CN105205253B - A kind of optimization method of bare cloth circular antenna array - Google Patents
A kind of optimization method of bare cloth circular antenna array Download PDFInfo
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Abstract
The invention discloses a kind of optimization methods of bare cloth circular antenna array, include the following steps：(1) round-about way is used to generate individual structure initial population；(2) hereditary pretreatment is carried out to population；(3) generalized crossover is carried out to population and broad sense makes a variation；(4) hereditary post-processing is carried out to population, according to fitness quality selective advantage individual；(5) iteration optimization obtains optimum individual and minimum peak sidelobe.The circular array of this method optimization is characterized in array element non-uniform Distribution on Circular Aperture, it is not limited on auxiliary annulus, this method can utilize the degree of freedom of array element to a greater extent, more efficient than traditional genetic algorithm, and aerial array can be made to obtain lower sidelobe level.
Description
Technical field
The present invention relates to array antenna design methods, specifically realize the dilute of more design constraints using Revised genetic algorithum
Cloth circular antenna array designs, and by means of the equidistant auxiliary annulus designed on circular aperture, is designed using circle ring array characteristic
Bare cloth circular array antenna makes it obtain peak sidelobe low as possible.
Background technology
Circular array antenna is one of most important array antenna type in multiple element antenna type, is widely used in communication neck
Domain and radio astronomy field.Circular antenna array has ideal direction character in its azimuth direction, while its is circular
Structure feature makes its wave beam, antenna gain and other property retentions basicly stable.Because more than circular antenna array has
Feature makes it be widely used in many engineering practices, but circular antenna array has relatively high peak sidelobe,
Therefore circular antenna array design has become important research topic.
Circular array antenna is pressed there are two types of the distributions of array element：One is array element from the annulus grid of the rule at a distance of half-wavelength
Upper sparse Sparse Array；Another kind is that antenna element is setting the random bare cloth within the scope of certain pore size of its array element spacing of timing restrictions
Thinned arrays.In recent years, has there is Statistic optimization in peak side-lobe Sparse Array of good performance in order to obtain, dynamic is advised
Draw the integrated approach such as method, genetic algorithm, simulated annealing, particle swarm optimization.And both at home and abroad for the Thinned arrays of degree of freedom bigger
Rarely has research.So the research of the Low sidelobe level to bare cloth circular array antenna, has very real meaning.
Invention content
The purpose of the present invention provides a kind of Revised genetic algorithum to optimize bare cloth circular antenna array, in constraint array element
Under the constraint of number, aperture and minimum spacing, the peak sidelobe of bare cloth circular array antenna is reduced as possible.
In order to achieve the above object, technical scheme is as follows.
In the case of constraining aperture, array element number and minimum spacing, it is based on Revised genetic algorithum, passes through secondary indication
The method of individual, using broad sense genetic manipulation, heredity pretreatment and heredity post-processing optimize element position, no longer constrain
Array element must be positioned on auxiliary annulus, increases the degree of freedom of structuring the formation of each array element, obtains lower peak sidelobe.
Model：On planar rondure bore, the model by the radiation characteristic of element position computing array antenna is：
Wherein
cosαn=sin θ cos (φ-φn)；U=sin θ cos φ；0≤θ≤π
V=sin θ sin φ；0≤φ≤2π；
λ is operation wavelength；
K=2 π/λ；
N is the number of optimized variable, i.e. array element sum；
0≤θ≤π andRespectively pitch angle and azimuth；
InFor excitation；
ψnFor the excitation phase of array element；
rnFor the polar coordinates radius of array element n；
φnFor angles of the array element n under polar coordinate system, θ is azimuth, and φ is pitch angle.
Constraint array element number is N, and under conditions of minimum array element spacing d, all array element has identical excitation, institute in aperture
To assume all array element In=1, ψn=0.Position by optimizing array element obtains lower peak sidelobe, optimizes letter
Number is：
Wherein D=[d1,d2,…,dN], fitness function is expressed as：
Object function is：
f(d1,d2,…,dN)=min { H (D) } (4)
Wherein dm、dnIndicate that m, the coordinate of n array element, d are minimum array element interval constraints, R is aperture, and Z is positive integer
Collection, FmaxMain lobe peak value, the θ of secondary lobe area E (θ, φ) andInterval be all areas in addition to main lobe region.
Detailed step is as follows：
1：The generation of initial population
In order to preferably optimize the element position of bare cloth circle ring array using the degree of freedom of array element.Using between complex vector C
Connect statement optimization individual.Fig. 2 is the uniform rings array of aperture r=(a+1) d, and a ∈ Z are annulus numbers, and d is array element spacing.
