CN108829988B - Rapid optimization method for hexagonal circularly polarized antenna array - Google Patents
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Abstract
The invention relates to a hexagonal circularly polarized antenna array and a rapid optimization method thereof. A hexagonal circularly polarized antenna array comprises an FR4 dielectric substrate, a feed network, a reflecting surface and a hexagonal radiation patch. A method for quickly optimizing a hexagonal circularly polarized antenna array comprises the following steps of (1) establishing a finite element model of a unit antenna to be optimized; (2) determining design variables of the unit antenna to be optimized; (3) Calling a parallel confidence lower limit optimization algorithm to optimize a finite element model of the initial unit antenna; (4) Obtaining an optimized result Y = (Y) 1 ,y 2 ,…,y n ) T Analyzing and utilizing the optimal design scheme Y opt Carrying out array formation to obtain a finite element model of an initial array to be optimized; (5) Determining design variables of a finite element model of an initial array to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm; (6) Calling a parallel confidence lower limit algorithm to optimize an initial array to be optimized; and (7) obtaining an optimization result of the antenna array.
Description
Technical Field
The invention relates to a hexagonal circularly polarized antenna array and a rapid optimization method thereof, and belongs to the technical field of electromagnetic fields.
Background
With the development of communication technology and internet of things, the requirements of various communication systems on antennas and array antennas on bandwidth, gain, size, polarization characteristics and the like are higher and higher, and the design of the antennas needs to introduce a high-dimensional multi-objective optimization algorithm due to the complexity of structure and design, the diversity of parameters, the multiplicity of the requirements and the like. The existing optimization design method is very dependent on the experience of designers, and when the parameters are many and the requirements on the results are high, the optimization algorithm is easy to fall into local optimization.
The conventional optimization algorithm, such as "application in antenna design of lijun genetic algorithm [ J ] mobile communication, 2000,24 (5): 41-43. Doi.
In order to improve the design efficiency, an optimization scheme based on a proxy model is gradually popularized, and the optimization scheme has unique advantages in a plurality of scientific analyses. For example, the Kriging proxy model mentioned in chinese patent application CN201610015224.9 has the advantages of minimized variance of unbiased estimation, high nonlinearity and strong adaptability, and on this basis, the present invention adopts effective measures such as Maximin latin hypercube sampling and parallel computation to further improve the efficiency of the proxy model.
Since the circularly polarized antenna can receive electromagnetic waves with any polarization and the electromagnetic waves radiated by the circularly polarized antenna can be received by the antenna with any polarization, the circularly polarized antenna is widely applied to wireless communication, such as documents "huang welcome spring, billow, zhufushen et al. 22-24,28.DOI:10.3969/j.issn.1004-373x.2009.07.007 ", the broadband circularly polarized array antenna has a higher relative bandwidth (44.14%) than the broadband circularly polarized array antenna.
Disclosure of Invention
The invention aims to: the present invention is directed to solving the above-mentioned problems of the prior art, and it is a first object of the present invention to disclose a hexagonal circularly polarized antenna array. The second objective of the present invention is to disclose a method for quickly optimizing a hexagonal circularly polarized antenna array.
The technical scheme is as follows: a hexagonal circular polarized antenna array comprises an FR4 dielectric substrate,
a feed network is etched on the bottom side of the FR4 dielectric substrate,
a reflecting surface is arranged on the top side of the FR4 dielectric substrate, four H-shaped gaps are etched at four corners of the reflecting surface in a centrosymmetric manner,
the reflecting surface is bonded with the four hexagonal radiation patches through the medium bolts, the hexagonal radiation patches are separated from the reflecting surface, the middle parts of the four hexagonal radiation patches are provided with strip-shaped gaps, and the strip-shaped gaps are matched with the H-shaped gaps on the reflecting surface.
Further, the characteristic impedance of a main feeder line of the feed network is 50 Ω.
Furthermore, the included angle between the strip-shaped gap in the middle of the hexagonal radiation patch and the H-shaped gap on the reflecting surface is 45 degrees.
Further, the distance between the hexagonal radiation patch and the reflection surface is 2mm.
A method for quickly optimizing a hexagonal circularly polarized antenna array comprises the following steps:
(1) Establishing a finite element model of the unit antenna to be optimized by using HFSS;
(2) Determining design variables of the unit antenna to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
selecting initial sample points of a parallel confidence lower limit algorithm by using a test design method, forming a point set X and an upper bound X of a variable to be optimized l And a lower bound x u Wherein the expression of point set X is as follows:
X＝(x 1 ,x 2 ,...,x i ,...,x n ) T
wherein
x i Is a m-dimensional vector, m is the number of design variables,
n is the number of sample points, and the corresponding actual response value is Y Response to ＝(y 1 ,y 2 ,…y i …,y n ) T ；
(3) Calling a parallel confidence lower limit optimization algorithm to optimize a finite element model of the initial unit antenna;
(4) Obtaining an optimized result Y Superior food ＝(y 1 ,y 2 ,…y i …,y n ) T Analyzing and utilizing the optimal design scheme Y opt Carrying out array formation to obtain a finite element model of an initial array to be optimized;
(5) Determining design variables of a finite element model of an initial array to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
since the finite element model of the initial array to be optimized needs to consider the influence of the feed network on the whole, the design parameters of the feed network must be used as a part of the initial sample point set, and thus the initial sample point set of the array is
In the formula
s is the number of sample points of the array;
(6) Calling a parallel confidence lower limit algorithm to optimize the initial array to be optimized;
(7) And obtaining an optimization result of the antenna array.
