CN106329153A - Combined optimization method used for synthesis of large-scale heterogeneous four-dimensional antenna array - Google Patents

Abstract

The invention discloses a combined optimization method used for synthesizing a large-scale heterogeneous four-dimensional antenna array which employs a pulse phase shift sequence. According to the combined method, a part of convexity of an original synthesis problem is fully utilized, and the original complicated synthesis problem is divided into two sub-problems; and then optimization is performed by two steps: step 1, rapidly optimizing an equivalent excitation amplitude (switch switch-on duration) and a static excitation phase with high efficiency according to constraint of a field at a center frequency by employing a convex optimization algorithm; and step 2, optimizing a switch switch-on initial time with the combination of a subarray optimization technology by employing a differential evolution algorithm according to the requirement of a directional diagram by a sideband so that the whole optimization problem can be rapidly solved with high efficiency. According to the method, the biggest innovation is the discovery of the essential characteristic of the original optimization problem, optimization is performed with the combination of the convex optimization algorithm and the differential evolution algorithm, the speed and the efficiency of the whole optimization process are greatly increased, and the effect of getting double the result with half the effort is achieved.

Description

A kind of combined optimization method comprehensive for large-scale isomery four-dimensional antenna array

Technical field

The invention belongs to antenna technical field, relate to large-scale isomery four-dimensional antenna array comprehensive, utilize one specifically Plant combined optimization method comprehensive isomery four-dimensional antenna array quickly and efficiently.The rapidly and efficiently property major embodiment of this combined optimization algorithm Taking full advantage of the part convexity of problem, convex optimized algorithm is being incorporated in the problem that large-scale isomery four-dimensional antenna array is comprehensive Go.

Background technology

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 it is the conformal array antenna being distributed only on same curved surface.For some special carrier, such as satellite, aircraft, naval vessels etc., due to The extremely limited space surface structured the formation of carrier itself and the requirement of other non-antenna performances, such topological structure is realizing During the characteristic requirements such as high-gain, Sidelobe, narrow beam, will necessarily be by the limited essential constraint of carrier physics bore so that sky Line engineer runs into 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, it is achieved at different planes, different curved surface or flat On face and curved surface, simultaneously designing antenna has become as the certainty of modern antennas development, owing to being by difference as such antenna The antenna array group battle array of topological structure forms, therefore we term it isomery battle array.But in various documents disclosed at home and abroad, right Isomery battle array carry out studying almost also in blank, therefore this is also a brand-new field and problem, has highly important Realistic meaning and theory value.

Array antenna complicated as isomery battle array, necessarily its required complexity that first we consider when design Feeding network, this is concerning the Cost Problems of antenna designed by us.And be set forth in nineteen sixties and rise in 20 The concept of century four-dimensional antenna array just, carrys out designing antenna by the introducing time as new one-dimensional degree of freedom, utilizes the time The amplitude that realizes of weighting equivalence and the weighting of phase place, can control and improve the radiation characteristic of antenna array, again can be the most quiet Designing narrow beam, Sidelobe and various shaped-beam under state excitation amplitude, this will greatly simplify wants feeding network Ask, therefore the thought of four-dimensional antenna is introduced in isomery battle array and will be advantageous to the design to isomery battle array feeding network, the most right Antenna structure machining accuracy, the feed precision of feeding network and the demand of tolerance are greatly reduced, and have great design flexibility.

Topological structure and the sideband characteristic of four-dimensional battle array due to isomery battle array so that the synthtic price index for isomery four-dimension battle array is led to It is often a large-scale array synthtic price index, and the current integrated approach for four-dimensional battle array is nearly all Stochastic Optimization Algorithms, such as Differential evolution algorithm (DE), particle cluster algorithm (PSO), simulated annealing algorithms (SA) etc., this kind of algorithm is at the comprehensive small-sized four-dimension During battle array, convergence is very fast, efficiency is higher, the most available.But the most then seeming unable to do what one wishes for large-scale four-dimensional battle array, convergence rate is very Slowly, extremely inefficient, the most feasible.Therefore develop new algorithm synthesis isomery four-dimensional antenna array and will have highly important engineering Meaning.

