CN105760632B - A kind of design method of the bare cloth concentric loop battle array based on Bessel function - Google Patents
A kind of design method of the bare cloth concentric loop battle array based on Bessel function Download PDFInfo
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Abstract
The design method for the bare cloth concentric loop battle array based on Bessel function that the present invention provides a kind of, which comprises using the annular radii of bare cloth concentric loop battle array as Optimal Parameters, several weeds individual is randomly generated, constitutes initial population；For each weeds individual, the minimum array number on annulus is determined according to annular radii, so that it is determined that the Peak sidelobe level of bare cloth ring array, the fitness value as weeds individual；Thus seed is generated to each weeds individual；The offspring individual composed by optimized variable annular radii and its parent individuality are put together and form new population, all individuals in the population are ranked up from small to large according to fitness value, the initial population that the individual of specified quantity is evolved as next round before only retaining eliminates remaining individual；The process is repeated, until meeting stopping criterion for iteration, exports the optimum individual in the last one population.
Description
Technical field
The present invention relates to radar, radio astronomy and satellite communication fields more particularly to a kind of based on Bessel function
The design method of bare cloth concentric loop battle array.
Background technique
Concentric loop battle array is widely used because of the unchanged covering of its orientation and 360 ° of orientation scan capability
In radar, radio astronomy and satellite communication (bibliography [1]: O.M.Bucci, S.Perna, and D.Pinchera, "
Synthesis of Isophoric Sparse Arrays Allowing Zoomable Beams and Arbitrary
Coverage in Satellite Communications,"IEEE Trans.Antennas Propagat,vol.63,
) etc. pp.1445-1457,2015 in fields.In the case that uniform concentric loop battle array refers to without excitation weighting, on concentric loop
Array element is uniformly distributed, and concentric loop is also uniformly distributed along radial.Although a burst of array structure of uniform concentric loop is simple, side
There is high directivity coefficient and well circle symmetry characteristic to figure, but be also up under its peak sidelobe best-case-
17.5dB.It is well known that reduce the peak sidelobe of uniform battle array, there are mainly two types of modes: first is that amplitude weighting, second is that position
Set weighting.But amplitude weighting will certainly be such that feeding network complicates, and when array is as transmitting antenna, non-homogeneous excitation meeting
Making all amplifiers of front end of emission can not work in same optimum state, to reduce the radiation efficiency (ginseng of entire array
Document [2]: O.M.Bucci, T.Isernia, and A.F.Morabito are examined, " An effective deterministic
procedure for the synthesis of shaped beams by means of uniform-amplitude
linear sparse arrays,"Antennas and Propagation,IEEE Transactions on,vol.61,
pp.169-175,2013).However, in the case where uniform excitation, using position weighting i.e. it is non-homogeneous structure the formation by the way of, not only
Array element number needed for the reduction of minor level may be implemented and can reduce array antenna to a certain extent simplifies feedback
Source network mitigates antenna weights, to realize the reduction of entire antenna system cost and cost.
For concentric loop battle array, the i.e. sparse concentric loop battle array of two kinds of non-homogeneous forms being primarily present at present and bare cloth
Concentric loop battle array (bibliography [3]: R.L.Haupt, " Optimized Element Spacing for Low Sidelobe
Concentric Ring Arrays,”IEEE Trans.Antennas Propagat.,vol.56,no.1,pp.266-268,
Jan.2008).Sparse concentric loop battle array refers to the excitation array element picked out and worked from uniform concentric loop battle array, i.e., uniformly same
All array elements have a two states in heart ring array: " open/work " state and " close/do not work " state, then therefrom choosing
It selects the array element to work and constitutes sparse concentric loop battle array (bibliography [4]: U.Singh and T.Kamal, " Synthesis
of thinned planar concentric circular antenna arrays using biogeography-based
optimisation,"IET Microwav.Antennas Propag.,vol.6,pp.822-829,May.2012).Compared to
Uniform concentric loop battle array, the sparse concentric loop battle array of even now can be reduced needed for array while reducing minor level
Array element number, but due to the asymmetry on sparse concentric loop battle array array structure, its directional diagram is caused no longer as uniformly same