Further, the step (3) comprises the following steps:
(31) Setting optimization parameters;
(311) The optimization parameters comprise the initial values of the unit antennas to be optimizedSet of starting sample points X = (X) 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variables to be optimized l And a lower bound x u Expectation value of ith optimization target
And the maximum iteration number Maxnumeval, and the iteration number k =1, wherein the optimization model of the unit antenna structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
Min f(x)
S.T.g(x)≤σ max ,
h(x)≤h U
x l ≤x≤x u
in the formula:
f i representing the actual response value of the unit antenna obtained by HFSS simulation, wherein the actual response value comprises an actual gain value, an actual impedance bandwidth value and an actual circular polarization bandwidth value;
g (x) is a stress constraint condition,
σ max for the maximum allowable stress value of the unit antenna,
h (x) is the condition of the section thickness of the unit antenna,
h U the maximum allowable section thickness of the unit antenna;
(312) Setting optimization objectives
(3121) Antenna ideal gain G for calculating far field electric field distribution of unit antenna lossfree Of the formula
In the formula (I), the compound is shown in the specification,
delta (x) is the antenna structure displacement,
x is the structural design variable of the antenna, including the structure size, shape, angle;
(3122) And calculating a gain loss value delta G of the unit antenna, wherein the calculation formula is as follows:
in the formula:
G real is the actual gain value of the unit antenna;
f 1 the actual gain value of the unit antenna obtained by HFSS simulation;
(313) Setting impedance bandwidth of unit antenna to be optimized
Circular polarization bandwidth of 1GHz to-be-optimized unit antenna
Is 0.2GHz;
(314) Starting optimization iteration of the unit antenna;
(32) Sampling according to an initial sample point set X = (X) of a unit antenna to be optimized by using Maximi Latin hypercube 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variable to be optimized l And a lower bound x u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and K is a two-dimensional matrix of m multiplied by n
n is the number of sample points and the number of finite element proxy models which need to be calculated in parallel,
m is the number of the design variables,
then, selecting the n samples in the sample space K by using a VBS script to establish a parallel element antenna finite element model, and carrying out n multiplied by p times of electromagnetic simulation on the element antenna finite element model, wherein p is the number of the targets to be optimized;
(33) Calling a finite element model of the initial unit antenna, calculating response values corresponding to the initial sample points in parallel, and storing the sample points and the corresponding response values into a sample point database;
(34) Calculating the actual response value f of each sample point by using MATLAB i And comparing the results, wherein:
f i including the gain value f in the direction of maximum radiation of the E-plane (phi =0 deg., theta =90 deg.) 1 Actual impedance bandwidth f of the element antenna 2 Actual circularly polarized bandwidth f of the element antenna 3 ，
f 2 ＝max(Δf|VSWR(f)＜1.9)
f 3 ＝max(Δf|AR(f)＜3)，
Wherein:
Δ f represents a frequency bandwidth satisfying the condition;
VSWR (f) represents a voltage standing wave ratio with frequency f as an argument;
AR (f) represents an axial ratio with frequency f as an argument;
respectively calculating the maximum bandwidth values meeting the respective corresponding conditions; when the maximum bandwidth is obtained, whether the frequency bandwidth contains a central frequency point or not must be considered, if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is discarded, and if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is updated into a sample space K;
(35) Constructing a Kriging agent model meeting a fitness function by using initial sample points and corresponding response values thereof, wherein the Kriging agent model is used as an initialization population of a genetic algorithm and is constructed in the following process,
(351) The expression of the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (2); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation and,
theta is a parameter vector to be solved in the Gaussian correlation function;
(352) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of the basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which,
m is the number of design variables,
n is the number of sample points and,
y is a response value column vector corresponding to the existing sample point;
(36) Obtaining the local optimal solution of the current agent model by combining the Kriging algorithm and the minimum confidence lower limit algorithm with the genetic algorithm
(37) Solving a global sampling model by using a genetic algorithm to obtain an optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) And save it to the sample pointIn a database; and the global optimal result is subjected to error analysis,
(38) Judging whether convergence occurs
If k = Maxnumeval or the optimization target termination condition f (x) is less than or equal to 3, ending the operation, and returning the current global optimum value and the corresponding sample point; if k is less than Maxnumeval, the step (39) is carried out;
(39) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (34).
Still further, step (33) comprises the steps of:
(331) Firstly, dividing initial sample points into a plurality of subdomains according to groups, distributing a subdomain for each process, and broadcasting by 0 process;
(332) Then, carrying out simulation calculation on each process in a given calculation range according to a minimum confidence lower limit algorithm;
(333) After the calculation of each process is completed, the 0 process collects and combines the response values of each group of sample points.
Still further, step (36) includes the steps of:
(361) The method comprises the steps of obtaining an agent model meeting a fitness function by combining Kriging and a minimum confidence lower limit algorithm as an initialized population of a genetic algorithm, carrying out simulation according to a response value of the population after evolution by an evolution strategy, updating a sample library, and then carrying out sample filling criterion by combining Kriging and the minimum confidence lower limit algorithm
Selecting a sample with the minimum fitness function value to perform simulation and find the optimal solution of the current agent model;
in the formula:
b is a balance constant used for adjusting the balance of the global search and the local search, and when b =0, the minimum confidence lower limit formula is equal to
The local searching capability is strong, when b → ∞ the global searching capability is remarkable, and at the moment
(362) The equilibrium constant b is selected in an automatic determination mode and is determined by the following formula:
(i,j＝1,2,...,N,i≠j)
in the formula (I), the compound is shown in the specification,
n is the total number of sample points before the kth iteration,
x i ，x j is any two sample points in the sample space K,
(363) Using genetic algorithm to solve local sampling model, and obtaining optimal solution x (k) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (k) ) And saves it to the sample point database.