In the document delivered at home and abroad and patent, isomery four-dimensional antenna array is carried out comprehensive few.2009 Year, professor Ou Yangjun of University of Electronic Science and Technology utilizes conformal spheric array and conformal cylindrical array to carry out isomery, not yet carries in literary composition And the concept of isomery battle array, but undoubtedly this belongs to the category of isomery battle array already.By surveying each unit at microwave dark room Active directional diagram, then according to vector field principle of stacking draws the Electric Field Distribution expression formula in far field under any width encourages mutually, And utilize the Gene hepatitis B vaccine optimization excitation width Sidelobe directional diagram that obtained under scanning mode mutually of improvement.Although to isomery The document that four-dimensional antenna array carries out studying is less, and major part is to adding time-modulation and not adding the grinding of conformal array of time-modulation Studying carefully, but conformal array is as a kind of special isomery battle array, the integrated approach of research conformal array can not for comprehensively having of isomery battle array The effect substituted.In the patent of Patent No. CN 104393414 A, it is proposed that a kind of based on time-modulation Conformal Phased Array The quick Pattern Synthesis method of row, utilizes at alternative projection algorithm and fast Fourier transform integrating center frequency respectively and the Directional diagram at one sideband, isolates static stimulation and switch sequential the most again, but it is just for two-dimensional directional figure, unit Quantity is the most less；In the patent of Patent No. CN 103178359 A, it is proposed that a kind of based on spherical crown Aperture field distribution be total to The method for designing of shape array antenna, utilizes the method to the parameter weighting of Bessel function to be adjusted Aperture field distribution, Continuous mouth to figuration variety classes wave beam calculates corresponding element excitation through distribution, recycling discrete method；2014, Xi'an Doctor Li Wentao of University of Electronic Science and Technology, he has comprehensively carried out correlational study to conformal circular cone four-dimensional antenna array, has passed through multiple target Particle swarm optimization algorithm combine the multi-form main polarization directional diagram combining Sidelobe of Bornstein, also inhibits intersection simultaneously Polarization.From the document delivered and patent, the method comprehensive for isomery battle array or conformal array is mainly based upon random optimization Method, the number of unit of array is the most fewer, therefore develops for the comprehensive high efficiency method of large-scale isomery battle array or conformal array urgently Needing to solve, the present invention arises at the historic moment the most in this context.

Essentially, isomery four-dimension battle array synthtic price index is a mathematical optimization problem seeking optimal solution, mathematically One optimization problem is typically all and divides with convex or non-convex, as long as optimization problem is convex or part is convex, So this optimization problem just can use convex optimized algorithm quickly, efficiently, accurately solve, and this solves or global optimum, And his convergence rate is also significantly faster than various Stochastic Optimization Algorithms.Therefore convex optimized algorithm is incorporated into isomery four-dimension battle array to combine Conjunction problem is gone will improve its overall efficiency greatly.

For any one isomery four-dimensional antenna array synthtic price index, it is all that the field at mid frequency and the field at sideband are entered Row constraint seeks the problem of optimal value, is i.e. the synthtic price index comprising multiple constraints.When we choose pulse phase shift During (Pulse Shifting) this sequential, the consideration that the constraints of isomery four-dimensional antenna array can be independent, at mid frequency Field be convex about optimized variable (static stimulation phase place and switch closing period), the field at sideband is about optimized variable (switch Guan Bi initial time) is non-convex, thus whole optimization problem to be part convex, therefore natural can introduce convex optimization Algorithm field at integrating center frequency, then the field at sideband uses differential evolution algorithm to be optimized, i.e. convex optimization Algorithm and differential evolution algorithm are united for comprehensive isomery four-dimension battle array, and so major part optimized variable can be by convex excellent Changing algorithm to obtain, fraction optimized variable then utilizes differential evolution algorithm optimization, thus it is four-dimensional to be greatly improved whole large-scale isomery The speed of battle array synthtic price index and efficiency.

Summary of the invention

In view of above-mentioned technical background, the present invention proposes the convex optimization of associating and the comprehensive large-scale isomery of differential evolution algorithm is four-dimensional Battle array, it is therefore intended that compared to the optimisation technique existed, the method for the proposition of the present invention can be quicker, significantly more efficient Comprehensive large-scale isomery four-dimension battle array.

Integrated processes proposed by the invention is mainly for the isomery four-dimension battle array of pulse phase shift sequential, according to different under this timing The feature of structure four-dimension battle array, whole combined optimization process can be divided into two steps.The first step, according to pact to directional diagram at mid frequency Bundle, utilizes convex optimized algorithm optimization equivalent excitation amplitude (switch closing period) and static stimulation phase place；Second step, On the basis of the first step, switch closing period and static stimulation phase place as it is known that according to directional diagram at the first sideband Requirement, utilize differential evolution algorithm only optimize switch Guan Bi initial time carry out suppressed sideband.

