CN106329153B - A kind of combined optimization method comprehensive for large-scale isomery four-dimensional antenna array - Google Patents
A kind of combined optimization method comprehensive for large-scale isomery four-dimensional antenna array Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q21/00—Antenna arrays or systems
- H01Q21/0087—Apparatus or processes specially adapted for manufacturing antenna arrays
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
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- H01Q1/00—Details of, or arrangements associated with, antennas
- H01Q1/27—Adaptation for use in or on movable bodies
- H01Q1/28—Adaptation for use in or on aircraft, missiles, satellites, or balloons
- H01Q1/285—Aircraft wire antennas
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q21/00—Antenna arrays or systems
- H01Q21/29—Combinations of different interacting antenna units for giving a desired directional characteristic
- H01Q21/293—Combinations of different interacting antenna units for giving a desired directional characteristic one unit or more being an array of identical aerial elements
- H01Q21/296—Multiplicative arrays
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Abstract
The invention discloses a kind of combined optimization methods for the comprehensive large-scale isomery four-dimensional antenna array for using pulse phase shift timing, this integrated processes takes full advantage of the part convexity of former synthtic price index, originally complicated synthtic price index is divided into two sub-problems, two steps are then divided into optimize, the first step takes convex optimized algorithm, according to the optimization equivalent excitation amplitude (closing the switch the duration) and static stimulation phase of the constraint at centre frequency rapidly and efficiently, second step, according at sideband to the requirement of directional diagram, initial time is closed the switch using the optimization of differential evolution algorithm combination submatrix optimisation technique, to enable the solution of entire optimization problem rapidly and efficiently.Maximum novelty of the invention is to have excavated the intrinsic propesties of former optimization problem, combines convex optimized algorithm and differential evolution algorithm optimizes, substantially increase the speed and efficiency of entire optimization process, achieved the effect that get twice the result with half the effort.
Description
Technical field
The invention belongs to antenna technical fields, are related to large-scale isomery four-dimensional antenna array synthesis, specifically utilize one
Kind combined optimization method quickly and efficiently integrates isomery four-dimensional antenna array.The rapidly and efficiently property major embodiment of this combined optimization algorithm
In the part convexity for the problem that takes full advantage of, convex optimized algorithm is introduced into the comprehensive problem of large-scale isomery four-dimensional antenna array
It goes.
Background technique
Up to the present, the topological structure of antenna array be nearly all the planar array antenna being distributed only on same plane or
It is the conformal array antenna being distributed only on same curved surface.For certain special carriers, such as satellite, aircraft, naval vessels etc., due to
The requirement of carrier itself the extremely limited space surface structured the formation and other non-antenna performances, such topological structure are being realized
It, will necessarily be by the limited essential constraint of carrier physics bore, so that day when the characteristic requirements such as high-gain, Sidelobe, narrow beam
Line engineer encounters technical bottleneck when designing the antenna performances such as high-gain, Sidelobe, narrow beam.Therefore based on single plane or
The traditional idea of single curved design antenna is necessarily required to be improved, and realizes in different planes, different curved surfaces or flat
The certainty that antenna has become modern antennas development is designed on face and curved surface simultaneously, due to being by difference as such antenna
The antenna array group battle array of topological structure forms, therefore we term it isomery battle arrays.It is right however at home and abroad in disclosed various documents
Isomery battle array studied almost also in blank, therefore this is also a completely new field and project, is had highly important
Realistic meaning and theoretical value.
The complicated array antenna as isomery battle array, the necessarily complexity needed for it that we consider first in design
Feeding network, this cost problem concerning antenna designed by us.And it is set forth in nineteen sixties and rises Yu Ershi
The concept of four-dimensional antenna array at the beginning of century designs antenna by introducing the time as new one-dimensional freedom degree, utilizes the time
The weighting for weighting equivalent realization amplitude and phase not only can control and improve the radiation characteristic of antenna array, but also can be uniform quiet
Narrow beam, Sidelobe and various shaped-beams are designed under state excitation amplitude, this, which will greatly simplify, wants feeding network
It asks, therefore the thought of four-dimensional antenna is introduced into isomery battle array will be advantageous to design to isomery battle array feeding network, while is right
Antenna structure machining accuracy, the feed precision of feeding network and the demand of tolerance greatly reduce, and have great design flexibility.
