CN116562143A - Antenna topology and parameter mixing optimization method based on normalized Gaussian network - Google Patents
Antenna topology and parameter mixing optimization method based on normalized Gaussian network Download PDFInfo
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Abstract
The invention discloses an antenna topology and parameter mixing optimization method based on a normalized Gaussian network. The method is based on an iterative machine learning auxiliary optimization algorithm architecture, a normalized Gaussian network is introduced to extract characteristics of antenna topology in each iteration of an algorithm, and a Gaussian process machine learning method is introduced to establish a proxy model between the extracted characteristics and the antenna performance; on the basis, an evolutionary algorithm is introduced to optimize the proxy model, the optimization result is restored to be the antenna topology, full-wave simulation tool is utilized to simulate and verify, whether the algorithm is terminated or not is judged, if not, the optimization and verification result is added into a data set to retrain the Gaussian process machine learning model, and the next algorithm iteration is carried out. Compared with the traditional topological optimization method based on pixel subdivision, the method can obtain a smooth antenna topological edge structure; the introduction of the machine learning method also greatly improves the algorithm efficiency.
Description
Technical Field
The invention belongs to the technical field of antenna design, and particularly relates to an antenna topology and parameter mixing optimization method based on a normalized Gaussian network.
Background
As a research problem focused on the professions of electromagnetic field and microwave technology, communication and information systems and the like, the topological optimization design of the antenna is always a hot spot and a difficult point of academic research. The traditional antenna topology optimization method can be divided into an antenna structure topology optimization design based on an evolutionary algorithm and an antenna structure topology optimization design based on a gradient algorithm. The method has the advantages that the method is easy to integrate with commercial software, has strong expandability, does not need sensitivity information, can search the globally optimal topological structure as far as possible, and has long time consumption and high requirement on computing resources; the method can effectively improve the solving efficiency of the antenna topological structure optimization problem, but is easy to sink into local optimization, and is difficult to integrate with commercial software due to the fact that sensitivity information is needed. In addition, the traditional antenna topology optimization method based on the pixelation method cannot obtain smooth topology edges, so that the achievable antenna performance is limited, and the practical processing is difficult.
Over the past decade, machine learning methods have been widely introduced into the design field of electronic devices such as antennas, passive devices, and circuit designs, and have achieved very good results. At present, most of antenna designs assisted by machine learning only consider parameter designs of antennas after antenna topology fixing, but cannot be applied to topology optimization designs of antennas.
Disclosure of Invention
The purpose of the invention is that: aiming at the problems, compared with the traditional antenna topology optimization design method, the antenna topology structure meeting design indexes and having smooth topology edges can be obtained very efficiently, and the antenna topology and parameter mixing optimization method based on the normalized Gaussian network is provided;
in order to achieve the above purpose, the present invention adopts the following technical scheme: an antenna topology and parameter mixing optimization method based on a normalized Gaussian network comprises the following steps:
step one: training an initial data set M through a Gaussian process machine learning method in an iterative process to obtain a proxy model R;
step two: introducing a genetic algorithm into the agent model R, optimizing the value of the characteristic value vector according to the antenna performance index, obtaining the value of the antenna performance index corresponding to different characteristic value vector values by using the agent model R obtained in the third step in the optimizing process, calculating the fitness function value required by the iteration of the genetic algorithm, and finally obtaining the optimal characteristic value vector combination X opt ；
Step three: combining the optimal eigenvalue vectors X using the transformation of the normalized Gaussian network in step one opt Converting to obtain a reconstructed antenna topological structure;
step four: full-wave simulation calculation is carried out on the reconstructed antenna topological structure to obtain the real performance Y of the antenna real And adding one to the iteration number;
step five: the true performance Y of the antenna real Respectively judging the iteration times, if the iteration times meet the termination condition, outputting a final antenna topological structure, and if the iteration times do not meet the termination condition, combining the optimal eigenvalue vector obtained by the iteration times with X opt And the true performance Y of the corresponding antenna real And adding the data into the data set M in the step one, and executing the steps one to four until the termination condition is met.