The present invention has a herein below:

Considering the isomery four-dimension battle array being made up of two arrays, multiple array isomery methods are similar to.In isomery four-dimension battle array each Antenna element connects the radio-frequency (RF) switch of a high speed, and switch function is U_mnp(t).Then the far-field distribution of this timing form is:

WhereinRepresent first array and the element pattern of second array respectively；I_1,mnp, I_2,rstRepresent first array and the static stimulation amplitude of second array respectively；α_1,mnp,α_2,rstRepresent first array respectively Static stimulation phase place with second array；β represents wave number,Represent spherical coordinate system end point of observationThe unit vector at place；Represent first array and the cell position vector of second array respectively.

This isomery four-dimensional antenna array is operated in mid frequency f₀, the time-modulation cycle T of switch_p, time-modulation frequency f_p= 1/T_p.There is the switch function U of pulsion phase shift time modulation system_mnpT () is expressed as:

$U_{mnp}\left(t\right)=\left\{\begin{array}{cc}1& t_{mnp}\≤t\≤t_{mnp}+{\mathrm{\τ}}_{mnp},0\≤t_{mnp},{\mathrm{\τ}}_{mnp}\≤T_p\\ 0& others\end{array}\right.---\left(2\right)$

t_mnpRepresent the switch Guan Bi initial time of control unit, τ_mnpRepresent the switch closing period of control unit. Theoretical according to Signals & Systems, the time-domain expression of the periodic function of switch can be launched at frequency domain by Fourier space:

$a_{mnp}^k=\frac{1}{T_p}\underset{0}{\overset{T_p}{\∫}}{U}_{mnp}\left(t\right)e^{-j2{\mathrm{\πf}}_{p}t}dt=\frac{{\mathrm{\τ}}_{mnp}}{T_p}\·\frac{sin\left({\mathrm{\πkf}}_p{\mathrm{\τ}}_{mnp}\right)}{{\mathrm{\πkf}}_p{\mathrm{\τ}}_{mnp}}\·e^{j-{\mathrm{k\πf}}_p({\mathrm{\τ}}_{mnp}+2t_{mnp})}---\left(3\right)$

The expression formula bringing the kth subharmonic that (1) formula obtains far field into is:

Consider that unit form is preferable point source, the uniform situation of static stimulation amplitude, i.e.I_1,mnp, I_2,rstIt is equal to 1, for convenience, triple summation forms is write as one and heavily sues for peace form, then:

Field at mid frequency and the field at the first sideband can be expressed as:

Knowable to the expression formula in above far field, the field at mid frequency about equivalence amplitude (switch closing period) and It is convex for static stimulation, and only relevant with the two variable, the field at the first sideband or at other sidebands is closed about switch It is non-convex for closing initial time.Physical relationship is shown in Fig. 1.

Therefore, whole combined optimization process can be divided into two steps.

The first step, utilizes convex optimized algorithm according to the constrained optimization equivalent excitation amplitude (switch to the field at mid frequency Closing period) and equivalent excitation phase place.I.e. find out solution W meeting following convex optimization problem.

$\underset{W}{min}\left(t\right)$

Or

$\underset{W}{min}\left(t\right)$

Wherein f_{r_main}Representing the normalization reference field distribution in main beam region, δ represents that foundation requires the maximum being manually set Secondary lobe value, D represents the steering vector being made up of scanning direction, and t represents the slack variable in convex optimization.

Second step, the W that the first step is solved as it is known that utilize differential evolution algorithm only optimize switch Guan Bi initial time Carve, carry out suppressed sideband.For large-scale isomery four-dimension battle array, optimized variable now still compares many, and convergence rate is relatively slow, because of This can be separated into some submatrixs the submatrix of original isomery four-dimension battle array, it is believed that all unit switch in same submatrix Guan Bi initial time is identical, then different between submatrix.So optimized variable number will be greatly reduced, thus accelerate convergence rate. How molecule battle array？It is divided into how many grades of submatrixs？Then demand and convergence rate according to concrete sidebands levels together decide on.In the present invention Example in the submatrix of all composition isomery four-dimension battle arrays be all divided into 16 submatrixs uniformly, be illustrated in fig. 2 shown below.

