CN116151096B - Multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method and system - Google Patents
Multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method and system Download PDFInfo
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Abstract
The invention discloses a noodleThe method and the system for optimizing the parameters of the circularly polarized microstrip antenna optimized towards multiple targets comprise the following steps: s1) initializing N groups of antenna structure parameters as a parent population P according to design requirements t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s The method comprises the steps of carrying out a first treatment on the surface of the S2) carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters; s3) performing electromagnetic calculation to obtain M antenna performance indexes corresponding to the working frequency points as optimization targets; s4) searching optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to M optimization targets, and turning to the step S2) until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized. According to the method, a multi-objective optimization algorithm is combined to optimize a plurality of antenna performance indexes, and the diversity of solutions is maintained in a high-dimensional space by introducing a dominant relationship and a reference point.
Description
Technical Field
The invention relates to the field of multi-objective optimization of antennas, in particular to a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method and system.
Background
At present, the methods for optimizing the antenna parameters are mainly divided into three types, namely methods based on an intelligent optimization algorithm, methods based on a neural network and methods based on combination of the intelligent optimization algorithm and the neural network. The intelligent optimization algorithm is mature in application in antenna design and mainly comprises a genetic algorithm, a particle swarm (Particle Swarm Optimization, PSO) algorithm, an ant colony algorithm and the like, takes antenna parameters as an optimization object, takes return loss as an optimization object, and continuously iterates until the proper antenna size is finally obtained. The antenna optimization design algorithm based on the neural network is mainly characterized in that the result of electromagnetic simulation software and the set antenna size are used as training data, and the characteristics of antenna parameters and antenna performance are continuously learned to realize that the electromagnetic characteristics of the related antenna can be obtained by directly inputting the antenna size data without electromagnetic software. Wherein Convolutional Neural Networks (CNNs) are the dominant. And an algorithm based on the combination of the two can be used for optimizing parameters through a traditional intelligent algorithm, and the electromagnetic performance is predicted through a neural network so as to replace electromagnetic simulation software, so that the optimization and design efficiency is improved.
In designing a circularly polarized microstrip antenna, an antenna designer may pay attention to the axial ratio of the antenna and the gain of the antenna, and may pay attention to the polarization ratio in a certain direction to determine the polarization characteristics in that direction, in addition to the return loss. For this reason, conventional intelligent optimization algorithms are no longer applicable because they cannot find suitable solutions in multidimensional space. The antenna optimization method using the neural network is difficult to predict a plurality of performance indexes through training, some performance optimizations may conflict with each other, and meanwhile, the network using CNN and the like may be in local optimum. For this purpose, an algorithm that is optimized for multiple objectives needs to be considered. At present, the more mature algorithms researched in the multi-objective optimization field at home and abroad are NSGA-II, SPEA2, MOPSO algorithms and the like, and as targets are increased (more than 3), the convergence performance of the algorithms is reduced, so that the optimization capability of the algorithms in a high-dimensional space is challenged. The NSGA-III algorithm maintains the diversity of the population by introducing a reference point mechanism, so that the optimal individual is not easy to lose, and local optimization is avoided.
However, literature optimized for multiple targets of circularly polarized antennas is not found in the existing algorithm for a while, mainly for single targets.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method and system. And optimizing the antenna parameters by adopting an NSGA-III algorithm based on self-adaption.
In order to achieve the above object, the present invention provides a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method, which includes:
step S1) initializing N groups of antenna structure parameters as a parent population P according to design requirements t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s ；
S2) carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters;
step S3), electromagnetic calculation is carried out to obtain M antenna performance indexes corresponding to the working frequency points, and the M antenna performance indexes are used as M optimization targets;
step S4) searching the optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to M optimization targets, and turning to step S2) until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized.
As a modification of the above method, the step S1) initializes the reference point Z according to the set optimization target number M s The method comprises the steps of carrying out a first treatment on the surface of the The method specifically comprises the following steps:
determining a reference point on a hyperplane, dividing each optimization target into H parts according to the set number M of the optimization targets, generating a set p= {0/H,1/H,2/H,.., H/H }, and randomly selecting M elements p from the set p = {0/H,1/H,2/H } j E p for meetingIs a component of the external boundary layerExamination point set Z s_boundary The method comprises the steps of carrying out a first treatment on the surface of the Generating a reference point set Z of an inner boundary layer according to the corresponding relation s_inside ；Z s_boundary and Zs_inside Merging to form a consistency reference point set Z s 。
As an improvement of the above method, the step S1) further includes: setting the initial value of the iteration times t as 1, and setting the maximum value of the iteration times t as t max 。
As an improvement of the above method, the step S2) specifically includes:
generating a script through an HFSS-MATLAB-API tool kit according to the N groups of antenna structure parameters, and carrying out electromagnetic modeling on the circularly polarized microstrip antenna by adopting HFSS three-dimensional electromagnetic simulation software based on the script.
