An antenna topology and parameter hybrid optimization method based on a normalized Gaussian network

Abstract

This invention discloses a hybrid optimization method for antenna topology and parameters based on a normalized Gaussian network (NGN). This method employs an iterative machine learning-assisted optimization algorithm architecture. In each iteration, a NGN is introduced to extract features from the antenna topology, and a Gaussian process machine learning (GSM) method is used to establish a surrogate model between the extracted features and antenna performance. Based on this, an evolutionary algorithm is introduced to optimize the surrogate model. The optimization result is then restored to the antenna topology, and the algorithm is verified using a full-wave simulation tool. The algorithm is then used to determine whether it terminates. If it does not terminate, the optimization and verification results are added to the dataset to retrain the GSM model for the next iteration. Compared to traditional pixel-based topology optimization methods, this method can obtain smooth antenna topology edge structures; the introduction of machine learning methods also significantly improves the algorithm's efficiency.

Description

Technical Field

[0001] This invention belongs to the field of antenna design technology, specifically relating to a method for hybrid optimization of antenna topology and parameters based on normalized Gaussian networks. Background Technology

[0002] Antenna topology optimization design, a key research area in fields such as electromagnetic fields and microwave technology, and communication and information systems, has always been a hot topic and a challenge in academia. Traditional antenna topology optimization methods can be divided into antenna topology optimization design based on evolutionary algorithms and antenna topology optimization design based on gradient algorithms. The former is easy to integrate with commercial software, has strong scalability, does not require sensitivity information, and can search for the globally optimal topology as much as possible, but it is time-consuming and has high computational resource requirements; the latter can effectively improve the solution efficiency of antenna topology optimization problems, but it is prone to getting trapped in local optima, and because it requires sensitivity information, it is difficult to integrate with commercial software. In addition, traditional antenna topology optimization methods based on pixelation methods cannot obtain smooth topological edges, thus limiting the achievable antenna performance and making them difficult to manufacture in practice.

[0003] Over the past decade, machine learning methods have been widely applied to the design of electronic devices, including antennas, passive components, and circuits, with significant success. However, most machine learning-assisted antenna designs currently only consider the parameter design of antennas with a fixed topology, and cannot be applied to antenna topology optimization. Summary of the Invention

[0004] The purpose of this invention is to address the above problems by providing a method for antenna topology and parameter hybrid optimization based on normalized Gaussian networks. This method can efficiently obtain antenna topology structures with smooth topological edges that meet design specifications, compared to traditional antenna topology optimization design methods.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: an antenna topology and parameter hybrid optimization method based on a normalized Gaussian network, comprising:

[0006] Step 1: In the iterative process, the initial dataset M is trained using the Gaussian process machine learning method to obtain the surrogate model R;

[0007] Step 2: In the surrogate model R, a genetic algorithm is introduced to optimize the values ​​of the eigenvalue vectors for antenna performance indicators. During the optimization process, the surrogate model R obtained in Step 3 is used to obtain the antenna performance indicator values ​​corresponding to different eigenvalue vector values. The fitness function value required for the genetic algorithm iteration is then calculated, ultimately yielding the optimal eigenvalue vector combination X. opt ;

[0008] Step 3: Use the transformation of the normalized Gaussian network from Step 1 to combine the optimal eigenvalue vectors X. opt The reconstructed antenna topology is obtained through conversion;

[0009] Step 4: Perform full-wave simulation calculations on the reconstructed antenna topology to obtain the antenna's true performance Y. real And increment the iteration count by one;

[0010] Step 5: Calculate the actual performance Y of the antenna. real The iteration count and iteration number are judged separately. If the termination condition is met, the final antenna topology is output. If the termination condition is not met, the optimal eigenvalue vector combination X obtained in this iteration is combined. opt and the actual performance Y of the corresponding antenna real Add it to the dataset M from step one, and execute steps one through four until the termination condition is met.