Further, the specific step of obtaining the initial data set M in the step one includes:
step A1: randomly sampling in the eigenvalue vector to obtain a combination X of eigenvalue vectors, and transforming the eigenvalue combination used for mapping the antenna topological structure in the eigenvalue vector by using a normalized Gaussian network to generate a series of different antenna topological structures;
step A2: and (3) generating a series of different antenna topological structures in the first step by using full-wave simulation software to obtain antenna performances Y corresponding to the new topological structures, and combining the characteristic value vector X and the antenna performances Y to form an initial data set M.
Further, the transformation of the normalized gaussian network includes:
let any point in the antenna topology design area Ω be x, and the material state at x is determined by function y (x), when y (x) is not less than 0, the material here is metal, when y (x) is less than 0, the material here is air, and the value formula of function y (x) is:
wherein the coefficient w i Is a characteristic parameter variable, and b i (x) Is a normalized Gaussian function;
the normalized Gaussian function b i (x) The value formula of (2) is as follows:
wherein G is i (x) For m×n two-dimensional gaussian functions uniformly distributed in the region to be designed, N is the number of combinations X of eigenvalue vectors;
the G is i (x) The formula of (2) is:
center μ of two-dimensional Gaussian function i Is positioned on m x n grid points evenly divided by taking a design area as a boundary, and sigma i Is a covariance matrix.
Further, the fitness function of the genetic algorithm in the second step converts the multi-objective optimization problem into a single-objective optimization problem by setting a corresponding penalty coefficient.
Further, the eigenvalue vector comprises eigenvalues corresponding to the antenna topological structure and values of parameters of the antenna topological structure, and the range of the eigenvalues corresponding to the antenna topological structure is [ -1,1].
Further, the termination condition is set to reach a maximum overlapNumber of generations limitation or true performance Y of antenna in this iteration real The optimization objective has been met.
The beneficial effects are that: the method provided by the invention not only can obtain smooth antenna topological edges, but also can greatly improve the design speed of antenna topological structure optimization, and improve the performance of the antenna structure finally obtained by optimization. And can be used in the topology optimization fields of different types of antennas, multiple antennas and the like.
Drawings
FIG. 1 is a block diagram of an algorithm for a normalized Gaussian network-based antenna topology and parameter mixture optimization method described in the present invention;
fig. 2 is a schematic diagram of the structure of the upper surface of a two-antenna system optimized by an embodiment of the present invention;
fig. 3 is a schematic view of the lower surface of a two-antenna system optimized by an embodiment of the present invention;
FIG. 4 is a schematic diagram showing the comparison between the system performance and the initial value of the two-antenna system obtained by optimizing the method according to the embodiment of the present invention;
FIG. 5 is a graph comparing the convergence rate of the optimization method described in the present invention with that of the conventional genetic algorithm in the practical example.
In the figure: 1. the upper layer area to be subjected to topological optimization design, the feeding point of the microstrip antenna, the topological structure of the upper surface of the dielectric plate and the lower layer area to be subjected to topological optimization.
Detailed Description
The invention is further explained below with reference to the drawings.
The invention provides an antenna topology and parameter mixing optimization method based on a normalized Gaussian network, which comprises the following steps:
step one: in the iterative process, training is carried out on the initial data set M through a Gaussian process machine learning method to obtain a proxy model R.
Step two: in the agent model R, a genetic algorithm is introduced, and the eigenvalue vector is valued according to the antenna performance indexAnd (5) optimizing. In the optimization process, the agent model R obtained in the step three is utilized to obtain the values of the antenna performance indexes corresponding to the vector values of different characteristic values, and the fitness function values required by the genetic algorithm iteration are calculated, so that the optimal characteristic value vector combination X is finally obtained opt 。
Step three: combining the optimal eigenvalue vectors X using the transformation of the normalized Gaussian network in step one opt And converting to obtain a reconstructed antenna topological structure.