Heart ring array has round symmetry characteristic like that.For concentric loop battle array, such non-homogeneous structure the formation to sacrifice directional diagram is used
Circle symmetry characteristic is not optimal come the reduction for realizing minor lobe and array element number.This is because concentric loop battle array may be implemented
Circle symmetry direction figure, this is its intrinsic advantages and intrinsic propesties as a kind of Typical Planar battle array, once the directional diagram integrated
Without circle symmetry characteristic, then can be substituted completely if the planar array of other forms such as rectangle plane battle array, concentric loop
The advantage of battle array can be weakened severely.In order to improve deficiency existing for sparse concentric loop battle array, propose in recent years another non-equal
Even battle array, that is, bare cloth concentric loop battle array.This kind of battle array refers to multiple concentric loops radially non-uniform Distribution, and array element is then along concentric loop
It is uniformly distributed, the radius by optimizing concentric loop is realized with the array number on corresponding annulus to be made while round symmetry direction figure
Minor level and array element number further decrease (bibliography [5]: O.M.Bucci and D.Pinchera, " A
Generalized Hybrid Approach for the Synthesis of Uniform Amplitude Pencil
Beam Ring-Arrays,"Antennas and Propagation,IEEE Transactions on,vol.60,
pp.174-183,2012)。
Currently, it is relatively fewer for the research of bare cloth concentric loop battle array, and in order to guarantee to generate round symmetry direction figure, it is existing
Research method be broadly divided into two classes: first is that in confinement ring adjacent member uniform intervals d=0.5 λ, then radius be rmAnnulus
On array number Nm=floor (2 π rm/ d) (array number can only be integer, and function floor (x) indicates to be rounded downwards), thus only
Optimization annular radii come integrate have circle symmetry direction figure bare cloth concentric loop battle array (bibliography [3]: R.L.Haupt,
“Optimized Element Spacing for Low Sidelobe Concentric Ring Arrays,”IEEE
Trans.Antennas Propagat., vol.56, no.1, pp.266-268, Jan.2008, bibliography [6]: Y.Jiang,
and S.Zhang,“An Innovative Strategy for Synthesis of Uniformly Weighted
Circular Aperture Antenna Array Based on the Weighting Density Method”IEEE,
Antennas Wireless Propa.Lett., vol.12, pp.725-728,2013), the major defect of such methods is phase
The spacing constraint of 0.5 λ of adjacent member is more so as to cause array number needed for array；Second is that first calculating concentric circles using related algorithm
Then the excitation amplitude of the radius of ring and equivalent continuous current ring utilizes evenly spaced constant amplitude array element discretization continuous current
Ring, it is possible thereby to determine evenly arranged array number (bibliography [5]: O.M.Bucci and on each annulus
D.Pinchera,"A Generalized Hybrid Approach for the Synthesis of Uniform
Amplitude Pencil Beam Ring-Arrays,"IEEE Trans.Antennas Propagat.,vol.60,
Pp.174-183,2012, bibliography [7]: M.Carlin, G.Oliveri, and A.Massa, " Hybrid BCS-
Deterministic Approach for Sparse Concentric Ring Isophoric Arrays,”IEEE
Trans.Antennas Propagat., vol.63, no.1, pp.378-383, Jan.2015, bibliography [8]: X.Zhao,
Q.Yang and Y.Zhang,“A Hybrid Method for the Optimal Synthesis of 3-D Patterns
of Sparse Concentric Ring Arrays,”IEEE Trans.Antennas Propagat.,vol.64,no.2,
pp.515-524,Feb.2016.).The above method can be realized optimization while being uniformly distributed array element number on annular radii and ring,
But it is required to the array element sum of previously given array, and only selects reasonable array element sum, could integrate and meet directional diagram out
It is required that bare cloth concentric loop battle array, therefore, these methods need just find out reasonable array element sum by test of many times, in turn
It just can determine that the distribution situation of array element on corresponding annulus.
Summary of the invention
It is an object of the invention to overcome drawbacks described above present in the design method of current bare cloth concentric loop battle array, propose
A kind of design method of the bare cloth concentric loop battle array based on Bessel function, this method are established using Bessel function characteristic
The numerical relation of annular radii and its minimum array number, so that the polymorphic type variable for optimizing annular radii and array number for one is excellent
Change problem is converted into the single categorical variable optimization problem for only optimizing annular radii, greatly reduces the calculation amount of optimization process
With the complexity of Optimized model.At the same time, this method ensure that circle symmetry direction figure reduces peak side-lobe while generation
Level reduces array element number, reduces entire antenna system cost and cost.
