CN115329558A - Cylindrical array antenna optimization method based on chaotic sparrow search algorithm - Google Patents
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Abstract
The invention provides a cylindrical array antenna optimization method based on a chaotic sparrow search algorithm, which comprises the following steps: (1) establishing a thin cloth cylindrical array model; (2) constructing a fitness function; (3) initializing a population by adopting a Tent chaotic sequence; (4) Calculating a fitness function value of an initial population individual, and recording the fitness function value of the optimal individual and a corresponding position of the fitness function value; (5) Sequencing individuals in the population according to fitness function values, and optimizing the positions of the individuals by adopting an updating strategy of a chaotic sparrow searching algorithm; (6) Comparing and updating the fitness function value in the process of updating the individual position by the algorithm, judging whether the maximum iteration times are reached or not after one iteration is completed, and if not, returning to the step (5); if yes, outputting an optimal arrangement scheme of the thin-cloth cylindrical array. The invention can effectively reduce the number of the cylindrical array antennas, reduce the peak side lobe level and has important reference significance for the practical application of the thin conformal array in an antenna system.
Description
Technical Field
The invention belongs to the field of array antennas, and relates to a sparse distribution optimization array method of a cylindrical array antenna, which is used for inhibiting side lobes of a sparse array antenna directional diagram.
Background
According to different arrangement forms of array elements, the array antenna can be divided into a one-dimensional linear array, a two-dimensional planar array and a three-dimensional conformal array. Because the radiation beams of the linear array and the planar array have the advantages of rapid scanning, beam forming and the like, the radiation beams are in a mature array form at present, but the radiation performance of the radiation beams is influenced by the value of a scanning angle due to the asymmetry of the linear array and the planar array, and the beam scanning range is limited. The circular array structure has structural symmetry, can realize 360-degree omnidirectional coverage on an azimuth angle, has ideal radiation performance on a pitch angle, and has small influence on the shape and gain of an antenna beam in the antenna scanning process, so that the circular array structure is widely concerned in the field.
In radar systems, there is a special type of array antenna, in which the elements are arranged on the outer surface of the radar platform such that the surface of the array antenna conforms to the outer shape of the radar platform, and such an antenna is called a conformal array antenna. The cylindrical array is the basis for researching conformal arrays, but the cylindrical array antenna needs more array units, and the directional pattern of the cylindrical array antenna has higher sidelobe level, so the sparse cylindrical array antenna with a low sidelobe radiation pattern, which can effectively inhibit interference signals, needs to be designed.
In recent years, with continuous development and progress of numerical calculation, sparse array synthesis is performed by using intelligent optimization algorithms such as a genetic algorithm, a particle swarm algorithm, a simulated annealing method, a differential evolution algorithm and the like, so that the purposes of reducing the number of array elements, reducing the cost of an antenna system, inhibiting the side lobe level of a directional diagram and the like are achieved, and the research on linear arrays and planar arrays is widely performed, but the research on conformal array antennas such as cylindrical antennas is less. With the complication of the antenna structure, when the traditional group intelligent optimization algorithm is used for processing a complex nonlinear problem, the solving efficiency is not high, and the situation that a local optimal solution is easy to fall exists, so that the optimization requirement of the antenna array cannot be met.
Disclosure of Invention
Aiming at the defects of the existing method, the invention provides a cylindrical array antenna optimization method based on a chaotic sparrow search algorithm, and the specific technical scheme is as follows:
a thin cloth optimization method of a cylindrical array antenna comprises the following steps:
the method comprises the following steps: determining parameters such as array radius, array height, array element number, minimum array element spacing and the like, and establishing a thin cloth cylindrical array model;
step two: selecting the sum of the maximum value of the cylindrical array azimuth directional pattern peak side lobe level and the maximum value of the pitch directional pattern peak side lobe level as an optimization target, and constructing a fitness function;
step three: adopting a chaotic sparrow search algorithm, regarding sparrow individuals as different cylindrical array antenna position distributions, wherein the dimension of the sparrow positions corresponds to the number of units contained in the array, and initializing a population by using a Tent chaotic sequence;
step four: calculating a fitness function value of an initial population individual, and recording the fitness function value of the optimal individual and the corresponding position distribution of the fitness function value;
step five: sorting the individuals in the population according to the corresponding fitness function values, dividing sparrows into two categories, namely an explorer and an enrollee, according to the fitness function values, randomly selecting part of the individuals in the population as cautionars, and updating the positions of the individuals by adopting different position updating strategies;
step six: continuously comparing and updating the objective function value in the process of continuously updating the self position of the sparrow, judging whether the maximum iteration times are reached or not after one iteration is completed, and if not, returning to the fifth step; if so, an optimal optimization scheme for a set of scrim cylinder arrays can be obtained.
