Electromagnetic metasurface unit structure optimization method based on constraint space mapping

Abstract

The invention discloses an electromagnetic metasurface unit structure optimization method based on constraint space mapping, and belongs to the technical field of electromagnetic metamaterial design. In order to solve the problems that in the prior art, constraint conditions are difficult to process in the metasurface unit structure optimization process, and optimization efficiency is low, the method mainly adopts the mode that multi-dimensional structure variables are mapped to a convex constraint space formed by inequality constraint conditions, and efficient optimization is carried out in combination with a multi-objective optimization algorithm. A structural variable vector is represented by using a direction vector and a proportionality coefficient, so that an initial solution generation process meeting complex constraints is simplified, and meanwhile, the global search capability of the algorithm and the convergence speed in a constraint space are improved. According to the method, the local optimal solution can be quickly converged under the complex constraint condition, and the Pareto optimal solution is effectively found, so that an efficient and accurate solution is provided for multi-objective optimization of the electromagnetic metasurface unit structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic metamaterial design, and specifically is a method for optimizing an electromagnetic metasurface unit structure based on constrained space mapping. Background Art

[0002] Electromagnetic metasurfaces are two-dimensional subwavelength structures with different geometric shapes. By properly designing the unit structure, the amplitude and phase of electromagnetic waves transmitted and reflected in a specific frequency band can be manipulated. They have been widely used to design various functional devices, such as frequency selective surfaces, perfect absorbers, and amplitude modulators. However, with the increasing diversity and complexity of metasurface application scenarios, the design optimization of metasurface unit structures has become more challenging. On the one hand, the design goals of metasurface unit structures not only need to meet specific electromagnetic indicators, but also need to meet other indicators of metasurface device application scenarios, such as smaller unit size, limited structural processing area, etc. On the other hand, structural optimization cannot destroy the geometric topological characteristics of the original unit structure, which makes the structural parameters limited to a complex constraint space, greatly increasing the difficulty of the optimization process. Therefore, the study of multi-objective optimization methods for metasurface unit structures that can meet complex constraints is indispensable.

[0003] Existing multi-objective optimization methods for metasurface unit structures are divided into two categories: those based on numerical simulation software and those based on neural networks. Methods based on numerical simulation software require the use of numerical simulation software to simulate the electromagnetic response of the metasurface unit, and on this basis calculate the fitness in the optimization algorithm. This type of method requires a large number of numerical simulations, especially when complex inequality constraints need to be met. This type of method will consume a lot of computing resources and time to search in the parameter space that does not meet the constraints, making the search inefficient and converging slowly under small population conditions. Methods based on neural networks require the preparation of large-scale data sets in advance to train neural networks used to replace numerical simulation software, and then use them for structural optimization. This type of method also has the problem of blindly searching in the parameter space that does not meet the inequality constraints. Summary of the invention

[0004] In order to address the shortcomings of the above-mentioned existing technologies, the present invention proposes an electromagnetic metasurface unit structure optimization method based on constraint space mapping, which uses direction vectors and proportional coefficients to map multidimensional structural variables into a convex constraint space composed of inequality constraints. Combined with a multi-objective optimization algorithm, multi-objective and high-efficiency optimization of metasurface unit structures that meet complex constraints is achieved.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for optimizing an electromagnetic metasurface unit structure based on constraint space mapping comprises the following steps:

[0007] 1) Determine the structural variables to be optimized of the electromagnetic metasurface unit structure, construct the objective function, and determine the inequality constraints of the structural variables;

[0008] 2) Establish a mapping relationship from structural variables to the convex constraint space composed of inequality constraints;

[0009] 3) Initialize the basic parameters of the genetic algorithm according to the objective function and mapping relationship, and construct genetic individuals. Each individual includes a genetic vector and a complete vector, and is randomly initialized;

[0010] 4) Modeling and simulation of the hypersurface unit structure are performed based on the structural variables contained in the complete vector of the individual, the objective function value is calculated, and then the fitness of the individual is evaluated based on the objective function value;

[0011] 5) Calculate the corresponding Pareto rank and crowding distance of each individual in the current population, and select the parent individuals participating in the genetic operation according to the Pareto rank and crowding distance;

[0012] 6) Performing crossover and mutation operations on the genetic vector of the selected parent individual to obtain the genetic vector of the offspring; obtaining the complete vector of the offspring according to the mapping relationship of the offspring genetic vector, thereby obtaining the offspring individual, and then evaluating the fitness of the offspring individual through step 4);

[0013] 7) All the offspring individuals and all the individuals in the original population are grouped together, the individuals that make up the next generation population are selected, and the iteration is repeated; after the iteration is completed, the structural variable vector is extracted from the complete vector of the individuals in the final population to achieve the optimization of the electromagnetic metasurface unit structure.

