CN108829988A - A kind of hexagon circular polarized antenna array and its fast Optimization - Google Patents
A kind of hexagon circular polarized antenna array and its fast Optimization Download PDFInfo
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Abstract
The present invention relates to a kind of hexagon circular polarized antenna array and its fast Optimizations.A kind of hexagon circular polarized antenna array, including FR4 medium substrate, feeding network, reflecting surface and hexagon radiation patch.A kind of fast Optimization of hexagon circular polarized antenna array, the finite element model for including the following steps (1), establishing element antenna to be optimized；(2), the design variable of element antenna to be optimized is determined；(3), parallel confidence lower limit optimization algorithm is called, the finite element model of initial cell antenna is optimized；(4) optimum results Y=(y is obtained1,y2,…,yn)T, analyze and utilize optimization design scheme YoptIt carries out group battle array and obtains the finite element model of original array to be optimized；(5) design variable of the finite element model of original array to be optimized and the initial sample point as parallel confidence lower limit algorithm are determined；(6) parallel confidence lower limit algorithm is called to optimize original array to be optimized；(7) optimum results of aerial array are obtained.
Description
Technical field
The present invention relates to a kind of hexagon circular polarized antenna array and its fast Optimizations, belong to electromagnetic field technology neck
Domain.
Background technique
With the development of the communication technology and Internet of Things, all kinds of communication systems are for antenna and array antenna in bandwidth, increasing
The requirement of benefit, size and polarization characteristic etc. is higher and higher, the following structure, the complexity of design, the diversity of parameter
And multiplicity of requirements above etc. makes the design of antenna need to introduce the optimization algorithm of higher-dimension multiple target.Existing optimization is set
Meter method is highly dependent on the experience of designer, and when parameter is many, and the requirement to result is more, optimization algorithm is held
Easily fall into local optimum.
Traditional optimization algorithm such as " application [J] mobile communication in Li Jun genetic algorithm Antenna Design, 2000,24
(5):41-43.DOI:Described in 10.3969/j.issn.1006-1010.2000.05.009. ", genetic algorithm be it is a kind of very
Classical global optimization approach, principle is simple, is highly suitable for the optimization of antenna structure, but non-due to working as Optimal Parameters
When often more, convergence rate has certain limitation compared with slow and lower therefore traditional efficiency global optimization approach.
In order to improve design efficiency, the prioritization scheme based on agent model is gradually popularized, and it is in many section's credits
Exclusive advantage is demonstrated by analysis.For example the Kriging being previously mentioned in Chinese patent application CN201610015224.9 acts on behalf of mould
Type, Kriging agent model has the advantages that the least squares optimization, non-linear high, adaptable of unbiased esti-mator, basic herein
On, present invention employs the effective measures such as Maximin Latin hypercube sampler body and parallel computation, further increase agent model
Efficiency.
Since the electromagnetic wave that circular polarized antenna can receive any polarized electromagnetic wave and its radiation can also be any
Polarized antenna receives, therefore it is widely used in wireless communications, such as document " Huang winter jasmine, the such as Zhang Tao, Zhang Fushun
High-gain broadband circular polarization microstrip antenna array studies [J] modern electronic technology, 2009,32 (7)：22-24,28.DOI：
10.3969/j.issn.1004-373X.2009.07.007. ", broadband circle polarized array antenna according to the present invention and this text
Compared to higher relative bandwidth (44.14%).
Summary of the invention
Goal of the invention：The present invention has made improvements in view of the above-mentioned problems of the prior art, i.e., first mesh of the invention
Be to disclose a kind of hexagon circular polarized antenna array.Second object of the present invention is to disclose a kind of hexagon circular polarisation day
The fast Optimization of linear array.
Technical solution：A kind of hexagon circular polarized antenna array, including FR4 medium substrate,
It is etched with feeding network in the bottom side of the FR4 medium substrate,
It is equipped with reflecting surface in the top side of the FR4 medium substrate, is carved in the quadrangle of reflecting surface according to centrosymmetric mode
It loses there are four H-type gap,
Reflecting surface is Nian Jie with four hexagon radiation patch by medium bolt, hexagon radiation patch and reflecting surface phase
From equipped with strip crevice in the middle part of four hexagon radiation patch, which matches with the H-type gap on reflecting surface.
Further, the trunk feeder characteristic impedance of the feeding network is 50 Ω.
Further, the angle in the H-type gap on the strip crevice and reflecting surface in the middle part of hexagon radiation patch is 45 °.
Further, the spacing between hexagon radiation patch and reflecting surface is 2mm.
A kind of fast Optimization of hexagon circular polarized antenna array, including：
(1), the finite element model of element antenna to be optimized is established using HFSS；
(2) design variable of element antenna to be optimized and the initial sample point as parallel confidence lower limit algorithm are determined；
It chooses the initial sample point of parallel confidence lower limit algorithm with test design method, forms point set X and to be optimized
The upper bound x of variablelWith lower bound xu, the expression formula of Point Set X is as follows：
X=(x1,x2,...,xn)T
Wherein
xiIt is m dimensional vector, m is the number of design variable,
N is sample point number, and corresponding real response value is Y=(y1,y2,…,yn)T；
(3), parallel confidence lower limit optimization algorithm is called, the finite element model of initial cell antenna is optimized；
(4) optimum results Y=(y is obtained1,y2,…,yn)T, analyze and utilize optimization design scheme YoptA group battle array is carried out to obtain
The finite element model of original array to be optimized；
(5) design variable of the finite element model of original array to be optimized is determined and as parallel confidence lower limit algorithm
Initial sample point；
Since the finite element model of original array to be optimized needs to consider feeding network to whole influence, it is therefore necessary to
Using the design parameter of feeding network as a part of initial sample point set, therefore the initial sample point set of array is
Xarr=(x1,x2,x3,...,xn)T
In formula
xiIt is m+u dimensional vector, u is the variable number of feeding network, is responded as Yarr_opt=(y1,y2,…,yn)T；
(6) parallel confidence lower limit algorithm is called to optimize original array to be optimized；
(7) optimum results of aerial array are obtained.