As an improvement of the above method, the step S3) specifically includes:
electromagnetic calculation is carried out through a solver of HFSS three-dimensional electromagnetic simulation software, M antenna performance indexes corresponding to a working frequency point Freq are obtained to serve as optimization targets, and the performance targets comprise return loss S11 Freq Axial Ratio Axial Ratio Freq Antenna Gain Freq And antenna polarization ratio corresponding to pitch angle or azimuth angle ThetaSatisfies the following formula:
as an improvement of the above method, the step S4) includes:
step S4-1) taking the antenna structure parameters as the population to be optimized, and for the iteration times t, when t=1, the population to be optimized is the first generation parent population P t When t is more than 1, the population to be optimized is the parent population P t And offspring population Q t Is a mixed population R of (2) t ；
Step S4-2) traversing P according to the optimization objective of step S3) t Or R is t Each individual s in (a) is subjected to rapid non-dominant rankingObtaining a plurality of non-dominant layers F= { F 1 ,F 2 …;
step S4-3) individual of the plurality of non-dominant layers is defined by F 1 Initially, a new population S is put into a layer by layer t Up to S t The number is not less than the number N of individuals in the population for the first time;
step S4-4) judgment S t If the number of (2) is equal to N, judging that S is t Put into a new parent population P t+1 Turning to step S4-5); if not, making the last non-dominant layer be h layer F h Layer 1F is then 1 To layer h-1F h-1 Individuals are put into a new parent population P t+1 In which the number of individuals is T, then from the h-th layer F h Selecting the rest K=N-T individuals, performing normalization, connection and screening operation, and placing new individuals into new parent population P t+1 At this time, the population number is N;
step S4-5) for New parent population P t+1 Respectively calculating fitness function V t And diversity metric G t Updating the crossover probability pc and the variation probability pm according to the current iteration times t;
step S4-6) performing adaptive binary crossover and adaptive polynomial variation according to the crossover probability pc and the variation probability pm updated in step S4-5) to generate a new offspring population Q t+1 ；
Step S4-7), adding 1 to the iteration number t, if the iteration number t does not reach the preset value t max New offspring population Q t+1 And a new parent population P t+1 Merging into a new mixed population R t+1 At this time, the population number is 2N, and R is t+1 Setting the structural parameters of the antenna as the structural parameters of the antenna, and turning to the step S2), otherwise turning to the step S4-8);
step S4-8) starting from population P t+1 And obtaining the antenna structure parameters, thereby realizing the optimization of the circularly polarized microstrip antenna parameters.
As an improvement of the above method, the step S4-2) specifically includes:
step S4-2-1) pair belongs to P t Or R is t Target function f(s) = { f of individual s 1 (s),f 2 (s),...,f M (s) } normalized and subjected to a fast non-dominant ordering resulting in a plurality of non-dominant layers f= { F 1 ,F 2 …, wherein the rapid non-dominant ranking employs a serial search method to optimize the population to be optimized according to a first objective function f 1 (s) carrying out ascending arrangement to obtain an arranged population P t rank And a corresponding sequential rank;
step S4-2-2) performs serial search ranking, the current non-dominant layer number front num=1, the initial non-dominant layer number P of each individual FrontNum =inf, inf represents infinity;
step S4-2-3) from the currently ranked population P t rank Individuals 1 st s i Initially, for each current non-dominant layer number P FrontNum Individuals with =inf are ranked, i=1;
step S4-2-4) traversing each individual S ranked rank < i in front of the individual j Wherein subscript j = 1,2, …, i-1;
if there is an individual s j Non-dominant layer number P of (2) FrontNum (s j ) =front num, then determine if there are s remaining M-1 targets i Is less than s j Is a function of the objective function of:
if so, then the description s i Non-dominating, the current individual s i Corresponding non-dominant layer number P FrontNum (s i ) =front num, i plus 1;
if not, then the description s i Is subject to no subject arrangement, i is increased by 1, go to step S4-2-4) until i is equal to the current population P t rank The number of individuals in (a);
if there is no individual s j Non-dominant layer number P of (2) FrontNum (s j ) "=front num, then s j For non-dominant, the corresponding non-dominant layer number P FrontNum (s i ) =front num, i is increased by 1, go to step S4-2-4) to execute until i equals the current population P t rank The number of individuals in (a);
adding 1 to the current non-dominant layer number front num, proceeding to step S4-2-3) for execution until for the next non-dominant layer numberEach individual is non-dominated ordered, i.e. there are no individuals whose non-dominated number of layers P FrontNum The front num at this time is the maximum non-dominant layer number.
As an improvement of the above method, the step S4-4) specifically includes:
judgment S t If the number of (2) is equal to N, judging that S is t Put into a new parent population P t+1 Turning to step S4-5); if not, the following processing is performed:
step S4-4-1) according to the minimum value of the target vector of the current populationFor each individual S e S of the population t Corresponding target vector f(s) = [ f 1 (s),f 2 (s),…,f M (s)]Mapping to a target vector f'(s):
and calculating the maximum point of the current population on each targetThe M maximum points form a hyperplane to obtain the intercept a on the coordinate axis corresponding to each target j Where j=1, 2, …, M, normalize each individual mapped target vector f'(s);
step S4-4-2) constructing a reference point set Z for the normalized hyperplane r With Z r ＝Z s ；
For the existing structured reference point Z e Z r Determining a reference line w corresponding to each reference point z, and calculating each individual S epsilon S t And the distance between each reference line, find the nearest reference point pi(s) of each individual s, get pi(s) correspondent reference line and distance d (s, pi (s)) between individual s at this moment, thus realize the connection between individual and reference point of the population;
step S4-4-3) let ithReference point z i ∈Z r And population P t+1 ＝S t /F h The number of connected individuals is ρ (z i )；
Step S4-4-4) generating a minimum connection number reference point set
Step S4-4-5) for randomDetermine the collection->Judgment set I i Whether or not it is empty +.>
If it isThen->And goes to step S4-4-4) to continue execution;
if it isAnd->Select the collection +.>Individuals s with smallest d (s, pi (s)) are placed into population P t+1 In this case-> and Fh ＝F h S, go to step S4-4-4) to continue execution;
if it isAnd->Then from the collection->Randomly selecting an individual s to be placed into the population P t+1 In this case and Fh ＝F h S, go to step S4-4-4) to continue until K individuals are obtained by screening and placed into population P t+1 Is a kind of medium.