To achieve the goals above, the design for the bare cloth concentric loop battle array based on Bessel function that the invention proposes a kind of
Method, which comprises using the annular radii of bare cloth concentric loop battle array as Optimal Parameters, P weeds individual, structure is randomly generated
At initial population；For each weeds individual, the minimum array number on annulus is determined according to annular radii, to calculate ring array
Directional diagram determines the Peak sidelobe level of bare cloth ring array, the fitness value as weeds individual；Thus to each weeds
Body generates seed；The offspring individual composed by optimized variable annular radii and its parent individuality are put together and form new kind
Group is ranked up all individuals in the population according to fitness value from small to large, and the individual of specified quantity is made before only retaining
For the initial population that next round is evolved, remaining individual is eliminated；The process is repeated, it is defeated until meeting stopping criterion for iteration
Optimum individual in the last one population out.
In above-mentioned technical proposal, the method is specifically included:
Step 1) is randomly generated P weeds individual, constitutes just using the annular radii of bare cloth concentric loop battle array as Optimal Parameters
Beginning population；And it is initial population that current population, which is arranged,；
Step 2) determines the minimum array number on annulus according to annular radii, to calculate circle for each weeds individual
Ring battle array directional diagram, determines the Peak sidelobe level of bare cloth ring array, the fitness value as weeds individual；
Each weeds individual in the current population of step 3) generates seed, the diffusion of kind subspace；
Step 4) calculates the fitness value for each seed that each weeds individual generates, and will be by optimized variable annular radii
Composed offspring individual and its parent individuality, which are put together, forms new population, and it is current population that the population, which is arranged,；
Step 5) judges whether individual amount reaches preset maximum value P in current populationmaxIf in current population
Individual amount is less than Pmax, it is transferred to step 3), i.e., all individuals in current population continue breeding and generate new seed, if currently
Individual amount in population is more than or equal to Pmax, it is transferred to step 6)；
All individuals in current population are ranked up by step 6) from small to large according to fitness value, P before only retainingmax
The initial population that the individual of a fitness value is evolved as next round eliminates remaining individual；It is to work as that this initial population, which is arranged,
Preceding population；
Step 7) judges whether to meet termination condition: if the number of iterations reaches maximum number of iterations itermaxOr current kind
Individual maximum adaptation angle value and minimum fitness value meet in group | fmax-fmin|≤10-6, if it is satisfied, being transferred to step 8)；It is no
Then, it is transferred to step 3), next round is executed and evolves；
Step 8) exports optimum individual, and the optimum individual is the individual in current population, the design of bare cloth concentric loop battle array
It finishes.
In above-mentioned technical proposal, the specific implementation process of the step 1) are as follows:
In front circular aperture radius R, annulus number M and adjacent ring minimum spacing drIn the case where given, by annular radii
As optimized variable, i.e. r=[r1,r2,…rM] as the weeds individual in invasive weed optimization algorithm；In optimization process, it is
Guarantee that array bore is constant, and meet the minimum spacing of adjacent ring, annular radii generates as follows:
Wherein random sub-vector a=[a1,a2,…aM-1], element aiIt is [0, R-Mdr] in random number, and a1≤a2≤…
≤aM-1, then the random sub-vector is generated by following formula:
A=sort ((R-Mdr)·rand(1,M-1)) (2)
According to above-mentioned formula (1) and (2), P such weeds individuals are randomly generated, constitute initial population P0=[r1,
r2,…rP]。
In above-mentioned technical proposal, the step 2) is specifically included:
Step 201) calculates the minimum array element of each annulus for each group of weeds being made of annular radii individual
Number；
For each group of weeds being made of annular radii individual, radius rmAnnulus on minimum array number Nm's
Determine that method is as follows:
Nm=round (β rm) (3)
Wherein, β=2 π/λ is wave number, and λ is；Round () is round function；
It calculatesWhereinCharacterization independent variable is β rmNmRank Bessel function；
IfThen enable Nm=Nm+ 1, then calculateUntilLast
NmFor required value.
Step 202) calculates the directional diagram of the bare cloth concentric loop battle array according to array number in annular radii and ring:
Wherein, the azimuth position of each array element is on ringThe direction
The Bessel series expression formula of figure are as follows:
In optimization process, directional diagram is calculated by above-mentioned Bessel series expression formula；
Step 203) determines Thinned arrays Peak sidelobe level according to directional diagram, and as the adaptation of corresponding weeds individual
Angle value f.