The flow chart of whole combined optimization process is shown in Fig. 3.

The novelty of the present invention is to develop a kind of combined optimization algorithm to isomery four-dimensional antenna array Sidelobe, lower sideband It is comprehensive that directional diagram has carried out rapidly and efficiently.Compared with prior art, the invention have the advantages that

1. by the constraints reasonable analysis of field at mid frequency and at sideband, the method taking step-by-step processing, The sufficiently complex synthtic price index of one script resolves into two relatively simple synthtic price index, in the general premise of problem of not losing Under reduce comprehensive difficulty.

The most sufficiently make use of the part convexity of this synthtic price index, the directional diagram at mid frequency is used convex optimized algorithm Carry out comprehensive, for traditional Stochastic Optimization Algorithms completely, while ensureing the global optimum solved, greatly carry High comprehensive speed and efficiency.

3., due to the nonconvex property of field at sideband, we use overall situation Stochastic Optimization Algorithms to carry out comprehensively, to guarantee the complete of solution Office's optimality, take in the inventive method is differential evolution algorithm, the most also can take other overall situation Stochastic Optimization Algorithms.

4., when utilizing differential evolution algorithm to carry out comprehensive to isomery four-dimensional antenna array sideband directional diagram, take submatrix excellent Change technology, takes into account Global Optimality and the convergence of algorithm speed of understanding, thus has heightened the speed of whole optimization problem further Degree and efficiency.

Accompanying drawing explanation

Fig. 1 is that integrated processes optimizes large-scale isomery four-dimension battle array optimized variable graph of a relation.

Fig. 2 is the illustraton of model that isomery four-dimension a period of time battle array based on simple model aircraft is divided into 16 submatrixs.

Fig. 3 is the flow chart of this combined optimization method.

Fig. 4 is that isomery four-dimension a period of time array element based on simple model aircraft is distributed naive model figure.

Fig. 5 is to optimize the two-dimensional directional figure at the mid frequency of gained in embodiment 1.

Fig. 6 is to optimize the two-dimensional directional figure at the first sideband of gained in embodiment 1.

Fig. 7 is to optimize the three-dimensional figure in u, v space at the mid frequency of gained in embodiment 1.

Fig. 8 is to optimize the three-dimensional figure in u, v space at the first sideband of gained in embodiment 1.

Fig. 9 is the case unit switch normalization closing period scattergram optimizing gained in embodiment 1.

Figure 10 is the head unit switch normalization closing period scattergram optimizing gained in embodiment 1.

Figure 11 is the starboard wing unit switch normalization closing period scattergram optimizing gained in embodiment 1.

Figure 12 is the port wing unit switch normalization closing period scattergram optimizing gained in embodiment 1.

Figure 13 is the case unit static stimulation PHASE DISTRIBUTION figure optimizing gained in embodiment 1.

Figure 14 is the head unit static stimulation PHASE DISTRIBUTION figure optimizing gained in embodiment 1.

Figure 15 is the starboard wing unit static stimulation PHASE DISTRIBUTION figure optimizing gained in embodiment 1.

Figure 16 is the port wing unit static stimulation PHASE DISTRIBUTION figure optimizing gained in embodiment 1.

Figure 17 is to optimize the two-dimensional directional figure at the mid frequency of gained and at the first two sideband in embodiment 2.

Figure 18 is to optimize the three-dimensional figure in u, v space at the mid frequency of gained in embodiment 2.

Figure 19 is to optimize the three-dimensional figure in u, v space at the first sideband of gained in embodiment 2.

Detailed description of the invention

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 forms, and structure is as shown in Figure 4.Case unit number is 4 × 10 × 16=640, has along generatrix direction 20 unit, 32, directrix direction unit, 4 represent unit symmetrical submatrix number, i.e. by the submatrix of 4 10 × 16 on fuselage Constituting, and between submatrix, the equivalent excitation amplitude (switch closing period) of unit is identical, head unit number is 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 for being 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=d_z=d_y=0.5 λ, h=d₁=0, d₂=0.25 λ, δ=-30dB