Step four: full-wave simulation calculation is carried out on the reconstructed antenna topological structure to obtain the real performance Y of the antenna real And the number of iterations is increased by one.
Step five: the true performance Y of the antenna real And the iteration times are respectively judged, and if the iteration times meet the termination conditions, the final antenna topological structure is output. If the optimal characteristic value vector combination X does not meet the termination condition, combining the optimal characteristic value vector combination X obtained by the iteration opt And the true performance Y of the corresponding antenna real And adding the data into the data set M in the step one, and executing the steps one to four until the termination condition is met.
As shown in fig. 1, in step A1, random sampling is performed in the eigenvalue vector to obtain a combination X of eigenvalue vectors. And then, the characteristic value combination used for mapping the antenna topological structure in the characteristic value vector is transformed by using a normalized Gaussian network, so as to generate a series of different antenna topological structures. The eigenvalue vector comprises eigenvalues corresponding to the antenna topological structure and values of parameters of the antenna topological structure, the range of the eigenvalues corresponding to the antenna topological structure is [ -1,1], and the values of the parameters of the antenna structure are given by a designer according to the range of required optimization.
The transformation process of the normalized gaussian network is as follows: let any point in topology design area Ω be x, and the material state at x be determined by function y (x), when y (x) is 0, the material here is metal, when y (x) < 0, the material here is air. The value of the function y (x) is determined by the following equation:
wherein the coefficient w i Is a characteristic parameter variable, and b i (x) Is a normalized gaussian function.
b i (x) The value formula of (2) is as follows:
wherein G is i (x) For m x n two-dimensional gaussian functions uniformly distributed in the area to be designed.
G i (x) The formula is:
its center mu i Is positioned on m x n grid points evenly divided by taking a design area as a boundary, and sigma i Is a covariance matrix.
In this embodiment, to reduce the number of characteristic parameters in the normalized gaussian network, the parameter μ is fixed in the optimization process i Sigma and i therefore, the number of the pass-through parts is n topo Characteristic parameter variable w i The same number is n para Along with the values of the antenna structure parameters, the generated antenna topology is adjusted. The data dimension of the combination X of eigenvalue vectors is k initial ×N。k initial The number of combinations X of eigenvalue vectors is represented. N represents the characteristic parameter variable w in the combination X of characteristic value vectors i Wherein n=n topo +n para 。n topo The number of the characteristic parameter matrixes is represented, and the value range of the characteristic value corresponding to the antenna topological structure in each characteristic parameter matrix is [ -1,1]。n para The number of the antenna structure parameters is represented.
In step A2, a series of different antenna topologies are generated in step one by using full-wave simulation software to obtain antenna performances Y corresponding to the new topologies, and then an initial data set M composed of a combination X of eigenvalue vectors and the antenna performances Y is entered into an iterative process.
In the iterative process, training is carried out on an initial data set M through a Gaussian process machine learning method to obtain a proxy model R. Wherein the relation between the combination of eigenvalue vectors X and the antenna performance Y is learned by training the initial dataset M.
Introducing a genetic algorithm into the agent model R, optimizing the value of the characteristic value vector according to the antenna performance index, obtaining the value of the antenna performance index corresponding to the different characteristic value vector values by using the agent model R obtained in the third step in the optimizing process, calculating the fitness function value required by the iteration of the genetic algorithm, and finally obtaining the optimal characteristic value vector combination X opt 。
The fitness function of the genetic algorithm in the second step can be designed by a designer according to the requirements of a design example, the design principle is consistent with that of a traditional heuristic algorithm-based antenna optimization method, and aiming at a multi-objective optimization problem, the multi-objective optimization problem can be converted into a single-objective optimization problem by setting a corresponding punishment coefficient.
Combining the optimal eigenvalue vectors X by utilizing the transformation of the normalized Gaussian network in the step one opt And (5) reconstructing to obtain a reconstructed antenna topological structure.