Further, the first step specifically comprises:
a cylinder array to be optimized is given, a spherical coordinate system is established by taking the circle center O of a bottom ring as the origin of coordinates, the radius of each ring on the cylinder is R, the number of array elements is P, the height of the cylinder is H, and the vertical distance between each layer of ring and the bottom ring is H m And theta is a pitch angle,
is the azimuth angle. Assuming that the antennas are distributed in constant amplitude, the amplitude weighting coefficient A mn =1, main beam radiation direction of array
Then it is roundThe directional pattern function of the column array model is:
wherein the wave number k =2 π/λ, λ is the wavelength, r m Is the radius of the mth circular ring,
is the azimuth angle theta of the nth (N =0,1, \8230;, N-1) array element on the mth (M =0,1, \8230;, M-1) ring m Pitch angle for the mth ring relative to the origin of coordinates:
θ m ＝arctan(R/h m ) (2)
in the formula, arctan represents an arctangent function, and the length r of a connecting line between any point on a circular ring and a coordinate origin m Obtained by the pythagorean theorem:
further, the second step is specifically:
the fitness function is taken as the sum of the maximum sidelobe level of the azimuth directional diagram and the maximum sidelobe level of the elevation directional diagram:
where max represents the maximum of the evaluation function, S 1 Expressed in θ = θ 0 The time array factor is in a side lobe interval on the azimuth tangent plane; in the same way, S 2 Is shown in
A sidelobe interval of the time matrix factor on the pitching tangent plane; if the zero power points of the azimuth directional diagram and the elevation directional diagram are respectively
And 2 psi 0 And satisfies the following conditions:
obtaining a fitness function optimization model of the cylindrical array:
wherein min represents the minimum value of the solving function, x and y are optimization variables and respectively represent the azimuth angles corresponding to the array elements on the cylinder
And height h m 。
Preferably, the number M of the rings and the number N of the array elements on a single ring should satisfy the constraint condition:
wherein, d c Is the minimum distance interval between adjacent array elements.
Preferably in the direction of the circle, azimuth
Is split into
Two parts, the angle of the handle to the azimuth
Indirectly convert to pairs x mn The search range is from [0 degrees, 360 degrees ]]Reduced to
Is the minimum angular separation of two adjacent array elements,
the minimum distance d between the two adjacent array elements c And the radius R of the cylindrical array satisfies the relationship:
wherein acos represents an inverse cosine function, and the minimum distance d between two adjacent array elements c Taking lambda/2;
it should be noted that, in the pitch direction, the vertical distance between each layer of ring and the bottom layer of ring is h m Resolution into y mn +(n-1)d c Two parts, handle pair h m Is indirectly converted into a solution of mn Is solved by ranging the search from [0, H]Reduced to [0, H- (M-1) · d c ]And h is a m Satisfies the following conditions:
further, the third step is specifically:
the cylindrical array antenna is unfolded along the height of the outer surface of the cylindrical array antenna, the cylindrical array is converted into a two-dimensional rectangular plane array, a chaotic sparrow search algorithm is adopted, sparrow individuals are regarded as different cylindrical array antenna position distributions, the dimension of the sparrow position corresponds to the number of units contained in the array, and the position information of sparrows, namely array layout, is obtained:
d i，g ＝x i，g +j·y i，g (i＝1，2，…，N P ；g＝1，2，…dim) (10)
tent chaos self-mapping generates a chaos sequence:
Z i+1 ＝(2Z i )mod1+rand(0，1)/N p T (11)
where mod is a remainder operation, rand (0, 1) represents a random number generated between (0, 1), N P The number of the population is T, and the maximum iteration number of the algorithm is T;
according to the constraint conditions, the Tent chaotic sequence is constrained to the set solving range:
wherein l bx And U bx Is the minimum and maximum values of the variable dx, l by And U by The minimum and maximum values of the variable dy.
Further, the fourth step is specifically:
substituting the position of each sparrow individual, namely the position of the array unit, into the fitness function, calculating the corresponding fitness function value according to the formula (4), and obtaining the fitness value of a sparrow group:
each row of the matrix represents a sparrow individual, namely a fitness function value of the array, the fitness function values corresponding to the sparrow individuals in the initial population are sorted, and the optimal fitness function value and the corresponding array position distribution of the fitness function value are recorded.