Under conditions of constraining the minimum spacing d of array element, the distribution of array element is indefinite on each annulus.I.e., it is assumed that adjacent meeting
The spacing of array element is not less than under conditions of d, is distributed k on i-th of annulusiA array element, kiIt can be indicated with following formula：
Wherein riIt is the radius of i-th of annulus,For downward rounding.Structure as shown in Figure 2, in known annulus hole
It is indefinite to have array element distribution under diameter.Assuming that minimum λ/2 array element spacing d=of constraint, can calculate the maximum on each annulus
Array number kiWith corresponding phase angular separation ρi, i.e., the angular separation of adjacent array element on same annulus, as shown in Table 1.
Table one
Because of kiA array element is evenly distributed on i-th of annulus, so ρiFor：
Complex vector C can be expressed as：
Wherein a=r/d-1 is annulus number, ki(i=1,2 ..., are a) the maximum array number on i-th of annulus, ρi(i=
1,2 ..., it is a) to have k on i-th of annulusiAverage angular separation when a array element.C constrains d and angular separation ρ with array elementiIt is related, therefore
Also related with array element number, so C can be considered constrained vector again.Auxiliary vector F on the basis of CtFollowing sub-step can be passed through
Suddenly it obtains:
1.1, assume oneReal number column vector M0, element value arranges from small to large in [0,0.5 λ] range
Sequence.By M0It is divided into a sections.Kth1A array element is in M0First segment, second segment has k2A array element, i.e., from (k1+ 1) (k is arrived1+k2+ 1) k2
A array element.So a sections contain M0Last kaA array element.Because array element is random distribution in each section, therefore is obtained
NewTie up random vector：
Vectorial η has following feature：Array element on each section is random distribution by size, and still (k+1) section is each
A element is not less than any one element in k sections.
1.2, assume a random vector [ξ1,ξ2,…,ξa]T, element value is embodied as in [0,2 π] range：
ζ=[ξ1,…,ξ1,ξ2,…,ξ2,…ξa,…,ξa]T (9)
First segment has k1A ξ1, and so on.It can thus be concluded that ζ also hasDimension, also there is a sections.The feature of ζ is different point
Element is the random number not waited in section, but the element in each section is equal.
1.3, on the basis of complex vector C, auxiliary vector FtAs shown in formula (10), using the element of η as plural number mould,
It is added on the corresponding moulds of complex vector C, using ζ elements as argument of a complex number, is added on the corresponding arguments of complex vector C, therefore assist
Vectorial FtIt can be expressed as：
It can prove FtMeet three design constraints, the degree of freedom of array element is also utilized well.
1.4, the bare cloth vector that individual vector u is made of N number of non-zero battle array member, andLocating vector S is able to record
Auxiliary vector FtIn which element be retained, locating vector is defined as follows：
Define 1：For vectorial I, if q-th of array element is sparse, with the relevant value for searching plain vector of q-th of array element
It is ' 0 ', is otherwise ' 1 '.
In locating vector FtOn the basis of, pass through sparse auxiliary vector FtIt can obtain individual vector I：
I=S.*Ft (11)
In view of FtAll contain with SThe one-dimensional array of a element, FtIndividual vector I can be obtained with S scalar multiplications.
Such as locating vector S is：
Therefore individual vector I can be expressed as：
It can prove that individual vector I is feasible solution in solution space, therefore it can all variables as an optimization.
Step 2：It independently repeats above operation M times, the initial population U being made of M I can be obtained.This unique life
At method, it ensure that each of initial population individual meets element number of array, the constraint of array aperture and minimum array element spacing.
Step 3：Heredity processing
Traditional genetic algorithm cannot directly describe individual, therefore will will produce infeasible solution.Infeasible solution in order to prevent
Generation, need the operation for changing some genetic algorithms.Modified operatings of genetic algorithm is known as generalized crossover and broad sense by us
Variation.
Define 2：Array element matrix：Array element matrix GA, each row are all a constraint matrix C, therefore are hadRow and M row.
Define 3：Population constraint matrix：Population constraint matrix GMIt is according to population searching matrix SM, from GAIn separate
's.
GM=SM.*GA (14)
Define 4：Heredity pretreatment：Before carrying out generalized crossover and broad sense variation, heredity is pre-processed from parent population U1
In obtain hereditary information matrix P
Wherein GMIt is population U1Population constraint matrix, | | indicate plural number modulo operation,For the operating angle of plural number
Symbol.
Define 5：Hereditary post-processing operation：After generalized crossover and broad sense variation, heredity post-processing is believed from heredity again
Cease construction population U in matrix P2
Wherein GMIt is and the relevant population constraint matrixes of population P.Offspring flocks P is from parent population P by wide simultaneously
It is obtained after justice is intersected and broad sense makes a variation.
