Sparse array design method for continuous multi-population particle swarm cooperation

Abstract

The invention discloses a sparse array design method for continuous multi-population particle swarm cooperation. The method comprises the following steps: firstly, giving a range of a grid middle part where an activeness grid is located; the initialization is that the first row, the last row and activity grids in the particle swarm X are all set to be 1, and random assignment between 0 and 1 is carried out on elements in the rows corresponding to the rest grids under the condition that the sparse rate requirement is met; in the iteration step, on the basis of the optimal particle grid concentration principle, updating is carried out by referring to the grid change probability of particles X, and when the grids are active grids, the closer to the centermost grid, the smaller the grid change probability is; when the grids are inactive grids, the grid change probability is a fixed value; the adjustable value grid change probability of the activeness grid is always smaller than the fixed value grid change probability of the inactiveness grid; carrying out information sharing and cooperative updating among the subgroups; and the X is output as the optimal sparse array layout after iteration is completed. The convergence speed of an intelligent algorithm can be increased, and a local optimal trap is avoided.

Description

Technical Field

[0001] The present invention belongs to radar communication technology, and in particular relates to a linear array sparse array technology. Background Art

[0002] Compared to traditional uniform array layouts, sparse arrays can reduce hardware complexity, save space, and reduce power consumption by reducing the number of array elements while maintaining array performance. However, sparse arrays introduce grating lobes and large sidelobes due to grid spacing issues, further deteriorating performance. Therefore, how to reduce sidelobes through a reasonable array layout has become an urgent engineering challenge for sparse arrays. Therefore, studying the problem of sparse linear arrays with intelligent algorithms has practical applications.

[0003] However, traditional sparse array design methods usually rely on empirical rules or manual adjustments and lack efficient optimization strategies. In recent years, intelligent algorithms, especially the particle swarm optimization algorithm (PSO), have become important research tools in sparse array design due to their strong global optimization capabilities and fast convergence speed. The particle swarm optimization algorithm performs well in the layout optimization of array units by simulating group intelligence and searching for the optimal solution through multiple iterations. However, traditional particle swarm optimization algorithms have some shortcomings, especially when dealing with sparse array design. The non-uniformity of the array layout may lead to slow convergence speed and even easy to fall into local optimal solutions. In addition, Boolean values ​​are often used for iteration, which greatly limits the diversity of particles and makes the problem more likely to fall into the trap of local optimal solutions, which cannot meet engineering needs. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a sparse array design scheme with adjustable sparse array grid activity in order to overcome the defects of existing sparse array designs based on intelligent algorithms in terms of convergence speed and local optimal traps.

[0005] The technical solution adopted by the present invention to solve the above technical problems is a sparse array design method for continuous multi-swarm particle swarm collaboration, comprising:

[0006] Parameter setting steps: Set the total number of grids, the number of particles in the particle swarm X, where each particle is a column in X, representing a sparse array layout, and a row in X corresponds to a grid; the probability that an array element is arranged on the element value grid; set the sparse rate, the total number of iterations, the number of subgroups, and the range of the middle of the grid where the given activity grid is located;

[0007] Initialization step: Initialize the particle swarm X based on the optimal particle grid concentration principle. The value of each element in the particle swarm velocity V is initially 0. Based on the optimal particle grid concentration principle, set the first row, the last row, and the activity grid of the particle swarm X to 1. Then, randomly assign values ​​between 0 and 1 to each element in the corresponding rows of the remaining grids while meeting the sparsity requirement.

[0008] Iterative steps: first update the particle swarm velocity V, then update X based on the optimal particle grid concentration principle, X = X + V; based on the optimal particle grid concentration principle, update X as the grid change probability X of the reference particle. When the grid is an active grid, the closer to the center grid, the smaller the grid change probability; when the grid is an inactive grid, the grid change probability is a fixed value; the adjustable value grid change probability of the active grid is always less than the fixed value grid change probability of the inactive grid; then perform information sharing and collaborative update on X among subgroups; determine whether the current number of iterations reaches the total number of iterations. If so, output X as the optimal sparse array layout; otherwise, return to the iterative step.