Further, the step five seeker location update comprises:
after the individuals in the population are sorted according to the corresponding fitness function values, the proportion of the individuals with better fitness occupying the population quantity is selected as P N (10% -20%) sparrow individuals were seekers, who updated their positions using the following formula:
wherein the content of the first and second substances,
is (0,1)]A uniform random number in between; q is a random number which follows standard normal distribution; l is a matrix with elements all being 1; r is 1 ∈(0，1) And ST represent the early warning value and the safety value, respectively.
Further, the step five follower location update comprises:
the rest of the individuals in the population except the seeker are used as followers, and the position is updated by adopting the following formula:
wherein x is p The optimal position occupied by the seeker at present; x is the number of worst Then the position of the current global worst individual in the population is represented and a is a matrix of 1 and-1 randomly.
Further, the step five alert position update includes:
randomly selecting the proportion of the number of the population as S N (10% -20%) sparrow individuals are cautionary and the position is updated using the following equation:
wherein x is best Is the current global optimum position; beta is a normally distributed random number; k ∈ [ -1,1]Is a random number; f. of i The fitness value of the current sparrow individual is obtained; f. of g And f w Respectively the fitness values of the current globally optimal individual and the worst individual; epsilon 0 Is a very small constant.
Compared with the prior art, the invention has the following advantages: the core content of the invention is to provide a novel sparse cylindrical array optimization method, which converts the cylindrical array optimization problem of a three-dimensional plane into the rectangular array optimization problem of a two-dimensional plane, reduces the complexity in the optimization process, and improves the search efficiency of the algorithm by reducing the search space of the optimization variables. The chaotic sparrow search algorithm is utilized to realize the improvement of the performance of the peak side lobe level of the equal amplitude weighted cylindrical array, and simulation experiments verify that the method provided by the invention can effectively reduce the peak side lobe level of the cylindrical array, and has certain reference value and significance for the sparse optimization design of the conformal antenna array and the practical application of the sparse optimization design in the antenna system.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a schematic view of a cylindrical array;
FIG. 3 (a) is a distribution diagram of array elements of a uniform cylindrical array;
FIG. 3 (b) is a three-dimensional directional diagram of a uniform cylindrical array;
FIG. 3 (c) is a normalized radiation pattern for a uniform cylindrical array azimuth;
FIG. 3 (d) is a normalized radiation pattern of uniform cylindrical array in elevation;
FIG. 4 (a) is a distribution diagram of array elements of a thin-cloth cylindrical array;
FIG. 4 (b) is a three-dimensional directional diagram of a sparse cylindrical array;
FIG. 4 (c) is a normalized radiation pattern for the azimuth direction of the sparse cylindrical array;
fig. 4 (d) is a normalized radiation pattern of the pitch of the sparse cylindrical array.
Detailed Description
The following embodiments of the present invention are provided by way of specific examples, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1, the implementation steps of the invention are as follows:
the method comprises the following steps: initializing array parameters, and establishing reference models of a thin-cloth cylindrical array and a cylindrical full array;
referring to fig. 2, the invention considers a cylindrical array of sparse cloth, and supposes that the cylindrical array has M circular rings, the radius of the circular ring is R, the number of units on the circular ring is N, and the vertical distance between the circular ring of the mth layer and the circular ring of the bottom layer is h m And obtaining an array factor of the cylindrical array:
where k is the wavenumber, k =2 π/λ, λ is the operating wavelength of the array, r m Is the radius of the mth circular ring,
is the azimuth angle, theta, of the nth array element on the mth ring m Pitch angle for the mth ring relative to the origin of coordinates:
θ m ＝arctan(R/h m ) (2)
length r of connecting line between any point on the ring and the origin of coordinates m ：
Step two: selecting the sum of the maximum value of the cylindrical array azimuth directional pattern peak side lobe level and the maximum value of the pitch directional pattern peak side lobe level as an optimization target, and constructing a fitness function:
where max represents the maximum of the evaluation function, S 1 Expressed in θ = θ 0 The time array factor is in a side lobe interval on the azimuth tangent plane; similarly, S2 is shown in
A side lobe interval of the time array factor on the pitching tangent plane; setting the zero power points of the azimuth directional diagram and the elevation directional diagram as
And 2 psi 0 To obtain S 1 、S 2 The value range of (A):
the fitness function optimization model of the cylindrical array is as follows:
min represents the minimum value of the solving function, x and y are optimization variables and respectively represent the azimuth angles corresponding to the array elements on the cylinder
And height h m 。
The number M of the circular rings and the number N of the array elements on a single circular ring meet the constraint condition:
in the direction of the circle, azimuth
Is split into
Two parts, the angle of the handle to the azimuth
Indirectly convert to pairs x mn The search range is from 0 degrees to 360 degrees]Reduced to
Is the minimum angular separation of two adjacent array elements,
the minimum distance d between the two adjacent array elements c And the radius R of the cylindrical array satisfies the relationship:
wherein acos represents the inverse cosine function, and the minimum distance d between two adjacent array elements c Taking lambda/2;
it is noted that in the pitch direction, h m The requirements are as follows:
the vertical distance between each layer of circular ring and the bottom layer of circular ring is h m Splitting into y mn +(n-1)d c Two parts, handle pair h m Indirectly translate to pair y mn Is solved by ranging the search from 0, H]Reduced to [0, H- (M-1). D c ]。
From the above analysis, it can be seen that by converting the cylindrical array optimization problem of the three-dimensional plane into the rectangular array optimization problem of the two-dimensional plane, the complexity in the optimization process is reduced, and by optimizing the variables
And h m Turn the solution problem into pair x mn And y mn Is solved questionAnd reducing the search space and improving the search efficiency of the algorithm.