As an improvement of the above method, the step S4-5) specifically includes:
the fitness function V of the t-th iteration is obtained according to the following steps t And diversity metric G t ：
wherein ,ωj For normalizing the weight corresponding to the objective function, satisfyW i For the fitness function corresponding to the ith individual of the t-th iteration,/th>For the t-th iteration population P t+1 The ith individual in (a)，i＝1,2,…,N，f j For individuals->Normalized j-th antenna performance index corresponding to the corresponding antenna at the working frequency point Freq or the angle Theta, j=1, 2, … and M;for the t-th iteration, population P t+1 I < th > non-dominant individual->And non-dominant individuals->The individual are the antenna structure parameters;
according to the current iteration times t, the fitness function V t And diversity metric G t Updating the crossover probability pc and the mutation probability pm:
wherein ,respectively the maximum and minimum value of the set crossover probability,/->The maximum value and the minimum value of the set mutation probability are respectively set.
In another aspect, the present invention provides a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization system, the system comprising:
an initialization module for according toDesign requirement, initializing N groups of antenna structure parameters as parent population P t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s ；
The electromagnetic modeling module is used for carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters;
the optimization target calculation module is used for carrying out electromagnetic calculation to obtain M antenna performance indexes corresponding to the working frequency points and used as M optimization targets;
and the multi-target optimization module is used for searching the optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to the M optimization targets, and transferring to the electromagnetic modeling module until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized.
Compared with the prior art, the invention has the advantages that:
1. according to the invention, a multi-objective optimization algorithm NSGA-III is combined, a plurality of antenna performance indexes can be optimized, and the diversity of solutions is maintained in a high-dimensional space by introducing a dominant relationship and a reference point;
2. the invention improves the exploration capacity of the decision space in the early stage and the convergence capacity in the later stage by adaptively updating the cross probability and the variation probability, and improves the optimizing efficiency.
Drawings
FIG. 1 is a flow chart of a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method of the invention;
FIG. 2 is a schematic diagram of the reference points of example 1;
fig. 3 is a schematic diagram of the structural dimensions of an antenna according to embodiment 1;
FIG. 4 is a schematic diagram of parameters of example 1S 11;
FIG. 5 is a schematic diagram of the axial ratio parameters of example 1;
FIG. 6 is a schematic diagram of polarization ratio of example 1;
fig. 7 is a schematic diagram of the antenna gain in embodiment 1.
Detailed Description
The invention aims to provide a circular polarization microstrip antenna parameter optimization algorithm based on a self-adaptive NSGA-III algorithm, which aims at comparing a plurality of performance indexes of attention of a circular polarization microstrip antenna and optimizes antenna parameters. Compared with the traditional optimization algorithm, the algorithm can optimize a plurality of indexes at the same time, the searching capability of the Pareto solution set is enhanced by improving the searching capability of the solution space in the early stage and the convergence capability in the later stage through self-adaptive updating of the crossover probability and the variation probability.
In order to achieve the above purpose, according to the invention, through an HFSS-MATLAB-API tool, VB script macro instruction control HFSS (High Frequency Structure Simulator) three-dimensional electromagnetic simulation software is compiled to conduct antenna modeling, an HFSS solver is called to obtain return loss, an axis ratio, antenna gain, antenna polarization ratio and the like, values corresponding to certain frequency points concerned in the values are recorded and are used as optimization targets to be transmitted back to MATLAB, then an adaptive NSGA-III algorithm is adopted to conduct optimization, antenna structure parameters are used as a population, the population is screened and combined through non-dominant sorting, and in each iteration, crossover probability and variation probability are adaptively updated according to iteration times, fitness function and diversity measurement, new offspring population and parent population, namely new structural parameters are transmitted to HFSS, and relevant parameters under a current structure are solved, and iteration is continued. And finally, ending when the maximum iteration times are reached, and obtaining a corresponding Pareto solution set.
The invention mainly uses an HFSS solver and a self-adaptive NSGA-III algorithm to obtain a proper Pareto solution set through continuously generating new antenna structure parameters. Pareto solutions sets are also referred to as non-dominant solutions, which are characterized by not weakening at least one objective function while not optimizing any objective function. Fig. 1 shows a flow chart of a circular polarization microstrip antenna parameter optimization algorithm based on the adaptive NSGA-III algorithm. The following are specific implementation steps.
Step 1) writing VB scripts in MATLAB by using related m programs and functions provided by HFSS-MATLAB-API. A set of antenna structure parameters is initialized in MATLAB as a first generation population,
step 2) initializing reference points for later screening of the population is also required. For convenience of explanation, take MFor example, =3, h=4, generated as follows: a. according to the Das and Dennis's method, each object is divided into 4 parts, and the set p= {0/H,1H,2/H, …, H/H }, from which three elements p are arbitrarily selected j E p constitutes a reference point in three-dimensional space, where the kth point can be represented as z k ＝(p k1 ,p k2 ,p k3 ) Satisfies the following conditionsFor example, (0, 1/4, 3/4), (1/4, 2/4, 1/4) etc., thereby obtaining the outer boundary layer reference point set Z s_boundary The method comprises the steps of carrying out a first treatment on the surface of the b. The reference point z obtained in the step a is obtained k ＝(p k1 ,p k2 ,p k3 ) Generating an inner boundary layer according to the corresponding relation>Where j=1, 2, …, M, as shown in fig. 2, thereby yielding an inner boundary layer reference point set Z s_inside . Total reference point set Z s Is the union of the outer boundary layer reference point set and the inner boundary layer reference point set and has Z s ＝Z s_boundary ∪Z s_inside It should be noted that the set of inner boundary layer reference points and the set of outer boundary layer reference points are on a hyperplane.
