CN106356641A - Array antenna designing method of polynomial and particle swarm mixing method - Google Patents

Abstract

The invention provides an array antenna designing method of a polynomial and particle swarm mixing method, and relates to a thinned array antenna. The array antenna designing method of the polynomial and particle swarm mixing method comprises the following steps: (1) setting parameters of an array antenna according to actual demands; (2) setting a control parameter of particle swarm optimization according to a parameter of the array antenna; (3) selecting an order n of a polynomial, and initializing a particle swarm; (4) solving position distribution of various array elements by using position vectors of particles; (5) calculating whether the particles meet a constraint condition or not according to a model constraint condition, namely calculating whether the particles are in a feasible region or not; (6) judging whether array element distribution shown by the particles is good or bad according to a fitness function and a penalty function, and updating the position vectors and speed vectors of the particles; (7) repeating the step (4), the step (5) and the step (6), and searching optimum of the various current particles and experienced global optimum of all the particles; and (8) carrying out iteration repeatedly, searching to obtain convergent optimal particles, substituting the position vectors of the optimal particles into an array element distribution polynomial, and solving the optimized array distribution.

Description

Multinomial and the array antenna design method of population mixed method

Technical field

The present invention relates to thinned array antenna, especially relate to the array antenna design of multinomial and population mixed method Method.

Background technology

Array antenna arrangement mode can be divided into all even uneven arrangement, is claimed by the array that the array element of uneven arrangement forms For Unequal distance array, otherwise it is equidistant array.Non-uniform spacing array mainly has the advantage that 1) there is phase with uniform intervals array Same main lobe width, when that is, aperture is approximate, needs less antenna element, reduces the expense of whole system；2) pass through to optimize Element position is distributed, and can be achieved with Sidelobe characteristic etc. amplitude feed, simplifies feed system.

Non-uniform spacing array can be divided into thinned array and thinning array according to the arrangement mode of array element.Thinning array is A kind of array of element position Arbitrary distribution, element position distribution has very big degree of freedom, it is possible to obtain radiation characteristic is more preferable Optimum results.Thinned array antenna passes through to adjust element position or element position and array element excitation controls the radiation of array special Property, optimizing degree of freedom is more than uniform array and thinned array, can reduce the Peak sidelobe level of antenna pattern further.Base In the above-mentioned advantage of thinning array, thinning array has in fields such as radar, navigation, communication and radio astronomies and is widely applied very much Potentiality.

The optimization design of thinned array antenna is with regard to the multivariate of position distribution, multiple constraint nonlinear problem.Up till now Till had that a large number of researchers propose various thinned array antenna Optimized arrays tradition approximate analytical methods and intelligent optimization is calculated Method.Wherein traditional approximate analytical method mainly includes based on the approximate Taylor's distribution of Poisson summation, exponential, is based on Fu Vertical leaf transformation approximate integration technology, the density taper pin method based on graphic technique are although these methods are obtained for thinning array relatively Optimize element position distribution, but be substantially during theoretical derivation used Approximate Equivalent so as to get termination Fruit be suboptimal solution it is impossible to obtain optimal solution truly, the effect of optimization to minor level is limited；Using calculating The perturbation method of machine numerical analysis techniques, the method for exhaustion, statistic law, the method for exhaustion can obtain the element position distribution of optimum, but by It is very difficult to apply in the more array design of array element number in the too big limitation of amount of calculation.

With the development of computer technology, intelligent optimization algorithm is widely used in the Pattern Synthesis kind of thinning array, bag Include genetic algorithm, simulated annealing, ant group algorithm, particle algorithm etc..Although however, these can only algorithm can be in overall model Enclose interior search optimal solution, but still solving precision and solving speed is high, Premature Convergence, calculating can be made when array element number is more Amount increases, and takies computer resource excessive.Therefore, finding the more optimal technology of structuring the formation is an important research direction.

Content of the invention

It is an object of the invention to provide a kind of array antenna design method of multinomial and population mixed method.

The present invention comprises the following steps:

1) parameter of setting array antenna according to the actual requirements；

2) parameter according to array antenna, sets the control parameter of particle cluster algorithm；

3) choose polynomial exponent number n, initialize population；

4) position distribution of each array element is tried to achieve with the position vector of particle；

5) according to model constraints, calculate particle whether meet the constraint condition, that is, whether this particle is in feasible zone；

6) quality of the array element distribution that particle represents is passed judgment on according to fitness function and penalty, and the position of more new particle Put vector velocity；

7) repeat step 4)～6), search for the global optimum that the optimum and all particle of each particle current lives through；

8) carry out successive ignition, search obtains the optimal particle restraining, then the position vector of optimal particle is substituted into array element Distribution polynomials, try to achieve the distribution of the array element after optimization.

In step 1) in, described parameter includes array aperture, array element number, array element minimum spacing constraints etc..