Due to the topological structure of isomery battle array and the sideband characteristic of four-dimensional battle array, so that the synthtic price index for isomery four-dimension battle array is logical
It is often one large-scale array synthtic price index, and is nearly all at present Stochastic Optimization Algorithms for the integrated approach of four-dimensional battle array, such as
Differential evolution algorithm (DE), particle swarm algorithm (PSO), simulated annealing algorithms (SA) etc., this kind of algorithm is in the small-sized four-dimension of synthesis
Convergence is very fast when battle array, efficiency is higher, still utilizes.But then seem unable to do what one wishes for large-scale four-dimensional battle array synthesis, convergence rate is very
Slowly, efficiency is extremely low or even infeasible.Therefore highly important engineering will be had by developing new algorithm synthesis isomery four-dimensional antenna array
Meaning.
In the document and patent delivered at home and abroad, the fewer and fewer of synthesis is carried out to isomery four-dimensional antenna array.2009
Year, professor Ou Yangjun of University of Electronic Science and Technology carries out isomery using conformal spheric array and conformal cylindrical array, not yet mentions in text
And the concept of isomery battle array, but unquestionable this already belongs to the scope of isomery battle array.By surveying each unit in microwave dark room
Active directional diagram, the field distribution expression formula in the far field in the case where any width mutually motivates then is obtained according to vector field principle of stacking,
And optimizes excitation width using improved Gene hepatitis B vaccine and mutually obtained the Sidelobe directional diagram under scanning mode.Although to isomery
The document that four-dimensional antenna array is studied is less, is largely to adding time-modulation and not plus the conformal array of time-modulation is ground
Study carefully, but conformal array is as a kind of special isomery battle array, studying the integrated approach of conformal array, have for the synthesis of isomery battle array can not
The effect of substitution.In the patent of 104393414 A of Patent No. CN, propose a kind of based on time-modulation Conformal Phased Array
The quick Pattern Synthesis method of column, using at alternative projection algorithm and Fast Fourier Transform (FFT) difference integrating center frequency and the
Directional diagram at one sideband finally isolates static stimulation and switch working sequence again, but it is just for two-dimensional directional figure, unit
Quantity is also less；In the patent of 103178359 A of Patent No. CN, a kind of being total to based on spherical crown Aperture field distribution is proposed
The design method of shape array antenna is adjusted Aperture field distribution using the method for the parameter weighting to Bessel function, obtains
Continuous mouth to figuration variety classes wave beam is distributed, and discrete method is recycled to calculate corresponding element excitation；2014, Xi'an
Doctor Li Wentao of University of Electronic Science and Technology, he has carried out correlative study to conformal circular cone four-dimensional antenna array synthesis, has passed through multiple target
The multi-form main polarization directional diagram for combining Sidelobe of particle swarm optimization algorithm combination Bornstein, while also inhibiting intersection
Polarization.From the document and patent delivered, the method comprehensive for isomery battle array or conformal array is mainly based upon random optimization
The number of unit of method, array is all fewer, therefore develops for the comprehensive high efficiency method of large-scale isomery battle array or conformal array urgently
It needs to solve, what the present invention exactly came into being in this context.
Essentially, isomery four-dimension battle array synthtic price index is the mathematical optimization problem for seeking optimal solution, mathematically
One optimization problem be typically all with it is convex or it is non-convex divide, as long as an optimization problem be convex or part be it is convex,
So this optimization problem can using convex optimized algorithm quickly, efficiently, it is accurate solve, and this solution or global optimum,
And his convergence rate is also significantly faster than various Stochastic Optimization Algorithms.Therefore it is comprehensive convex optimized algorithm to be introduced into isomery four-dimension battle array
It goes greatly improve its overall efficiency in conjunction problem.
For any one isomery four-dimensional antenna array synthtic price index, be all to the field at centre frequency and the field at sideband into
The problem of optimal value is sought in row constraint is the synthtic price index comprising multiple constraint conditions.When we choose pulse phase shift
When (Pulse Shifting) this timing, the consideration that the constraint condition of isomery four-dimensional antenna array can be independent, at centre frequency
Field about optimized variable (static stimulation phase and close the switch the duration) be it is convex, the field at sideband is about optimized variable
(closing the switch initial time) is non-convex, so entire optimization problem is that part is convex, therefore nature can introduce convex optimization
Algorithm is for the field at integrating center frequency, and then the field at sideband is optimized using differential evolution algorithm, i.e., convex optimization
Algorithm and differential evolution algorithm are united for integrating isomery four-dimension battle array, and optimized variable most of in this way can be by convex excellent
Change algorithm to find out, fraction optimized variable then utilizes differential evolution algorithm to optimize, so that it is four-dimensional to greatly improve entire large-scale isomery
The speed and efficiency of battle array synthtic price index.