Step 3) and modeling according to the structural parameters, calling the HFSS solver to obtain M concerned performance indexes such as return loss (S11), axial Ratio (Axial Ratio), antenna Gain (Gain), antenna polarization Ratio (Polarization Ratio) and the like, and setting concerned solving frequency Freq and angle Theta when calling the relevant solving function.
Step 4) normalize the M objective function values corresponding to each individual returned by HFSS, where the normalized function may be a piecewise function or a polynomial function, as shown below, taking m=4 as an example,
step 5) for individuals s e P when t=1 t Or individuals s.epsilon.R when t > 1 t Target function f(s) = { f 1 (s),f 2 (s),f 3 (s),f 4 (s) } performing a fast non-dominant ordering to produce a plurality of non-dominant layers f= { F 1 ,F 2 …. Wherein the rapid non-dominant sorting adopts a serial search method, and the population to be optimized is arranged in ascending order according to a first objective function (such as axial ratio) to obtain an arranged population P t rank And a corresponding sequential rank.
Starting to perform serial search ordering, wherein the current non-dominant layer number is front num=1, and the initial non-dominant layer number P of each individual FrontNum ＝Inf，
Step 5-1) from the currently ranked population P t rank First individual s i (i=1) starting, for each current non-dominant layer number P FrontNum Individual ones of the =inf are ordered,
step 5-2) traversing each individual s ranked in front of this individual (rank < i) j Where j=1, 2, …, i-1,
if there is an individual s j Non-dominant layer number P of (2) FrontNum (s j ) =front num, then determine if s exists for the remaining M-1 targets i Is less than s j Is a function of the target function of (a):
if present, then specify s i Non-dominating, the current individual s i Corresponding non-dominant layer number P FrontNum (s i ) The case of =front num, where i=i+1;
if not, then the s is described i Is governed by not proceedingNon-dominant permutation, where i=i+1, returns to step 5-2) until i equals the current population P t rank The number of individuals in the population.
If there is no individual s j Non-dominant layer number P of (2) FrontNum (s j ) "=front num, then s j For non-dominant, the corresponding non-dominant layer number P FrontNum (s i ) =front num, i=i+1, then go back to step 5-2) until i equals the current population P t rank The number of individuals in the population.
After the above steps are completed, the current non-dominant layer number front num=front num+1, and the process returns to step 5-1) until each individual is subjected to non-dominant ranking, i.e. there is no individual whose non-dominant layer number P FrontNum The front num at this time is the maximum non-dominant layer number.
Step 6) individual of the plurality of non-dominant layers is defined by F 1 Layer start, F 2 Layer F 3 Layer by layer, … into a new population S t Later until S t The number of individuals in the system is not less than N for the first time, and S is judged t Whether or not the number of (2) is equal to N:
if yes, S is t Put into a new parent population P t+1 Turning to step 7);
if not, making the last non-dominant layer be h layer F h Layer 1F is then 1 To layer h-1F h-1 Individuals are put into a new parent population P t+1 In which the number of individuals is T, then from the h-th layer F h Selecting the rest K=N-T individuals, performing normalization, connection and screening operations, and placing new individuals into new parent population P t+1 In this case, the number of the population is N. (it should be noted that, since the current objective function has been normalized in step 4), no normalization operation is required at this time, and if the antenna designer uses other function mapping methods in step 4) to cause the result to be non-normalized, normalization is required at this time, i.e. normalization operation is optional), and for the reference point after normalization operation, there is Z r ＝Z s 。
Step 6-1) minimum target vector according to the current populationValue ofFor each individual S e S of the population t Corresponding target vector f(s) = [ f 1 (s),f 1 (s),…,f M (s)]Mapped to a target vector f'(s), with
And calculating the maximum point of the current population on each targetThe M maximum points form a hyperplane to obtain the intercept a on the coordinate axis corresponding to each target j Where j=1, 2, …, M, normalize each individual mapped target vector f'(s), there is
Step 6-2) for the normalized hyperplane construction reference point set, there is Z r ＝Z s . For the existing structured reference point Z e Z r Determining a reference line w corresponding to each reference point z, wherein the reference line is a straight line passing through the origin and the reference point, and calculating each individual S epsilon S as shown in figure 2 t And the distance between the individual reference lines, namely, the nearest reference point pi(s) of each individual s is found, and the distance d (s, pi (s)) between the reference line corresponding to pi(s) and the individual s is obtained at the moment, so that the connection between the population of individuals and the reference point is realized.
Step 6-3) let the ith reference point z i ∈Z r And population P t+1 ＝S t /F h The number of connected individuals is ρ (z i ) Step 6-3-1) generating a minimum connection number reference point set
Step 6-3-2) for randomDetermine the collection->Judging set->Whether or not it is empty +.>
If it isThen->And returns to step 6-3-1) to continue execution;
if it isJudging the number of connections->Whether or not 0:
if it isSelect the collection +.>Individuals s with smallest d (s, pi (s)) are placed into population P t+1 In this case and Fh ＝F h S, returning to the step 6-3-1) to continue execution;
if it isThen from the collection->Randomly selecting an individual s to be placed into the population P t+1 In this case and Fh ＝F h And/s, returning to the step 6-3-1) to continue execution. Step 6-3) is executed until K individuals are obtained by screening and placed into the population P t+1 Is a kind of medium. The screening operation is completed at this time.