In step 2) in, described parameter includes number of particles, optimizing space bound, inertia weight, aceleration pulse, iteration Number of times etc..

In step 3) in, described polynomial exponent number n selection range is 2～9；With regard to polynomial exponent number n in the present invention Select permeability, in theory for, polynomial exponent number is higher, and multinomial more approaches optimized position distribution function, But during actual optimization, the multinomial of too high exponent number can lead to optimum results easily to converge to infeasible domain, and too high Exponent number can increase amount of calculation and the optimization time of algorithm, so compromise considers it is proposed that selecting polynomial exponent number n to be 4～6 Rank.

The present invention, in optimizing spatially lower range, removes to optimize polynomial coefficient with particle cluster algorithm, polynomial The lower limit in the optimizing space of each coefficient is -100～-1, and the upper limit is 1～100.Optimized variable bound with regard to population Setting problem, in theory for the bound of optimized variable can be whole real number field, but if scope is too big Optimized algorithm can be led to be absorbed in local convergence after the iterationses setting, do not reach optimal solution, and hunting zone is excessive The optimal speed of algorithm can be affected, so suggestion selects less bound scope.

All array elements in the present invention are mutually encouraged using constant amplitude etc..

The invention provides a kind of method that is combined of element position polynomial repressentation and particle cluster algorithm is realizing Thinned arrays The optimal design of array antenna array element distribution, the present invention does not directly optimize element position, but by optimizing polynomial coefficient, Connect optimization element position distribution, lead to too small amount of multinomial coefficient and control most element positions, advantageously reduce intelligent algorithm Operand.Additionally, the array antenna through optimization design has low-sidelobe level, the phase feeding network such as simplest constant amplitude, Both decreased radiation loss, reduced design and manufacturing cost again, had in fields such as radar, navigation, communication and radio astronomies Potential commercial value.

Compared with the method for designing of existing thinned array antenna, the remarkable advantage of the present invention is as follows:

1st, optimize the coefficient of array element distribution polynomials by particle cluster algorithm, efficiently reduce the operand of algorithm；

2nd, have the advantages that particle cluster algorithm flow process simple, in high precision, fast convergence rate, the array element distribution after optimization is Excellent solution, has the low characteristic of array minor level；

3rd, array element mutually encourages using with constant amplitude etc., has simplest feeding network, greatly reduces and be designed and manufactured as This.

Brief description

Fig. 1 is the thinned array antenna schematic diagram symmetrical with regard to array center of the embodiment of the present invention.

Fig. 2 is that the multinomial of the embodiment of the present invention is divided with the right half part array element of population mixed method thinned array antenna Cloth position.

Fig. 3 is the antenna pattern with population mixed method thinned array antenna for the multinomial of the embodiment of the present invention.

Specific embodiment

Following examples will combine accompanying drawing, and the present invention is further illustrated.

The design procedure of the embodiment of the present invention is as follows:

Step 1: the parameter of setting array antenna according to the actual requirements: array aperture, array element number, array element minimum spacing are about Bundle condition；

The thinned linear arrays antenna of the present embodiment is symmetrical with regard to array center, the element number of array m=16 on the right side of array, that is, Array element sum is 2m=32, array aperture l=20 λ, minimum spacing d between array element_c=λ/2, wherein λ are the operation wavelength of array, First element position d₁≥0.5d_c, last element position d_m=l/2, as shown in Figure 1.

Step 2: according to the parameter of array antenna, set the control parameter of particle cluster algorithm: number of particles, optimizing are spatially Lower limit, inertia weight, aceleration pulse, iterationses；

In the present embodiment, population number of particles is 100, and optimized variable is { d₁,d₂,d₃,…d₁₆, wherein d_iFor i-th gust The position of unit, dimension d=n, aceleration pulse c₁=2.05 and c₂=2.05, inertia weight w is set as:

$\begin{array}{cc}w=w_{max}-\frac{t}{t}(w_{max}-w_{min})& w\&element;\[0.2,0.9\]\end{array}---\left(1\right)$

Wherein, w_max, w_minIt is respectively the minimum and maximum value of w, total iterationses are set to t=2000, and t represents t Secondary iteration；In solution room, the lower boundary of each dimension is set to x_min=[- 1, -10, -10 ... -10], coboundary is set to x_max=[1, 10,10,…10]；

Step 3: choose polynomial order n, initialize population；

In the present embodiment, exponent number n selects 4,5,6 to be optimized design respectively.Random initializtion population, obtains primary Position vector x₁={ x₁₁,x₁₂,…x_1dAnd velocity v₁={ v₁₁,v₁₂,…,v_1d}；The position vector x of i-th particle_i ={ x_i1,x_i2,…x_idAnd velocity v_i={ v_i1,v_i2,…,v_id}；

Step 4: try to achieve the position distribution of each array element with the position vector of particle；

Polynomial expression is formula (2a) with the corresponding relation of array element numbering, element position distribution and multinomial coefficient relation For formula (2b), using the position vector of particle as polynomial coefficient, try to achieve the position distribution of each array element.