Summary of the invention
In view of above-mentioned technical background, the invention proposes combining, the comprehensive large-scale isomery of convex optimization and differential evolution algorithm is four-dimensional
Battle array, it is therefore intended that compared to already existing optimisation technique, the method for proposition of the invention can be quicker, significantly more efficient
Comprehensive large size isomery four-dimension battle array.
Integrated processes proposed by the invention mainly for pulse phase shift timing isomery four-dimension battle array, according to different under this timing
The characteristics of structure four-dimension battle array, entire combined optimization process can be divided into two steps.The first step, according at centre frequency to the pact of directional diagram
Beam utilizes convex optimized algorithm optimization equivalent excitation amplitude (closing the switch the duration) and static stimulation phase；Second step, In
On the basis of the first step, closing the switch duration and static stimulation phase as it is known that according to directional diagram at the first sideband
Requirement, only optimized using differential evolution algorithm and close the switch initial time come suppressed sideband.
The present invention has the following contents:
Consider that the isomery four-dimension battle array being made of two arrays, multiple array isomery methods are similar.It is each in isomery four-dimension battle array
Antenna element meets the RF switch of a high speed, switch function Umnp(t).The then far-field distribution of this timing form are as follows:
WhereinRespectively indicate the element pattern of first array and second array；I1,mnp,
I2,rstRespectively indicate the static stimulation amplitude of first array and second array；α1,mnp,α2,rstRespectively indicate first array
With the static stimulation phase of second array；β indicates wave number,Indicate spherical coordinate system end point of observationThe unit vector at place；Respectively indicate the cell position vector of first array and second array.
This isomery four-dimensional antenna array works in centre frequency f0, the time-modulation cycle T of switchp, time-modulation frequency fp=
1/Tp.Switch function U with pulse phase shifted time modulation systemmnp(t) it indicates are as follows:
tmnpIndicate control unit closes the switch initial time, τmnpIndicate control unit closes the switch the duration.
According to signal and Systems Theory, the time-domain expression of the periodic function of switch can be unfolded by Fourier space in frequency domain:
Bring the expression formula that (1) formula obtains the kth subharmonic in far field into are as follows:
Consider that unit form is ideal point source, the uniform situation of static stimulation amplitude, i.e.,
I1,mnp,I2,rstIt is equal to 1, for convenience, triple summation forms is write as one and are summed again form, then:
The field at field and the first sideband at centre frequency can respectively indicate are as follows:
From the expression formula in the above far field it is found that field from centre frequency about equivalent amplitude (closing the switch the duration) and
It is convex for static stimulation, and only related with the two variables, the field at the first sideband or at other sidebands is closed about switch
It is non-convex for closing for initial time.Physical relationship is shown in Fig. 1.
Therefore, entire combined optimization process can be divided into two steps.
The first step, using convex optimized algorithm according to the constrained optimization equivalent excitation amplitude (switch to the field at centre frequency
Closing period) and equivalent excitation phase.Find out the solution W for meeting following convex optimization problem.
Or
Wherein fr_mainIndicate that the normalization in main beam region refers to field distribution, δ indicates the maximum being manually set according to requirement
Minor lobe value, D indicate that the steering vector being made of scanning direction, t indicate the slack variable in convex optimization.
Second step, the W that the first step solves as it is known that only optimized using differential evolution algorithm close the switch starting when
It carves, carrys out suppressed sideband.For large-scale isomery four-dimension battle array, optimized variable at this time is still relatively more, and convergence rate is slower, because
The submatrix of original isomery four-dimension battle array can be separated into several submatrixs by this, it is believed that all unit switch in the same submatrix
It is identical to be closed initial time, it is then different between submatrix.Optimized variable number will be greatly reduced in this way, to accelerate convergence rate.
How molecule battle array it is divided into how many grades of submatrixs then codetermined according to the demand of specific sidebands levels and convergence rate.In the present invention
Example in it is all constitute isomery four-dimension battle arrays submatrixs be all uniformly divided into 16 submatrixs, be illustrated in fig. 2 shown below.