Further, step (3) includes the following steps：
(31) Optimal Parameters are set；
(311) Optimal Parameters include the initial sample point set X=(x of element antenna to be optimized1,x2,...,xn)T, to excellent
Change the upper bound x of variablelWith lower bound xu, i-th optimization aim desired valueAnd maximum number of iterations Maxnumeval, and
The number of iterations k=1 is set, and the Optimized model of element antenna structure is：
Find x=[x1,x2,…,xm]T
Min f(x)
S.T.g(x)≤σmax,
h(x)≤hU
xl≤x≤xu
In formula：
fiIndicate by the HFSS element antenna emulated real response value, real response value include actual gain value,
Practical impedance bandwidth value, practical circular polarisation bandwidth value；
Indicate the desired value of the element antenna of design；
G (x) is stress constraint condition,
σmaxFor the maximum permissible stress value of element antenna,
H (x) is element antenna sectional thickness condition,
hUFor maximum allowable element antenna sectional thickness；
(312) optimization aim is set
(3121) the antenna the perfect Gain G of the far field field distribution of computing unit antennalossfree, formula is
In formula,
For far field direction of observation, θ is point of observation vector with the angle between z-axis,It is arrived for point of observation vector projection
The angle between same x-axis on the face xoy,
δ (x) is antenna structure displacement,
X is the structure design variable of antenna, including structure size, shape, angle；
(3122) the gain loss value Δ G of computing unit antenna, calculation formula are as follows：
In formula：
GrealFor the actual gain value of element antenna；
f1Actual gain value for the element antenna emulated by HFSS；
For the gain desired value of the element antenna of design, value 9.03dBi；
(313) impedance bandwidth of element antenna to be optimized is setFor the circular polarisation bandwidth of 1GHz, element antenna to be optimizedFor 0.2GHz；
(314) start the Optimized Iterative of element antenna；
(32) using Maximin latin hypercube sampling according to the initial sample point set X=of element antenna to be optimized
(x1,x2,...,xn)T, variable to be optimized upper bound xlWith lower bound xu, random sample is generated as the finite element for needing parallel computation
Agent model initial sample, sample space K is determined according to the value range of initial sample and each parameter using MATLAB,
K is the two-dimensional matrix of a m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
M is the number of parameters for needing to optimize,
Then this n sample is chosen in sample space K using VBS script establish parallel element antenna finite element mould
Type carries out n × p Electromagnetic Simulation to the finite element model of element antenna, and p is the target number for needing to optimize；
(33) finite element model of calling initial cell antenna, the corresponding response of the initial sample point of parallel computation, and will
These sample points and its corresponding response are saved in sample point database；
(34) the real response value f of each sample point is calculated using MATLABiAnd result is compared, wherein：
fiYield value f including (φ=0 °, θ=90 °) in the greatest irradiation direction of the face E1, the practical impedance band of element antenna
Wide f2, the practical circular polarisation bandwidth f of element antenna3,
f2=max (Δ f | VSWR (f) < 1.9)
f3=max (Δ f | AR (f) < 3),
Wherein：
Δ f indicates the frequency bandwidth for meeting condition；
VSWR (f) is indicated using frequency f as the voltage standing wave ratio of independent variable；
AR (f) is indicated using frequency f as the axis of independent variable ratio；
Calculate separately the maximum bandwidth value for meeting respective respective conditions；The frequency range must be first considered when taking maximum bandwidth
It whether include center frequency point；Cast out if not including center frequency point, if comprising updating in sample space K；
(35) mould is acted on behalf of using the Kriging that initial sample point and its corresponding response construction meet fitness function
Type, initialization population of the Kriging agent model as GA algorithm, construction process is as follows,
(351) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(352) for arbitrary point x0, using Kriging algorithm construction agent model predicted value and prediction variance,
Expression formula is：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(36) using Kriging algorithm, GA algorithm obtains the part of current agent model in conjunction with minimum confidence lower limit algorithm
Optimal solution
(37) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)It is updated as one
Point calls agent model to calculate the corresponding response f (x of the optimal solution(global)), and be saved into sample point database；
And global optimum's result is subjected to error analysis,
(38) judge whether to restrain
If k=Maxnumeval or when meeting optimization aim termination condition f (x)≤3, terminate this operation, and return
Return current global optimum and its corresponding sample point；Step (39) are transferred to if k < Maxnumeval；
(39) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(34)。
Further, step (33) includes the following steps：
(331) initial sample point is divided into several subdomains by group first, for each process distribute a subdomain, and by 0 into
Journey broadcast；
(332) then by each process in given computer capacity, emulation meter is carried out according to confidence lower limit algorithm is minimized
It calculates；
(333) after each process calculates, the response of each group sample point is collected simultaneously merging data by 0 process.
Further, step (36) includes the following steps：
(361) it combines to obtain the agent model for meeting fitness function with minimum confidence lower limit algorithm using Kriging
As the initialization population of GA algorithm, evolution strategy is to be emulated according to the response of population after evolution, updates sample database, so
Criterion is filled with the sample that minimum confidence lower limit algorithm combines by Kriging afterwards
The sample with minimum fitness function value is selected to execute the optimal solution for emulating and finding current agent model；
In formula：
It is the predicted value of unknown point,
For indicating that prediction standard is poor,
B is the equilibrium constant, for adjusting the balance of global search and local search, as b=0, is minimized under confidence
Limit formula is equal toLocal search ability is strong, and as b → ∞, ability of searching optimum is significant, at this time
(362) equilibrium constant b is chosen by the way of automatically determining, and is determined by following formula：
(i, j=1,2 ..., N, i ≠ j)
In formula,
N is sample point sum before kth time iteration,
For the equilibrium constant automatically determined,
xi, xjIt is any two sample point in sample space K,
(363) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point,
Agent model is called to calculate the corresponding response f (x of the optimal solution(k)), and be saved into sample point database.
Further, the error analysis in step (37) the specific steps are：
(371) preferably 5 groups of samples and its response in sample database are chosen；
(372) with this 5 groups of samples for initial sample, new sample estimates data are generated simultaneously according to mismachining tolerance ± 0.1%
Establish corresponding finite element model；
(373) HFSS is called to be emulated and taken the response and this group of sample estimates pair of each group of optimal sample
The response answered asks every group of mean square error as error estimate；If optimization aim has multiple, found out in the group respectively
After the mean square error of response corresponding to each optimization aim, then take its root mean square whole as this group these mean square errors
The error estimate of body；
(374) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective i.e.