Further, the error analysis in step (37) includes the following specific steps:
(371) Selecting 5 groups of better samples in the sample database and response values thereof;
(372) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error of +/-0.1 percent, and establishing a corresponding finite element model;
(373) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(374) The error estimation value is minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
Further, the step (6) comprises the steps of:
(61) Setting optimization parameters of an initial array to be optimized;
(611) The array optimization parameters include an initial set of sample points for the array
Upper and lower bounds x of variables to be optimized l 'and x' u And the expected value of the ith optimization objective
The optimization model of the array structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
MinΔG(x)
h(x)≤h U
x' l ≤x≤x' u
in the formula (I), the compound is shown in the specification,
ag (x) represents the gain loss value corresponding to the sample point x,
g (x) is a stress constraint condition,
σ e for the normal operating stress of the e-th cell,
h (x) is the thickness condition of the array section, and h (x) is less than or equal to 4mm;
h U the maximum allowable array cross-sectional thickness;
(612) Calculating the maximum gain loss value of the E surface, wherein the expression is
In the formula (I), the compound is shown in the specification,
y opt_gain (x) Represents an optimal gain value of the element antenna,
y arr_gain (x) Representing the gain response value for the current sample point of the array,
n represents the number of array elements;
(62) Sampling according to an initial sample point set X = (X) of an antenna array to be optimized by using Maximi Latin hypercube 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variables to be optimized l 'and lower boundary x' u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and K is a two-dimensional matrix of m multiplied by n
n is the number of sample points and the number of finite element proxy models which need to be calculated in parallel,
m is the number of the design variables,
then, selecting the n samples in the matrix K by using a VBS script to establish an array parallel proxy model, and carrying out n x p times of electromagnetic simulation on the proxy model, wherein p is the number of targets needing to be optimized;
(63) Calling a finite element model of an initial array to be optimized, calculating response values corresponding to initial sample points in parallel, and storing the sample points and the response values corresponding to the sample points into a sample point database;
(64) Obtaining actual response value of each sample point by using MATLAB
Comparing the results to obtain a gain loss value delta G (x) corresponding to the sample point x;
(65) Constructing a Kriging agent model meeting a fitness function as an initialization population of a genetic algorithm by using initial sample points and corresponding response values, wherein the specific steps of constructing the Kriging agent model are as follows:
(651) The expression of the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (a); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation of the signal,
theta is a parameter vector to be solved in the Gaussian correlation function;
(652) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which,
m is the number of design variables,
n is the number of sample points,
y is a response value column vector corresponding to the existing sample point;
(66) Solving a local sampling model by using a genetic algorithm to obtain an optimal solution x (k) As an updateCalling a proxy model to calculate a response value f (x) corresponding to the optimal solution (k) ) And storing the data into a sample point database;
(67) Using genetic algorithm to solve global sampling model, and obtaining optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) Storing the data into a sample point database, and carrying out error analysis on the global optimal result;
(68) Judging whether to converge
If k = Maxnumeval or the optimization target termination condition Δ G of the antenna array to be optimized is not more than 3, entering the step (7) and returning the current global optimum value and the corresponding sample point; if k is less than Maxnumeval, the step (69) is carried out;
(69) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (64).
Further, the error analysis in step (67) includes the following steps:
(671) Selecting 5 groups of better samples in the sample database and response values thereof;
(672) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error of +/-0.1 percent, and establishing a corresponding finite element model;
(673) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(674) The error estimation value is minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
Has the advantages that: the hexagonal circularly polarized antenna array and the rapid optimization method thereof disclosed by the invention have the following beneficial effects:
1. the optimal structure parameters can be automatically searched under given design indexes and conditions, the whole optimization process does not need manual intervention, and the optimization result is real and reliable;
2. the invention provides help for the design of a complex antenna structure and a large-scale antenna array, greatly reduces the time for optimizing the parameters of the antenna structure and improves the efficiency of the antenna design;
3. the unit antenna and the array designed by the invention have good performance and are suitable for the application of ISM frequency band;
4. the invention has important guiding significance and value to engineering application, expands the application range of MATLAB-HFSS-API, and can be widely applied to the optimization of arrays with complex structures.
Drawings
FIG. 1 is an exploded view of a finite element model of a unit antenna;
fig. 2 is an exploded view of a hexagonal circular polarized antenna array according to the present disclosure;
fig. 3 is a perspective view of a hexagonal circular polarized antenna array according to the present disclosure;
fig. 4 is a schematic flow chart of a method for optimizing a hexagonal circularly polarized antenna array according to the present invention;
FIG. 5 is a schematic flow chart of parallel confidence lower limit optimization algorithm for optimizing an antenna;
FIG. 6 is a flow diagram of a parallel computing mechanism;
FIG. 7a is a graph of the optimal return loss and 3-dB axial ratio for a unit antenna;
FIG. 7b is the optimal pattern for the element antenna;
FIG. 8a is a graph of the optimal 3-dB axial ratio for a hexagonal circularly polarized antenna array;
FIG. 8b is a graph of the optimal return loss for a hexagonal circularly polarized antenna array;
FIG. 8c is an optimal directional diagram of a hexagonal circularly polarized antenna array;
wherein:
1-hexagon radiation patch
2-reflecting surface
3-FR4 dielectric substrate
4-feed network
The specific implementation mode is as follows:
the following describes in detail specific embodiments of the present invention.
As shown in fig. 2 and 3, a hexagonal circular polarized antenna array comprises an FR4 dielectric substrate 3,
a feed network 4 is etched on the bottom side of the FR4 dielectric substrate 3,
the top side of the FR4 dielectric substrate 3 is provided with a reflecting surface 2, four H-shaped gaps are etched at four corners of the reflecting surface 2 in a centrosymmetric mode,
reflecting surface 2 bonds with four hexagonal radiation paster 1 through the medium bolt, and hexagonal radiation paster 1 is kept away from with reflecting surface 2 mutually, and four hexagonal radiation paster 1 middle parts are equipped with the bar gap, and this bar gap cooperatees with the H type gap on the reflecting surface 2.
