-wave antenna parameterized model, and the electromagnetic simulation program is called to calculate the verification electromagnetic simulation performance response of each antenna performance target corresponding to the complete original design parameters. The electromagnetic simulation performance response of each verification sample is used as the target response value of the verification sample. The complete original design parameters and each target response value are associated and stored in the full parameter sample set according to the same verification sample identifier. The number of newly added verification samples in the current round is increased by one count unit.

9. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 8, characterized in that, Each time the verification sample is added to the full parameter sample set, the current number of optimization iterations and the performance convergence index corresponding to the current Pareto solution set are obtained. When the total number of samples in the full parameter sample set reaches the preset total number of samples, or when the performance convergence index meets the preset performance convergence threshold condition, it is determined that the preset convergence condition is met, and the millimeter-wave antenna design parameters are output. If the preset convergence condition is not met and the number of newly added validation samples in the current round is less than the preset update threshold, the current sensitive parameter index sequence, the current non-sensitive parameter index sequence, the current mean vector, the current principal component loading matrix, the current dynamic mixed feature map, and each of the mixed feature Gaussian process regression models are maintained, and the multi-objective optimization continues to be performed. If the preset convergence condition is not met and the number of newly added validation samples in the current round reaches the preset update threshold, the number of newly added validation samples in the current round is reset, and each of the full-parameter Gaussian process regression models is reconstructed in sequence, the sensitivity index of each original design parameter is redetermined, the sensitive parameter set and the non-sensitive parameter set are regenerated, principal component analysis is performed again, the current dynamic mixed feature map is reformed, and each of the mixed feature Gaussian process regression models is reconstructed.

10. The millimeter-wave antenna design optimization method based on dynamic hybrid feature modeling according to claim 1, characterized in that, The millimeter-wave antenna is a substrate integrated waveguide slot array antenna. The substrate integrated waveguide slot array antenna includes an upper radiating layer, a lower feeding layer, and an adhesive layer located between the upper radiating layer and the lower feeding layer. The upper radiating layer is provided with 14 radiating slots. The 14 radiating slots are symmetrically distributed in pairs along the center line of the array, and each radiating slot has the same slot width. The original design parameters include the lengths of the first to seventh radial slots. to The offset distance of the first to seventh radiation slots relative to the center line of the array to Center-to-center distance between adjacent longitudinal radial gaps Distance between the central radiating slot and the feed port The distance between the short-circuit holes on both sides of the radiation cavity and the center of the radiation gap Distance between the center of the feed layer gap and the short-circuit end and the positional offset of the matching holes around the power supply gap. , , and ; The target frequency band is set from 76 GHz to 81 GHz. The antenna performance targets include the maximum value of the reflection coefficient amplitude in decibels and the maximum value of the E-plane sidelobe level in the target frequency band. The millimeter-wave antenna design parameters output when the preset convergence condition is met are written into the parameterized model file of the substrate integrated waveguide slot array antenna.

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