[0014] Furthermore, in step 2), a method for establishing a mapping relationship from a structural variable to a convex constraint space formed by inequality constraints is as follows: a fixed point in the convex constraint space is selected to represent the position of a structural variable, and a mapping relationship is established, wherein the mapping relationship includes a proportionality coefficient, an upper bound of a modulus length, and a direction vector; wherein the modulus length vector is calculated based on the relationship between the structural variable and the inequality constraints, and then the minimum value in the modulus length vector is calculated to obtain the upper bound of the modulus length; and according to the upper bound of the modulus length, the range of the proportionality coefficient is adjusted so that it satisfies the inequality constraints.

[0015] Furthermore, the basic parameters initialized in step 3) include: the number of objective functions, the number of populations, the total number of iterations, the number of structural variables to be optimized, the crossover coefficient, the coefficient of variation, the crossover rate, the mutation rate, the genetic upper bound vector and the genetic lower bound vector.

[0016] Furthermore, in step 3), the genetic vector is a column vector composed of a direction vector and a proportional coefficient, and the complete vector is a column vector composed of a structural variable vector.

[0017] Furthermore, the step of randomly initializing the genetic vector and the complete vector in step 3) includes:

[0018] Set the initial fixed point, randomly generate the direction vector and proportional coefficient for each genetic individual, and obtain the genetic vector;

[0019] According to the established mapping relationship, the randomly generated genetic vector is converted into the corresponding structural variable vector to obtain a complete vector.

[0020] Furthermore, in step 5), the fast non-dominated solution sorting algorithm and the crowding distance calculation algorithm are used to calculate the corresponding Pareto rank and crowding distance of the complete vector of each individual in the current population.

[0021] Furthermore, in step 5), the parent individuals participating in crossover and mutation are selected according to the Pareto rank and the crowding distance, and the steps include: randomly selecting 2 individuals from the population for comparison, and selecting the individual with a higher Pareto rank of the complete vector; if the ranks are the same, comparing the crowding distances, and selecting the individual with a larger crowding distance of the complete vector; if the crowding distances are the same, randomly selecting one of them; wherein the sampling of the individuals adopts replacement sampling; and repeating the operation until the new population size reaches the original population size.

[0022] Furthermore, in step 7), after all the offspring individuals and all the individuals in the original population are formed into a set, the Pareto rank and crowding distance of the complete vector of the individuals in the set are calculated; the individuals are sorted from small to large according to the Pareto rank, and for individuals of the same rank, they are sorted from large to small according to the crowding distance, and finally only the top N individuals are retained as the next generation population; the parent individuals participating in the genetic operation are selected through step 5), and the chromosome population is evolved.

[0023] The beneficial effects achieved by the present invention are as follows:

[0024] 1. The present invention maps multidimensional structural variables into a convex constraint space composed of inequality constraints, which can effectively limit the search range of the algorithm and avoid invalid simulation of structures that do not meet the constraints, thereby significantly improving the optimization efficiency and accelerating the convergence speed.

[0025] 2. The present invention simplifies the process of generating effective initial solutions under complex constraints by using direction vectors and proportional coefficients to represent structural variables, while enhancing the global search capability of the algorithm in the constraint space, which helps to achieve excellent optimization results under small population conditions.

[0026] 3. By limiting the search space to the constraint space, the present invention can quickly converge to the local optimal solution under complex constraint conditions, and effectively find the Pareto optimal solution in combination with a multi-objective genetic algorithm, providing an efficient solution for the multi-objective optimization of the metasurface unit structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the electromagnetic metasurface unit structure to be optimized.