[0009] Preferably, information sharing and collaboration among subgroups to update the grid position of each subgroup in X are achieved based on a leadership group discussion mechanism, wherein the leadership group discussion mechanism includes:

[0010] Mechanism a. Distinguish between good particles and poor particles, and replace poor particles with good particles in the sub-group according to the set probability;

[0011] Mechanism b. triggering mechanism a according to conditional probability, where the greater the number of iterations the conditional probability satisfies, the smaller the probability of triggering mechanism a;

[0012] Mechanism c. Particles in the subgroup undergo mutation updates with a preset low probability;

[0013] Mechanism d. Randomly exchange particles in a sub-population with a preset low probability.

[0014] Specifically, the parameter setting steps are as follows: given the total number of grids is M, the number of particles in the particle group X is N, Represents the real number field, sets the total number of iterations to G and the number of subgroups to N s , the range of the activity grid is determined by giving the starting position coefficient qp and the ending position coefficient zp of the activity grid;

[0015] In the initialization step, all grid cells where the particle is located in the position interval (M*qp, M*zp) are set to 1.

[0016] The iterative steps specifically include:

[0017] The grid position of the best historical performance pbest iCalculation steps: Take X as the grid position pbest of the best historical performance i ; Based on the result of the particle swarm X rounding function, the sparse array layout is obtained, and then the peak sidelobe level value psll_vec of all particles is obtained according to the directional pattern i ;

[0018] Optimal grid position gbest i Calculation steps: Divide the particle swarm X evenly into N s subgroups, psll_vec i Divided into N s The peak sidelobe level value s_psll_vec of the subgroup i,l , l is the subgroup number variable, l=0,1,…N s ; Take each subgroup s_psll_vec i,l The minimum value is taken as the optimal peak sidelobe level sbest_psll of each subgroup i (l); optimal position of subgroup sbest_pos i is sbest_psll i (l) The corresponding particle position; combined with N s sbest_pos i,l Get the optimal grid position gbest of all particles in the current iteration i ;

[0019] Steps to update X and X's velocity V based on the optimal particle grid concentration principle: Use X and the best historical performance grid position pbest i and the optimal grid position gbest of the current iteration i Update the particle swarm velocity V; then update X with reference to the particle grid change probability;

[0020] The steps of sharing information and collaborating among subgroups in X to update the grid positions of each subgroup are implemented based on the leadership group discussion mechanism;

[0021] Update the peak sidelobe level value psll_vec of all particles according to X i Steps;

[0022] Output judgment step: judge whether the number of iterations i reaches the total number of iterations G. If so, take the current X as the optimal sparse array layout; otherwise, return to the iteration step.

[0023] Specifically, qp is set to 25%, zp is set to 70%, and the grid located in the middle 45% of the entire grid area is the activity grid.

[0024] Specifically, the probability of grid change P(x) is calculated as follows:

[0025]

[0026] x is the xth grid in X, and P(x) represents the probability of the xth grid changing.

[0027] Specifically, the specific method for updating the grid change probability P(x) of the reference particle is:

[0028] A judgment parameter sj1 with a value between (0,1) is randomly generated. If the x-th grid satisfies P(x)>sj1, X will use the latest element in V at row x and column j to update the element in X at row x and column j. If a negative value appears in X, it will be updated to 0, and if a value greater than 1 appears, it will be updated to 1. When the grid in X is traversed, the update of X for the i-th iteration is completed.

[0029] Specifically, use X and the grid position pbest with the best historical performance i and the optimal grid position gbest of the current iteration i The method to update the particle swarm velocity V is:

[0030]

[0031] Among them, V(:,j) represents the jth row in X, that is, the velocity of the jth particle, w represents the dynamically updated inertia weight parameter, c1, c2 represent the first and second parameter learning factors, r1, r2 represent the first and second random vectors, pbest i (:,j) represents pbest i The jth row in the middle;

[0032] The dynamically updated inertia weight parameter w=w_max-((w_max-w_min)*i / G); w_min and w_max are the preset minimum and maximum inertia weight parameters respectively.

[0033] Preferably, the method for distinguishing excellent particles from poor particles in mechanism a is:

[0034] The standardized fitness is used as an indicator to distinguish excellent particles from poor particles. In the i-th iteration, the peak sidelobe level values ​​of all particle groups are normalized to obtain the calculated standardized fitness norm_fitness. i ,

[0035]

[0036] Among them, eps is the anti-zero factor;

[0037] norm_fitnessi Synchronize to each subgroup to obtain the fitness of each subgroup particle sb_norm_fitness i ; Find the standardized fitness sb_norm_fitness in the subgroup i Particles with a value below 0.5 are considered poor particles, and the rest are considered excellent particles.