For optimal design parameters.
Further, step (6) includes the following steps：
(61) Optimal Parameters of original array to be optimized are set；
(611) array optimization parameter includes the initial sample point set X of arrayarr=(x1,x2,...,xn)T, variable to be optimized
Bound x 'lAnd x'uAnd the desired value of i-th of optimization aimThe Optimized model of array structure is：
In formula,
The corresponding gain loss value of Δ G (x) representative sample point x,
The maximum gain loss function in a direction that array needs to optimize is represented,
G (x) is stress constraint condition,
σeFor the normal work stress of e-th of unit,
For average allowable stress value,
H (x) is array sectional thickness condition, h (x)≤4mm；
hUFor maximum allowable array sectional thickness；
(612) face E maximum gain penalty values are calculated, expression formula is
In formula,
yopt_gain(x) optimal gain values of representative unit antenna,
yarr_gain(x) the gain response value of the current sample point of array is represented,
N represents array element quantity；
(62) using Maximin latin hypercube sampling according to the initial sample point set X=of aerial array to be optimized
(x1,x2,...,xn)T, variable to be optimized upper bound x 'lWith lower bound x'uRandom sample is generated as needing the limited of parallel computation
The initial sample of the agent model of member, determines sample space according to the value range of initial sample and each parameter using MATLAB
K, K are the two-dimensional matrixes of a m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
The number of parameters that m needs to optimize,
Then this n sample is chosen in matrix K using VBS script and establish the parallel agent model of array, to agent model
N × p Electromagnetic Simulation is carried out, p is the target number for needing to optimize；
(63) finite element model of calling original array to be optimized, the corresponding response of the initial sample point of parallel computation,
And these sample points and its corresponding response are saved in sample point database；
(64) the real response value of each sample point is obtained using MATLABAnd result is compared, and obtain sample
The corresponding gain loss value Δ G (x) of this x；
(65) meet the Kriging agent model of fitness function using initial sample point and its corresponding response construction
As the initialization population of GA algorithm, constructing Kriging agent model, specific step is as follows：
(651) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(652) for arbitrary point x0, using Kriging algorithm construction agent model predicted value and prediction variance,
Expression formula is：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(66) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point, adjust
The corresponding response f (x of the optimal solution is calculated with agent model(k)), and be saved into sample point database；
(67) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)It is updated as one
Point calls agent model to calculate the corresponding response f (x of the optimal solution(global)), and be saved into sample point database,
And global optimum's result is subjected to error analysis；
(68) judge whether to restrain
If k=Maxnumeval or when meeting the optimization aim termination condition Δ G≤3 of aerial array to be optimized, into
Enter step (7) and returns to current global optimum and its corresponding sample point；Step is transferred to if k < Maxnumeval
(69)；
(69) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(64)。
Further, specific step is as follows for the error analysis in step (67)：
(671) preferably 5 groups of samples and its response in sample database are chosen；
(672) with this 5 groups of samples for initial sample, new sample estimates data are generated simultaneously according to mismachining tolerance ± 0.1%
Establish corresponding finite element model；
(673) HFSS is called to be emulated and taken the response and this group of sample estimates pair of each group of optimal sample
The response answered asks every group of mean square error as error estimate；If optimization aim has multiple, found out in the group respectively
After the mean square error of response corresponding to each optimization aim, then take its root mean square whole as this group these mean square errors
The error estimate of body；
(674) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective i.e.
For optimal design parameters.
Beneficial effect：A kind of hexagon circular polarized antenna array disclosed by the invention and its fast Optimization have following
Beneficial effect：
1. can given design objective and under the conditions of the optimal structural parameters of Automatic-searching, entire optimization process is not required to
Manual intervention is wanted, and optimum results are true and reliable；
2. the present invention provides help for complicated antenna structure, large-scale antenna Array Design, a day knot is greatly reduced
The time of structure parameter optimization and the efficiency for improving Antenna Design；
3. element antenna designed by the present invention and array performance are good, it is suitable for the application of ISM band；
4. the present invention has great importance and value to engineer application, that has expanded MATLAB-HFSS-API uses model
It encloses, allows to be used widely in the optimization of structure is complicated array.
Detailed description of the invention
Fig. 1 is the explosive view of the finite element model of element antenna；
Fig. 2 is a kind of explosive view of hexagon circular polarized antenna array disclosed by the invention；
Fig. 3 is a kind of perspective view of hexagon circular polarized antenna array disclosed by the invention；
Fig. 4 is a kind of flow diagram of the optimization method of hexagon circular polarized antenna array disclosed by the invention；
Fig. 5 is the flow diagram that parallel confidence lower limit optimization algorithm optimizes antenna；
The flow diagram of Fig. 6 parallel computation mechanism；
The optimal return loss and 3-dB axis that Fig. 7 a is element antenna are than figure；
Fig. 7 b is the optimal direction figure of element antenna；
Fig. 8 a is a kind of optimal 3-dB axis of hexagon circular polarized antenna array than figure；
Fig. 8 b is a kind of optimal return loss plot of hexagon circular polarized antenna array；
Fig. 8 c is a kind of optimal direction figure of hexagon circular polarized antenna array；
Wherein：
1- hexagon radiation patch
2- reflecting surface
3-FR4 medium substrate
4- feeding network
Specific embodiment：
Detailed description of specific embodiments of the present invention below.
As shown in Figures 2 and 3, a kind of hexagon circular polarized antenna array, including FR4 medium substrate 3,
It is etched with feeding network 4 in the bottom side of FR4 medium substrate 3,
It is equipped with reflecting surface 2 in the top side of FR4 medium substrate 3, is etched in the quadrangle of reflecting surface 2 according to centrosymmetric mode
There are four H-type gap,
Reflecting surface 2 is Nian Jie with four hexagon radiation patch 1 by medium bolt, hexagon radiation patch 1 and reflecting surface 2
Mutually from equipped with strip crevice in the middle part of four hexagon radiation patch 1, which matches with the H-type gap on reflecting surface 2
It closes.