Step three: initializing a population by using a Tent chaotic sequence;
the cylindrical array antenna is unfolded along the height of the outer surface of the cylindrical array antenna, and the cylindrical array is converted into a two-dimensional rectangular plane array, so that the position information of a sparrow individual and the antenna array is obtained:
d i，g ＝x i，g +j·y i，g (i＝1，2，…，N P ；g＝1，2，…dim) (10)
tent chaos self-mapping generates a chaos sequence:
Z i+1 ＝(2Z i )mod1+rand(0，1)/N p T (11)
where mod is a remainder operation, rand (0, 1) represents a random number generated between (0, 1), N P The number of the population is T, and the maximum iteration number of the algorithm is T;
and according to the constraint conditions of the set variables, constraining the variables x and y in the set solving range:
wherein l bx And U bx Is the minimum and maximum of the variable x, l by And U by The minimum and maximum values for the variable y. Compared with an initial population generated randomly, the chaotic motion has the characteristics of randomness, uniformity and ergodicity, the population is initialized through the Tent chaotic sequence, the rapid search and optimization of sparrow individuals on the neighborhood are enhanced, and the randomness of an algorithm is improved.
Step four: calculating a fitness function value of the initial population individuals and recording the fitness function value of the optimal individual and the corresponding position distribution of the optimal individual;
substituting the position of each sparrow individual, namely the position of the array unit into the fitness function, calculating the corresponding fitness function value according to the formula (4), and obtaining the fitness value of the sparrow population:
each row of the matrix represents a sparrow individual, namely a fitness function value of the array, the fitness function values corresponding to the sparrow individuals in the initial population are sorted, and the optimal fitness function value and the corresponding array position distribution of the fitness function value are recorded.
Step five: updating the position of the antenna array by adopting different updating strategies of a sparrow algorithm so as to realize the optimization of a fitness function value;
after the individuals in the population are sorted according to the corresponding fitness function values, the proportion of the individuals with better fitness occupying the population quantity is selected as P N (10% -20%) sparrow individuals were seekers, who updated their positions using the following formula:
wherein the content of the first and second substances,
is (0, 1)]A uniform random number in between; q is a random number which obeys standard normal distribution; l is a matrix with elements all being 1; r 1 E (0, 1) and ST represent the early warning value and the safety value, respectively.
The following equation is adopted for updating the position of the seeker as the follower for individuals other than the seeker:
wherein x is p The optimum position occupied by the seeker at present; x is the number of worst Then the position of the current global worst individual in the population is represented and a is a matrix formed randomly by 1 and-1.
Randomly selecting the proportion of the number of the population as S N (10% -20%) sparrow individuals are cautionary and the position is updated using the following equation:
wherein x is best Is the current global optimum position; beta is a normally distributed random number; k ∈ [ -1,1]Is a random number; f. of i The fitness value of the current sparrow individual is obtained; f. of g And f w Respectively the fitness values of the current globally optimal individual and the worst individual; epsilon 0 Is a very small constant.
Step six: and judging whether the maximum iteration times is reached, if so, terminating the cycle, finishing the algorithm, storing and outputting the finally obtained optimal array position distribution, and if not, repeating the step five.