In the fourth step, full-wave simulation calculation is carried out on the reconstructed antenna topological structure to obtain the real performance Y of the antenna real And the number of iterations is increased by one.
In the fifth step, the real performance Y of the antenna real Respectively judging the iteration times, if the iteration times meet the termination condition, outputting a final antenna topological structure, and if the iteration times do not meet the termination condition, combining the optimal eigenvalue vector obtained by the iteration times with X opt And the true performance Y of the corresponding antenna real And adding the data into the data set M in the third step, and executing the third to sixth steps until the termination condition is met.
The termination condition is set to reach the maximum iteration number limit or the real performance Y of the antenna in this iteration real Optimization has been satisfiedA target.
As shown in fig. 2-3, a typical structure of two microstrip antennas in a mimo system comprises a layer of a height h=1.6 mm and a width w 1 Length l=36.9 mm 1 Dielectric plate with dielectric constant of 4.6 =24 mm. The upper layer of the dielectric plate is provided with two widths w 2 Length l =11.15 mm 2 Microstrip patch antenna to be optimized, the design interval of the length is [11,12.5 ]]mm. Spacing g between two microstrip patch antennas 1 =1.75mm. Width g between patch antennas 2 =1.4 mm, height l 1 =24 mm. The area surrounded by a dashed box on the upper layer of the dielectric plate is regarded as an upper layer area 1 to be subjected to topology optimization design. The feeding point 2 of the microstrip antenna is comprised between the two microstrip patch antennas. The lower layer of the dielectric plate is a metal ground plane, wherein the width surrounded by a dotted line frame is g 3 =2.7 mm, height l 1 The rectangular region=24 mm is the lower region 5 to be topologically optimized. The optimization target is |S in the working frequency range of 5.725-5.825GHz 11 I and S 21 I, fitness function is set to:
wherein c 1 =5 and c 2 =1 is a coefficient, f 1 And f 2 Respectively represent the worst S in the operating frequency band 11 I and S 21 The dB value of i is set to be,and->Respectively represent worst |S in working frequency band 11 I and S 21 Design of i reference dB value of target, |s 11 I represents the input match in antenna performance Y, |s 21 I represents the gain or loss in antenna performance Y.
The shadow filling in fig. 2 and 3 is obtained by the topology optimization design method of the first to fifth stepsPartial and optimized l 2 . The shaded filled portions in fig. 2 and 3 are the optimized topology 3 on the upper surface of the dielectric slab and the topology 4 on the lower surface of the dielectric slab. Optimized l 2 =11.87 mm. Fig. 4 presents a comparison of the results of the initial design and optimization using the proposed topology optimization method. Under the initial design, the worst |S in the working frequency band 11 I and S 21 The I is-4.2 dB and-6.4 dB respectively, and the worst I S in the working frequency band is the worst after the optimization 11 I and S 21 The I is-12.3 dB and-27.1 dB respectively, and the performance of the antenna system is greatly improved.
In this embodiment, the design area initially designed as the upper and lower surfaces is not topologically optimized, the upper surface is left empty, and the lower surface is copper coated.