$f\left(m\right)=x_0+x_1\frac{m}{m}+x_2{\left(\frac{m}{m}\right)}^2+...x_n{\left(\frac{m}{m}\right)}^n---\left(2a\right)$

$d_m=\frac{l}{2}\·f\left(m\right)=\frac{l}{2}\[x_0+x_1\frac{m}{m}+x_2{\left(\frac{m}{m}\right)}^2+...x_n{\left(\frac{m}{m}\right)}^n\]---\left(2b\right)$

Wherein, d_mRefer to the array element distribution of m-th array element, wherein x_iRepresent position vector in i-th value, x₀=1- (x₁ +x₂+…x_n).

Step 5: according to model constraints, calculate particle whether meet the constraint condition, that is, whether this particle is in feasible zone；

The present embodiment model constraints is formula (3), the position vector of particle is substituted in formula (3), judges that this particle is No in feasible zone.

$\begin{array}{cc}s.t.& g(x_1,x_2,...x_n)=\left\{\begin{array}{cc}\[f\left(m\right)-\frac{1}{l}{d}_c\]\&greaterequal;0& m=1\\ \[f\left(m\right)-f(m-1)-\frac{2}{l}{d}_c\]\&greaterequal;0& m=2,3...m\end{array}\right.\end{array}---\left(3\right)$

Step 6: the quality of the array element distribution that particle represents is passed judgment on according to fitness function and penalty, and more new particle Position vector and velocity；

With the Peak sidelobe level of thinning array antenna pattern as optimization aim, its fitness function is formula to the present invention (4a):

$fitness(d_1,d_2,...d_m)=max\left|\frac{2\underset{m=1}{\overset{m}{\mathrm{\σ}}}{a}_{m}cos\left({\mathrm{ud}}_m\right)}{e_{max}}\right|---\left(4a\right)$

Wherein, a_mNormalization for array element encourages amplitude, u=k (sin θ-sin θ_main), k is that the propagation in free space is normal Number, θ is the angle gust between axle and radiation direction, θ_mainIt is the angle of main radiation direction and battle array axle, the Thinned arrays of the present embodiment Arrange each array element excitation amplitude all equal, i.e. a_m=1, e_maxIt is antenna pattern main lobe maximum.

Penalty is formula (4b):

$p\left(x\right)=\mathrm{\ξ}\·\[\underset{i=1}{\overset{m}{\mathrm{\σ}}}\left|min(0,g_i(x_1,x_2,...x_n\left)\right)\right|\]---\left(4b\right)$

Wherein penalty weighter factor ξ=10⁸, x=(x₁,x₂,…x_n) it is the n multinomial representing element position function Coefficient；

It is formula (4c) that fitness function and penalty are combined into a new object function:

$f(x_1,x_2,...x_n)=\left\{\begin{array}{cc}fitness(x_1,x_2,...x_n)& x\&element;f\\ \mathrm{\ξ}\·\[\underset{i=1}{\overset{m}{\mathrm{\σ}}}\left|\min (0,g_i(x_1,x_2,...x_n\left)\right)\right|\]& x\&notelement;f\end{array}\right.---\left(4c\right)$

Wherein f is the feasible zone meeting formula (3) constraints.

The present embodiment is to the selection of particle in the following ways:

(1) if two particle x_iAnd x_jIt is all feasible solution, then directly compare both fitness value fitness (x_i) With fitness (x_j), select fitness value minimum for excellent；

(2) if two particle x_iAnd x_jIt is all infeasible solution, then compare penalty value p (x_i) and p (x_j), choose The little particle of penalty value is excellent；

(3) if particle x_iIt is feasible solution, particle x_jIt is infeasible solution, then choose x_iFor excellent particle.

The equation of the speed and position that update i-th particle in the present embodiment is formula (5a) and (5b):

$v_i^t=w\·v_i^{t-1}+c_1{r}_{1i}^t\·({\mathrm{pbest}}_i^t-x_i^{t-1})+c_2{r}_{2i}^t\·({\mathrm{gbest}}^t-x_i^{t-1})---\left(5a\right)$

$x_i^t=x_i^{t-1}+v_i^t---\left(5b\right)$

Wherein, t is the current iterationses of algorithm,WithIt is i-th particle position arrow in the t-1 time iteration Amount and velocity；pbest_i={ p_i1,p_i2,…p_idBe the optimum that i-th particle is lived through position, gbest={ p_g1, p_g2,,p_gdIt is optimized position in the optimal location that all particles live through.