Step 7) respectively obtaining fitness functions V of the t-th iteration according to the following formula t And diversity metric G t ：
wherein ,ωj For normalizing the weight corresponding to the objective function, satisfyW i For the fitness function corresponding to the ith individual of the t-th iteration,/th>For the t-th iteration population P t+1 I=1, 2, …, N, and obtaining the fitness function V of the population after weighted averaging t 。f j For individuals->Corresponding antennaNormalized j-th antenna performance index corresponding to the working frequency Freq or the angle Theta, wherein j=1, 2, …, M; />For the t-th iteration, population P t+1 I < th > non-dominant individual->And non-dominant individuals->The individual are the antenna structure parameters;
step 8) according to the current iteration times t, the fitness function V t And diversity metric G t Updating the crossover probability pc and the mutation probability pm:
wherein ,respectively the maximum and minimum value of the set crossover probability,/->The maximum value and the minimum value of the set mutation probability are respectively set.
Step 9) according to the updated self-adaptive cross probability pc and self-adaptive variation probability pm, the population P is subjected to t+1 Binary crossover and polynomial variation are carried out to obtain a offspring population Q t+1 And the offspring population Q t+1 And parent population P t+1 Merging into a new population R t+1 。
Step 9-1) at population P t+1 Conducting a tournamentSelecting from P each time t+1 The two individuals are selected randomly for comparison, the individual with the smallest adaptation value (in the invention, the smaller the adaptation value is, the more excellent the individual is) is selected, and the individuals are put into the new population T one by one t+1 Up to a new population T t+1 The number of individuals in (a) reaches N.
Step 9-2) the newly obtained population T t+1 1 st to 1 st of (a)The individual is used as the parent population P1, the +.>To->Individual as parent population P2, T t+1 =p1.u.p2. A random number mu e (0, 1) is generated for each individual per gene, where the gene is a certain structural parameter of the antenna to be optimized. Calculating the uniform distribution factor beta c (μ)，
wherein ηc For the cross distribution index, 20 to 30 is generally used. For each gene of each individual, a random number r epsilon (0, 1) is generated,
where pc is the adaptive crossover probability. From P1, P2, offspring populations Q1, Q2 are obtained, with
Step 9-3) polynomial variation is performed on the offspring populations Q1, Q2 obtained in step 9-2). For each individual gene, a random number μ∈ (0, 1) is generated, calculatedCalculating the uniform distribution factor beta m (μ)，
wherein ηm The mutation distribution index is generally 20 to 30. For each individual, each gene, a random number r epsilon (0, 1) is generated,
where pm is the adaptive variation probability.
For a new population M new =q1.gtorg2, jth individual m j ∈M new The corresponding jth new individual q j Through variation of the rear part of the water tank is provided with a water tank,
wherein And->An upper bound and a lower bound for each individual. New N individuals q j Composition of a New offspring population Q t+1 。
Step 10) iteration times t=t+1, judging whether t is smaller than t max ：
If less, then the new offspring population Q t+1 And parent population P t+1 Is combined into R t+1 The number of individuals was 2N. R is R t+1 Sending the antenna parameters into the HFSS as new antenna parameters for electromagnetic modeling and calculation, and returning to the step 3) for continuous execution;
otherwise, exit, population P t+1 The optimized structural parameters are obtained.
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
Example 1
The embodiment 1 of the invention provides a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method.
In this embodiment, multi-objective optimization is performed on a single-frequency circularly polarized microstrip antenna, the frequency point of the antenna is 2.65GHz, the polarization mode is left-hand circularly polarization (LHCP), the plate medium is Rogers RT/duroid 6002 (tm), the dielectric constant σ=2.94, and the loss tangent tan δ=0.0012. The optimization targets are as follows: optimization objectives need to be described including but not limited to this.
Initializing a reference point, wherein the target number M=4, the population number N=100, and generating the reference point according to the method, wherein the reference point is shown in table 1.
Table 1 reference point coordinates (m=4, h=6)
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Initializing a set of antenna configuration parameters is shown in table 2:
TABLE 2 initial parameter configuration of antenna Structure size (Unit: mm)
| W | 23.5 |
| L | 20 |
| L_GND | 13 |
| W1 | 3.6 |
| L1 | 12 |
| W2 | 2.2 |
| L2 | 15 |
| W3 | 2.2 |
| L3 | 19 |
| H | 1.5 |
And the antenna structure is shown in figure 3. The parameters are initially imported into the HFSS to carry out electromagnetic simulation, and the following objective function results are obtained:
| Axial Ratio | S11 | Gain | Polarization Ratio |
| 1.15dB | -19dB | -7.5dB | 17.12dB |
gain and Polarization Ration do not meet the optimization criteria, for W, L, W 1 、L 1 、W 2 、L 2 、W 3 、L 3 、L GND And optimizing a plurality of antenna parameters. Random numbers are generated for each parameter under each individual, with rand k ∈[0,1]K=1, 2, … 9, then the actual antenna parameters are obtained according to the following mapping, as in table 3:
TABLE 3 parameter populations to be optimized for antennas (Unit: mm)
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The present example was optimized for the following variables, whereby individuals in the population were initialized, with a medium height H of 1.5mm, which was constant:
the individual (antenna size) is led into HFSS for electromagnetic calculation, the corresponding objective function value is returned, the corresponding objective function value is normalized, the normalized function is shown in the description of the previous step 4), the objective function value corresponding to each individual at the time of t=1 is obtained, and part of the results are shown in table 4.
