CN113311395A

CN113311395A - Subarray division and subarray weight combined optimization method based on genetic algorithm

Info

Publication number: CN113311395A
Application number: CN202110685185.4A
Authority: CN
Inventors: 陈希信; 王洋; 李坡; 弓盼; 张庆海
Original assignee: Nanjing Vocational University of Industry Technology NUIT
Current assignee: Nanjing Vocational University of Industry Technology NUIT
Priority date: 2021-06-21
Filing date: 2021-06-21
Publication date: 2021-08-27
Anticipated expiration: 2041-06-21
Also published as: CN113311395B

Abstract

The invention discloses a subarray division and subarray weight combined optimization method based on a genetic algorithm, which comprises the following steps: s1, establishing a coding scheme of the genetic algorithm chromosome, wherein the subarray division adopts Grefenstette coding, and the subarray weight adopts binary coding; s2, determining a cost function of subarray division and subarray weight combined optimization; and S3, establishing an optimization iteration process of the genetic algorithm, and giving an optimal subarray division structure and subarray weight after convergence, thereby forming a difference beam. According to the invention, the sub-array division adopts Grefenstette coding to avoid the individual deletion or repetition problem of binary coding, the sub-array weight adopts binary coding, and the two codes form a mixed chromosome for optimization iteration of a genetic algorithm to perform combined optimization solution, so that an ideal difference beam is formed, and the performance of radar sum and difference monopulse angle measurement and the target tracking capability of radar are improved.

Description

Subarray division and subarray weight combined optimization method based on genetic algorithm

Technical Field

The invention relates to the technical field of subarray division of array antennas, in particular to a method for jointly optimizing subarray division and subarray weight based on a genetic algorithm.

Background

In a large array antenna radar, the subarray technology can greatly reduce the implementation difficulty and the manufacturing cost of a system, so that the subarray technology is widely adopted. However, what subarray technique is adopted has a great influence on the performance of the radar system, and is a problem of high concern.

In many radar systems, the sum beam of the array antenna is usually used for target detection, and the sum beam and the difference beam are used for target angle measurement together, so that the sum beam is required to be optimally formed at an array element level, the difference beam is optimally formed at a subarray level through a subarray technology, and at the moment, subarray division and subarray weight of the difference beam need to be jointly optimized and solved. In the literature (L Lopez P, Rodri i guez J A, areas F. Subarray weighting for the difference patterns of monobasic antennas: joint optimization of subarray configurations and weights [ J ]. IEEE trans. on AP,2001,49(11):1606-1608.) a binary-coding-based genetic algorithm is used to partition subarrays and perform digital difference beamforming. The subarray division actually needs to search for separation points among array elements, the separation points are random numbers, and if a genetic algorithm based on binary coding is adopted, individual deletion or repetition is generated, so that the problem is difficult to avoid.

Disclosure of Invention

This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.

The present invention has been made in view of the above and/or problems occurring in the existing binary-coded genetic algorithms.

Therefore, the invention aims to provide a subarray division and subarray weight combined optimization method based on a genetic algorithm, wherein Grefenstette codes are adopted for subarray division to avoid the individual deletion or repetition problem of binary codes, binary codes are adopted for subarray weights, and a mixed chromosome is formed by the two codes to be used for optimization iteration of the genetic algorithm.

To solve the above technical problem, according to an aspect of the present invention, the present invention provides the following technical solutions:

a subarray division and subarray weight combined optimization method based on a genetic algorithm comprises the following steps:

s1, establishing a coding scheme of the genetic algorithm chromosome, wherein the subarray division adopts Grefenstette coding, and the subarray weight adopts binary coding;

s2, determining a cost function of subarray division and subarray weight combined optimization;

and S3, establishing an optimization iteration process of the genetic algorithm, and giving an optimal subarray division structure and subarray weight after convergence, thereby forming a difference beam.