The flow chart of entire combined optimization process is shown in Fig. 3.
The novelty of the present invention is develop a kind of combined optimization algorithm to isomery four-dimensional antenna array Sidelobe, lower sideband
Directional diagram has carried out synthesis rapidly and efficiently.Compared with prior art, the invention has the following advantages that
1. by the constraint condition reasonable analysis at centre frequency and at sideband, the method for taking step-by-step processing,
The one sufficiently complex synthtic price index of script resolves into two relatively simple synthtic price index, is not losing the general premise of problem
Under reduce comprehensive difficulty.
2. the part convexity of the synthtic price index is adequately utilized, convex optimized algorithm is used to the directional diagram at centre frequency
It is integrated, for traditional complete Stochastic Optimization Algorithms, while guaranteeing the global optimum of solution, is greatly mentioned
High comprehensive speed and efficiency.
3. due at sideband nonconvex property, we are integrated using global Stochastic Optimization Algorithms, complete with ensure to solve
Office's optimality, what is taken in the method for the present invention is differential evolution algorithm, can also take other global Stochastic Optimization Algorithms certainly.
4. it is excellent to take submatrix when integrating using differential evolution algorithm to isomery four-dimensional antenna array sideband directional diagram
Change technology, takes into account the Global Optimality and convergence speed of the algorithm of understanding, so that the speed of entire optimization problem further be turned up
Degree and efficiency.
Detailed description of the invention
Fig. 1 is that integrated processes optimize large-scale isomery four-dimension battle array optimized variable relational graph.
Fig. 2 is the illustraton of model that the four-dimensional a period of time battle array of the isomery based on simple model aircraft is divided into 16 submatrixs.
The flow chart of Fig. 3 combined optimization method thus.
Fig. 4 is that the four-dimensional a period of time array element of the isomery based on simple model aircraft is distributed naive model figure.
Fig. 5 is the two-dimensional directional figure optimized at resulting centre frequency in embodiment 1.
Fig. 6 is the two-dimensional directional figure optimized at resulting first sideband in embodiment 1.
Fig. 7 is the three-dimensional figure for optimizing the space u, v at resulting centre frequency in embodiment 1.
Fig. 8 is the three-dimensional figure for optimizing the space u, v at resulting first sideband in embodiment 1.
Fig. 9 is to optimize resulting case unit switch normalization closing period distribution map in embodiment 1.
Figure 10 is to optimize resulting head unit switch normalization closing period distribution map in embodiment 1.
Figure 11 is to optimize resulting starboard wing unit switch in embodiment 1 to normalize closing period distribution map.
Figure 12 is to optimize resulting port wing unit switch in embodiment 1 to normalize closing period distribution map.
Figure 13 is to optimize resulting case unit static stimulation phase distribution figure in embodiment 1.
Figure 14 is to optimize resulting head unit static stimulation phase distribution figure in embodiment 1.
Figure 15 is to optimize resulting starboard wing unit static stimulation phase distribution figure in embodiment 1.
Figure 16 is to optimize resulting port wing unit static stimulation phase distribution figure in embodiment 1.
Figure 17 is the two-dimensional directional figure optimized at resulting centre frequency and at the first two sideband in embodiment 2.
Figure 18 is the three-dimensional figure for optimizing the space u, v at resulting centre frequency in embodiment 2.
Figure 19 is the three-dimensional figure for optimizing the space u, v at resulting first sideband in embodiment 2.