[0011] Furthermore, the specific steps for obtaining the initial dataset M in step one include:

[0012] Step A1: Randomly sample within the eigenvalue vector to obtain the combination of eigenvalue vectors X. Then, transform the eigenvalue combination in the eigenvalue vector used to map the antenna topology using a normalized Gaussian network to generate a series of different antenna topologies.

[0013] Step A2: Use full-wave simulation software to calculate a series of different antenna topologies generated in Step 1, obtain the antenna performance Y corresponding to these new topologies, and then combine the combination of eigenvalue vectors X and antenna performance Y to form the initial dataset M.

[0014] Furthermore, the transformation of the normalized Gaussian network includes:

[0015] Let x be any point within the antenna topology design region Ω, and let the material state at x be determined by the function y(x). When y(x) ≥ 0, the material at x is metal; when y(x) < 0, the material at x is air. The formula for the value of the function y(x) is:

[0016]

[0017] Where the coefficient w i For characteristic parameter variables, and b i (x) is a normalized Gaussian function;

[0018] The normalized Gaussian function b i The formula for determining the value of (x) is:

[0019]

[0020] Gi (x) represents m×n two-dimensional Gaussian functions uniformly distributed within the region to be designed, and N is the number of combinations of eigenvalue vectors X;

[0021] The G i The formula for (x) is:

[0022]

[0023] The center μ of the two-dimensional Gaussian function i Located on m×n grid points uniformly divided by the design area, Σ i Let be the covariance matrix.

[0024] Furthermore, in step two, the fitness function of the genetic algorithm transforms the multi-objective optimization problem into a single-objective optimization problem by setting a corresponding penalty coefficient.

[0025] Furthermore, the feature vector includes the feature value corresponding to the antenna topology and the values ​​of the antenna topology structural parameters, and the feature value corresponding to the antenna topology has a value range of [-1, 1].

[0026] Furthermore, the termination condition is set to reaching the maximum number of iterations limit or the actual performance Y of the antenna in this iteration. real The optimization objective has been met.

[0027] Beneficial effects: The method provided by this invention can not only obtain smooth antenna topology edges, but also greatly improve the design speed of antenna topology optimization and enhance the performance of the final optimized antenna structure. Furthermore, it can be applied to topology optimization for various types of antennas, including multi-antenna systems. Attached Figure Description

[0028] Figure 1 This is a flowchart of an algorithm for a hybrid optimization method of antenna topology and parameters based on a normalized Gaussian network, as described in this invention.

[0029] Figure 2 This is a schematic diagram of the upper surface structure of a two-antenna system optimized according to an embodiment of the present invention;

[0030] Figure 3 This is a schematic diagram of the lower surface structure of a two-antenna system optimized according to an embodiment of the present invention;

[0031] Figure 4 This is a schematic diagram comparing the system performance of the two-antenna system optimized by the optimization method of the present invention with the initial value in an implementation example;

[0032] Figure 5This is a comparison chart of the convergence speed of the optimization method described in this invention and the traditional genetic algorithm in an implementation example.

[0033] In the figure: 1. The upper region to be topology optimized; 2. The feed point of the microstrip antenna; 3. The topology of the upper surface of the dielectric substrate; 4. The topology of the upper surface of the dielectric substrate; 5. The lower region to be topology optimized. Detailed Implementation

[0034] The invention will now be further explained with reference to the accompanying drawings.

[0035] This invention provides a method for hybrid optimization of antenna topology and parameters based on normalized Gaussian networks, comprising:

[0036] Step 1: In the iterative process, the initial dataset M is trained using the Gaussian process machine learning method to obtain the surrogate model R.

[0037] Step 2: In the surrogate model R, a genetic algorithm is introduced to optimize the values ​​of the eigenvalue vectors for antenna performance indicators. During the optimization process, the surrogate model R obtained in Step 3 is used to obtain the antenna performance indicator values ​​corresponding to different eigenvalue vector values. The fitness function value required for the genetic algorithm iteration is then calculated, ultimately yielding the optimal eigenvalue vector combination X. opt .