As a further preferable embodiment of the present invention, the step S1 is to establish a coding scheme of genetic algorithm chromosomes, wherein the subarray division uses grefenttte coding, the subarray weights use binary coding, specifically,

s1-1), dividing N array elements in the N element array into M sub-arrays which are mutually adjacent, wherein the number of the array elements of the M sub-array is N_mM is 1,2, so, M, N is N₁+N₂+…+N_M(ii) a N is a natural number and an even number, and M is a predetermined natural number and an even number;

the N-element array is an N-element uniform linear array, and a received signal of the N-element array directly forms a sum beam after passing through a phase shifter, an array element attenuator and two-stage summation operation; adding a subarray attenuator to the output end of the subarray after the received signals of the N-element array pass through a phase shifter, an array element attenuator and a primary summation operation, and synthesizing output signals of the subarray into a difference beam after passing through the subarray attenuator;

s1-2), in the chromosome population of the genetic algorithm, each chromosome is composed of M/2+1 genes;

the first gene describes a sub-array division scheme, and Grefenstette coding is adopted, namely based on the symmetry of a uniform linear array, N/2 array elements of the linear array are divided into M/2 sub-arrays to obtain M/2-1 separation points, and then the M/2-1 separation points are converted into Grefenstette codes;

the latter M/2 genes respectively represent the weight values of the M/2 sub-arrays, and binary coding is adopted, namely the M/2 genes are formed by 8-bit binary codes;

wherein, the weight of the subarray is converted from binary coding gene to real number by the formula,

in the formula, g_mIs the weight of the mth subarray, h_m+1(k) Denotes the kth position of the m +1 gene in the chromosome, a being an intermediate variable.

As a further preferred embodiment of the present invention, the step S2 determines a cost function for joint optimization of subarray division and subarray weight, specifically,

the maximum side lobe level of the difference beam pattern is brought close to a desired side lobe level, and therefore a cost function is used,

min[|α-α_d|D(α-α_d)] (2)

where α is the current difference beam pattern maximum sidelobe level, α_dFor the desired side lobe level, D (-) is a step function, i.e.

As a further preferred scheme of the present invention, the step S3 establishes an optimization iterative process of the genetic algorithm, and gives an optimal subarray division structure and subarray weights after convergence, thereby forming a difference beam, specifically, S3-1), generating an initial chromosome population;

randomly generating M/2-1 different natural numbers on the interval of 1-N/2-1 as subarray separation points, and converting the M/2-1 separation points into Grefenstette codes; randomly generating M/2 different 8-bit binary random sequences as subarray weights; the Grefenstette code and M/2 binary sequences form a chromosome of a genetic algorithm; repeating the above processes to generate a plurality of chromosomes, wherein the plurality of chromosomes form an initial chromosome population;

s3-2), evaluating the fitness value;

calculating a difference beam pattern corresponding to each chromosome, then obtaining the maximum side lobe level of each difference beam pattern, substituting the obtained maximum side lobe level into a formula (2), evaluating each chromosome in a population by taking the reciprocal of the formula (2) as a fitness value, finding out the chromosome with the current best fitness value, namely the maximum fitness value, and the chromosome with the worst fitness value, namely the chromosome with the minimum fitness value, and then replacing the worst chromosome with the optimal chromosome, thereby generating the next generation;

s3-3), selecting operation;

selecting by roulette according to the fitness value obtained in the step S3-2);

s3-4), Grefenstette coding;

before crossing and mutation, converting natural numbers in a first gene into Grefenstette codes;

s3-5), and performing crossover operation;

adopting discrete two-point intersection;

s3-6), mutation operation;

chromosome with probability P_m(ii) mutation, if the grefentte code is mutated, the coding of the mutated position is replaced by any of the remaining M/2-2 grefentte codes to generate a new chromosome; if the binary code is mutated, the code of the mutated position is replaced by any one of the remaining 4M-1 binary codes to generate a new chromosome;

s3-7), Grefenstette code inverse transformation;

after crossing and mutation, the Grefenstette code in the first gene is inversely converted into subarray separation points;

s3-8), evaluating the fitness value again;