The effect of the invention is further illustrated by the following simulation experiment:
1) Setting simulation parameters: the array radius R =2 lambda, the height H =4.5 lambda, the beam pointing direction is (180 degrees, 90 degrees), and all array elements are cylindrical arrays with equal amplitude and omnidirectional.
2) Emulation content
Simulation content of experiment 1: when the cylindrical array is a uniform full array, the total array element number is P =240, the number of circular rings is M =10, and the number of units on each circular ring is N =24.
Simulation content of experiment 2: performing sparse optimization on the cylindrical array with the same aperture, setting the sparse rate (the ratio of the number of the array elements after sparse to the number of the array elements when the array is full) to be 50%, namely the number of the array elements after sparse P =120, setting the population size pop =100 in simulation, the iteration frequency Iter =1000 and the proportion of an explorer P N =0.2, ratio of alert person S N =0.2, safety value ST =0.8. The aim is to minimize the sum of the maximum sidelobe levels of the azimuth tangent plane and the elevation tangent plane in the directional diagram of the array antenna obtained after the thinning.
Fig. 3 is a simulation result of a uniform array, and if a cylindrical array antenna is spread along the height of the outer surface of the cylindrical array antenna, the distribution diagram of the array elements under the condition of a uniform full array is given by fig. 3 (a), which has a similar structure to a rectangular planar array; FIG. 3 (b) is a normalized three-dimensional pattern of a uniform array; fig. 3 (c) (d) are the azimuth and elevation normalized radiation patterns of the uniform array, respectively, and it can be seen from the figure that the maximum sidelobe level in azimuth is-8.08 dB, the maximum sidelobe level in elevation is-13.6 dB, and the sum of the azimuth and elevation peak sidelobe levels is-21.68 dB for the cylindrical array when the array is uniformly full.
Fig. 4 is a simulation result diagram of a thin cloth cylindrical array obtained by using chaotic sparrow search algorithm optimization, fig. 4 (a) is an array element distribution diagram of the thin cloth array which is formed by expanding the cylindrical array along the height, and the distance between adjacent array elements meets the condition that the array aperture is fixed, and is more than half wavelength; FIG. 4 (b) is a normalized three-dimensional pattern of a scrim array; fig. 4 (c) and (d) are the azimuth normalized radiation pattern and the pitch normalized radiation pattern of the thin-cloth array respectively, and it can be seen from the figure that the maximum side lobe level of the azimuth is-13.12 dB, the maximum side lobe level of the pitch is-13.83 dB, and the sum of the peak side lobe level of the azimuth and the pitch is-26.95 dB, compared with the uniform cylindrical array under the same aperture, the thin-cloth cylindrical array realizes the good suppression of the side lobe level of the azimuth while reducing the number of half array elements.
The result shows that the invention carries out sparse distribution synthesis on the cylindrical conformal array under the condition of fixing the array aperture, realizes the optimization of the peak side lobe level under the condition of obviously reducing the array element number, and can better meet the application requirement of the current low side lobe cylindrical conformal array antenna.
In summary, the invention provides a novel optimization design method of a cylindrical array, which converts a three-dimensional cylindrical array optimization problem into a two-dimensional rectangular array optimization problem for simplification, and simultaneously adopts Tent chaotic sequence to initialize a population, thereby enhancing the rapid search and optimization of an individual on the neighborhood and improving the randomness of an algorithm. The method can effectively inhibit the peak side lobe level of the cylindrical array antenna, and has important reference value and significance for the practical application of the thin-cloth conformal array in an antenna system.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (8)
1. A cylindrical array antenna optimization method based on a chaotic sparrow search algorithm is characterized by comprising the following steps:
the method comprises the following steps: establishing a thin cloth cylindrical array model, initializing array parameters:
a cylinder array to be optimized is given, a cylinder coordinate system is established by taking the circle center O of a bottom surface ring as the origin of coordinates, the radius of each ring on a cylinder is R, the number of array elements is P, the height of the cylinder is H, and the vertical distance between each layer of ring and the bottom layer of ring is H m And theta is a pitch angle,
is the azimuth angle. Assuming that the antennas are distributed in equal amplitude, the amplitude weighting coefficient A mn =1, main beam radiation direction of array
Obtaining a directional diagram function of the thin-cloth cylindrical array antenna;
step two: selecting the sum of the maximum value of the cylindrical array azimuth directional pattern peak side lobe level and the maximum value of the pitch directional pattern peak side lobe level as an optimization target, and constructing a fitness function;
step three: initializing a population by adopting a Tent chaotic sequence;
step four: calculating a fitness function value of an initial population individual, and recording the fitness function value of the optimal individual and the corresponding position distribution of the fitness function value;
step five: sorting the individuals in the population according to the corresponding fitness function values, dividing sparrows into two categories, namely an explorer and an enrollee, according to the fitness function values, randomly selecting part of the individuals in the population as alerters, and updating the positions of the individuals by adopting different position updating strategies;
step six: comparing and updating the objective function values in the process of continuously updating the individual positions by the algorithm, judging whether the maximum iteration times are reached or not after one iteration is completed, and returning to the fifth step if the maximum iteration times are not reached; if yes, an optimal arrangement scheme of a group of thin cylindrical arrays can be obtained.