Table 4 normalized objective function (m=4, t=1)
| Individual body | f1 | f2 | f3 | f4 |
| 1 | 1 | 0.66 | 1 | 1 |
| 2 | 1 | 0.66 | 1 | 1 |
| 3 | 1 | 1 | 1 | 1 |
| 4 | 1 | 0.33 | 1 | 1 |
| 5 | 0.974866034 | 0.66 | 1 | 0.66 |
| ...... | ...... | ...... | ...... | ...... |
The non-dominant ordering is then performed, layering is performed, and N parent individuals are generated as a new parent population P t+1 Calculate fitness function V t And diversity metric G t Wherein the weights w are normalized i Are 1/4, and the maximum value and the minimum value of the crossover probability and the mutation probability are respectivelyIn this example, the cross distribution index η c 20, mutation distribution index η m 20. At this time, the population fitness V is calculated t 0.819, diversity measure G t For 2.0301, the Euclidean distance in calculating, for example, the individual x and the individual y can be calculated by +.>
Obtaining a offspring population Q through self-adaptive crossing and self-adaptive mutation t+1 T=t+1, the new offspring population and parent population P t+1 New population R obtained after combination t+1 Then, the HFSS is led in to carry out electromagnetic modeling and electromagnetic calculation to obtain the objective function of each individual, and a new round of normalization is carried out according to the steps of the flow chartA one-degree, non-dominant ordering, etc., iterating over time. The individual at t=5 and the corresponding normalized objective function partial results are shown in table 5, with the normalized objective function of table 5 (m=4, t=5)
| Individual body | f1 | f2 | f3 | f4 |
| 1 | 1 | 0.33 | 1 | 0.66 |
| 2 | 0.692505174 | 0.33 | 1 | 0.66 |
| 3 | 0.01004419 | 0.66 | 1 | 0 |
| 4 | 1 | 0.33 | 1 | 0.66 |
| 5 | 0.007621894 | 0.66 | 1 | 0 |
| ...... | ...... | ...... | ...... | ...... |
At this time, population fitness V t 0.627, diversity metric G t 1.6940. It can be seen that the population as a whole is evolving in a good direction, the diversity metric is smaller than when t=1, as inferior individuals are eliminated.
Through continuous iteration until t=t max Finally, the optimized microstrip antenna is obtained, and the dimensions are shown in table 6.
TABLE 6 optimized antenna size (Unit: mm)
The performance of the antenna is shown in fig. 4 to 7, where fig. 4 is an S11 parameter, fig. 5 is an axial ratio parameter, fig. 6 is a polarization ratio, fig. 7 is an antenna gain, and performance indexes corresponding to each frequency point or angle are shown in table 7.
Table 7 antenna performance
| Axial Ratio | S11 | Gain | Polarization Ratio |
| 1.16dB | -24.6dB | 0.35dBi | 26.05dB |
The optimization result of the circularly polarized microstrip antenna meets the objective, and it is notable that the result only meets the design requirement, and is not the best result, and there is room for further optimization.
Example 2
The embodiment 2 of the invention provides a multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization system, which is realized based on the method of the embodiment 1, and comprises the following steps:
an initialization module for initializing N groups of antenna structure parameters as parent population P according to design requirements t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s ；
The electromagnetic modeling module is used for carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters;
the optimization target calculation module is used for carrying out electromagnetic calculation to obtain M antenna performance indexes corresponding to the working frequency points and used as M optimization targets;
and the multi-target optimization module is used for searching the optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to the M optimization targets, and transferring to the electromagnetic modeling module until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized.