calculating a difference beam pattern corresponding to each chromosome, acquiring a current fitness value, evaluating each chromosome in the population through the current fitness value again, finding out a current optimal chromosome and a worst chromosome, and replacing the worst chromosome with the optimal chromosome;

s3-9), circulation and termination;

and if the fitness value does not reach the acceptable magnitude or the optimization iteration process does not reach the preset maximum evolution algebra, returning to the step S3-3), continuing the loop process from the step S3-3) to the step S3-8), and otherwise, terminating the loop to obtain the optimal chromosome and give the optimal subarray division structure and subarray weight.

As a further preferable scheme of the invention, the value range of a in the formula (1) is 0-31.875 dB, g_mThe value range of (a) is 0.0255-1.

Compared with the prior art, the invention has the beneficial effects that:

the method provided by the invention can jointly optimize and solve the problems of subarray division and subarray weight calculation of the large array antenna, can form a difference beam with ideal main lobe shape and main-to-side lobe ratio for the radar adopting the sum beam and the difference beam to carry out monopulse angle measurement, and is favorable for improving the performance of the sum and difference monopulse angle measurement of the radar and the target tracking capability of the radar.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail with reference to the accompanying drawings and detailed embodiments, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise. Wherein:

FIG. 1 is a flow chart of a method for joint optimization of subarray division and subarray weight based on genetic algorithm according to the present invention;

FIG. 2 is a diagram of array element level and wave beam and sub-array level difference wave beam of a method for sub-array division and sub-array weight joint optimization based on a genetic algorithm;

FIG. 3 is the structure of a mixed-code chromosome;

FIG. 4 is an evolutionary process of a genetic algorithm;

FIG. 5 is a subarray level difference beam pattern of the genetic algorithm of the method for jointly optimizing subarray division and subarray weight based on the genetic algorithm of the present invention.

Detailed Description

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described herein, and it will be apparent to those of ordinary skill in the art that the present invention may be practiced without departing from the spirit and scope of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.

Next, the present invention will be described in detail with reference to the drawings, wherein for convenience of illustration, the cross-sectional view of the device structure is not enlarged partially according to the general scale, and the drawings are only examples, which should not limit the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The invention provides a subarray division and subarray weight combined optimization method based on a genetic algorithm.

With reference to fig. 1, the method for joint optimization of subarray division and subarray weight based on genetic algorithm provided by the present invention includes the following steps:

Wherein S1 establishes a coding scheme of genetic algorithm chromosome, wherein subarray division adopts Grefenstette coding, subarray weight adopts binary coding, specifically,

s1-1), dividing N array elements in the N element array into M sub-arrays which are mutually adjacent, wherein the number of the array elements of the M sub-array is N_mM is 1,2, …, M, N is N₁+N₂+...+N_M(ii) a N is a natural number and an even number, and M is a predetermined natural number and an even number;

the N-ary array is an N-ary uniform linear array, and as shown in fig. 2, a received signal of the N-ary array directly forms a sum beam after passing through a phase shifter, an array element attenuator and two-stage summation operation; and adding a subarray attenuator at the output end of the subarray after the received signals of the N-element array pass through a phase shifter, an array element attenuator and a primary summation operation, and synthesizing the output signals of the subarray into a difference beam after passing through the subarray attenuator.

As shown in fig. 2, for an N-element uniform linear array, a phase shifter and an array element attenuator are connected behind each array element for controlling the sidelobe level and direction of the sum beam. In the sum and difference beamforming of FIG. 2, the weights of the array element attenuators w_nN is optimal for sum beamforming, whereas the weight of the subarray division and the subarray attenuators { g } is optimal_mM is unknown, 1, 2. On the basis that the number M of the subarrays is predetermined, the invention simultaneously optimizes and solves the subarray division and the weight of the attenuator of the subarray through a genetic algorithm, thereby providing more ideal difference beams.

the first gene describes a subarray division scheme, and Grefenstette coding is adopted, namely based on the symmetry of a uniform linear array, N/2 array element arrays of the linear array are divided into M/2 subarrays to obtain M/2-1 separation points, and then the M/2-1 separation points are converted into Grefenstette codes;

The value range of a in the formula (1) is 0-31.875 dB, g_mThe value range of (a) is 0.0255-1; if the number of genes is too small, the accuracy is insufficient, and if it is too large, the accuracy is not necessarily high.