Further, the characteristic impedance of the main feeder of the feed network 4 is 50 Ω.
Further, the angle between the strip-shaped gap in the middle of the hexagonal radiation patch 1 and the H-shaped gap on the reflection surface 2 is 45 °.
Further, the distance between the hexagonal radiation patch 1 and the reflection surface 2 is 2mm.
As shown in fig. 4, a method for quickly optimizing a hexagonal circularly polarized antenna array includes:
(1) Establishing a finite element model of the element antenna to be optimized by using HFSS (structure shown in FIG. 1);
(2) Determining design variables of the unit antenna to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
selecting initial sample points of a parallel confidence lower limit algorithm by using a test design method, forming a point set X and an upper bound X of a variable to be optimized l And a lower bound x u Wherein the expression of point set X is as follows:
X＝(x 1 ,x 2 ,...,x i ,...,x n ) T
wherein
x i Is a m-dimensional vector, m is the number of design variables,
n is the number of the sample points,corresponding to an actual response value of Y Response to ＝(y 1 ,y 2 ,…y i …,y n ) T ；
(3) Calling a parallel confidence lower limit optimization algorithm to optimize a finite element model of the initial unit antenna;
(4) Obtaining an optimized result Y Superior food ＝(y 1 ,y 2 ,…y i …,y n ) T Analyzing and utilizing the optimal design scheme Y opt Carrying out array formation to obtain a finite element model of an initial array to be optimized;
(5) Determining design variables of a finite element model of an initial array to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
since the finite element model of the initial array to be optimized needs to consider the influence of the feed network on the whole, the design parameters of the feed network must be used as a part of the initial sample point set, and thus the initial sample point set of the array is
In the formula
s is the number of sample points of the array;
(6) Calling a parallel confidence lower limit algorithm to optimize an initial array to be optimized;
(7) And obtaining the optimization result of the antenna array.
Further, as shown in fig. 5, the step (3) includes the steps of:
(31) Setting optimization parameters;
(311) The optimization parameters include an initial sample point set X = (X) of the unit antenna to be optimized 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variable to be optimized l And a lower bound x u Expectation value of ith optimization goal
And the maximum iteration number Maxnumeval, and the iteration number k =1, wherein the optimization model of the unit antenna structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
Min f(x)
S.T.g(x)≤σ max ,
h(x)≤h U
x l ≤x≤x u
in the formula:
f i representing the actual response value of the unit antenna obtained by HFSS simulation, wherein the actual response value comprises an actual gain value, an actual impedance bandwidth value and an actual circular polarization bandwidth value;
g (x) is a stress constraint condition,
σ max for the maximum allowable stress value of the unit antenna,
h (x) is the condition of the section thickness of the unit antenna,
h U the maximum allowable section thickness of the unit antenna;
(312) Setting optimization objectives
(3121) Antenna ideal gain G for calculating far field electric field distribution of unit antenna lossfree Of the formula
In the formula (I), the compound is shown in the specification,
delta (x) is the antenna structure displacement,
x is the structural design variable of the antenna, including the structure size, shape, angle;
(3122) And calculating a gain loss value delta G of the unit antenna, wherein the calculation formula is as follows:
in the formula:
G real is the actual gain value of the unit antenna;
f 1 the actual gain value of the unit antenna obtained by HFSS simulation;
(313) Setting impedance bandwidth of unit antenna to be optimized
Circular polarization bandwidth of 1GHz to-be-optimized unit antenna
Is 0.2GHz;
(314) Starting optimization iteration of the unit antenna;
(32) Sampling by using Maximi Latin hypercube according to an initial sample point set X = (X is the number of the unit antenna to be optimized) 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variable to be optimized l And a lower bound x u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and K is a two-dimensional matrix of m multiplied by n
n is the number of sample points and the number of finite element proxy models which need to be calculated in parallel,
m is the number of the design variables,
then, selecting the n samples in the sample space K by using a VBS script to establish a parallel element antenna finite element model, and carrying out n multiplied by p times of electromagnetic simulation on the element antenna finite element model, wherein p is the number of the targets to be optimized;
(33) Calling a finite element model of the initial unit antenna, calculating response values corresponding to the initial sample points in parallel, and storing the sample points and the corresponding response values into a sample point database;
(34) Calculating the actual response value f of each sample point by using MATLAB i And comparing the results, wherein:
f i including a gain value f in the direction of maximum radiation of the E-plane (phi =0 deg., theta =90 deg.) 1 Actual impedance bandwidth f of the element antenna 2 Actual circularly polarized bandwidth f of the element antenna 3 ，
f 2 ＝max(Δf|VSWR(f)＜1.9)
f 3 ＝max(Δf|AR(f)＜3)，
Wherein:
Δ f represents a frequency bandwidth satisfying the condition;
VSWR (f) represents a voltage standing wave ratio with frequency f as an argument;
AR (f) represents an axial ratio with frequency f as an argument;
respectively calculating the maximum bandwidth values meeting respective corresponding conditions; when the maximum bandwidth is obtained, whether the frequency bandwidth contains a central frequency point or not must be considered, if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is discarded, and if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is updated into a sample space K;
(35) Constructing a Kriging agent model which meets a fitness function by using the initial sample points and the corresponding response values, wherein the Kriging agent model is used as an initialization population of a genetic algorithm, the construction process is as follows,
(351) The expression for the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (2); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation and,
theta is a parameter vector to be solved in the Gaussian correlation function;
(352) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which,
m is the number of design variables,
n is the number of sample points and,
y is a response value column vector corresponding to the existing sample point;
(36) Obtaining the local optimal solution of the current agent model by using the Kriging algorithm and the minimum confidence lower limit algorithm in combination with the genetic algorithm
(37) Using genetic algorithm to solve global sampling model, and obtaining optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) And storing the result in a sample point database, and feeding the global optimal result into the databaseAnalyzing errors;
(38) Judging whether to converge
If k = Maxnumeval or the optimization target termination condition f (x) is less than or equal to 3, ending the operation, and returning the current global optimum value and the corresponding sample point; if k is less than Maxnumeval, the step (39) is carried out;
(39) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (34).