[0038] Specifically, mechanism b is: randomly set a random number sj2 between 0 and 1, and trigger mechanism a only when sj2≤(1-i / G).

[0039] The present invention is based on continuous particle changes, which enriches the diversity of the particle process, and adds dynamic weights and random mutations in all steps to further increase the diversity of particles; further, through the applicant's long-term experiments and observations of data, the idea of ​​"optimal particle grid concentration" was proposed for the first time, and applied to the intelligent algorithm, which accelerated the convergence speed of the particle swarm algorithm and provided theoretical support for future exploration of large grids; further, the present invention also proposed the idea of ​​"leadership group discussion mechanism" for the first time and applied it to the algorithm, giving particles more possibilities to escape the trap of local optimal solutions.

[0040] The beneficial effect of the present invention is that it can accelerate the convergence speed of the intelligent algorithm, avoid the local optimal trap, and further reduce the side lobes of the directional pattern, and it is more difficult to meet the engineering requirements for sparse array design. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Flowchart of the present invention;

[0042] Figure 2 The lowest sidelobe iteration diagram for the comparative search of each algorithm on the 32-grid grid;

[0043] Figure 3 This is the distribution diagram of the optimal array element positions in the 32-grid;

[0044] Figure 4 It is the 32-grid optimal position direction map;

[0045] Figure 5 The lowest sidelobe iteration graph of 100 iterations of the comparative search of each algorithm on 64 grids;

[0046] Figure 6 This is the distribution map of the optimal array element positions in the 64-grid;

[0047] Figure 7 It is the 64-grid optimal position direction map;

[0048] Figure 8 The lowest sidelobe iteration graph of 100 iterations of the comparative search of each algorithm on 128 grids;

[0049] Figure 9 This is the optimal array element position distribution map for 128 grids;

[0050] Figure 10 It is the optimal position direction map of 128 grids;

[0051] Figure 11 The lowest sidelobe iteration graph of 10,000 iterations of the comparative search of each algorithm on 64 grids;

[0052] Figure 12 The lowest sidelobe iteration graph of 10,000 iterations of the comparative search for each algorithm on a 128-grid grid. DETAILED DESCRIPTION

[0053] The specific embodiments and working principles of the present invention are further described in detail below with reference to the accompanying drawings. Figure 1 The sparse array design method shown in the figure specifically comprises the following steps:

[0054] Step 1) Given the total number of grids as M, the number of particles in the particle swarm X as N, the grid represents the potential position of the array element (i.e., the discrete position point after gridding), each particle represents a sparse array layout, and the particle swarm represents the parallel candidate solution in the group, i.e., the candidate sparse array layout, where the element value represents the probability that the array element is arranged on the grid, and the value range is 0 to 1, 0 means that the grid has no array element arranged, and 1 means that the grid has array element arranged; considering the comprehensive consideration, the sparsity rate is set to 0.77, the total number of iterations is given as G, the main beam pointing is θ0, and the number of subgroups is given as N. s , given the starting position coefficient of the activity grid is qp, the ending position coefficient is zp, and the number of iterations is i;

[0055] Let the grid position of the optimal historical performance of each particle from the beginning of iteration to the i-th time be The corresponding sidelobe level is represents the field of real numbers;

[0056] Let the optimal grid position of all particles from the beginning of iteration to the i-th time be gbest i , and its corresponding sidelobe level value is gbest_psll i ;

[0057] Let the optimal peak sidelobe level of all subgroups be And initialized to all 0 vectors, the optimal position corresponding to the optimal peak sidelobe level value of all subgroups is The optimal position sbest_pos corresponding to the optimal peak sidelobe level value of each subgroup i (l), l=0,1,…N s ;

[0058] Let the peak sidelobe level of all particles in the i-th iteration be expressed as The peak sidelobe level of all particles in the i-th iteration of the l-th subgroup is expressed as The corresponding grid position is

[0059] Step 2) After long-term experiments on the distribution of optimal particle grid positions, the applicant proposed the concept of "optimal particle grid concentration" and verified it by traversing a smaller number of grids. The verification found that when initializing the particle swarm, initializing it according to the "optimal particle grid concentration" principle will greatly accelerate the algorithm iteration speed, that is, prioritize the array elements to be concentrated in the central grid area. Therefore, the specific method of the initialization step is as follows:

[0060] Let i = 0, and the particle swarm First, set all the values ​​of 0, and then perform the following initialization operations on X:

[0061] a) The first and last grids are fixed with one element, that is, the first and Mth rows in X are both 1;

[0062] b) Set all rows corresponding to the activity grid to 1, that is, set all grids where the particle is located in the position interval (M*q, p M*z) to 1; the activity grid refers to a grid located in the central area determined according to the principle of "optimal particle grid concentration", with the starting position ratio coefficient of the central area being qp and the ending position ratio coefficient being zp; the number of activity grids is M*qp-M*zp, and the number of activity grids is set to an appropriate ratio based on the total number of array elements. In practice, the ratio is 45%, that is, qp is 25%, zp is 70%, and the grid located in the middle 45% of the entire grid area is the activity grid;

[0063] c) Randomly assign values ​​between 0 and 1 to the elements in the corresponding rows of the remaining grids while meeting the sparsity requirement. If the activity grid accounts for 45%, remove the grids at the beginning and end, and the number of grids that need to be randomly initialized is MM*45%-2.

[0064] d) Then initialize the particle swarm velocity All values ​​are set to 0;

[0065] Iteration steps:

[0066] Update i = i + 1;

[0067] Step 3) Based on the current particle swarm X, the peak sidelobe level value psll_vec of all particles in the i-th iteration is calculated using the rounding function. i :

[0068]

[0069] Where, direction θ∈ sidelobe area, T represents transposition, F j (θ) represents the direction map obtained from the sparse array layout of the kth particle, F j (θ)=(B(:,j)⊙a(θ0)) H a(θ), H represents the conjugate transpose, B = round(X), round is the rounding function. If the value of an element in X is in the range [0, 0.5), the corresponding element in B is assigned 0; if the value of an element in X is in the range [0.5, 1], the corresponding element in B is assigned 1; B(:, j) is the j-th column of the matrix B, representing the array element selection sequence of the sparse array layout corresponding to the j-th particle, a(θ) represents the steering vector when the array is full; the value of j ranges from 1 to N;

[0070] Pass X to the grid position pbest of the best historical performance i , and its corresponding psll_vec i The minimum value is passed to gbest_psll i , at this time i=0:

[0071] gbest_psll i =min(psll_vec i )

[0072] Calculate the optimal peak sidelobe level among all particles in the i-th iteration as gbest_psll i As an indicator to measure algorithm performance in simulation experiments.

[0073] Step 4) Divide the particle group X evenly into N s subgroups and calculate the subgroup sequence where the best particles are located;

[0074] For the lth subgroup at the i-th iteration, the peak sidelobe level values ​​psll_vec of all particles are obtained. i Take out the part of the lth subgroup to get the optimal peak sidelobe level sbest_psll of the subgroup i (l):

[0075] sbest_psll i (l)=min(psll_vec i ((l-1)×N / N s +1:l×NN s )),l=0,1,…N s ;

[0076] sbest_psll i (l) is to take psll_veci The minimum value of the lth subgroup corresponds to the grid position sbest_pos of the optimal performance of the subgroup i is sbest_psll i (l) The particle position, 1:l×N / N s Represents 1 to l×N / N s At this time, the peak sidelobe level value of all particles in the i-th iteration of the l-th subgroup is expressed as:

[0077] s_psll_vec i,l =psll_vec i (((l-1)×NN s +1):(l×NN s )),l=1,2,…N s ;

[0078] s_psll_vec i,l Is to take the subgroup in psll_vec i The level of the corresponding position is used as its value, and the grid positions of all particles in the corresponding subgroup are Combine N s sbest_pos i,l The optimal grid position among all particles is gbest i ;

[0079] Step 5) Based on the principle of "optimal particle grid concentration" mentioned in the previous step, we iteratively solve the problem by making the area where the activity grid is located change with a lower probability, while the areas outside this area change normally with a preset standard probability. To maintain the aperture size, the first and last grids are fixed with 1 element. The update method for the i-th iteration is as follows:

[0080] Update the speed V of X:

[0081]

[0082] Among them, V(:,j) represents the velocity of the jth particle in X, w represents the dynamically updated inertia weight parameter, c1, c2 represent parameter learning factors, vector r1, r2 represents a random vector, pbest i (:,j) represents the grid position of the best historical performance of the jth particle from the beginning of the iteration to the i-th time, gbest i Represents the optimal grid position of all particles from the beginning of iteration to the i-th time.