2. The method of claim 1, wherein the pattern function of the sparse cylindrical array antenna is:
wherein the wave number k =2 pi/lambda, lambda is the wavelength, r m Is the radius of the mth circular ring,
is the azimuth angle, theta, of the nth array element on the mth ring m The pitch angle of the mth ring relative to the origin of coordinates, theta m Expressed as:
θ m ＝arctan(R/h m )
wherein arctan represents an arctangent function, and the length r of a connecting line between any point on a circular ring and a coordinate origin m It can be derived from the pythagorean theorem:
wherein R is the radius of the ring, h m Is the vertical distance between the circular ring at the mth layer and the circular ring at the bottom layer.
3. The method of claim 1, wherein the fitness function is the sum of the maximum azimuth pattern sidelobe level and the maximum elevation pattern sidelobe level, expressed as:
where max represents the maximum of the evaluation function, S 1 Expressed in θ = θ 0 A sidelobe interval of the time matrix factor on the azimuth tangent plane; in the same way, S 2 Is shown in
A side lobe interval of the time array factor on the pitching tangent plane; setting the zero power points of the azimuth directional diagram and the elevation directional diagram as
And 2 psi 0 And satisfies the following conditions:
S 2 ＝{θ|θ min ≤θ≤θ 0 -ψ 0 ∪θ 0 +ψ 0 ≤θ≤θ max }
the fitness function optimization model of the cylindrical array is as follows:
min represents the minimum value of the solving function, x and y are optimization variables and respectively represent the azimuth angles corresponding to the array elements on the cylinder
And height h m 。
4. The method of claim 1, using Tent chaotic sequence to initialize a population, wherein:
generating an initial population by Tent chaos, wherein the Tent chaos self-mapping generates a chaos sequence:
Z i+1 ＝(2Z i )mod1+rand(0,1)/N p T
where mod is a remainder operation, rand (0, 1) represents a random number generated between (0, 1), N P The number of the population is T, and the maximum iteration number of the algorithm is T;
and constraining the generated chaos sequence to the set solving range:
wherein l bx And U bx Is a variable d x Minimum and maximum values of l by And U by Is a variable d y Minimum and maximum values of.
5. The method of claim 1, wherein the different location update policies are seeker location updates, follower location updates, alert location discovery updates.
6. The method of claim 5, wherein the seeker location update policy is:
after the individuals in the population are sorted according to the magnitude of the fitness function value corresponding to the individuals, the proportion of the individuals with better fitness occupying the population quantity is selected as P N (10% -20%) sparrow individuals were seekers, who updated their positions using the following formula:
wherein the content of the first and second substances,
is (0,1)]Q is a random number following a standard normal distribution, L is a matrix with elements all being 1, and R is a uniform random number between 1 E (0, 1) and ST are respectively an early warning value and a safety value.
7. The method of claim 5, wherein the follower location update policy is:
the other individuals in the population, except the seeker, as followers, update their positions using the following equation:
wherein x is p For the optimum position currently occupied by the seeker, x worst And A is a matrix formed by 1 and-1 randomly, wherein A is the position of the current global worst individual in the population.
8. The method according to claim 5, wherein the alert position update policy is:
randomly selecting the proportion of the number of the population as S N (10% -20%) sparrow individuals are cautionary and the position is updated using the following equation:
wherein x is best For the current global optimum position, β is a random number of normal distribution, and K is [ -1,1]A random number in the interval, f i Is the fitness value of the current sparrow individual, f g And f w Fitness values, ε, for the current globally optimal and worst individuals, respectively 0 Is an extremely small constant.
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| CN116796640B (en) * | 2023-06-26 | 2024-05-03 | 北京理工大学 | Conformal sparse array optimization method based on snake optimization algorithm |
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