Step 7: repeat step 4～6, the history optimum pbest of search each particle current_i={ p_i1,p_i2,…p_idAnd Global optimum gbest={ the p that all particles live through_g1,p_g2,…p_gd}.

Step 8: carry out successive ignition, search obtains the particle of the optimum of convergence, recycles the position vector back substitution of particle Enter polynomial expression, try to achieve the distribution of the array element after optimization.

After k iteration, the optimal particle of the convergence searching is final gbest={ p_g1,p_g2,…p_gd, this reality Apply example in n=4,5,6 make the multinomial optimized coefficients that obtain as shown in table 1, by the multinomial coefficient of table 1 substitute into formula (2a) and (2b) array element distribution after being optimized in, element position distribution is as shown in Fig. 2 adopt the many of different rank as can be seen from Figure 2 Item formula optimizes the element position of thinning array, and the optimization element position distribution obtaining is approximately the same.Finally, element position is divided Cloth substitutes in the direction schema (6) of array:

$f\left(u\right)=2\underset{m=1}{\overset{m}{\mathrm{\σ}}}{a}_m\cos \left({\mathrm{ud}}_m\right)---\left(6\right)$

Table 1

	x0	x1	x2	x3	x4	x5	x6
								N=4	-0.034	1.0000	-0.958	1.737	-0.745
N=5	-0.0210	0.6790	1.209	-3.948	5.586	-2.505
								N=6	-0.0120	0.470	2.746	-8.038	10.000	-4.164	-0.002

Thinned array antenna directional diagram after final optimization pass is as shown in figure 3, the Thinned arrays that obtain of 4～6 rank multinomial optimizations Row antenna pattern radiation characteristic in visual field is good, and Peak sidelobe level is about -20.41db.Using multinomial and particle Group's hybrid optimization algorithm optimizes the distribution of thinning array element position, in the not many array of array element number, by choosing 4～6 Rank multinomial represents that element position is distributed, and the various dimensions problem optimizing each element position is converted into optimizing multinomial coefficient Problem, decreases the number of optimized variable, decreases amount of calculation and operation time.And same array element number and array aperture When, mixed method is lower than directly obtaining Peak sidelobe level using particle swarm optimization algorithm.Illustrate that the present invention is a kind of feasible Solution thinning array Optimization Design.

With a n-order polynomial, the present invention parameter needed for initialization system according to the actual requirements, represents that element position is distributed, Optimize this polynomial coefficient with particle cluster algorithm again, pass judgment on the quality of array element distribution using fitness and penalty, pass through Successive ignition is searched for, and obtains the array distribution of optimum.The method that element position polynomial repressentation is combined with particle cluster algorithm, leads to Cross and optimize polynomial coefficient, indirectly optimize element position distribution, lead to too small amount of multinomial coefficient and control most array element positions Put, advantageously reduce the operand of intelligent algorithm, lift array antenna performance, present invention incorporates particle cluster algorithm flow process is simple Single, operational precision is high, the feature of fast convergence rate, finds object function by using particle swarm optimization algorithm optimized multinomial Formula coefficient combines, and realizes the optimization design of thinned array antenna.

Claims (6)

1. multinomial and the array antenna design method of population mixed method are it is characterised in that comprise the following steps:

1) parameter of setting array antenna according to the actual requirements；

2) parameter according to array antenna, sets the control parameter of particle cluster algorithm；

3) choose polynomial exponent number n, initialize population；

4) position distribution of each array element is tried to achieve with the position vector of particle；

5) according to model constraints, calculate particle whether meet the constraint condition, that is, whether this particle is in feasible zone；

6) quality of the array element distribution that particle represents is passed judgment on according to fitness function and penalty, and the position arrow of more new particle Amount and velocity；

7) repeat step 4)～6), search for the global optimum that the optimum and all particle of each particle current lives through；

8) carry out successive ignition, search obtains the optimal particle restraining, then the position vector of optimal particle is substituted into array element distribution Multinomial, tries to achieve the distribution of the array element after optimization.

2. the array antenna design method of multinomial as claimed in claim 1 and population mixed method is it is characterised in that in step In rapid 1), described parameter includes array aperture, array element number, array element minimum spacing constraints.

3. the array antenna design method of multinomial as claimed in claim 1 and population mixed method is it is characterised in that in step In rapid 2), described parameter includes number of particles, optimizing space bound, inertia weight, aceleration pulse, iterationses.

4. the array antenna design method of multinomial as claimed in claim 1 and population mixed method is it is characterised in that in step In rapid 3), described polynomial exponent number n selection range is 2～9.

5. the array antenna design method of multinomial as claimed in claim 4 and population mixed method is it is characterised in that described Polynomial exponent number n is 4～6 ranks.

6. the array antenna design method of multinomial as claimed in claim 1 and population mixed method is it is characterised in that in step In rapid 4), all array elements are mutually encouraged using constant amplitude etc..