In summary, according to the method disclosed by the invention, HFSS is subjected to antenna modeling and simulation in a script form through HFSS-MATLAB-API, the performance of the circularly polarized antenna, such as return loss, axial ratio, antenna gain, antenna polarization ratio and the like, are taken as optimization targets, and the optimal structural parameters are searched through an adaptive NSGA-III algorithm. In the face of multi-objective antenna optimization problems, the number of iterations of conventional genetic algorithms increases and it is difficult to find a suitable solution to optimize multiple objectives, whereas CNN-based antenna optimization algorithms require more diverse and complex sample data to learn and may fall into local optimizations. The NSGA-III algorithm is a parallel global optimization algorithm, the diversity of solutions is maintained in a high-dimensional space by introducing dominant relations and reference points, and meanwhile, the self-adaptive change cross probability and variation probability in the invention strengthen the capability of searching Pareto solution sets.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (7)
1. A multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization method, the method comprising:
step S1) initializing N groups of antenna structure parameters as a parent population P according to design requirements t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s ；
S2) carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters;
step S3), electromagnetic calculation is carried out to obtain M antenna performance indexes corresponding to the working frequency points, and the M antenna performance indexes are used as M optimization targets;
step S4) searching optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to M optimization targets, and turning to step S2) until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized;
in the step S1), initializing a reference point Z according to the set optimization target number M s The method comprises the steps of carrying out a first treatment on the surface of the The method specifically comprises the following steps:
determining a reference point on a hyperplane, dividing each optimization target into H parts according to the set number M of the optimization targets, generating a set p= {0/H,1/H,2/H, …, H/H }, and randomly selecting M elements p from the set p = {0/H,1/H,2/H, …, H/H } j E p for meetingIs set of outer boundary layer reference points Z s_boundary The method comprises the steps of carrying out a first treatment on the surface of the Generating a reference point set Z of an inner boundary layer according to the corresponding relation s_inside ；Z s_boundary and Zs_inside Merging to form a consistency reference point set Z s ；
The step S2) specifically includes:
generating a script through an HFSS-MATLAB-API tool kit according to the N groups of antenna structure parameters, and carrying out electromagnetic modeling on the circularly polarized microstrip antenna by adopting HFSS three-dimensional electromagnetic simulation software based on the script;
the step S3) specifically includes:
electromagnetic calculation is carried out through a solver of HFSS three-dimensional electromagnetic simulation software, M antenna performance indexes corresponding to a working frequency point Freq are obtained to serve as optimization targets, and the optimization targets comprise return loss S11 Freq Axial Ratio Axial Ratio Freq Antenna Gain Freq And antenna polarization ratio corresponding to pitch angle or azimuth angle ThetaSatisfies the following formula:
2. the method for optimizing parameters of a circularly polarized microstrip antenna for multi-objective optimization according to claim 1, wherein said step S1) further comprises: setting the initial value of the iteration times t as 1, and setting the maximum value of the iteration times t as t max 。
3. The method for optimizing parameters of a circularly polarized microstrip antenna for multi-objective optimization according to claim 2, wherein said step S4) comprises:
step S4-1) taking the antenna structure parameters as the population to be optimized, and for the iteration times t, when t=1, the population to be optimized is the first generation parent population P t When t is more than 1, the population to be optimized is the parent population P t And offspring population Q t Is a mixed population R of (2) t ；
Step S4-2) traversing P according to the optimization objective of step S3) t Or R is t Each individual s in the tree is subjected to rapid non-dominant sorting to obtain a plurality of non-dominant layers F= { F 1 ,F 2 …;
step S4-3) individual of the plurality of non-dominant layers is defined by F 1 Initially, a new population S is put into a layer by layer t Up to S t The number is not less than the number N of individuals in the population for the first time;
step S4-4) judgment S t If the number of (2) is equal to N, judging that S is t Put into a new parent population P t+1 Turning to step S4-5); if not, making the last non-dominant layer be h layer F h Layer 1F is then 1 To layer h-1F h-1 Individuals are put into a new parent population P t+1 In which the number of individuals is T, then from the h-th layer F h Selecting the rest K=N-T individuals, performing normalization, connection and screening operation, and placing new individuals into new parent population P t+1 At this time, the population number is N;
step S4-5) for New parent population P t+1 Respectively calculating fitness function V t And diversity metric G t Updating the crossover probability pc and the variation probability pm according to the current iteration times t;
step S4-6) performing adaptive binary crossover and adaptive polynomial variation according to the crossover probability pc and the variation probability pm updated in step S4-5) to generate a new offspring population Q t+1 ；
Step S4-7), adding 1 to the iteration number t, if the iteration number t does not reach the preset value t max New offspring population Q t+1 And a new parent population P t+1 Merging into a new mixed population R t+1 At this time, the population number is 2N, and R is t+1 Setting the structural parameters of the antenna as the structural parameters of the antenna, and turning to the step S2), otherwise turning to the step S4-8);
step S4-8) starting from population P t+1 And obtaining the antenna structure parameters, thereby realizing the optimization of the circularly polarized microstrip antenna parameters.
4. The method for optimizing parameters of a circularly polarized microstrip antenna for multi-objective optimization according to claim 3, wherein said step S4-2) specifically comprises:
step S4-2-1) pair belongs to P t Or R is t Target function f(s) = { f of individual s 1 (s),f 2 (s),...,f M (s) } normalized and subjected to a fast non-dominant ordering resulting in a plurality of non-dominant layers f= { F 1 ,F 2 …, wherein the rapid non-dominant ranking employs a serial search method to optimize the population to be optimized according to a first objective function f 1 (s) carrying out ascending arrangement to obtain an arranged population P t rank And a corresponding sequential rank;
step S4-2-2) performs serial search ranking, the current non-dominant layer number front num=1, the initial non-dominant layer number P of each individual FrontNum =inf, where Inf represents infinity;
step S4-2-3) from the currently ranked population P t rank Is the 1 st individual s i Initially, for each current non-dominant layer number P FrontNum Individuals with =inf are ranked, i=1;
step S4-2-4) traversing the rowEach individual s in front of this individual rank < i j Wherein subscript j = 1,2, …, i-1;
if there is an individual s j Non-dominant layer number P of (2) FrontNum (s j ) =front num, then determine if there are s remaining M-1 targets i Is less than s j Is a function of the objective function of:
if so, then the description s i Non-dominating, the current individual s i Corresponding non-dominant layer number P FrontNum (s i ) =front num, i plus 1;
if not, then the description s i Is subject to no subject arrangement, i is increased by 1, go to step S4-2-4) until i is equal to the current population P t rank The number of individuals in (a);
if there is no individual s j Non-dominant layer number P of (2) FrontNum (s j ) "=front num, then s j For non-dominant, the corresponding non-dominant layer number P FrontNum (s i ) =front num, i is increased by 1, go to step S4-2-4) to execute until i equals the current population P t rank The number of individuals in (a);
adding 1 to the current non-dominant layer number front num, proceeding to step S4-2-3) until each individual is non-dominant ordered, i.e. there is no individual whose non-dominant layer number P FrontNum The front num at this time is the maximum non-dominant layer number.