[0083] Specifically:

[0084] w=w_max-((w_max-w_min)*i / G);

[0085] w_min and w_max are the preset minimum and maximum inertia weight parameters, respectively, and G is the total number of given iterations;

[0086] Update X according to the probability P(x) of the particle grid change:

[0087]

[0088] x is the xth grid in X, that is, the grid sequence number, P(x) represents the probability of the xth grid changing, M*0.5 represents the most central grid, M*0.25<x<M*0.75 indicates that the xth grid is the activity grid. The closer the activity grid is to the most central grid, the smaller P(x), that is, P(x) of the activity grid changes with the distance from the most central grid.

[0089] When the grid is active, the closer it is to the center, the smaller the probability of grid change. When the grid is inactive, the probability of grid change is fixed, with a value of 0.5 in this embodiment. The adjustable probability of grid change for the active grid is always lower than the fixed probability of grid change for the inactive grid. This ensures that the active grid area always changes with a lower probability.

[0090] A judgment parameter sj1 is randomly generated between (0,1). If P(x) > sj1 for the xth grid, X will be updated with the element in the xth row, jth column of V using the most recent element in the xth row, jth column of V, where X(x,j) = X(x,j) + V(x,j). If a negative value appears in X, it is updated to 0; if a value greater than 1 appears, it is updated to 1. Once all grid cells in X are traversed, the update of X for the i-th iteration is complete.

[0091] Step 6) Based on the "leadership group discussion mechanism" proposed by the applicant, information sharing and collaboration between subgroups are realized to update s_pos i,l ,l=1,2,…N s The “Leadership Group Discussion Mechanism” includes:

[0092] Mechanism a. Assigning high-performing groups to lower-performing groups to set an example: Calculate and propose a metric to distinguish high-performing from low-performing groups. Groups below this metric are considered low-performing groups, while the remaining groups are high-performing. Low-performing groups are replaced by high-performing groups with a certain probability. Optionally, this metric needs to reach half the performance of the top group.

[0093] Mechanism b. The probability of triggering mechanism a should take into account that the team should perform frequent updates in the early stage and reduce the number of updates in the later stage. That is, the greater the current number of iterations, the smaller the probability of triggering mechanism a.

[0094] Mechanism c. To prevent group solidification, members within the group are allowed to mutate and update with a low probability;

[0095] Mechanism d. To prevent group solidification, members of different groups are allowed to randomly exchange with each other with a low probability to achieve collaborative updates.

[0096] When the "leadership group discussion mechanism" is implemented in the present invention, the group is a subgroup and the members are particles. The specific implementation method is as follows:

[0097] Mechanism a. Use standardized fitness as an indicator to distinguish excellent subgroups from poor subgroups. In the i-th iteration, the peak sidelobe level values ​​of all particle groups are normalized to obtain the calculated standardized fitness norm_fitness i ,

[0098]

[0099] psll_vec i represents the peak sidelobe level value of all particle swarms in the i-th iteration, and eps is the anti-zero factor;

[0100] psll_vec has been used before i Synchronize to each subgroup s_psll_vec i,l ; Now, norm_fitness i Synchronize to each subgroup to obtain the fitness of each subgroup particle sb_norm_fitness i ;

[0101] Find the standardized fitness sb_norm_fitness of the subgroup i For particles below 0.5, the particle is used to cover the particles in the atomic group with a certain probability, s_pos i,l (1:M,j g ) = s_pos i,l (1:M,j b ), where j g represents the jth of the lth subgroup in the i-th iteration g Excellent particles (i.e. s_pos i,l The jth g The entire column of elements from the 1st to the Mth row of the column), j b Indicates that the poor particles with a normalized fitness below 0.5 are selected from the lth subgroup in the i-th iteration. The certain probability here is a probability pre-set according to actual needs.

[0102] Mechanism b. The probability of triggering mechanism a is set in the following way:

[0103] Randomly set a random number sj2 between 0 and 1. Only when sj2≤(1-i / G) is the optimal particle s_pos in the subgroup guaranteed. i If not operated, trigger mechanism a.