In above-mentioned technical proposal, the step 3) is specifically included:
Step 301) determines that each weeds individual in current population produces seed bearing number；
Each weeds individual in population produces seed bearing number by minimax in its fitness value f and current population
Fitness value decision, and it is in a linear relationship with the fitness value of itself, and the seed number that each weeds individual generates is Nseed:
Wherein, SmaxWith SminRespectively indicate the maximum seed number and minimum seed number that single weeds can be generated, fmax、fmin
Respectively indicate maximum adaptation angle value individual in current population and minimum fitness value；Floor () function is to be rounded letter downwards
Number；
Step 302) calculates the standard deviation of the kind subspace diffusion of weeds individual；
The seed that weeds individual generates is diffused near its parent according to normal distribution random number, and the mean value of normal distribution
For the position of its parent weeds, corresponding standard deviation sigma are as follows:
In above formula, iter is current iteration number, and initial value is set as 1, itermaxIt is greatest iteration set by algorithm
Number, σinitialWith σfinialRespectively preset standard deviation initial value and end value, n are the non-linear modulation factor；
Step 303) produces seed bearing number according to each weeds individual and standard deviation generates seed；
K-th of seed that p-th of weeds individual generates in population are as follows:
rp,k=N (rp,σ2) (8)
And meet the element in seed
Each seed represents one group of new annular radii.
The present invention has the advantages that
1, method of the invention is closed using the numerical value that Bessel function characteristic establishes annular radii and its minimum array number
System, so that converting one for a polymorphic type variable optimization problem about annular radii and array number only optimizes annular radii
Single categorical variable optimization problem, greatly reduce the calculation amount of optimization process and the complexity of Optimized model, realize simultaneously
Optimize while annular radii is with array number；
2, the bare cloth concentric loop battle array of method of the invention design can realize directional diagram entire with array element as few as possible
Orientation it is unchanged covering be orientation aboutCircularly symmetric radiation characteristic, and peak side-lobe electricity can be effectively reduced
It is flat；
3, method of the invention, which ensure that, reduces peak sidelobe while round symmetry direction figure generates, reduce annulus
The array element number of battle array, reduces entire antenna system cost and cost.
Detailed description of the invention
Fig. 1 is bare cloth concentric loop Array Model of the invention；
Fig. 2 is the bare cloth concentric loop battle array design method flow chart of the invention based on Bessel function；
Fig. 3 is the array element layout for the bare cloth concentric loop battle array that the present invention designs on the round mouth face that radius is 5 λ；
Fig. 4 is bare cloth concentric loop battle array orientation section directional diagram given by Fig. 3；
Fig. 5 is the array element layout for the bare cloth concentric loop battle array that the present invention integrates on round mouth face of the radius by 25 λ；
Fig. 6 is bare cloth concentric loop battle array orientation section directional diagram given by Fig. 5.
Specific embodiment
The invention proposes a kind of novel design methods to realize bare cloth concentric loop battle array, by optimizing bare cloth circle simultaneously
Ring radius is uniformly distributed array element number with it to realize there is Sidelobe, the circle for expecting beam angle using array element as few as possible
Symmetry direction figure.According to array factor theory it is found that bare cloth concentric loop battle array pattern function can be launched into Bessel function
The summation of series will make directional diagram have circle symmetry characteristic well, i.e., be only the function of pitching angle theta and and azimuthIt is unrelated,
It so requires only to retain zeroth order major event in the Bessel function summation formula of equal value of directional diagram, and remaining high-order Bessel function
Item can be ignored.It is well known that equally distributed array number is more on concentric loop, remainder is smaller, and the circle of directional diagram is symmetrical
Characteristic is better, when array number more to a certain degree when, remainder is essentially close to 0, and the circle symmetry characteristic of directional diagram will not be with battle array
The increase of first number and have significant change.This is to say, for any given annular radii, there are least array number is right with it
It should realize round symmetry direction figure.On this basis, by the independent variable of detailed analysis Bessel function and order to function sheet
The influence of body, method of the invention establish concentric loop radius with the relationship of the minimum array number needed for it to guarantee to justify
The generation of symmetry direction figure.Have benefited from the establishment of above-mentioned relation, then use invasive weed optimization algorithm with annular radii be it is excellent
Optimization while to annular radii and array number can be realized by changing variable.
For a better understanding of the technical solution of the present invention, making below in conjunction with attached drawing to embodiments of the present invention further
Description.