Utilize this combined optimization algorithm optimization equivalent excitation amplitude (switch closing period), static stimulation phase place, open Close and close the isomery four-dimension battle array that initial time this unit sum comprehensive is 2464, be quickly obtained a secondary lobe for- 28.52dB, the first sideband is the directional diagram of-15.79dB, such as Fig. 5, shown in Fig. 6, Fig. 7, Fig. 8.Fig. 9, Figure 10, Figure 11, Tu12Shi Optimizing the normalized equivalent excitation amplitude (switch closing period) obtained, Figure 13, Figure 14, Figure 15, Figure 16 are to optimize The static stimulation phase place arrived, it should be noted that during the first step in combined process i.e. utilizes convex optimized algorithm to carry out comprehensively During directional diagram at frequency of heart, institute be about the cost time 1 hour about 30 points, this is to be spent well below Stochastic Optimization Algorithms The time taken, owing to adding submatrix optimisation technique in second step, optimized variable sum is only 64, and differential evolution algorithm is also Can restrain rapidly.

Embodiment 2: based on (θ under simple model aircraft scanning mode₀=45.,) Sidelobe isomery four-dimension battle array is comprehensive

Considering isomery matrix number totally 3 in the case of this, by cylindrical body curved surface battle array, head planar array, starboard wing is put down Face battle array composition, i.e. removes the unit on port wing when example 1, and cell distribution form is constant.Case unit number is 4 × 10 × 10=400, has 20 unit, 20, directrix direction unit along generatrix direction, and 4 represent the symmetrical submatrix of unit Number, is i.e. made up of the submatrix of 4 10 × 10 on fuselage, and the equivalent excitation amplitude (switch closing period) of unit between submatrix 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 symmetrical, switching sequence selects pulse phase shift, and static stimulation amplitude is for being uniformly distributed, and other major parameters are as follows:

d₃=d₄=d₅=d_z=d_y=0.5 λ, h=d₁=0, d₂=0.25 λ

Also with this combined optimization algorithm optimization equivalent excitation amplitude (switch closing period), static stimulation phase Position, switch Guan Bi initial time this unit sum comprehensive is the isomery four-dimension battle array of 1584, quickly combine a secondary lobe for- 25.08dB, the first sideband is the directional diagram of-10.01dB, such as Figure 17, shown in Figure 18, Figure 19.It should be noted that in comprehensive mistake The first step the spent time in journey is about about 1 hour, adds submatrix optimisation technique, optimized variable sum in second step Being only 48, differential evolution algorithm also can be restrained rapidly.

This combined optimization algorithm is despite proposing for isomery four-dimension battle array, but its application is never only limited to this, any Similar large-scale optimization problem all rapidly and efficiently can solve by the method.

Be above to be familiar with field of the present invention engineers and technicians provide to the present invention and the description of embodiment thereof, These descriptions should be considered to be illustrative and not restrictive.Engineers and technicians can be accordingly in invention claims Thought combines particular problem and does concrete operation and implement, and naturally also according to the above, embodiment can be done a series of change More.Above-mentioned these are regarded as the coverage of the present invention.

Claims (3)

1. the present invention proposes a kind of method combining convex optimization and the comprehensive large-scale isomery four-dimension battle array of differential evolution algorithm, its feature It is fully to have excavated the mathematics essence of large-scale isomery four-dimension battle array synthtic price index, the part convexity that the most former optimization problem exists.Cause We are divided into two simple optimization problems former optimization problem for this, are divided into two steps for the simple optimization problem of the two and carry out Solve.I.e. to convex problematic portion, we take convex optimization method to carry out comprehensively, and for non-convex problematic portion, we utilize difference to enter Change algorithm to be optimized.Making full use of the two algorithm institute inherent advantages own, realization rapidly and efficiently is to large-scale isomery four Tie up the comprehensive, to reach the effect got twice the result with half the effort of battle array.

The most according to claim 1, to carry out large-scale isomery four-dimension battle array comprehensive for combined optimization method, it is characterised in that mid frequency The secondary lobe characteristics such as the directional diagram at place has；When carrying out comprehensive to sideband directional diagram, major part optimized variable is calculated by convex optimization Method determines, recycles submatrix optimisation technique, and the optimized variable of differential evolution algorithm can be greatly reduced so that differential evolution algorithm is also Can Fast Convergent.The two Global Optimality being possible not only to guarantee optimize the solution of gained of associating, and the efficiency solved compared to Traditional randomized optimization process also can be greatly improved.

The most according to claim 1, combined optimization method, be further characterized in that it is not only applicable to large-scale isomery four-dimension battle array Comprehensively, for other any kind of arrays, as long as meeting the central idea of this integrated processes, we can take the method to enter Row is comprehensive, and therefore its versatility is stronger.