[0038] Step 3: Use the transformation of the normalized Gaussian network from Step 1 to combine the optimal eigenvalue vectors X. opt The reconstructed antenna topology is obtained through conversion.

[0039] Step 4: Perform full-wave simulation calculations on the reconstructed antenna topology to obtain the antenna's true performance Y. real And increment the iteration count by one.

[0040] Step 5: Calculate the actual performance Y of the antenna. real The iteration count and iteration number are evaluated separately. If the termination condition is met, the final antenna topology is output. If the termination condition is not met, the optimal eigenvalue vector combination X obtained in this iteration is processed. opt and the actual performance Y of the corresponding antenna real Add it to the dataset M from step one, and execute steps one through four until the termination condition is met.

[0041] like Figure 1As shown, in step A1, random sampling is performed within the eigenvalue vector to obtain a combination X of eigenvalue vectors. Then, the eigenvalue combination used to map the antenna topology in the eigenvalue vector is transformed using a normalized Gaussian network to generate a series of different antenna topologies. The eigenvalue vector includes the eigenvalues ​​corresponding to the antenna topology and the values ​​of the antenna topology structural parameters. The eigenvalues ​​corresponding to the antenna topology range from [-1, 1], and the values ​​of the antenna structural parameters are given by the designer according to the desired optimization range.

[0042] The transformation process of a normalized Gaussian network is as follows: Let x be any point within the topology design region Ω, and let the material state at x be determined by the function y(x). When y(x) ≥ 0, the material at this point is metal; when y(x) < 0, the material at this point is air. The value of the function y(x) is determined by the following formula:

[0043]

[0044] Where the coefficient w i For characteristic parameter variables, and b i (x) is the normalized Gaussian function.

[0045] b i The formula for determining the value of (x) is:

[0046]

[0047] G i (x) represents m×n two-dimensional Gaussian functions uniformly distributed within the region to be designed.

[0048] G i The formula for (x) is:

[0049]

[0050] Its center μ i Located on m×n grid points uniformly divided by the design area, Σ i Let be the covariance matrix.

[0051] In this embodiment, to reduce the number of feature parameters in the normalized Gaussian network, the parameter μ is fixed during the optimization process. i and Σ i Therefore, it can be done by having a number of n topo Feature parameter variable w i The same number is n para The values ​​of the antenna structure parameters are used together to adjust the generated antenna topology. The data dimension of the combination of eigenvalue vectors X is k. initial ×N. k initialThis represents the number of combinations of eigenvalue vectors X. N represents the characteristic parameter variable w in the combination of eigenvalue vectors X. i The number of, where N = n topo +n para n topo n represents the number of feature parameter matrices, and the range of eigenvalues ​​corresponding to the antenna topology in each feature parameter matrix is ​​[-1, 1]. para This indicates the number of possible values ​​for the antenna structure parameters.

[0052] In step A2, a series of different antenna topologies generated in step one are calculated using full-wave simulation software to obtain the antenna performance Y corresponding to these new topologies. Then, the initial dataset M composed of the combination of feature vectors X and antenna performance Y is entered into the iterative process.

[0053] In step one, during the iterative process, the initial dataset M is trained using a Gaussian process machine learning method to obtain the surrogate model R. Specifically, training on the initial dataset M learns the relationship between the combination of feature vectors X and the antenna performance Y.

[0054] In step two, a genetic algorithm is introduced into the surrogate model R to optimize the values ​​of the eigenvalue vectors for antenna performance indicators. During the optimization process, the surrogate model R obtained in step three is used to obtain the antenna performance indicator values ​​corresponding to different eigenvalue vector values. Based on this, the fitness function value required for the iteration of the genetic algorithm is calculated, and finally, the optimal eigenvalue vector combination X is obtained. opt .

[0055] In step two, the fitness function of the genetic algorithm can be designed by the designer according to the requirements of the design instance. The design principle is consistent with the traditional antenna optimization method based on heuristic algorithms. For multi-objective optimization problems, the multi-objective optimization problem can be transformed into a single-objective optimization problem by setting the corresponding penalty coefficient.