Further, as shown in fig. 6, the step (33) includes the steps of:
(331) Firstly, dividing initial sample points into a plurality of subdomains according to groups, distributing one subdomain for each process, and broadcasting by 0 process;
(332) Then, carrying out simulation calculation on each process in a given calculation range according to a minimum confidence lower limit algorithm;
(333) After the calculation of each process is completed, the 0 process collects and combines the response values of each group of sample points.
Still further, step (36) includes the steps of:
(361) Combining Kriging and minimum confidence lower limit algorithm to obtain an agent model meeting a fitness function as an initialized population of the genetic algorithm, simulating according to the response value of the population after evolution by the evolution strategy, updating a sample library, and then combining the Kriging and the minimum confidence lower limit algorithm to obtain a sample filling criterion
Selecting a sample with the minimum fitness function value to execute simulation and finding the optimal solution of the current agent model;
in the formula:
b is a balance constant used for adjusting the balance of the global search and the local search, and when b =0, the minimum confidence lower limit formula is equal to
The local searching capability is strong, when b → ∞ the global searching capability is remarkable, and at the moment
(362) The equilibrium constant b is selected in an automatic determination mode and is determined by the following formula:
(i,j＝1,2,...,N,i≠j)
in the formula (I), the compound is shown in the specification,
n is the total number of sample points before the kth iteration,
x i ，x j is any two sample points in the sample space K,
(363) Using genetic algorithm to solve local sampling model, and obtaining optimal solution x (k) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (k) ) And saves it to the sample point database.
Further, the error analysis in step (37) includes the following specific steps:
(371) Selecting 5 groups of better samples in a sample database and response values thereof;
(372) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error +/-0.1%, and establishing a corresponding finite element model;
(373) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(374) The error estimation value is the minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
Further, the step (6) comprises the following steps:
(61) Setting optimization parameters of an initial array to be optimized;
(611) The array optimization parameters include an initial set of sample points for the array
Upper and lower bounds x of the variable to be optimized l 'and x' u And the expected value of the ith optimization objective
The optimization model of the array structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
MinΔG(x)
h(x)≤h U
x' l ≤x≤x' u
in the formula (I), the compound is shown in the specification,
ag (x) represents the gain loss value corresponding to the sample point x,
g (x) is a stress constraint condition,
σ e for the normal operating stress of the e-th cell,
h (x) is the thickness condition of the array section, and h (x) is less than or equal to 4mm;
h U the maximum allowable array cross-sectional thickness;
(612) Calculating the maximum gain loss value of the E surface, wherein the expression is
In the formula (I), the compound is shown in the specification,
y opt_gain (x) Represents an optimal gain value of the element antenna,
y arr_gain (x) Representing the gain response value for the current sample point of the array,
n represents the number of array elements;
(62) Sampling according to an initial sample point set X = (X) of an antenna array to be optimized by using Maximi Latin hypercube 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variable to be optimized l 'and lower boundary x' u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and the K is a two-dimensional matrix of m multiplied by n
n is the number of sample points and the number of finite element proxy models which need to be calculated in parallel,
m is the number of the design variables,
then, selecting the n samples in the matrix K by using a VBS script to establish an array parallel proxy model, and carrying out n x p times of electromagnetic simulation on the proxy model, wherein p is the number of targets needing to be optimized;
(63) Calling a finite element model of an initial array to be optimized, calculating response values corresponding to initial sample points in parallel, and storing the sample points and the response values corresponding to the sample points into a sample point database;
(64) Obtaining actual response value of each sample point by using MATLAB
Comparing the results to obtain a gain loss value delta G (x) corresponding to the sample point x;
(65) Constructing a Kriging agent model meeting a fitness function by using the initial sample points and the corresponding response values thereof as an initialization population of a genetic algorithm, wherein the specific steps of constructing the Kriging agent model are as follows:
(651) The expression of the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (2); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation and,
theta is a parameter vector to be solved in the Gaussian correlation function;
(652) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of the basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which the vector is,
m is the number of design variables,
n is the number of sample points,
y is a response value column vector corresponding to the existing sample point;
(66) Solving a local sampling model by using a genetic algorithm to obtain an optimal solution x (k) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (k) ) And storing the data into a sample point database;
(67) Solving a global sampling model by using a genetic algorithm to obtain an optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) Storing the data into a sample point database, and carrying out error analysis on the global optimal result;
(68) Judging whether to converge
If k = Maxnumeval or the optimization target termination condition Δ G of the antenna array to be optimized is not more than 3, entering the step (7) and returning the current global optimum value and the corresponding sample point; if k is less than Maxnumeval, the step (69) is carried out;
(69) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (64).