Step 4：Generalized crossover operates and broad sense mutation operation
Intersecting with traditional genetic algorithm, generalized crossover is used for exchanging the element of the non-zero mould of two chromosome, so
The element of element mould is reset afterwards.Reset operation makes mould vector meet the property of η.Detailed reset operation is as follows：Mould vector, i.e.,
| P | column vector, be segmented into a sections, find out each section of minimum element first.Assuming that i-th section of least member is w, then
It is compared with the mould of each element of (i-1) section, if the mould of some element of (i-1) is more than w, uses w
It replaces.Similarly, after executing generalized crossover, in order to meet ζ properties, two column vectorsElement need to reset.
Broad sense variation changes the hereditary information of parent individuality.First one is randomly choosed from a row of hereditary information matrix P
A element is used if this element is 0It substitutes, riThe element maximum norm planted less than i sections is more than element minimum modulus, φi∈
[0,2π].If the element of selection is non-zero, substituted with 0.In this process, non-in order to meet the constraint of element number of array
The number of neutral element must remain unchanged.Secondly, resetting also makes the property that vector meets η, and angle vector is made to meet ζ's
Property.Finally, angularly amount can reconstruct hereditary information matrix P (the new hereditary information for representing offspring) to mould vector sum.
Traditional genetic algorithm directly carries out intersecting on the coding of optimized variable and mutation operation, and generalized crossover and wide
Justice variation is operated on hereditary information matrix P, not direct operation optimization variable, it is derivative from genetic process and
Come, S, η and the ζ of parent can be used to replace；On the other hand, including traditional genetic algorithm, the two broad sense genetic manipulations are all
It can ensure that the hereditary information of offspring is effective, i.e. Sson,ηsonAnd ζsonIt is effective.Operation described above, we term it wide
Justice is intersected and broad sense mutation operation.Generalized crossover and broad sense mutation operation so that correcting Genetic algorithm searching faster has preferably
Convergence property.
It is pre-processed by heredity, generalized crossover and broad sense variation and heredity post-processing optimize initial population, and iteration obtains most
Excellent individual obtains lower peak sidelobe.The present invention proposes on the basis of uniform rings array, utilizes sparse vector
Secondary indication individual, instead of the method for the directly description individual of traditional genetic algorithm.Use broad sense genetic manipulation, heredity pretreatment
It can ensure that individuals all in an iterative process is all feasible solution with heredity post-processing so that the efficiency for correcting genetic algorithm is big
It is big to improve.
Description of the drawings
The model of Fig. 1 bare cloth planar circular arrays
Uniform 9 circle ring arrays of Fig. 2
The antenna pattern of Fig. 3 examples
Fig. 4 examples work as φ=0 °, φ=45 °, and far-field pattern when φ=90 °
The array element distribution map of Fig. 5 examples
Specific implementation mode
It elaborates below to optimal enforcement mode of the present invention
The embodiment of the present invention is given below.By attached drawing it is found that the present invention to aperture and bare cloth rate by optimizing battle array
First position, it was demonstrated that the validity and feasibility of method.Fig. 1 is the illustraton of model of bare cloth circular loop antenna array.The example is that optimization is set
Meter parameter is the λ of aperture r≤4.5, and bare cloth rate 70% and array number are the bare cloth circular loop antenna battle array of 184 (removing the array element on the center of circle)
The element position of row.Fig. 3 be optimal planar circular array far field radiation pattern, in φ planes PSLL be-
22.723dB, worst PSLL are -22.051dB.Fig. 4 is in φ=0 °, φ=45 °, and far-field pattern when φ=90 °.
Optimal array element distribution is as shown in Figure 5.
Claims (4)
1. a kind of optimization method of bare cloth circular antenna array, includes the following steps：
Step 1：The individual of intermediate description is generated, initial population is built；
Wherein, steps are as follows for the initial population generation：
Step 1.1：In the case where meeting constraint of the adjacent array element spacing not less than d, it is distributed k on i-th of annulusiA array element,Wherein riIt is the radius of i-th of annulus,For downward rounding, because of kiA array element is evenly distributed on i-th
On a annulus, thus on same annulus adjacent array element angular separation ρiForThus construction complex vector C is：
Wherein, a=(R/d) -1 is annulus number, kiFor the maximum array number on i-th of annulus；
Step 1.2：By the auxiliary vector F constructedtInitial individuals are obtained with locating vector S；
ConstructionTie up random vectorFirst segment has k1A element, a sections have ka
A element, for all elements value in [0,0.5 λ] range, λ is operation wavelength, and the element on each section is random distribution by size
, and each element of (k+1) section is not less than any one element in k sections；
Construct a random vector [ξ1,ξ2,L,ξa]T, for each element value in [0,2 π] range, the first element repeats k1It is secondary, a-th
Element repeats kaIt is secondary, it is embodied as ζ=[ξ1,L,ξ1,ξ2,L,ξ2,L,ξa,L,ξa]T, andDimensional vector is characterized as：No
Element is unequal in same segmentation, but element is equal in each section；
On the basis of complex vector C, using the element of η as plural number mould, be added on the corresponding moulds of complex vector C, using ζ elements as
Argument of a complex number is added on the corresponding arguments of complex vector C, therefore auxiliary vector FtIt can be expressed as：
Step 1.3：On the basis of locating vector S, pass through scalar multiplication auxiliary vector FtIt can obtain individual vector I：
I=S.*Ft
FtAll contain with SThe one-dimensional vector of a element, FtThe individual vector I of bare cloth form can be obtained with S scalar multiplications；
It independently repeats above operation M times, the initial population being made of M I can be obtained；
Step 2：Selective advantage individual, and hereditary pretreatment is carried out to population；
Step 3:Generalized crossover and broad sense mutation operation are carried out to population；
Step 4：Hereditary post-processing is carried out to population, completes hereditary information extraction；
Step 5：Iteration executes the operation optimization population of step 2~4, finally obtains the optimal array of sidelobe level.