An example of a grephentette code: let N be 20, the subarray separation point s: [2,13,16,18], which may be encoded as gredenstette code s': [2,12,14,15], as follows:

by separating points s by array elements₀:[1,2,3,…,19]For reference, take the first number from s, i.e. "2", and place it in s₀Is taken as the Grefenstette code, namely "2", and then is taken as the following step s₀Delete this number to get updated s₀:[1,3,…,19]。

And repeating the process, and continuously processing each number in the s to obtain the Grefenstette code of the s.

The detailed encoding process is shown in table 1, wherein the first column is the sub-array separation points, the second column is the sequential array element separation points, and the third column is the resulting gredenstette code.

TABLE 1Grefenstette coding procedure

The Grefenstette code obtained by the conversion is easy to transform the original subarray separation point by the inverse process of the Grefenstette code.

The chromosome needs to be coded when a genetic algorithm is applied, the invention optimizes the subarray division and the subarray weight simultaneously, the Grefenstette coding is adopted for the subarray division, the binary coding is adopted for the subarray weight, and the two form a mixed coding chromosome so as to avoid the individual deletion or repetition problem of the binary coding. For the uniform linear array, considering the symmetry of the array, only half of the array surface needs to be optimized, and half of the array is divided into M/2 sub-arrays, so that M/2-1 separation points exist, and the separation points are converted into M/2-1 Grefenstette codes. The latter M/2 genes respectively represent the weights of the M/2 subarrays, and each gene is composed of 8-bit binary codes. The hybrid coding chromosome structure is shown in FIG. 3.

Wherein, in step S2, a cost function for joint optimization of subarray division and subarray weight is determined, specifically,

min[|α-α_d|D(α-α_d)] (2)

Wherein, step S3 is to establish an optimized iterative process of the genetic algorithm, and to provide an optimal subarray division structure and subarray weights after convergence, thereby forming a difference beam, specifically,

s3-1), generating an initial chromosome population;

randomly generating M/2-1 different natural numbers on the interval of 1-N/2-1 as subarray separation points, and converting the M/2-1 separation points into Grefenstette codes; randomly generating M/2 different 8-bit binary random sequences as subarray weights; the Grefenstette code and M/2 binary sequences form a chromosome of a genetic algorithm; repeating the above process to generate a plurality of chromosomes, wherein the plurality of chromosomes form an initial chromosome population, and the structure of the chromosome population is shown in FIG. 3;

s3-2), evaluating the fitness value;

s3-3), selecting operation;

s3-4), Grefenstette coding;

s3-5), and performing crossover operation;

adopting discrete two-point intersection;

the parent generation is as follows,

f_p＝{G_p,1,...,|G_p,i,...,G_p,j,|...,G_p,M/2-1；b_p，1,...,|b_p,k,...,b_p,l,|...,b_p,4M}

f_q＝{G_q,1,...,|G_q,i,...,G_q,j,|...,G_q,M/2-1；b_q,1,...,|b_q,k,...,b_q,l,|...,b_q,4M}

after the intersection of the two points, the child is,

s_p＝{G_p,1,...,|G_q,i,...,G_q,j,|...,G_p,M/2-1；b_p,1,...,|b_q,k,...,b_q,l,|...,b_p,4M}

s_q＝{G_q,1,...,|G_p,i,...,G_p,j,|...,G_q,M/2-1；b_q,1,...,|b_p,k,...,b_p,l,|...,b_q,4M}；

s3-6), mutation operation;