5. The method for optimizing parameters of a circularly polarized microstrip antenna for multi-objective optimization according to claim 4, wherein said step S4-4) specifically comprises:
judgment S t If the number of (2) is equal to N, judging that S is t Put into a new parent population P t+1 Turning to step S4-5); if not, the following processing is performed:
step S4-4-1) according to the minimum value of the target vector of the current populationFor each individual S e S of the population t Corresponding toTarget vector f(s) = [ f 1 (s),f 2 (s),…,f M (s)]Mapping to a target vector f'(s):
and calculating the maximum point of the current population on each targetThe M maximum points form a hyperplane to obtain the intercept a on the coordinate axis corresponding to each target j Where j=1, 2, …, M, normalize each individual mapped target vector f'(s);
step S4-4-2) constructing a reference point set Z for the normalized hyperplane r With Z r ＝Z s ；
For the existing structured reference point Z e Z r Determining a reference line w corresponding to each reference point z, and calculating each individual S epsilon S t And the distance between each reference line, find the nearest reference point pi(s) of each individual s, get pi(s) correspondent reference line and distance d (s, pi (s)) between individual s at this moment, thus realize the connection between individual and reference point of the population;
step S4-4-3) let the ith reference point z i ∈Z r And population P t+1 ＝S t /F h The number of connected individuals is ρ (z i )；
Step S4-4-4) generating a minimum connection number reference point set
Step S4-4-5) for randomDetermine the collection->Judging set->Whether or not it is empty +.>
If it isThen->And goes to step S4-4-4) to continue execution;
if it isAnd->Select the collection +.>Individuals s with smallest d (s, pi (s)) are placed into population P t+1 In this case and Fh ＝F h S, go to step S4-4-4) to continue execution;
if it isAnd->Then from the collection->One of which is randomly selectedIndividuals s are put into population P t+1 In this case and Fh ＝F h S, go to step S4-4-4) to continue until K individuals are obtained by screening and placed into population P t+1 Is a kind of medium.
6. The method for optimizing parameters of a circularly polarized microstrip antenna for multi-objective optimization according to claim 5, wherein said step S4-5) specifically comprises:
the fitness function V of the t-th iteration is obtained according to the following steps t And diversity metric G t ：
wherein ,ωj For normalizing the weight corresponding to the objective function, satisfyW i For the fitness function corresponding to the ith individual of the t-th iteration,/th>For the t-th iteration population P t+1 I=1, 2, …, N, f j For individuals->Corresponding toNormalized j-th antenna performance index corresponding to the working frequency point Freq or the angle Theta of the antenna, wherein j=1, 2, … and M;for the t-th iteration, population P t+1 I < th > non-dominant individual->And non-dominant individuals->The individual are the antenna structure parameters;
according to the current iteration times t, the fitness function V t And diversity metric G t Updating the crossover probability pc and the mutation probability pm:
wherein ,respectively the maximum and minimum value of the set crossover probability,/->The maximum value and the minimum value of the set mutation probability are respectively set.
7. A multi-objective optimization-oriented circularly polarized microstrip antenna parameter optimization system, the system comprising:
an initialization module for initializing N groups of antenna structure parameters as parent according to design requirementPopulation P t The number of individuals in the population is N, and a reference point set Z is initialized according to the set optimization target number M s ；
The electromagnetic modeling module is used for carrying out electromagnetic modeling on the circularly polarized microstrip antenna according to the antenna structure parameters;
the optimization target calculation module is used for carrying out electromagnetic calculation to obtain M antenna performance indexes corresponding to the working frequency points and used as M optimization targets;
the multi-target optimization module is used for searching for optimal structural parameters of the antenna through a self-adaptive NSGA-III algorithm according to M optimization targets, and transferring the optimal structural parameters to the electromagnetic modeling module until the set conditions are met, so that the optimal structural parameters of the antenna are obtained, and the parameter optimization of the circularly polarized microstrip antenna is realized;
the initialization module initializes a reference point Z according to the set optimization target number M s The method comprises the steps of carrying out a first treatment on the surface of the The method specifically comprises the following steps:
determining a reference point on a hyperplane, dividing each optimization target into H parts according to the set number M of the optimization targets, generating a set p= {0/H,1/H,2/H,.., H/H }, and randomly selecting M elements p from the set p = {0/H,1/H,2/H } j E p for meetingIs set of outer boundary layer reference points Z s_boundary The method comprises the steps of carrying out a first treatment on the surface of the Generating a reference point set Z of an inner boundary layer according to the corresponding relation s_inside ；Z s_boundary and Zs_inside Merging to form a consistency reference point set Z s ；
The processing of the electromagnetic modeling module specifically comprises the following steps:
generating a script through an HFSS-MATLAB-API tool kit according to the N groups of antenna structure parameters, and carrying out electromagnetic modeling on the circularly polarized microstrip antenna by adopting HFSS three-dimensional electromagnetic simulation software based on the script;
the processing of the optimization target calculation module specifically comprises the following steps:
electromagnetic calculation is carried out through a solver of HFSS three-dimensional electromagnetic simulation software, M antenna performance indexes corresponding to a working frequency point Freq are obtained to serve as optimization targets, and the optimization targets comprise echoesLoss S11 Freq Axial Ratio Axial Ratio Freq Antenna Gain Freq And antenna polarization ratio corresponding to pitch angle or azimuth angle ThetaSatisfies the following formula:
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