2. the method as described in claim 1 is unique in that, by auxiliary annulus, realize a kind of array element on Circular Aperture
Unequal distance round bare cloth antenna array design method, and be not necessarily limited each array element must design auxiliary annulus on, ensure battle array
It arranges aperture, array element interval and array element sum and meets given constraint.
3. the method as described in claim 1, which is characterized in that the feature of genetic manipulation is as follows：
(1) object of genetic manipulation is not parent population itself, and the genetic manipulation object of this method is hereditary information matrix P, is
It is especially extracted from parent population, correspondingly, before calculating fitness value, new population need to be reconstructed, restructuring procedure is extraction process
Inverse process；
(2) content of genetic manipulation is different from basic genetic algorithmic, is made a variation using generalized crossover and broad sense,
Generalized crossover is used for exchanging the element of two individual non-zero moulds, then also to reset the sequence of element；Detailed resetting
Operation is as follows：It finds out in a section, finds out each section of minimum element first, then by each element of itself and previous adjacent segment
Mould be compared, if the mould of some element of the last period is big, exchange；
Broad sense variation changes the hereditary information of parent individuality, and an element is randomly choosed first from hereditary matrix column, if
This element is 0, is usedIt substitutes, it is desirable that riLess than this section in a section maximum norm and be more than minimum modulus, φiIt is 0 to 2 π ranges
Random value, if selection element be non-zero, with 0 substitute, in this process, the number of nonzero element remains unchanged.
4. the method as described in claim 1, which is characterized in that the function for calculating fitness is：
Wherein, electric field strength E is the secondary lobe area of antenna pattern function when element position is arbitrary on disk bore, electric-field strength
The specific computation model for spending E is as follows：
Wherein, d1,d2,…,dNIt is the position coordinates expression of array element
cosαn=sin θ cos (φ-φn)；
N is the number of optimized variable, i.e. array element sum；
λ is operation wavelength；
K=2 π/λ；
θ、Respectively pitch angle and azimuth；
InFor excitation；
ψnFor the phase of array element；
rnFor the radius in the polar coordinates of array element n；
φnFor angle positions of the array element n in polar coordinate system；
dm、dnIndicate that m, the coordinate of n array element, d are minimum array element interval constraints, R is aperture, and Z is positive integer collection；
U=sin θ cos φ；0≤θ≤π；
V=sin θ sin φ；0≤φ≤2π；
FFmaxMain lobe peak value, the θ in E (θ, φ) andInterval be all secondary lobe regions in addition to main lobe region.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0238964A2 (en) * | 1986-03-24 | 1987-09-30 | Siemens Aktiengesellschaft | Cut-off filter for integrated optics |
| CN1725556A (en) * | 2005-07-07 | 2006-01-25 | 哈尔滨工业大学 | Intelligent antenna compound wave beam forming method based on genetic algorithm |
| CN104900988A (en) * | 2015-05-21 | 2015-09-09 | 电子科技大学 | Method for designing thin cloth circular antenna array through changing auxiliary grid circle radius |
-
2015
- 2015-09-18 CN CN201510601278.9A patent/CN105205253B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0238964A2 (en) * | 1986-03-24 | 1987-09-30 | Siemens Aktiengesellschaft | Cut-off filter for integrated optics |
| CN1725556A (en) * | 2005-07-07 | 2006-01-25 | 哈尔滨工业大学 | Intelligent antenna compound wave beam forming method based on genetic algorithm |
| CN104900988A (en) * | 2015-05-21 | 2015-09-09 | 电子科技大学 | Method for designing thin cloth circular antenna array through changing auxiliary grid circle radius |
Non-Patent Citations (1)
| Title |
|---|
| 稀布天线阵列的优化布阵技术研究;陈客松;《中国优秀博士学位论文全文数据库》;20080115;第17-25、58-60、95、98页 * |
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