the parent generation is as follows,

f_p＝{G_p,1,...,G_p,i,G_p,i+1,...,G_p,M/2-1；b_p,1,...,b_p,k,b_p,k+1,...,b_p,4M}

if the Grefenstette code is mutated, the obtained offspring is,

s_p＝{G_p,1,...,G_p,j,G_p,i+1,...,G_p,M/2-1；b_p,1,...,b_p,k,b_p,k+1,...,b_p,4M}

wherein G is_p,jFor removing G in the parent_p,iAny one of outer M/2-2 Grefenstette codes;

if the binary code is mutated, the obtained offspring is,

s_p＝{G_p,1,...,G_p,i,G_p,i+1,...,G_p,M/2-1；b_p,1,...,b_p,l,b_p,k+1,...,b_p,4M}

wherein, b_p,lFor b in the parent generation_p,kAny one of the outer 4M-1 binary codes;

s3-7), Grefenstette code inverse transformation;

s3-8), evaluating the fitness value again;

s3-9), circulation and termination;

Referring to fig. 4 and 5, the optimization design method of the present invention is verified by simulation examples using the method of joint optimization of subarray division and subarray weight based on genetic algorithm of the present invention.

Considering a 40-element uniform linear array, the distance between array elements is half wavelength, the Taylor window of-35 dB is adopted for array element level and wave beam, the linear array is divided into 10 sub-arrays, and considering the symmetry of the array, only the genetic algorithm is needed to be utilized to carry out optimization processing on half array surface, 4 separation points among 5 sub-arrays and the weighted values output by the 5 sub-arrays are searched, the sub-arrays of the other half array surface are symmetrically divided, and the weighted values are the opposite numbers.

After 50 iteration cycles, the algorithm tends to converge, and the convergence process is shown in fig. 4, where the subarray interval point is [2,13,16,18] (see table 1), and the subarray level weights are [0.3073,1.0000,0.6131,0.3278,0.1014 ]. The poor beam pattern calculated after convergence, as shown in fig. 5, can be seen that the main lobe has a good shape, the side lobe levels are uniformly distributed (about-28 dB), and there is no significant grating lobe.

While the invention has been described above with reference to an embodiment, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In particular, the various features of the disclosed embodiments of the invention may be used in any combination, provided that no structural conflict exists, and the combinations are not exhaustively described in this specification merely for the sake of brevity and resource conservation. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. a method for sub-array division and sub-array weight joint optimization based on genetic algorithm, is characterized in that, comprises the following steps:

S1. Establish a coding scheme for genetic algorithm chromosomes, in which the sub-array division adopts Grefenstette coding, and the sub-array weights adopt binary coding;

S2. Determine the cost function of sub-array division and sub-array weight joint optimization;

S3, establish the optimization iterative process of the genetic algorithm, and give the optimal sub-array division structure and sub-array weights after convergence, thereby forming a difference beam.

2. a kind of method for subarray division and subarray weight joint optimization based on genetic algorithm according to claim 1, is characterized in that, described step S1 establishes the coding scheme of genetic algorithm chromosome, and wherein subarray division adopts Grefenstette coding , the sub-array weights are coded in binary, specifically,

S1-1), divide the N array elements in the N-element array into M sub-arrays adjacent to each other, the number of array elements of the m-th sub-array is N _m , m=1,2,...,M, which satisfies N =N ₁ +N ₂ +...+N _M ; N is a natural number and an even number, and M is a predetermined natural number and an even number;

Among them, the N-element array is an N-element uniform linear array, and the received signal of the N-element array directly forms a sum beam after passing through a phase shifter, an array element attenuator and a two-stage summation operation; the received signal of the N-element array passes through a phase shifter. , array element attenuator and sub-array attenuator is added to the sub-array output after the first-level summation operation, and the sub-array output signal is synthesized into a difference beam after the sub-array attenuator;

S1-2), in the chromosome group of the genetic algorithm, each chromosome is composed of M/2+1 genes;

The first gene describes the subarray division scheme, and uses Grefenstette coding, that is, based on the symmetry of the uniform linear array, the N/2 array elements of the linear array are divided into M/2 subarrays, and M/2-1 partitions are obtained. points, and then convert M/2-1 split points to Grefenstette codes;

The following M/2 genes respectively represent the weights of M/2 subarrays, which are coded in binary, that is, composed of M/2 8-bit binary codes;

Among them, the conversion formula of the weight of the sub-array from the binary encoded gene to the real number is,

g _m = 10 ^-a/20 ,

In the formula, g _m is the weight of the m-th subarray, h _m+1 (k) represents the k-th position of the m+1-th gene in the chromosome, and a is an intermediate variable.