Further, the trunk feeder characteristic impedance of feeding network 4 is 50 Ω.
Further, the strip crevice at 1 middle part of hexagon radiation patch and the angle in the H-type gap on reflecting surface 2 are
45°。
Further, the spacing between hexagon radiation patch 1 and reflecting surface 2 is 2mm.
As shown in figure 4, a kind of fast Optimization of hexagon circular polarized antenna array, including：
(1), the finite element model of element antenna to be optimized is established using HFSS (structure is as shown in Figure 1)；
(2) design variable of element antenna to be optimized and the initial sample point as parallel confidence lower limit algorithm are determined；
It chooses the initial sample point of parallel confidence lower limit algorithm with test design method, forms point set X and to be optimized
The upper bound x of variablelWith lower bound xu, the expression formula of Point Set X is as follows：
X=(x1,x2,...,xn)T
Wherein
xiIt is m dimensional vector, m is the number of design variable,
N is sample point number, and corresponding real response value is Y=(y1,y2,…,yn)T；
(3), parallel confidence lower limit optimization algorithm is called, the finite element model of initial cell antenna is optimized；
(4) optimum results Y=(y is obtained1,y2,…,yn)T, analyze and utilize optimization design scheme YoptA group battle array is carried out to obtain
The finite element model of original array to be optimized；
(5) design variable of the finite element model of original array to be optimized is determined and as parallel confidence lower limit algorithm
Initial sample point；
Since the finite element model of original array to be optimized needs to consider feeding network to whole influence, it is therefore necessary to
Using the design parameter of feeding network as a part of initial sample point set, therefore the initial sample point set of array is
Xarr=(x1,x2,x3,...,xn)T
In formula
xiIt is m+u dimensional vector, u is the variable number of feeding network, is responded as Yarr_opt=(y1,y2,…,yn)T；
(6) parallel confidence lower limit algorithm is called to optimize original array to be optimized；
(7) optimum results of aerial array are obtained.
Further, as shown in figure 5, step (3) includes the following steps：
(31) Optimal Parameters are set；
(311) Optimal Parameters include the initial sample point set X=(x of element antenna to be optimized1,x2,...,xn)T, to excellent
Change the upper bound x of variablelWith lower bound xu, i-th optimization aim desired valueAnd maximum number of iterations Maxnumeval, and
The number of iterations k=1 is set, and the Optimized model of element antenna structure is：
Find x=[x1,x2,…,xm]T
Min f(x)
S.T.g(x)≤σmax,
h(x)≤hU
xl≤x≤xu
In formula：
fiIndicate by the HFSS element antenna emulated real response value, real response value include actual gain value,
Practical impedance bandwidth value, practical circular polarisation bandwidth value；
Indicate the desired value of the element antenna of design；
G (x) is stress constraint condition,
σmaxFor the maximum permissible stress value of element antenna,
H (x) is element antenna sectional thickness condition,
hUFor maximum allowable element antenna sectional thickness；
(312) optimization aim is set
(3121) the antenna the perfect Gain G of the far field field distribution of computing unit antennalossfree, formula is
In formula,
For far field direction of observation, θ is point of observation vector with the angle between z-axis,It is arrived for point of observation vector projection
The angle between same x-axis on the face xoy,
δ (x) is antenna structure displacement,
X is the structure design variable of antenna, including structure size, shape, angle；
(3122) the gain loss value Δ G of computing unit antenna, calculation formula are as follows：
In formula：
GrealFor the actual gain value of element antenna；
f1Actual gain value for the element antenna emulated by HFSS；
For the gain desired value of the element antenna of design, value 9.03dBi；
(313) impedance bandwidth of element antenna to be optimized is setFor the circular polarisation bandwidth of 1GHz, element antenna to be optimizedFor 0.2GHz；
(314) start the Optimized Iterative of element antenna；
(32) using Maximin latin hypercube sampling according to the initial sample point set X=of element antenna to be optimized
(x1,x2,...,xn)T, variable to be optimized upper bound xlWith lower bound xu, random sample is generated as the finite element for needing parallel computation
Agent model initial sample, sample space K is determined according to the value range of initial sample and each parameter using MATLAB,
K is the two-dimensional matrix of a m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
M is the number of parameters for needing to optimize,
Then this n sample is chosen in sample space K using VBS script establish parallel element antenna finite element mould
Type carries out n × p Electromagnetic Simulation to the finite element model of element antenna, and p is the target number for needing to optimize；
(33) finite element model of calling initial cell antenna, the corresponding response of the initial sample point of parallel computation, and will
These sample points and its corresponding response are saved in sample point database；
(34) the real response value f of each sample point is calculated using MATLABiAnd result is compared, wherein：
fiYield value f including (φ=0 °, θ=90 °) in the greatest irradiation direction of the face E1, the practical impedance band of element antenna
Wide f2, the practical circular polarisation bandwidth f of element antenna3,
f2=max (Δ f | VSWR (f) < 1.9)
f3=max (Δ f | AR (f) < 3),
Wherein：
Δ f indicates the frequency bandwidth for meeting condition；
VSWR (f) is indicated using frequency f as the voltage standing wave ratio of independent variable；
AR (f) is indicated using frequency f as the axis of independent variable ratio；
Calculate separately the maximum bandwidth value for meeting respective respective conditions；The frequency range must be first considered when taking maximum bandwidth
It whether include center frequency point；Cast out if not including center frequency point, if comprising updating in sample space K；
(35) mould is acted on behalf of using the Kriging that initial sample point and its corresponding response construction meet fitness function
Type, initialization population of the Kriging agent model as GA algorithm, construction process is as follows,
(351) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(352) for arbitrary point x0, using Kriging algorithm construction agent model predicted value and prediction variance,
Expression formula is：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(36) using Kriging algorithm, GA algorithm obtains the part of current agent model in conjunction with minimum confidence lower limit algorithm
Optimal solution
(37) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)It is updated as one
Point calls agent model to calculate the corresponding response f (x of the optimal solution(global)), and be saved into sample point database,
And global optimum's result is subjected to error analysis；
(38) judge whether to restrain
If k=Maxnumeval or when meeting optimization aim termination condition f (x)≤3, terminate this operation, and return
Return current global optimum and its corresponding sample point；Step (39) are transferred to if k < Maxnumeval；
(39) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(34)。
Further, as shown in fig. 6, step (33) includes the following steps：
(331) initial sample point is divided into several subdomains by group first, for each process distribute a subdomain, and by 0 into
Journey broadcast；
(332) then by each process in given computer capacity, emulation meter is carried out according to confidence lower limit algorithm is minimized
It calculates；
(333) after each process calculates, the response of each group sample point is collected simultaneously merging data by 0 process.