Further, the error analysis in step (67) comprises the following steps:
(671) Selecting 5 groups of better samples in a sample database and response values thereof;
(672) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error of +/-0.1 percent, and establishing a corresponding finite element model;
(673) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(674) The error estimation value is the minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
The antenna related by the invention is a broadband hexagonal circularly polarized microstrip antenna array adopting slot coupling, the specific structure is shown in figures 2 and 3, the central working frequency point is 5.8GHz, the impedance bandwidth is 4.48 GHz-7.04 GHz (44.14%), the axial ratio bandwidth is 5.4 GHz-5.99 GHz (10.2%), the requirement of the whole ISM waveband (5.725 GHz-5.875 GHz) is met, and the gain of the E plane in the maximum radiation direction (phi =0 degrees, theta =90 degrees) is 11.155dBi. The impedance bandwidth is wider than that of an antenna array (23%) with a circular radiating patch, and the circular polarization performance is greatly improved compared with that (8.9%).
TABLE 1
Note: step here refers to the number of iteration steps; the number of times of non-calling finite element calculation software is increased, and the finite element calculation software is called every time of iteration
The number of times is determined by the number of samples produced per iteration, rather than a simple multiple relationship. The array example is the same.
TABLE 2
| x1 | 13mm | x5 | 6mm | x9 | 0.8mm | x13 | 2mm |
| x2 | 25mm | x6 | 1.25mm | x10 | 36mm | x14 | 25.86mm |
| x3 | 1mm | x7 | 0.5mm | x11 | x10 | x15 | 0deg |
| x4 | 12.1mm | x8 | 7.5mm | x12 | 1mm | x16 | 45deg |
Table 1 shows a comparison between two algorithms used to optimize the antenna elements, one is a serial minimum confidence threshold algorithm and the other is a parallel minimum confidence threshold algorithm. The optimization objective of the cell is similar to the overall objective of the array optimization, expressed as
In particular y opt_gain (x)＝9.03，
Table 2 gives the results of optimizing the antenna element structure size using parallel and serial optimization methods (the smaller the value of the objective function, the closer it is to the set target). The antenna element optimization results are shown in fig. 1.
Optimization example
The invention uses the above-mentioned novel hexagonal circular polarized antenna array structure as an optimization object, the number of optimized design variables is 15, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, and since it needs to be compared with a serial algorithm, here, in order to improve efficiency (reduce serial optimization program running time), the optimization target is only set to the gain loss value Δ G at the maximum directional point (Φ =0 °, θ =90 °) (x-axis vertical direction), and then compares other results in the optimized sample response value to be appropriate. All relevant parameters adopted by the serial optimization program and the parallel optimization program are the same, and the termination conditions are the same. The results and comparisons of the tandem optimization program are shown in tables 3 and 4 of the attached documents. The array optimization results are described in fig. 7a, 7b, 8a, 8b and 8 c.
TABLE 3
TABLE 4
| Serial optimization program | Parallel optimization program | |
| Optimal results | 3.68 | 2.85 |
| Iterative algebra satisfying termination condition | 100 | 95 |
| Time spent in optimizing program | 81948 seconds | 43422 seconds |
The embodiments of the present invention have been described in detail. However, the present invention is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present invention.
Claims (6)
1. A method for quickly optimizing a hexagonal circularly polarized antenna array is characterized by comprising the following steps:
(1) Establishing a finite element model of the unit antenna to be optimized by using HFSS;
(2) Determining design variables of the unit antenna to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
selecting initial sample points of a parallel confidence lower limit algorithm by using a test design method, forming a point set X and an upper bound X of a variable to be optimized l And a lower bound x u Wherein the expression of point set X is as follows:
X＝(x 1 ,x 2 ,...,x i ,...,x n ) T wherein:
x i is a m-dimensional vector, m is the number of design variables,
n is the number of sample points, and the corresponding actual response value is Y Response to ＝(y 1 ,y 2 ,…y i …,y n ) T ；
(3) Calling a parallel confidence lower limit optimization algorithm to optimize a finite element model of the initial unit antenna;
(4) Obtaining an optimized result Y Youyou (an instant noodle) ＝(y 1 ,y 2 ,…y i …,y n ) T Analyzing and utilizing the optimal design solution Y opt Carrying out array formation to obtain a finite element model of an initial array to be optimized;
(5) Determining design variables of a finite element model of an initial array to be optimized and using the design variables as initial sample points of a parallel confidence lower limit algorithm;
since the finite element model of the initial array to be optimized needs to consider the influence of the feed network on the whole, the design parameters of the feed network must be used as a part of the initial sample point set, and thus the initial sample point set of the array is
In the formula
s is the number of sample points of the array;
(6) Calling a parallel confidence lower limit algorithm to optimize the initial array to be optimized;
(7) Obtaining an optimization result of the antenna array, wherein:
the step (3) comprises the following steps:
(31) Setting optimization parameters;
(311) The optimization parameters include an initial sample point set X = (X) of the unit antenna to be optimized 1 ,x 2 ,...,x i ,...,x n ) T To be treatedUpper bound x of optimization variables l And a lower bound x u Expectation value of ith optimization target
And the maximum iteration number Maxnumeval, and the iteration number k =1, wherein the optimization model of the unit antenna structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
Min f(x)
S.T.g(x)≤σ max ,
h(x)≤h U
x l ≤x≤x u
in the formula:
f i representing the actual response value of the unit antenna obtained by HFSS simulation, wherein the actual response value comprises an actual gain value, an actual impedance bandwidth value and an actual circular polarization bandwidth value;
g (x) is a stress constraint condition,
σ max for the maximum allowable stress value of the unit antenna,
h (x) is the condition of the section thickness of the unit antenna,