[0028] Figure 2 It is a flow chart of a multi-objective optimization algorithm based on constraint space mapping.

[0029] Figure 3 It is the algorithm search curve graph.

[0030] Figure 4 It is the Pareto front diagram obtained by final optimization.

[0031] Figure 5 This is the optimized metasurface unit structure diagram.

[0032] Figure 6 It is the simulated S21 curve from 22GHz to 28GHz. DETAILED DESCRIPTION

[0033] In order to make the various technical features and advantages or technical effects in the above technical solutions of the present invention more obvious and easy to understand, the following embodiments are described in detail with reference to the accompanying drawings.

[0034] The embodiment of the present invention specifically discloses a method for optimizing an electromagnetic metasurface unit structure based on constraint space mapping, wherein a design frequency of 22 GHz to 28 GHz is selected, and the electromagnetic metasurface unit structure to be optimized is as follows: Figure 1 As shown, the unit is a square with a side length D of 1.42 mm. The dielectric constant of dielectric layer 1 is 6.874, and the tangent loss angle is 0.0161; the dielectric constant of dielectric layer 2 is 2.1; the dielectric constant of dielectric layer 3 is 6.756, and the tangent loss angle is 0.0133; the etched layer is approximately an ohmic sheet with no thickness, and the square resistance is 0.6Ω. The simulation frequency band is 22GHz~28GHz, and the number of sampling points is 1001. The processing steps of this method are as follows:

[0035] Step 1. Establish a mathematical model for multi-objective optimization of the metasurface unit structure.

[0036] The structural parameters of the metasurface unit structure to be optimized are: There are 6 size parameters in total, namely n=6.

[0037] Construct the minimization objective function minF i ,i∈{1,2,...,k}, where Fi is the ith objective function, and k is the number of objective functions. In this embodiment, there are 3 objective functions, i.e., k=3, which are:

[0038]

[0039]

[0040]

[0041] The three objective functions correspond to the average transmission loss from 24.25 GHz to 25.25 GHz, the longitudinal etching ratio, and the etching area ratio, respectively.

[0042] Based on the modeling expression of structural variables, the inequality constraints are expressed as Where A is the coefficient matrix, whose number of rows is m, corresponding to the number of inequality constraints, and whose number of columns is n, corresponding to the number of structural variables; is a restriction vector with 1 column and m rows, corresponding to the constants in the inequality constraints.

[0043] In this embodiment, the constraints are specifically: There are 12 in total, that is, m=12.

[0044] The corresponding A is equal to b is equal to

[0045] 2. Establish a mapping relationship from multidimensional structural variables to the convex constraint space composed of inequality constraints.

[0046] Any structural variable vector in the convex constraint space composed of inequality constraints can be determined by a fixed point located in this convex constraint space To express: Where β is the proportional coefficient, β∈[0,1], a is the upper bound of the modulus, α≥0, is a direction vector with dimension n. The calculation formula for the modulus upper bound α is in is the modulus length vector, dimension is m, The meaning of is the modulus vector The jth dimension of . The modulus vector The calculation formula is in is the restriction vector of the inequality constraint. When one dimension of is 0, or When one dimension of is less than 0, The value of the corresponding dimension in is set to +∞. When one dimension of is equal to 0, it is necessary to check Whether the minimum value of all dimensional values ​​except 0 satisfies the constraint condition, if so, the upper bound α of the modulus length is equal to the minimum value, if not, the upper bound α of the modulus length is equal to 0.

[0047] 3. Electromagnetic metasurface unit structure based on constrained space mapping, such as Figure 2 The process shown.

[0048] 3.1 Initialize the basic parameters of the algorithm. The number of objective functions is k = 3, the population size is N = 40, the total number of iterations is Gen = 150, the current number of iterations is iter, the number of structural variables to be optimized is n = 6, the crossover coefficient is δ1 = 20, the coefficient of variation is δ2 = 20, the crossover rate is 1, the variation rate is γ = 1 / 7, and the upper bound vector of genetic individuals is The lower bound vector of genetic individuals is

[0049] 3.2 Construct the genetic vector and complete vector of the individual. The genetic vector refers to the vector involved in the crossover and mutation operations, and the complete vector refers to the vector involved in the fitness calculation and as the optimization result. The genetic vector is expressed as is the direction vector and a column vector of proportionality coefficients β. The complete vector is represented as is the structure variable vector The genetic vector and complete vector of the t-th individual in the population are expressed as and Where t∈{1,2,...,N}. The genetic vector corresponds one-to-one to the complete vector.