According to the invention, based on an iterative machine learning auxiliary optimization algorithm architecture, in each iteration of an algorithm, a normalized Gaussian network is introduced to extract characteristics of antenna topology, and a Gaussian process machine learning method is introduced to establish a proxy model between the extracted characteristics and the antenna performance. On the basis, a genetic algorithm is introduced to optimize the agent model, and then the optimization result is restored to the antenna topology. And the full-wave simulation tool is utilized for simulation and verification, whether the algorithm is terminated is judged, if not, the optimization and verification result is added into the data set to retrain the Gaussian process machine learning model, and the next algorithm iteration is carried out. Compared with the traditional topological optimization method based on pixel subdivision, the method can obtain a smooth antenna topological edge structure. The introduction of the machine learning method also greatly improves the algorithm efficiency. The method can be used in the topology optimization fields of different types of antennas, multiple antennas and the like.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (6)
1. An antenna topology and parameter mixing optimization method based on a normalized Gaussian network is characterized by comprising the following steps:
step one: training an initial data set M through a Gaussian process machine learning method in an iterative process to obtain a proxy model R;
step two: introducing a genetic algorithm into the agent model R, optimizing the value of the characteristic value vector according to the antenna performance index, obtaining the value of the antenna performance index corresponding to different characteristic value vector values by using the agent model R obtained in the third step in the optimizing process, calculating the fitness function value required by the iteration of the genetic algorithm, and finally obtaining the optimal characteristic value vector combination X opt ；
Step three: combining the optimal eigenvalue vectors X using the transformation of the normalized Gaussian network in step one opt Converting to obtain a reconstructed antenna topological structure;
step four: full-wave simulation calculation is carried out on the reconstructed antenna topological structure to obtain the real performance Y of the antenna real And adding one to the iteration number;
step five: the true performance Y of the antenna real Respectively judging the iteration times, if the iteration times meet the termination condition, outputting a final antenna topological structure, and if the iteration times do not meet the termination condition, combining the optimal eigenvalue vector obtained by the iteration times with X opt And the true performance Y of the corresponding antenna real And adding the data into the data set M in the step one, and executing the steps one to four until the termination condition is met.
2. The method for optimizing antenna topology and parameter mixture based on normalized gaussian network according to claim 1, wherein the step of obtaining the initial data set M in the step one comprises the specific steps of:
step A1: randomly sampling in the eigenvalue vector to obtain a combination X of eigenvalue vectors, and transforming the eigenvalue combination used for mapping the antenna topological structure in the eigenvalue vector by using a normalized Gaussian network to generate a series of different antenna topological structures;
step A2: and (3) generating a series of different antenna topological structures in the first step by using full-wave simulation software to obtain antenna performances Y corresponding to the new topological structures, and combining the characteristic value vector X and the antenna performances Y to form an initial data set M.
3. The method for optimizing antenna topology and parameter mixture based on normalized gaussian network according to claim 1 or 2, wherein the transformation of the normalized gaussian network comprises:
let any point in the antenna topology design area Ω be x, and the material state at x is determined by function y (x), when y (x) is not less than 0, the material here is metal, when y (x) is less than 0, the material here is air, and the value formula of function y (x) is:
wherein the coefficient w i Is a characteristic parameter variable, and b i (x) Is a normalized Gaussian function;
the normalized Gaussian function b i (x) The value formula of (2) is as follows:
wherein G is i (x) For m×n two-dimensional gaussian functions uniformly distributed in the region to be designed, N is the number of combinations X of eigenvalue vectors;
the G is i (x) The formula of (2) is:
center μ of two-dimensional Gaussian function i Is positioned on m x n grid points evenly divided by taking a design area as a boundary, and sigma i Is a covariance matrix.
4. The method for optimizing antenna topology and parameter mixture based on normalized Gaussian network according to claim 1, wherein the fitness function of the genetic algorithm in the second step converts the multi-objective optimization problem into a single-objective optimization problem by setting a corresponding penalty coefficient.
5. The method for optimizing antenna topology and parameter mixture based on normalized gaussian network according to claim 1 or 2, wherein said eigenvalue vector comprises eigenvalues corresponding to antenna topology and values of parameters of antenna topology, and the range of values of eigenvalues corresponding to antenna topology is [ -1,1].
6. The method of optimizing antenna topology and parameters mixture based on a normalized gaussian network according to claim 1, characterized in that said termination condition is set to reach a maximum iteration number limit or the real performance Y of the antenna in this iteration real The optimization objective has been met.
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| CN117574783B (en) * | 2024-01-16 | 2024-03-22 | 天津工业大学 | Antenna optimization method, device, equipment and medium based on depth Gaussian process |
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