[0056] In step three, the optimal eigenvalue vector X is combined using the transformation of the normalized Gaussian network from step one. opt Reconstruction is performed to obtain the reconstructed antenna topology.

[0057] In step four, the reconstructed antenna topology is subjected to full-wave simulation calculations to obtain the antenna's true performance Y. real And increment the iteration count by one.

[0058] In step five, the actual performance Y of the antenna will be... real The iteration count and iteration number are judged separately. If the termination condition is met, the final antenna topology is output. If the termination condition is not met, the optimal eigenvalue vector combination X obtained in this iteration is combined. opt and the actual performance Y of the corresponding antennareal Add it to dataset M from step three, and execute steps three through six until the termination condition is met.

[0059] The termination condition is set to either reaching the maximum number of iterations or the actual performance Y of the antenna in this iteration. real The optimization objective has been met.

[0060] like Figure 2-3 As shown, a typical multi-output (MIMO) system has two microstrip antennas. This multi-antenna structure includes a dielectric substrate with a height h = 1.6 mm, a width w1 = 36.9 mm, a length l1 = 24 mm, and a dielectric constant of 4.6. Above the dielectric substrate are two microstrip patch antennas with a width w2 = 11.15 mm and a length l2 to be optimized, with a designed length range of [11, 12.5] mm. The spacing between the two microstrip patch antennas is g1 = 1.75 mm. The width between the patch antennas is g2 = 1.4 mm, and the height is l1 = 24 mm. The area enclosed by the dashed frame on the upper layer of the dielectric substrate is considered as upper region 1, where topology optimization is to be performed. The area between the two microstrip patch antennas includes the feed point 2 of the microstrip antennas. Below the dielectric substrate is a metallic ground plane, where the rectangular area enclosed by the dashed frame with a width g3 = 2.7 mm and a height l1 = 24 mm is lower region 5, where topology optimization is to be performed. The optimization target is |S| within the operating frequency band of 5.725-5.825 GHz. 11 |and|S 21 The fitness function is set as follows:

[0061]

[0062] Where c1 = 5 and c2 = 1 are coefficients, and f1 and f2 represent the worst |S| within the operating frequency band. 11 |and|S 21 | dB value, and These represent the worst |S| within the operating frequency band. 11 |and|S 21 |The design reference target dB value,|S 11 | represents the input matching in antenna performance Y, |S 21 | represents the gain or loss in the antenna performance Y.

[0063] The topology optimization design method described in steps one through five above is used to obtain... Figure 2 and Figure 3 The shaded portion and the optimized l2. Figure 2 and Figure 3 The shaded areas represent the optimized topology 3 on the upper surface of the dielectric substrate and the optimized topology 4 on the lower surface of the dielectric substrate. The optimized l2 = 11.87 mm. Figure 4 A comparison is presented between the initial design and the results optimized using the proposed topology optimization method. Under the initial design, the worst |S... 11 |and|S 21 The values ​​are -4.2dB and -6.4dB respectively. After optimization, the worst |S| in the operating frequency band is... 11 |and|S 21 The values ​​were -12.3dB and -27.1dB respectively, which greatly improved the performance of the antenna system.

[0064] In this embodiment, the initial design did not perform topology optimization on the design areas of the upper and lower surfaces, leaving the upper surface empty and the lower surface copper-clad.

[0065] This invention is based on an iterative machine learning-assisted optimization algorithm architecture. In each iteration, a normalized Gaussian network is introduced to extract features from the antenna topology, and a Gaussian process machine learning method is used to establish a surrogate model between the extracted features and antenna performance. Based on this, a genetic algorithm is introduced to optimize the surrogate model, and the optimization result is then restored to the antenna topology. Full-wave simulation tools are used for verification, and the algorithm is used to determine whether it terminates. If it does not terminate, the optimization and verification results are added to the dataset to retrain the Gaussian process machine learning model for the next iteration. Compared to traditional pixel-based topology optimization methods, this method can obtain a smooth antenna topology edge structure. The introduction of machine learning methods also greatly improves the algorithm efficiency. This method can be used for topology optimization of various types of antennas, multi-antenna systems, etc.