Specific embodiment
Embodiment 1: comprehensive based on the Sidelobe isomery four-dimension battle array under the non-scanning mode of simple model aircraft
Consider an isomery four-dimension battle array, isomery matrix number totally 4, by cylindrical body curved surface battle array, head planar array,
Left and right wingpiston battle array composition, structure are as shown in Figure 4.Case unit number is 4 × 10 × 16=640, is had along generatrix direction
20 units, 32, directrix direction unit, 4 indicate the symmetrical submatrix numbers of unit, i.e., by 4 10 × 16 submatrixs on fuselage
Constitute, and between submatrix unit equivalent excitation amplitude (closing the switch the duration) it is identical, head unit number be 4 × 16 × 16
=1024, starboard wing number of unit is 4 × 10 × 10=400, and port wing number of unit is 4 × 10 × 10=400, and is all class
It is similar to the symmetrical of fuselage.Switching sequence selects pulse phase shift, and static stimulation amplitude is to be uniformly distributed, and referential array is one
Chebyshev's planar array of 44 × 44=1936 unit.Other major parameters are as follows:
d3=d4=d5=dz=dy=0.5 λ, h=d1=0, d2=0.25 λ, δ=- 30dB
Using this combined optimization algorithm optimization equivalent excitation amplitude (closing the switch the duration), static stimulation phase is opened
Close the isomery four-dimension battle array for closing that the comprehensive unit sum of initial time is 2464, be quickly obtained a minor lobe be-
28.52dB, the first sideband are the directional diagram of -15.79dB, such as Fig. 5, Fig. 6, Fig. 7, shown in Fig. 8.Fig. 9, Figure 10, Figure 11, Tu12Shi
Optimize obtained normalized equivalent excitation amplitude (closing the switch the duration), Figure 13, Figure 14, Figure 15, Figure 16 are to optimize
The static stimulation phase arrived, it should be noted that the first step in combined process is carried out in comprehensive using convex optimized algorithm
When directional diagram at frequency of heart, the spent time be about 1 hour 30 points or so, this is spent well below Stochastic Optimization Algorithms
The time taken, due to joined submatrix optimisation technique in second step, optimized variable sum is only 64, differential evolution algorithm
It can restrain rapidly.
Embodiment 2: based on (θ under simple model aircraft scanning mode0=45.,) Sidelobe isomery four-dimension battle array synthesis
Isomery matrix number totally 3 are considered in the case of this, by cylindrical body curved surface battle array, head planar array, starboard wing is flat
Face battle array composition, i.e., remove the unit on port wing, cell distribution form is constant in the case of example 1.Case unit number be 4 ×
10 × 10=400 has 20 units along generatrix direction, and 20, directrix direction unit, 4 indicate the symmetrical submatrix of unit
Number, i.e., be made of on fuselage 4 10 × 10 submatrixs, and between submatrix unit equivalent excitation amplitude (closing the switch the duration)
Identical, head unit number is 4 × 14 × 14=784, and starboard wing number of unit is 4 × 10 × 10=400, and is all analogous to
Fuselage it is symmetrical, switching sequence select pulse phase shift, static stimulation amplitude be uniformly distributed, other major parameters are as follows:
d3=d4=d5=dz=dy=0.5 λ, h=d1=0, d2=0.25 λ
Also with this combined optimization algorithm optimization equivalent excitation amplitude (closing the switch the duration), static stimulation phase
Position closes the switch the isomery four-dimension battle array that the comprehensive unit sum of initial time is 1584, quickly combine a minor lobe be-
25.08dB, the first sideband are the directional diagram of -10.01dB, such as Figure 17, Figure 18, shown in Figure 19.It should be noted that integrating
The first step the spent time in journey is about 1 hour or so, joined submatrix optimisation technique, optimized variable sum in second step
Only 48, differential evolution algorithm can also restrain rapidly.
This combined optimization algorithm despite for isomery four-dimension battle array propose, but its application be never only limited to this, it is any
Similar large-scale optimization problem all can rapidly and efficiently be solved with the method.
It is the description to the present invention and its embodiment provided to the engineers and technicians in familiar field of the present invention above,
These descriptions should be considered to be illustrative and not restrictive.Engineers and technicians can be accordingly in invention claims
Thought combination particular problem is done specific operation and is implemented, and naturally also can do a series of change to embodiment according to the above
More.Above-mentioned these are regarded as coverage of the invention.
Claims (1)
1. a kind of combined optimization method comprehensive for large-scale isomery four-dimensional antenna array, it is characterised in that large-scale isomery four-dimension day
Linear array synthtic price index resolves into Pattern Synthesis and the first sideband directional diagram at centre frequency and inhibits two simplified step-by-step optimizations
Problem, specific Optimization Steps are as follows:
Step 1: centre frequency prescription being integrated to figure, according to, to the constraint of directional diagram, utilizing convex optimization at centre frequency
Algorithm optimization goes out one group and closes the switch duration and static stimulation phase；
Step 2: the first sideband directional diagram being inhibited, according to step 1, has closed the switch duration and equivalent excitation phase
Know, optimized variable only remains and closes the switch initial time, further according to the requirement of directional diagram at the first sideband, utilizes differential evolution algorithm
Only optimization closes the switch initial time and carrys out suppressed sideband.
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