h U the maximum allowable section thickness of the unit antenna;
(312) Setting optimization objectives
(3121) Antenna ideal gain G for calculating far field electric field distribution of unit antenna lossfree Of the formula
In the formula (I), the compound is shown in the specification,
delta (x) is the antenna structure displacement,
x is the structural design variable of the antenna, including the structure size, shape, angle;
(3122) And calculating a gain loss value delta G of the unit antenna, wherein the calculation formula is as follows:
in the formula:
G real is the actual gain value of the unit antenna;
f 1 actual gain values of the unit antennas obtained by HFSS simulation;
(313) Setting impedance bandwidth of unit antenna to be optimized
Circular polarization bandwidth of 1GHz to-be-optimized unit antenna
Is 0.2GHz;
(314) Starting optimization iteration of the unit antenna;
(32) Sampling according to an initial sample point set X = (X) of a unit antenna to be optimized by using Maximi Latin hypercube 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x of variable to be optimized l And a lower bound x u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and the K is a two-dimensional matrix of m multiplied by n
n is the number of the sample points,
m is the number of the design variables,
then, selecting the n samples in the sample space K by using a VBS script to establish a parallel element antenna finite element model, and carrying out n multiplied by p times of electromagnetic simulation on the element antenna finite element model, wherein p is the number of the targets to be optimized;
(33) Calling a finite element model of the initial unit antenna, calculating response values corresponding to the initial sample points in parallel, and storing the sample points and the corresponding response values into a sample point database;
(34) Calculating the actual response value f of each sample point by using MATLAB i And comparing the results, wherein:
f i including the gain value f in the direction of maximum radiation of the E-plane (phi =0 deg., theta =90 deg.) 1 Actual impedance bandwidth f of the element antenna 2 Actual circularly polarized bandwidth f of the element antenna 3 ，
f 2 ＝max(Δf|VSWR(f)＜1.9)
f 3 ＝max(Δf|AR(f)＜3)，
Wherein:
Δ f represents a frequency bandwidth satisfying the condition;
VSWR (f) represents a voltage standing wave ratio with frequency f as an argument;
AR (f) represents an axial ratio with frequency f as an argument;
respectively calculating the maximum bandwidth values meeting the respective corresponding conditions; when the maximum bandwidth is obtained, whether the frequency bandwidth contains a central frequency point or not must be considered, if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is discarded, and if the frequency bandwidth does not contain the central frequency point, the frequency bandwidth is updated into a sample space K;
(35) Constructing a Kriging agent model meeting a fitness function by using initial sample points and corresponding response values thereof, wherein the Kriging agent model is used as an initialization population of a genetic algorithm and is constructed in the following process,
(351) The expression of the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (a); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation of the signal,
theta is a parameter vector to be solved in the Gaussian correlation function;
(352) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which the vector is,
m is the number of the design variables,
n is the number of the sample points,
y is a response value column vector corresponding to the existing sample point;
(36) Obtaining the local optimal solution of the current agent model by using the Kriging algorithm and the minimum confidence lower limit algorithm in combination with the genetic algorithm
(37) Using genetic algorithm to solve global sampling model, and obtaining optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) And subjecting it toStoring the data into a sample point database; and the global optimal result is subjected to error analysis,
(38) Judging whether convergence occurs
If k = Maxnumeval or the optimization target termination condition f (x) is not more than 3, ending the operation, and returning the current global optimum value and the corresponding sample point; if k is less than Maxnumeval, then the step (39) is carried out;
(39) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (34).
2. The method for fast optimization of a hexagonal circularly polarized antenna array according to claim 1, wherein the step (33) comprises the steps of:
(331) Firstly, dividing initial sample points into a plurality of subdomains according to groups, distributing one subdomain for each process, and broadcasting by 0 process;
(332) Then, carrying out simulation calculation on each process in a given calculation range according to a minimum confidence lower limit algorithm;
(333) After the calculation of each process is completed, the 0 process collects and combines the response values of each group of sample points.
3. The method for rapidly optimizing a hexagonal circularly polarized antenna array according to claim 1, wherein the step (36) comprises the steps of:
(361) The method comprises the steps of obtaining an agent model meeting a fitness function by combining Kriging and a minimum confidence lower limit algorithm as an initialized population of a genetic algorithm, carrying out simulation according to a response value of the population after evolution by an evolution strategy, updating a sample library, and then carrying out sample filling criterion by combining Kriging and the minimum confidence lower limit algorithm
Selecting a sample with the minimum fitness function value to execute simulation and finding the optimal solution of the current agent model;
in the formula:
b is a balance constant used for adjusting the balance of the global search and the local search, and when b =0, the minimum confidence lower limit formula is equal to
The local searching capability is strong, when b → ∞ the global searching capability is remarkable, and at the moment
(362) The balance constant b is selected in an automatic determination mode and is determined by the following formula:
in the formula (I), the compound is shown in the specification,
n is the total number of sample points before the kth iteration,
x i ，x j is any two sample points in the sample space K,
(363) Solving a local sampling model by using a genetic algorithm to obtain an optimal solution x (k) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (k) ) And saves it to the sample point database.