3. a kind of method for sub-array division and sub-array weight joint optimization based on genetic algorithm according to claim 2, it is characterized in that, described step S2 determines the cost function of sub-array division and sub-array weight joint optimization, specifically for,

The maximum sidelobe level of the difference beam pattern is approximated to a desired sidelobe level, so the cost function is used as,

min[|α-α _d |D(α-α _d )] (2)

where α is the current maximum sidelobe level of the difference beam pattern, _αd is the desired sidelobe level, and D( ) is the step function, namely

4. a kind of method based on genetic algorithm sub-array division and sub-array weight joint optimization according to claim 3, it is characterized in that, described step S3 establishes the optimization iterative process of genetic algorithm, provides optimal after convergence. The sub-array divides the structure and the sub-array weights to form a difference beam, specifically,

S3-1), generate the initial chromosome population;

Randomly generate M/2-1 different natural numbers as sub-matrix separation points in the interval 1～N/2-1, and then convert M/2-1 separation points into Grefenstette codes; randomly generate M/2 different natural numbers The 8-bit binary random sequence is used as the subarray weight; this Grefenstette code and M/2 binary sequences constitute a chromosome of the genetic algorithm; repeat the above process to generate several chromosomes, and several chromosomes constitute the initial chromosome population;

S3-2), evaluate the fitness value;

Calculate the difference beam pattern corresponding to each chromosome, then obtain the maximum side lobe level of each difference beam pattern, substitute the obtained maximum side lobe level into equation (2), and use the inverse of equation (2) as The fitness value evaluates each chromosome in the population, and finds the current best, that is, the chromosome with the largest fitness value and the worst, that is, the chromosome with the smallest fitness value, and then replaces the worst chromosome with the optimal chromosome. to produce the next generation;

S3-3), select operation;

According to the fitness value obtained in step S3-2), a roulette wheel is used for selection operation;

S3-4), Grefenstette coding;

Convert the natural numbers in the first gene to Grefenstette codes before crossover and mutation;

S3-5), cross operation;

Use discrete two-point intersection;

S3-6), mutation operation;

The chromosome is mutated with probability P _m , if the Grefenstette code is mutated, the coding of the mutated position is replaced by any one of the remaining M/2-2 Grefenstette codes to generate a new chromosome; if the binary code is mutated , then the coding of the mutated position is replaced by any one of the remaining 4M-1 binary codes to generate a new chromosome;

S3-7), Grefenstette encoding inverse conversion;

After crossover and mutation, the Grefenstette codes in the first gene are inversely converted to subarray separation points;

S3-8), evaluate the fitness value again;

Calculate the difference beam pattern corresponding to each chromosome, obtain the current fitness value, evaluate each chromosome in the population again through the current fitness value, find the current optimal chromosome and the worst chromosome, and then use the optimal chromosome replace the worst chromosome;

S3-9), cycle and termination;

If the fitness value does not reach an acceptable value or the optimization iterative process does not reach the preset maximum evolutionary algebra, return to step S3-3) and continue the loop process from step S3-3) to step S3-8), otherwise terminate the loop , get the optimal chromosome, and give the optimal sub-array division structure and sub-array weights.

5. a kind of method of sub-array division and sub-array weight joint optimization based on genetic algorithm according to claim 3, it is characterized in that, the value range of a in formula (1) is 0～31.875dB, g _m The value ranges from 0.0255 to 1.