[0050] 3.3 Randomly generate initial genetic vector and complete vector. First, set the initial fixed point Then the genetic vectors of all individuals Set to in is the direction vector corresponding to the genetic vector of the tth individual in the population, β t is the proportional coefficient corresponding to the genetic vector of the tth individual in the population, rand n×1 is a column vector of dimension n whose elements satisfy a uniform distribution between 0 and 1. rand 1×1 To satisfy the uniform distribution of random numbers between 0 and 1. According to the mapping relationship in step 2, we can calculate Corresponding

[0051] 3.4 Evaluate the fitness of individuals. The structure variables included are used to model and simulate the corresponding metasurface units to obtain the required electromagnetic parameters; the average transmission loss from 24.25 GHz to 25.25 GHz is calculated based on the electromagnetic parameters. The longitudinal etching ratio and the etching area ratio are calculated based on the structure vector. The fitness of the complete individual vector is then evaluated based on the calculated objective function value, and the individual fitness is equal to the vector composed of the three objective function values.

[0052] 3.5 Use the fast non-dominated solution sorting algorithm and crowding distance calculation algorithm to obtain the corresponding Pareto rank and crowding distance of each complete individual vector in the current population.

[0053] 3.6 According to the Pareto rank and crowding distance, the binary tournament principle is used to select the genetic individual vectors participating in crossover and mutation. Specifically, two individuals are randomly selected from the population for comparison, and the individual with a higher Pareto rank is selected. If the ranks are the same, the crowding distance is compared and the individual with a larger crowding distance is selected. If the crowding distances are the same, one of them is randomly selected. The sampling of individuals is carried out with replacement sampling. Repeat the operation until the new population size reaches the original population size.

[0054] 3.7 Simulate binary crossover and polynomial mutation on the obtained genetic individual vector to obtain the genetic individual vector of the offspring. Then, according to the mapping relationship established in step 2, the obtained offspring genetic individual vector is converted into the corresponding structural variable vector to obtain the complete individual vector of the offspring. Then, the fitness of the complete individual vector is evaluated according to step 3.4.

[0055] 3.8 Based on the Pareto rank and crowding distance, use the elite retention strategy to generate a new generation of population. Specifically, the complete individual vectors of all offspring obtained in step 3.7 and the original complete individual vectors are combined into a set, and the Pareto rank and crowding distance of the set are calculated according to step 3.5. They are sorted from small to large according to their Pareto rank. For individuals of the same rank, they are sorted from large to small according to the crowding distance. Finally, only the top N chromosomes are retained as the chromosome population of the next generation. Then iter is increased by 1, and the step 3.6 is returned to iterative evolution of the chromosome population until iter is equal to Gen, then the iteration is stopped and the optimization is completed.

[0056] The hypervolume index (HV) is used to measure the comprehensive performance of the optimization algorithm, such as Figure 3 The algorithm converged after 50 generations, and the Pareto frontier finally optimized is shown in Figure 4 In order to achieve a trade-off between the three objectives, the points [0.502 0.448 0.107 0.0821 0.0584 0.0136] in the Pareto frontier are selected. TAs the final optimization result, the super surface unit structure generated by the optimized structural variables is shown in Figure 5 As shown in Figure 2, the simulation S21 results at 22 GHz to 28 GHz are as follows: Figure 6 As shown, it can be seen that the optimized structural parameters enable the metasurface to achieve an average transmission loss of 3.88dB in the 5GNR n251 frequency band, a longitudinal etching ratio of 89.1%, and an etching area of ​​35.3%.

[0057] Although the present invention has been disclosed as above by way of embodiments, it is not intended to limit the present invention. Appropriate modifications or equivalent substitutions of the technical solutions of the present invention made by ordinary technicians in the field should all be included in the protection scope of the present invention. The protection scope of the present invention shall be based on what is defined in the claims.