Further, step (36) includes the following steps：
(361) it combines to obtain the agent model for meeting fitness function with minimum confidence lower limit algorithm using Kriging
As the initialization population of GA algorithm, evolution strategy is to be emulated according to the response of population after evolution, updates sample database, so
Criterion is filled with the sample that minimum confidence lower limit algorithm combines by Kriging afterwards
The sample with minimum fitness function value is selected to execute the optimal solution for emulating and finding current agent model；
In formula：
It is the predicted value of unknown point,
For indicating that prediction standard is poor,
B is the equilibrium constant, for adjusting the balance of global search and local search, as b=0, is minimized under confidence
Limit formula is equal toLocal search ability is strong, and as b → ∞, ability of searching optimum is significant, at this time
(362) equilibrium constant b is chosen by the way of automatically determining, and is determined by following formula：
(i, j=1,2 ..., N, i ≠ j)
In formula,
N is sample point sum before kth time iteration,
For the equilibrium constant automatically determined,
xi, xjIt is any two sample point in sample space K,
(363) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point,
Agent model is called to calculate the corresponding response f (x of the optimal solution(k)), and be saved into sample point database.
Further, step (error analysis in 37 the specific steps are：
(371) preferably 5 groups of samples and its response in sample database are chosen；
(372) with this 5 groups of samples for initial sample, new sample estimates data are generated simultaneously according to mismachining tolerance ± 0.1%
Establish corresponding finite element model；
(373) HFSS is called to be emulated and taken the response and this group of sample estimates pair of each group of optimal sample
The response answered asks every group of mean square error as error estimate；If optimization aim has multiple, found out in the group respectively
After the mean square error of response corresponding to each optimization aim, then take its root mean square whole as this group these mean square errors
The error estimate of body；
(374) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective i.e.
For optimal design parameters.
Further, step (6) includes the following steps：
(61) Optimal Parameters of original array to be optimized are set；
(611) array optimization parameter includes the initial sample point set X of arrayarr=(x1,x2,...,xn)T, variable to be optimized
Bound x 'lAnd x'uAnd the desired value of i-th of optimization aimThe Optimized model of array structure is：
In formula,
The corresponding gain loss value of Δ G (x) representative sample point x,
The maximum gain loss function in a direction that array needs to optimize is represented,
G (x) is stress constraint condition,
σeFor the normal work stress of e-th of unit,
For average allowable stress value,
H (x) is array sectional thickness condition, h (x)≤4mm；
hUFor maximum allowable array sectional thickness；
(612) face E maximum gain penalty values are calculated, expression formula is
In formula,
yopt_gain(x) optimal gain values of representative unit antenna,
yarr_gain(x) the gain response value of the current sample point of array is represented,
N represents array element quantity；
(62) using Maximin latin hypercube sampling according to the initial sample point set X=of aerial array to be optimized
(x1,x2,...,xn)T, variable to be optimized upper bound x 'lWith lower bound x'uRandom sample is generated as needing the limited of parallel computation
The initial sample of the agent model of member, determines sample space according to the value range of initial sample and each parameter using MATLAB
K, K are the two-dimensional matrixes of a m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
The number of parameters that m needs to optimize,
Then this n sample is chosen in matrix K using VBS script and establish the parallel agent model of array, to agent model
N × p Electromagnetic Simulation is carried out, p is the target number for needing to optimize；
(63) finite element model of calling original array to be optimized, the corresponding response of the initial sample point of parallel computation,
And these sample points and its corresponding response are saved in sample point database；
(64) the real response value of each sample point is obtained using MATLABAnd result is compared, and obtain sample
The corresponding gain loss value Δ G (x) of this x；
(65) meet the Kriging agent model of fitness function using initial sample point and its corresponding response construction
As the initialization population of GA algorithm, constructing Kriging agent model, specific step is as follows：
(651) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(652) for arbitrary point x0, using Kriging algorithm construction agent model predicted value and prediction variance,
Expression formula is：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(66) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point, adjust
The corresponding response f (x of the optimal solution is calculated with agent model(k)), and be saved into sample point database；
(67) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)It is updated as one
Point calls agent model to calculate the corresponding response f (x of the optimal solution(global)), and be saved into sample point database,
And global optimum's result is subjected to error analysis；
(68) judge whether to restrain
If k=Maxnumeval or when meeting the optimization aim termination condition Δ G≤3 of aerial array to be optimized, into
Enter step (7) and returns to current global optimum and its corresponding sample point；Step is transferred to if k < Maxnumeval
(69)；
(69) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(64)。
Further, specific step is as follows for the error analysis in step (67)：
(671) preferably 5 groups of samples and its response in sample database are chosen；
(672) with this 5 groups of samples for initial sample, new sample estimates data are generated simultaneously according to mismachining tolerance ± 0.1%
Establish corresponding finite element model；
(673) HFSS is called to be emulated and taken the response and this group of sample estimates pair of each group of optimal sample
The response answered asks every group of mean square error as error estimate；If optimization aim has multiple, found out in the group respectively
After the mean square error of response corresponding to each optimization aim, then take its root mean square whole as this group these mean square errors
The error estimate of body；
(674) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective i.e.
For optimal design parameters.