As shown in Figure 1, concentric loop Array Model of the present invention are as follows: array center has array element always, remaining battle array
Member is located on each concentric loop, stipulated that array element is circumferentially uniformly arranged, the radially non-homogeneous arrangement of concentric loop, in array
It each array element isotropism and uniformly motivates.The concentric loop battle array is located in xoy plane, and z-axis is array normal direction, far field
Observed direction at point P is；Wherein θ is pitch angle,For azimuth.
As shown in Fig. 2, a kind of design method of the bare cloth concentric loop battle array based on Bessel function, which comprises
Step 1) is randomly generated P weeds individual, constitutes just using the annular radii of bare cloth concentric loop battle array as Optimal Parameters
Beginning population；And it is initial population that current population, which is arranged,；
In front circular aperture radius R, annulus number M and adjacent ring minimum spacing drIn the case where given, by annular radii
As optimized variable, i.e. r=[r1,r2,…rM] as the weeds individual in invasive weed optimization algorithm；In optimization process, it is
Guarantee that array bore is constant, and meet the minimum spacing of adjacent ring, annular radii generates as follows:
Wherein random sub-vector a=[a1,a2,…aM-1], element aiIt is [0, R-Mdr] in random number, and a1≤a2≤…
≤aM-1, then the random sub-vector is generated by following formula:
A=sort ((R-Mdr)·rand(1,M-1)) (2)
According to above-mentioned formula (1) and (2), P such weeds individuals are randomly generated, constitute initial population P0=[r1,
r2,…rP]；
Step 2) determines the minimum array number on annulus according to annular radii, to calculate circle for each weeds individual
Ring battle array directional diagram, determines the Peak sidelobe level of bare cloth ring array, the fitness value as weeds individual；
Step 201) calculates the minimum array element of each annulus for each group of weeds being made of annular radii individual
Number；
According to high-order Bessel function characteristic it is found that in order to obtain round symmetry direction figure, for each group by annular radii
The weeds individual constituted, radius rmAnnulus on minimum array number NmDetermination method it is as follows:
Nm=round (β rm) (3)
Wherein, β=2 π/λ is wave number, and λ is；Round () is round function；
It calculatesWhereinCharacterization independent variable is β rmNmRank Bessel function；
IfThen enable Nm=Nm+ 1, then calculateUntilLast
NmFor required value.
Step 202) calculates the directional diagram of the bare cloth concentric loop battle array according to array number in annular radii and ring:
Wherein, the azimuth position of each array element is on ringThe direction
The Bessel series expression formula of figure are as follows:
In optimization process, directional diagram is thus calculated；
Step 203) determines Thinned arrays Peak sidelobe level according to directional diagram, and as the adaptation of corresponding weeds individual
Angle value f；
Each weeds individual in the current population of step 3) generates seed, the diffusion of kind subspace；
Step 301) determines that each weeds individual in current population produces seed bearing number；
Each weeds individual in population produces seed bearing number by minimax in its fitness value f and current population
Fitness value decision, and it is in a linear relationship with the fitness value of itself, and the seed number that each weeds individual generates is Nseed:
Wherein, SmaxWith SminRespectively indicate the maximum seed number and minimum seed number that single weeds can be generated, fmax、fmin
Respectively indicate maximum adaptation angle value individual in current population and minimum fitness value；Floor () function is to be rounded letter downwards
Number；
Step 302) calculates the standard deviation of the kind subspace diffusion of weeds individual；
The seed that weeds individual generates is diffused near its parent according to normal distribution random number, and the mean value of normal distribution
For the position of its parent weeds, corresponding standard deviation sigma are as follows:
In above formula, iter is current iteration number, and initial value is set as 1, itermaxIt is greatest iteration set by algorithm
Number, σinitialWith σfinialRespectively preset standard deviation initial value and end value, n are the non-linear modulation factor；
Step 303) produces seed bearing number according to each weeds individual and standard deviation generates seed；
K-th of seed that p-th of weeds individual generates in population are as follows:
rp,k=N (rp,σ2) (9)
And meet the element in seed
Each seed represents one group of new annular radii,
Step 4) calculates the fitness value for each seed that each weeds individual generates, and will be by optimized variable annular radii
Composed offspring individual and its parent individuality, which are put together, forms new population, and it is current population that the population, which is arranged,；
Step 5) judges whether individual amount reaches preset maximum value P in current populationmaxIf in current population
Individual amount is less than Pmax, it is transferred to step 3), i.e., all individuals in current population continue breeding and generate new seed, if currently
Individual amount in population is greater than Pmax, it is transferred to step 6)；
All individuals in current population are ranked up by step 6) from small to large according to fitness value, P before only retainingmax
The initial population that the individual of a fitness value is evolved as next round eliminates remaining individual；This song initial population, which is arranged, is
Current population；
Step 7) judges whether to meet termination condition: if the number of iterations reaches maximum number of iterations itermaxOr current kind
Individual maximum adaptation angle value and minimum fitness value meet in group | fmax-fmin|≤10-6, it is transferred to step 8)；Otherwise, it is transferred to step
It is rapid 3), execute next round evolve；
Step 8) exports optimum individual, and the optimum individual is the individual in current population, the design of bare cloth concentric loop battle array
It finishes.