Claims

1. A method for optimizing electromagnetic metasurface unit structure based on constraint space mapping, characterized in that: The following steps are involved: 1) Determine the structural variables to be optimized of the electromagnetic metasurface unit structure, construct the objective function, and determine the inequality constraints of the structural variables; 2) Establish a mapping relationship from structural variables to the convex constraint space composed of inequality constraints; 3) Initialize the basic parameters of the genetic algorithm according to the objective function and mapping relationship, and construct genetic individuals. Each individual includes a genetic vector and a complete vector, and is randomly initialized; 4) Modeling and simulation of the hypersurface unit structure are performed based on the structural variables contained in the complete vector of the individual, the objective function value is calculated, and then the fitness of the individual is evaluated based on the objective function value; 5) Calculate the corresponding Pareto rank and crowding distance of each individual in the current population, and select the parent individuals participating in the genetic operation according to the Pareto rank and crowding distance; 6) Performing crossover and mutation operations on the genetic vector of the selected parent individual to obtain the genetic vector of the offspring; obtaining the complete vector of the offspring according to the mapping relationship of the offspring genetic vector, thereby obtaining the offspring individual, and then evaluating the fitness of the offspring individual through step 4); 7) All offspring individuals and all individuals in the original population are combined into a set, and the individuals that make up the next generation population are selected, and the iteration is repeated; After the iteration is completed, the structural variable vector is extracted from the complete vector of the individuals in the population finally obtained to achieve the optimization of the electromagnetic metasurface unit structure.

2. The method according to claim 1, characterized in that The method for establishing a mapping relationship from the structural variable to the convex constraint space composed of inequality constraints in step 2) is: select a fixed point in the convex constraint space to represent the position of a structural variable, and establish a mapping relationship, which includes a proportional coefficient, an upper limit of the modulus length, and a direction vector; wherein, the modulus length vector is calculated based on the relationship between the inequality constraints and the structural variables, and then the minimum value in the modulus length vector is calculated to obtain the upper limit of the modulus length; according to the upper limit of the modulus length, the range of the proportional coefficient is adjusted so that it satisfies the inequality constraints.

3. The method according to claim 1, characterized in that The basic parameters initialized in step 3) include: the number of objective functions, the number of populations, the total number of iterations, the number of structural variables to be optimized, the crossover coefficient, the coefficient of variation, the crossover rate, the mutation rate, the genetic upper bound vector and the genetic lower bound vector.

4. The method according to claim 1, characterized in that In step 3), the genetic vector is a column vector composed of a direction vector and a proportional coefficient, and the complete vector is a column vector composed of a structural variable vector.

5. The method according to claim 1, characterized in that The steps of randomly initializing the genetic vector and the complete vector in step 3) include: Set the initial fixed point, randomly generate the direction vector and proportional coefficient for each genetic individual, and obtain the genetic vector; According to the established mapping relationship, the randomly generated genetic vector is converted into the corresponding structural variable vector to obtain a complete vector.

6. The method according to claim 1, characterized in that In step 5), the fast non-dominated solution sorting algorithm and the crowding distance calculation algorithm are used to calculate the corresponding Pareto rank and crowding distance of the complete vector of each individual in the current population.

7. The method according to claim 1, characterized in that In step 5), the parent individuals participating in crossover and mutation are selected according to the Pareto rank and crowding distance, and the steps include: randomly selecting 2 individuals from the population for comparison, and selecting the individual with a higher Pareto rank of the complete vector; if the ranks are the same, comparing the crowding distances, and selecting the individual with a larger crowding distance of the complete vector; if the crowding distances are the same, randomly selecting one of them; the sampling of the individuals adopts replacement sampling; and repeating the operation until the new population size reaches the original population size.

8. The method according to claim 1, characterized in that In step 7), after all the offspring individuals and all the individuals in the original population are grouped together, the Pareto rank and crowding distance of the complete vector of the individuals in the group are calculated; the individuals are sorted from small to large according to the Pareto rank, and for individuals of the same rank, they are sorted from large to small according to the crowding distance, and finally only the top N individuals are retained as the next generation population; the parent individuals participating in the genetic operation are selected through step 5) to evolve the chromosome population.

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