Antenna according to the present invention is a kind of broadband hexagon circular polarization microstrip antenna array column using slot-coupled, tool
Body structure is as shown in Figures 2 and 3, and center working frequency points are 5.8GHz, and impedance bandwidth is 4.48GHz~7.04GHz
(44.14%), axial ratio bandwidth be 5.4GHz~5.99GHz (10.2%), meet entire ISM band (5.725GHz~
Requirement 5.875GHz), the gain of (φ=0 °, θ=90 °) is 11.155dBi in the greatest irradiation direction of the face E.The impedance bandwidth
It is wider as the aerial array (23%) of radiation patch than using circle, and circular polarisation performance changes greatly compared to having very much therewith (8.9%)
It is kind.
Table 1
Note：Here Step refers to iterative steps；Non- calling finite element analysis software number when each iteration, calls limited
First software for calculation
Number is determined by the sample size that each iteration generates, rather than simple multiple proportion.Array example and this phase
Together.
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 provides two kinds of algorithms used by optimization antenna element and is compared, and one is serial minimum confidence lower limits to calculate
Method, one is parallel minimum confidence lower limit algorithms.The optimization aim of unit is similar with array optimization general objective, and expression formula is
Specially yopt_gain(x)=9.03,Table 2 provide using parallel with it is serial excellent
The structure size result of change method optimization antenna element (target function value is smaller, indicates its target closer to setting).It
Line unit optimization result is as shown in Figure 1.
Optimize example
The present invention is optimized using novel hexagon circular polarized antenna array structure mentioned above as optimization object
Design variable number is 15, respectively x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
Due to needing to compare with serial algorithm, here in order to improve efficiency and (reduce serial optimization program runtime), optimize mesh
Mark is only set as at the maximum direction of directional diagram the gain loss value Δ G of (φ=0 °, θ=90 °) (x-axis is straight up), then
Compare other results in the sample responses value of optimization to take suitably.Serial optimization program and parallel optimization program use all
All, termination condition is all the same for relevant parameter.Serial parallel optimizes the result of program and compares, and sees the table 3 and table of attached drawing document
4.Array optimization result is as described in Fig. 7 a, Fig. 7 b, Fig. 8 a, Fig. 8 b and Fig. 8 c.
Table 3
Table 4
| Serial optimization program | Parallel optimization program | |
| Optimal result | 3.68 | 2.85 |
| Meet termination condition iterative algebra | 100 | 95 |
| Optimize program the spent time | 81948 seconds | 43422 seconds |
Embodiments of the present invention are elaborated above.But present invention is not limited to the embodiments described above,
Technical field those of ordinary skill within the scope of knowledge, can also do without departing from the purpose of the present invention
Various change out.
Claims (10)
1. a kind of hexagon circular polarized antenna array, which is characterized in that including FR4 medium substrate,
It is etched with feeding network in the bottom side of the FR4 medium substrate,
It is equipped with reflecting surface in the top side of the FR4 medium substrate, is etched in the quadrangle of reflecting surface according to centrosymmetric mode
Four H-type gaps,
Reflecting surface is Nian Jie with four hexagon radiation patch by medium bolt, and hexagon radiation patch is with reflecting surface mutually from four
Strip crevice is equipped in the middle part of a hexagon radiation patch, which matches with the H-type gap on reflecting surface.
2. a kind of hexagon circular polarized antenna array according to claim 1, which is characterized in that the master of the feeding network
Dry feeder line characteristic impedance is 50 Ω.
3. a kind of hexagon circular polarized antenna array according to claim 1, which is characterized in that in hexagon radiation patch
The angle in the H-type gap on the strip crevice and reflecting surface in portion is 45 °.
4. a kind of fast Optimization of hexagon circular polarized antenna array, which is characterized in that include the following steps：
(1), the finite element model of element antenna to be optimized is established using HFSS；
(2), the design variable of element antenna to be optimized and the initial sample point as parallel confidence lower limit algorithm are determined；
The initial sample point of parallel confidence lower limit algorithm is chosen with test design method, forms point set X and variable to be optimized
Upper bound xlWith lower bound xu, the expression formula of Point Set X is as follows：
X=(x1,x2,...,xn)T
Wherein
xiIt is m dimensional vector, m is the number of design variable,
N is sample point number, and corresponding real response value is Y=(y1,y2,…,yn)T；
(3), parallel confidence lower limit optimization algorithm is called, the finite element model of initial cell antenna is optimized；
(4) optimum results Y=(y is obtained1,y2,…,yn)T, analyze and utilize optimization design scheme YoptA group battle array is carried out to obtain to excellent
The finite element model of the original array of change；
(5) design variable of the finite element model of original array to be optimized is determined and as the initial of parallel confidence lower limit algorithm
Sample point；
Since the finite element model of original array to be optimized needs to consider feeding network to whole influence, it is therefore necessary to will present
The a part of the design parameter of electric network as initial sample point set, therefore the initial sample point set of array is
Xarr=(x1,x2,x3,...,xn)T
In formula
xiIt is m+u dimensional vector, u is the variable number of feeding network, is responded as Yarr_opt=(y1,y2,…,yn)T；
(6) parallel confidence lower limit algorithm is called to optimize original array to be optimized；
(7) optimum results of aerial array are obtained.
5. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 4, which is characterized in that step
Suddenly (3) include the following steps：
(31) Optimal Parameters are set；
(311) Optimal Parameters include the initial sample point set X=(x of element antenna to be optimized1,x2,...,xn)T, change to be optimized
The upper bound x of amountlWith lower bound xu, i-th optimization aim desired valueAnd maximum number of iterations Maxnumeval, and be arranged
The Optimized model of the number of iterations k=1, element antenna structure is：
In formula：
fiIndicate to include actual gain value, practical resistance by the real response value of the HFSS element antenna emulated, real response value
Anti- bandwidth value, practical circular polarisation bandwidth value；
Indicate the desired value of the element antenna of design；
G (x) is stress constraint condition,
σmaxFor the maximum permissible stress value of element antenna,
H (x) is element antenna sectional thickness condition,
hUFor maximum allowable element antenna sectional thickness；
(312) optimization aim is set
(3121) the antenna the perfect Gain G of the far field field distribution of computing unit antennalossfree, formula is
In formula,
For far field direction of observation, θ is point of observation vector with the angle between z-axis,For point of observation vector projection to the face xoy
On same x-axis between angle,
δ (x) is antenna structure displacement,
X is the structure design variable of antenna, including structure size, shape, angle；
(3122) the gain loss value Δ G of computing unit antenna, calculation formula are as follows：
In formula：
GrealFor the actual gain value of element antenna；
f1Actual gain value for the element antenna emulated by HFSS；
For the gain desired value of the element antenna of design, value 9.03dBi；
(313) impedance bandwidth of element antenna to be optimized is setFor the circular polarisation bandwidth of 1GHz, element antenna to be optimizedFor
0.2GHz；
(314) start the Optimized Iterative of element antenna；
(32) using Maximin latin hypercube sampling according to the initial sample point set X=(x of element antenna to be optimized1,
x2,...,xn)T, variable to be optimized upper bound xlWith lower bound xu, generate generation of the random sample as the finite element for needing parallel computation
The initial sample for managing model, determines that sample space K, K are according to the value range of initial sample and each parameter using MATLAB
The two-dimensional matrix of one m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
M is the number of parameters for needing to optimize,
Then this n sample is chosen in sample space K using VBS script establish parallel element antenna finite element model, it is right
The finite element model of element antenna carries out n × p Electromagnetic Simulation, and p is the target number for needing to optimize；
(33) call initial cell antenna finite element model, the corresponding response of the initial sample point of parallel computation, and by these
Sample point and its corresponding response are saved in sample point database；
(34) the real response value f of each sample point is calculated using MATLABiAnd result is compared, wherein：
fiYield value f including (φ=0 °, θ=90 °) in the greatest irradiation direction of the face E1, the practical impedance bandwidth f of element antenna2,
The practical circular polarisation bandwidth f of element antenna3,
f2=max (Δ f | VSWR (f) < 1.9)
f3=max (Δ f | AR (f) < 3),
Wherein：
Δ f indicates the frequency bandwidth for meeting condition；
VSWR (f) is indicated using frequency f as the voltage standing wave ratio of independent variable；
AR (f) is indicated using frequency f as the axis of independent variable ratio；
Calculate separately the maximum bandwidth value for meeting respective respective conditions；First whether the frequency range must be considered when taking maximum bandwidth
Include center frequency point；Cast out if not including center frequency point, if comprising updating in sample space K；
(35) meet the Kriging agent model of fitness function using initial sample point and its corresponding response construction,
Initialization population of the Kriging agent model as GA algorithm, construction process is as follows,
(351) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(352) for arbitrary point x0, utilize the predicted value and prediction variance of the agent model of Kriging algorithm construction, expression formula
For：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(36) using Kriging algorithm, GA algorithm obtains the local optimum of current agent model in conjunction with minimum confidence lower limit algorithm
Solution
(37) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)As a update point, adjust
The corresponding response f (x of the optimal solution is calculated with agent model(global)), and be saved into sample point database；And it will be complete
Office's optimal result carries out error analysis,
(38) judge whether to restrain
If k=Maxnumeval or when meeting optimization aim termination condition f (x)≤3, terminate this operation, and return and work as
Preceding global optimum and its corresponding sample point；Step (39) are transferred to if k < Maxnumeval；
(39) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(34)。
6. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 5, which is characterized in that step
Suddenly (33) include the following steps：
(331) initial sample point is divided into several subdomains by group first, distributes a subdomain for each process, and wide by 0 process
It broadcasts；
(332) then by each process in given computer capacity, simulation calculation is carried out according to confidence lower limit algorithm is minimized；
(333) after each process calculates, the response of each group sample point is collected simultaneously merging data by 0 process.
7. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 5, which is characterized in that step
Suddenly (36) include the following steps：
(361) combine to obtain using Kriging with minimum confidence lower limit algorithm the agent model for meeting fitness function as
The initialization population of GA algorithm, evolution strategy be emulated according to the response of population after evolution, update sample database, then by
Kriging fills criterion with the sample that minimum confidence lower limit algorithm combines
The sample with minimum fitness function value is selected to execute the optimal solution for emulating and finding current agent model；
In formula：
It is the predicted value of unknown point,
For indicating that prediction standard is poor,
B is the equilibrium constant, and for adjusting the balance of global search and local search, as b=0, it is public to minimize confidence lower limit
Formula is equal toLocal search ability is strong, and as b → ∞, ability of searching optimum is significant, at this time
(362) equilibrium constant b is chosen by the way of automatically determining, and is determined by following formula：
(i, j=1,2 ..., N, i ≠ j)
In formula,
N is sample point sum before kth time iteration,
For the equilibrium constant automatically determined,
xi, xjIt is any two sample point in sample space K,
(363) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point, call
Agent model calculates the corresponding response f (x of the optimal solution(k)), and be saved into sample point database.
8. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 5, which is characterized in that step
Suddenly the error analysis in (37) the specific steps are：
(371) preferably 5 groups of samples and its response in sample database are chosen；
(372) with this 5 groups of samples for initial sample, new sample estimates data is generated according to mismachining tolerance ± 0.1% and are established
Corresponding finite element model；
(373) HFSS is called to be emulated and taken the response of each group of optimal sample and this group of sample estimates corresponding
Response asks every group of mean square error as error estimate；If optimization aim has multiple, find out in the group respectively each
After the mean square error of response corresponding to optimization aim, then take its root mean square as this group whole these mean square errors
Error estimate；
(374) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective as most
Excellent design parameter.
9. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 4, which is characterized in that step
Suddenly (6) include the following steps：
(61) Optimal Parameters of original array to be optimized are set；
(611) array optimization parameter includes the initial sample point set X of arrayarr=(x1,x2,...,xn)T, variable to be optimized it is upper
Lower bound x 'lWith x 'uAnd the desired value of i-th of optimization aimThe Optimized model of array structure is：
Find x=[x1,x2,…,xm]T
MinΔG(x)
h(x)≤hU
x′l≤x≤x′u
In formula,
The corresponding gain loss value of Δ G (x) representative sample point x,
The maximum gain loss function in a direction that array needs to optimize is represented,
G (x) is stress constraint condition,
σeFor the normal work stress of e-th of unit,
For average allowable stress value,
H (x) is array sectional thickness condition, h (x)≤4mm；
hUFor maximum allowable array sectional thickness；
(612) face E maximum gain penalty values are calculated, expression formula is
In formula,
yopt_gain(x) optimal gain values of representative unit antenna,
yarr_gain(x) the gain response value of the current sample point of array is represented,
N represents array element quantity；
(62) using Maximin latin hypercube sampling according to the initial sample point set X=(x of aerial array to be optimized1,
x2,...,xn)T, variable to be optimized upper bound x 'lWith lower bound x 'uRandom sample is generated as the finite element for needing parallel computation
The initial sample of agent model determines sample space K, K according to the value range of initial sample and each parameter using MATLAB
It is the two-dimensional matrix of a m × n, wherein
N is sample point number, and needs the number of the agent model of the finite element of parallel computation,
The number of parameters that m needs to optimize,
Then this n sample being chosen in matrix K using VBS script and establishing the parallel agent model of array, n is carried out to agent model
× p Electromagnetic Simulation, p are the target number for needing to optimize；
(63) finite element model of calling original array to be optimized, the corresponding response of the initial sample point of parallel computation, and will
These sample points and its corresponding response are saved in sample point database；
(64) the real response value of each sample point is obtained using MATLABAnd result is compared, and obtain sample point x
Corresponding gain loss value Δ G (x)；
(65) using initial sample point and its corresponding response construction meet the Kriging agent model of fitness function as
The initialization population of GA algorithm, specific step is as follows for construction Kriging agent model：
(651) expression formula of Kriging algorithm is as follows：
In formula,
β is regression parameter vector to be asked,
The column vector that q (x) is made of polynomial basis function,
Z (x) is that a mean value is 0, and variance isRandom process；Statistical nature is as follows：
E [Z (x)]=0
In formula,
xi, xjIt is any two sample point in sample space K,
Rij(θ,xi,xj) it is Gauss correlation function,
θ is parameter vector to be asked in Gauss correlation function；
(652) for arbitrary point x0, utilize the predicted value and prediction variance of the agent model of Kriging algorithm construction, expression formula
For：
In formula,
Q is basic function matrix,
R is correlation function matrix, and other parameters expression formula is as follows：
r(x0)=[R (θ, x0,x1),R(θ,x0,x2),…,R(θ,x0,xn)]T
In formula,
xiIt is m dimensional vector,
M is design variable number,
N is the number of existing sample point,
Y is the existing corresponding response column vector of sample point；
(66) spot sampling's model, obtained optimal solution x are solved using genetic algorithm(k)As a update point, generation is called
Reason model calculates the corresponding response f (x of the optimal solution(k)), and be saved into sample point database；
(67) global sampling pattern, obtained optimal solution x are solved using genetic algorithm(global)As a update point, adjust
The corresponding response f (x of the optimal solution is calculated with agent model(global)), and be saved into sample point database, and will be complete
Office's optimal result carries out error analysis；
(68) judge whether to restrain
If k=Maxnumeval or when meeting the optimization aim termination condition Δ G≤3 of aerial array to be optimized, into step
Suddenly (7) and current global optimum and its corresponding sample point are returned to；Step (69) are transferred to if k < Maxnumeval；
(69) k=k+1 is enabled, update sample point database using current global optimum's sample and its response and turns to step
(64)。
10. a kind of fast Optimization of hexagon circular polarized antenna array according to claim 9, which is characterized in that
Specific step is as follows for error analysis in step (67)：
(671) preferably 5 groups of samples and its response in sample database are chosen；
(672) with this 5 groups of samples for initial sample, new sample estimates data is generated according to mismachining tolerance ± 0.1% and are established
Corresponding finite element model；
(673) HFSS is called to be emulated and taken the response of each group of optimal sample and this group of sample estimates corresponding
Response asks every group of mean square error as error estimate；If optimization aim has multiple, find out in the group respectively each
After the mean square error of response corresponding to optimization aim, then take its root mean square as this group whole these mean square errors
Error estimate；
(674) error estimate is minimum and reaches optimal response value and sample corresponding to that group of engineering objective as most
Excellent design parameter.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109687092A (en) * | 2018-12-25 | 2019-04-26 | 深圳市鼎耀科技有限公司 | A kind of low section omnidirectional circular-polarized antenna |
| CN110011032A (en) * | 2019-02-21 | 2019-07-12 | 成都中技智慧企业管理咨询有限公司 | A kind of open/close control device and method of airborne emergency communication system antenna |
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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 |
| CN109687092A (en) * | 2018-12-25 | 2019-04-26 | 深圳市鼎耀科技有限公司 | A kind of low section omnidirectional circular-polarized antenna |
| CN110011032B (en) * | 2019-02-21 | 2021-08-27 | 唐尚禹 | Retraction control device and method for airborne emergency communication system antenna |
| CN110011032A (en) * | 2019-02-21 | 2019-07-12 | 成都中技智慧企业管理咨询有限公司 | A kind of open/close control device and method of airborne emergency communication system antenna |
| CN112563764A (en) * | 2021-02-19 | 2021-03-26 | 成都天锐星通科技有限公司 | Antenna design method and device and electronic equipment |
| 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 |
| WO2022174689A1 (en) * | 2021-02-19 | 2022-08-25 | 成都天锐星通科技有限公司 | Antenna design method and apparatus, and electronic device |
| CN113013640A (en) * | 2021-03-04 | 2021-06-22 | 西安电子科技大学 | Low RCS high-gain circularly polarized array antenna based on polarization conversion super-surface |
| CN112949137A (en) * | 2021-03-18 | 2021-06-11 | 大连理工大学 | Lightweight design method for hoisting machine head sheave based on radial basis function proxy model |
| 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 |
| CN115173073A (en) * | 2022-06-24 | 2022-10-11 | 四川大学 | Aperiodic artificial magnetic conductor printed dipole antenna |
| CN115173073B (en) * | 2022-06-24 | 2023-08-29 | 四川大学 | Aperiodic artificial magnetic conductor printed dipole antenna |
| CN117574783A (en) * | 2024-01-16 | 2024-02-20 | 天津工业大学 | Antenna optimization method, device, equipment and medium based on depth Gaussian process |
| 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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