Preferably, initial population size P=20, population maximum-norm Pmax=50, maximum number of iterations itermax=50,
Maximum seed number Smax=5, minimum seed number Smin=1, standard deviation initial value σinitial=0.5, standard deviation end value σinitial=
0.002, non-linear modulation factor of n=3, the minimum interval d of adjacent ringr=0.5 λ.
The design method of bare cloth concentric loop battle array based on Bessel function proposed by the invention can further pass through
Simulation example in detail below is verified and is illustrated.
Simulation example 1:
Front the radius R=5 λ, concentric circles number of rings M=7 of the bare cloth concentric loop battle array of example 1.It is excellent using the method for the present invention
Change the annular radii for designing the bare cloth concentric loop battle array and be uniformly distributed array element number on its ring, simulation result shows institute of the present invention
The calculating time needed is 20s, the radius r of each concentric loopmArray element number Nm, which is uniformly distributed, with it is shown in Table 1, the array element cloth of array
Office has circle symmetry characteristic well, it is unchanged to realize 360 ° of orientations as shown in figure 3, the array element sum of the array is 175
Covering, orientation section directional diagram as shown in figure 5, and directional diagram peak sidelobe be -27.1dB.In identical array bore
Uniform battle array needed for array number be 341, corresponding peak sidelobe be -17.4dB, compare it is found that method of the invention not
48.7% bay is only saved, and peak sidelobe is reduced into 9.7dB.
Table 1
Simulation example 2:
Example 2 is the bare cloth concentric loop battle array of comprehensive annulus number M=26 on the round mouth face of radius R=25 λ, it is intended to which verifying is originally
Superiority of the method for invention in comprehensive wide aperture array.Simulation result shows that 26 rings as composed by 2042 array elements are dilute
The peak sidelobe that cloth concentric loop battle array is realized on round mouth face of the radius by 25 λ is -32.9dB.Fig. 5 gives the battle array
The array element of column is laid out, and Fig. 6 is the section directional diagram of each orientation.As a comparison, battle array needed for the uniform completely battle array of identical bore
First sum up to 7987, however its peak sidelobe realized but is only -17.5dB, then in this case,
Method of the invention can only be realized with 25.6% array number in the case where guaranteeing directional diagram circle symmetry characteristic-
The Sidelobe of 32.9dB, this engineering significance and application value with highly significant.
It should be noted last that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting.Although ginseng
It is described the invention in detail according to embodiment, those skilled in the art should understand that, to technical side of the invention
Case is modified or replaced equivalently, and without departure from the spirit and scope of technical solution of the present invention, should all be covered in the present invention
Scope of the claims in.