[0066] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for hybrid optimization of antenna topology and parameters based on normalized Gaussian networks, characterized in that, include: Step 1: In the iterative process, the initial dataset M is trained using the Gaussian process machine learning method to obtain the surrogate model R; Step 2: In the surrogate model R, a genetic algorithm is introduced to optimize the values ​​of the eigenvalue vectors for antenna performance indicators. During the optimization process, the surrogate model R obtained in Step 3 is used to obtain the antenna performance indicator values ​​corresponding to different eigenvalue vector values. The fitness function value required for the genetic algorithm iteration is then calculated, ultimately yielding the optimal eigenvalue vector combination X. opt ; Step 3: Use the transformation of the normalized Gaussian network from Step 1 to combine the optimal eigenvalue vectors X. opt The reconstructed antenna topology is obtained through conversion; Step 4: Perform full-wave simulation calculations on the reconstructed antenna topology to obtain the antenna's true performance Y. real And increment the iteration count by one; Step 5: Calculate the actual performance Y of the antenna. real The iteration count and iteration number are judged separately. If the termination condition is met, the final antenna topology is output. If the termination condition is not met, the optimal eigenvalue vector combination X obtained in this iteration is combined. opt and the actual performance Y of the corresponding antenna real Add it to the dataset M from step one, and execute steps one through four until the termination condition is met.

2. The antenna topology and parameter hybrid optimization method based on normalized Gaussian network according to claim 1, characterized in that, The specific steps for obtaining the initial dataset M in step one include: Step A1: Randomly sample within the eigenvalue vector to obtain the combination of eigenvalue vectors X. Then, transform the eigenvalue combination in the eigenvalue vector used to map the antenna topology using a normalized Gaussian network to generate a series of different antenna topologies. Step A2: Use full-wave simulation software to calculate a series of different antenna topologies generated in Step 1, obtain the antenna performance Y corresponding to these new topologies, and then combine the combination of eigenvalue vectors X and antenna performance Y to form the initial dataset M.

3. The antenna topology and parameter hybrid optimization method based on normalized Gaussian network according to claim 1 or 2, characterized in that, The transformation of the normalized Gaussian network includes: Let x be any point within the antenna topology design region Ω, and let the material state at x be determined by the function y(x). When y(x) ≥ 0, the material at x is metal; when y(x) < 0, the material at x is air. The formula for the value of the function y(x) is: Where the coefficient w i For characteristic parameter variables, and b i (x) is a normalized Gaussian function; The normalized Gaussian function b i The formula for determining the value of (x) is: G i (x) represents m×n two-dimensional Gaussian functions uniformly distributed within the region to be designed, and N is the number of combinations of eigenvalue vectors X; The G i The formula for (x) is: The center μ of the two-dimensional Gaussian function i Located on m×n grid points uniformly divided by the design area, Σ i Let be the covariance matrix.

4. The antenna topology and parameter hybrid optimization method based on normalized Gaussian network according to claim 1, characterized in that, In step two, the fitness function of the genetic algorithm transforms the multi-objective optimization problem into a single-objective optimization problem by setting an appropriate penalty coefficient.

5. The antenna topology and parameter hybrid optimization method based on normalized Gaussian network according to claim 1 or 2, characterized in that, The eigenvalue vector includes the eigenvalues ​​corresponding to the antenna topology and the values ​​of the antenna topology structural parameters. The eigenvalues ​​corresponding to the antenna topology have a range of [-1, 1].

6. The antenna topology and parameter hybrid optimization method based on normalized Gaussian network according to claim 1, characterized in that, The termination condition is set to reaching the maximum number of iterations or the actual performance Y of the antenna in this iteration. real The optimization objective has been met.

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