4. The method for rapidly optimizing a hexagonal circularly polarized antenna array according to claim 1, wherein the error analysis in step (37) comprises the following specific steps:
(371) Selecting 5 groups of better samples in a sample database and response values thereof;
(372) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error of +/-0.1 percent, and establishing a corresponding finite element model;
(373) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(374) The error estimation value is minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
5. The method for rapidly optimizing a hexagonal circularly polarized antenna array according to claim 1, wherein the step (6) comprises the steps of:
(61) Setting optimization parameters of an initial array to be optimized;
(611) The array optimization parameters include an initial set of sample points for the array
Upper and lower bounds x 'of variables to be optimized' l And x' u And the expected value of the ith optimization objective
The optimization model of the array structure is as follows:
Find x＝[x 1 ,x 2 ,…,x m ] T
Min ΔG(x)
h(x)≤h U
x' l ≤x≤x' u
in the formula (I), the compound is shown in the specification,
ag (x) represents the gain loss value corresponding to the sample point x,
g (x) is a stress constraint condition,
σ e for the normal operating stress of the e-th cell,
h (x) is the thickness condition of the array section, and h (x) is less than or equal to 4mm;
h U the maximum allowed array cross-sectional thickness;
(612) Calculating the maximum gain loss value of the E surface, wherein the expression is
In the formula (I), the compound is shown in the specification,
y opt_gain (x) Represents an optimal gain value of the unit antenna,
y arr_gain (x) Representing the gain response value for the current sample point of the array,
n represents the number of array elements;
(62) Initial sampling according to the antenna array to be optimized using Maximin Latin hypercubeSample point set X = (X) 1 ,x 2 ,...,x i ,...,x n ) T Upper bound x 'of variables to be optimized' l And lower boundary x' u Generating a random sample as an initial sample of a proxy model of a finite element needing parallel computation, and determining a sample space K by using MATLAB according to the initial sample and the value range of each parameter, wherein K is a two-dimensional matrix of m multiplied by n, and K is a two-dimensional matrix of m multiplied by n
n is the number of sample points and the number of finite element proxy models which need to be calculated in parallel,
m is the number of the design variables,
then, selecting the n samples in the matrix K by using a VBS script to establish an array parallel proxy model, and carrying out n multiplied by p times of electromagnetic simulation on the proxy model, wherein p is the number of targets needing to be optimized;
(63) Calling a finite element model of an initial array to be optimized, calculating response values corresponding to initial sample points in parallel, and storing the sample points and the response values corresponding to the sample points into a sample point database;
(64) Obtaining actual response value of each sample point by using MATLAB
Comparing the results to obtain a gain loss value delta G (x) corresponding to the sample point x;
(65) Constructing a Kriging agent model meeting a fitness function by using the initial sample points and the corresponding response values thereof as an initialization population of a genetic algorithm, wherein the specific steps of constructing the Kriging agent model are as follows:
(651) The expression for the Kriging algorithm is as follows:
in the formula (I), the compound is shown in the specification,
beta is the regression parameter vector to be solved,
q (x) is a column vector consisting of polynomial basis functions,
z (x) is a mean of 0 and a variance of
The random process of (a); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula (I), the compound is shown in the specification,
x i ，x j is any two sample points in the sample space K,
R ij (θ,x i ,x j ) Is a function of the gaussian correlation and,
theta is a parameter vector to be solved in the Gaussian correlation function;
(652) For an arbitrary point x 0 The predicted value and the predicted variance of the agent model constructed by the Kriging algorithm have the expression as follows:
in the formula (I), the compound is shown in the specification,
q is a matrix of basis functions,
r is a correlation function matrix, and other parameter expressions are as follows:
r(x 0 )＝[R(θ,x 0 ,x 1 ),R(θ,x 0 ,x 2 ),…,R(θ,x 0 ,x n )] T
in the formula (I), the compound is shown in the specification,
x i is a vector of dimensions m in which the vector is,
m is the number of the design variables,
n is the number of the sample points,
y is a response value column vector corresponding to the existing sample point;
(66) Solving a local sampling model by using a genetic algorithm to obtain an optimal solution x (k) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (k) ) And storing the data into a sample point database;
(67) Solving a global sampling model by using a genetic algorithm to obtain an optimal solution x (global) As an update point, calling the proxy model to calculate the response value f (x) corresponding to the optimal solution (global) ) Storing the data into a sample point database, and carrying out error analysis on the global optimal result;
(68) Judging whether to converge
If k = Maxnumeval or the optimization target termination condition Δ G of the antenna array to be optimized is satisfied with or less than 3, the step (7) is entered and the current global optimum value and the corresponding sample point are returned; if k is less than Maxnumeval, the step (69) is carried out;
(69) Let k = k +1, update the sample point database with the current global optimal sample and its response value and go to step (64).
6. The method for rapidly optimizing a hexagonal circularly polarized antenna array according to claim 5, wherein the error analysis in step (67) comprises the following steps:
(671) Selecting 5 groups of better samples in a sample database and response values thereof;
(672) Taking the 5 groups of samples as initial samples, generating new estimation sample data according to the machining error +/-0.1%, and establishing a corresponding finite element model;
(673) Calling HFSS to simulate, taking the response value of the optimal sample of each group and the response value corresponding to the group of estimation samples, and solving the mean square error of each group as an error estimation value; if the optimization targets are multiple, respectively calculating the mean square error of the response value corresponding to each optimization target in the group, and then taking the mean square error of the mean square errors as the error estimation value of the group;
(674) The error estimation value is the minimum and the optimal response value and the sample corresponding to the group reaching the engineering index are the optimal design parameters.
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| CN109687092B (en) * | 2018-12-25 | 2020-12-01 | 深圳市鼎耀科技有限公司 | Low-profile omnidirectional circularly polarized antenna |
| CN113296538A (en) * | 2019-02-21 | 2021-08-24 | 重庆好德译信息技术有限公司 | Control system of high-altitude folding and unfolding mechanism |
| CN112563764B (en) * | 2021-02-19 | 2021-05-14 | 成都天锐星通科技有限公司 | Antenna design method and device and electronic equipment |
| CN113013640B (en) * | 2021-03-04 | 2022-01-28 | 西安电子科技大学 | Low RCS high-gain circularly polarized array antenna based on polarization conversion super-surface |
| CN112949137B (en) * | 2021-03-18 | 2022-10-21 | 大连理工大学 | Lightweight design method for hoisting machine head sheave based on radial basis function proxy model |
| CN115173073B (en) * | 2022-06-24 | 2023-08-29 | 四川大学 | Aperiodic artificial magnetic conductor printed dipole antenna |
| 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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