Claims (3)
1. a kind of bare cloth concentric loop array antenna, which is characterized in that the bare cloth concentric loop array antenna includes several
Array element a, wherein array element is laid in array center；Using array center as the center of circle, concentric loop radially non-uniform Distribution；Its
Remaining array element is laid on each concentric loop, and the array element on each annulus is uniformly distributed；Each array element isotropism；
In front circular aperture radius R, annulus number M and adjacent ring minimum spacing drIn the case where given, each annular radii rm,1
Minimum array number N on≤m≤M and m-th of annulusmThe determination process of optimal value specifically include:
Step 1) is randomly generated P weeds individual, constitutes initial kind using the annular radii of bare cloth concentric loop battle array as Optimal Parameters
Group；And it is initial population that current population, which is arranged,；
Step 2) determines the minimum array number on annulus according to annular radii, to calculate ring array for each weeds individual
Directional diagram determines the Peak sidelobe level of bare cloth ring array, the fitness value as weeds individual；
Each weeds individual in the current population of step 3) generates seed, the diffusion of kind subspace；
Step 4) calculates the fitness value for each seed that each weeds individual generates, and will be by optimized variable annular radii institute group
At offspring individual and its parent individuality put together and form new population, and it is current population that the population, which is arranged,；
Step 5) judges whether individual amount reaches preset maximum value P in current populationmaxIf individual in current population
Number is less than Pmax, it is transferred to step 3), i.e., all individuals in current population continue breeding and generate new seed, if current population
In individual amount be more than or equal to Pmax, it is transferred to step 6)；
All individuals in current population are ranked up by step 6) from small to large according to fitness value, P before only retainingmaxIt is a suitable
The initial population for answering the individual of angle value to evolve as next round eliminates remaining individual；It is current kind that this initial population, which is arranged,
Group；
Step 7) judges whether to meet termination condition: if the number of iterations reaches maximum number of iterations itermaxOr in current population
The maximum adaptation angle value of individual and minimum fitness value meet | fmax-fmin|≤10-6, if it is satisfied, being transferred to step 8)；Otherwise,
It is transferred to step 3), next round is executed and evolves；
Step 8) exports optimum individual, and the optimum individual is optimal annular radii rm,1≤m≤M；
The step 2) specifically includes:
Step 201) calculates the minimum array number of each annulus for each group of weeds being made of annular radii individual；
For each group of weeds being made of annular radii individual, radius rmAnnulus on minimum array number NmDetermination
Method is as follows:
Nm=round (β rm) (3)
Wherein, β=2 π/λ is wave number, and λ is wavelength；Round () is round function；
It calculatesWhereinCharacterization independent variable is β rmNmRank Bessel function；If
Then enable Nm=Nm+ 1, then calculateUntilLast NmFor required value；
Step 202) calculates the directional diagram of the bare cloth concentric loop battle array according to array number in annular radii and ring:
Wherein, the azimuth position of each array element is on ringDirection figure
Bessel series expression formula are as follows:
In optimization process, directional diagram is calculated by above-mentioned Bessel series expression formula；
Step 203) determines bare cloth ring array Peak sidelobe level according to directional diagram, and as the adaptation of corresponding weeds individual
Angle value f.
2. bare cloth concentric loop array antenna according to claim 1, which is characterized in that the specific implementation of the step 1)
Process are as follows:
Using annular radii as optimized variable, i.e. r=[r1,r2,…rM] as the weeds individual in invasive weed optimization algorithm；
In optimization process, to guarantee that array bore is constant, and meet the minimum spacing of adjacent ring, annular radii generates as follows:
Wherein random sub-vector a=[a1,a2,…aM-1], element aiIt is [0, R-Mdr] in random number, and a1≤a2≤…≤
aM-1, then the random sub-vector is generated by following formula:
A=sort ((R-Mdr)·rand(1,M-1)) (2)
According to above-mentioned formula (1) and (2), P such weeds individuals are randomly generated, constitute initial population P0=[r1,r2,…
rP]。
3. bare cloth concentric loop array antenna according to claim 2, which is characterized in that the step 3) specifically includes:
Step 301) determines that each weeds individual in current population produces seed bearing number；
Each weeds individual in population produces seed bearing number and is adapted to by minimax in its fitness value f and current population
Angle value decision, and it is in a linear relationship with the fitness value of itself, and the seed number that each weeds individual generates is Nseed:
Wherein, SmaxWith SminRespectively indicate the maximum seed number and minimum seed number that single weeds can be generated, fmax、fminRespectively
Indicate maximum adaptation angle value individual in current population and minimum fitness value；Floor () function is downward bracket function；
Step 302) calculates the standard deviation of the kind subspace diffusion of weeds individual；
The seed that weeds individual generates is diffused near its parent according to normal distribution random number, and the mean value of normal distribution is it
The position of parent weeds, corresponding standard deviation sigma are as follows:
In above formula, iter is current iteration number, and initial value is set as 1, itermaxIt is maximum number of iterations set by algorithm,
σinitialWith σfinialRespectively preset standard deviation initial value and end value, n are the non-linear modulation factor；
Step 303) produces seed bearing number according to each weeds individual and standard deviation generates seed；
K-th of seed that p-th of weeds individual generates in population are as follows:
rp,k=N (rp,σ2) (8)
And meet the element in seed
Each seed represents one group of new annular radii.
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