[0104] Mechanism c. Let the particles in the subgroup perform mutation updates with a lower probability: that is, i,l Add a random smaller number to each element of column j:

[0105]

[0106] Where l, j represents the sequence number of the subgroup and the sequence number of the particle, l = 0, 1, ... N s , j=((l-1)×NN s +1),…,(l×NN s ), e j′ represents the standard basis vector of size M×1, and the random number j′=rand((l-1)×NN s +1):(l×NN s )), s_pos i,l e j′ Indicates that at s_pos i,l Randomly select a column from the ,ub is a column vector of all 1s that is consistent with the size of a particle, (s_pos i,l e j′ -0.5)*ub / 10 is the random smaller number mentioned above, / 10 is used to ensure that the number is small enough to avoid mutation after updating s_pos i,l When the number of elements in (1:M,j) exceeds 1 or 0, clamp is the truncation function, clamp(x) = max(0, min(x,1)).

[0107] Of course, based on this principle, there are many other algorithms that can achieve the update effect of mutation update.

[0108] The specific implementation of mechanism d. allowing random exchange of members in a subgroup with a lower probability is:

[0109]

[0110] The same size fragment (f3:f4) of the particle j2 of the selected l2 subgroup is exchanged with the selected fragment (f1:f2) of the particle j1 of the l1 subgroup. f3:f4 represents the fragment starting from the f3th row and ending at the f4th row.

[0111] Specifically, the lower probability between mechanism c and mechanism d is a probability below 0.1 or a probability below 0.2.

[0112] The result after subgroup information sharing and collaboration update is N s s_pos i,l Passed to X.

[0113] Step 7) The peak sidelobe level values ​​s_psll_vec of all particles in the lth subgroup of the i-th iteration are i,l All are returned to psll_vec according to the corresponding position i :

[0114] psll_vec i (((l-1)×NN s +1):(l×NN s ))=s_psll_vec i,l ,l=1,2,…N s ;

[0115] psll_vec i (((l-1)×NN s +1):(l×NN s )) refers to the peak sidelobe level value s_psll_vec of all particles of the lth subgroup of the i-th iteration i,l All are returned to psll_vec according to the corresponding position i .

[0116] Step 8) Determine whether the number of iterations i reaches the specified number G. If so, take the current X as the optimal sparse array layout; otherwise, return to step 3).

[0117] In order to make the purpose, technical solution and technical effect of the present invention clearer, the present invention is further described in detail through simulation experiments.

[0118] This experiment simulated a continuous multi-swarm particle swarm collaboration algorithm based on a sparse grid with adjustable activity. In the following simulations, the array structure was a linear array, the carrier frequency was 16.5GHz, the grid spacing was fixed at 10.5mm, the element sparsity was optimized at 77% after repeated experiments, the particle swarm size was 4000, the number of subgroups was 40, and the main beam pointing direction was set to 0°.

[0119] Simulation Experiment 1: In this experiment, a linear array with 16 grids was used to traverse the grid to find the optimal grid element position. Finally, the optimal element position with a sidelobe below -15dB and a sparse ratio was selected to verify our previous conjecture. The simulation results are shown in Table 1 below:

[0120] Table 1 The lowest sidelobe values ​​and element position distribution of the 16-grid optimal performance

[0121] Optimal sidelobe value (dB) The position of the element in the grid ("1" indicates the element exists, "0" indicates the element does not exist) -15.7365 1111111111111010 -15.5925 1101111111111111 -15.5925 1111111111110111 -15.5629 1011111111111001 -15.5629 1111111111101001 -15.2536 1011111111111101 -15.2536 1111111111110101

[0122] Through experiment 1, it can be found that a good grid position has continuous concentration in the middle.

[0123] Simulation experiment 2: In this simulation, a linear array with 32 grids is used, and the algorithm proposed in this paper is used to perform intelligent search for the optimal grid. The lowest sidelobe iteration diagram of the 32-grid algorithm is shown in the figure. Figure 2 As shown, the 32-grid optimal array element position distribution diagram is as follows Figure 3 As shown, the 32-grid optimal position direction map is as follows Figure 4 As shown in Experiment 2. Figure 3 This further verifies our conjecture about “optimal grid concentration continuity” and the algorithm proposed in this invention has been further applied. Figure 2 The continuous multi-population particle swarm collaboration algorithm based on sparse array grid with adjustable activity can achieve extremely fast convergence. It converges to the optimal value only in the 6th iteration, and the lowest sidelobe is also significantly improved compared with other algorithms.

[0124] Simulation experiment 3: In this simulation, a linear array with 64 grids is used, and the algorithm proposed in this paper is used to perform intelligent search for the optimal grid. The lowest sidelobe iteration diagram of 100 iterations of the 64-grid algorithm comparison search is shown in the figure. Figure 5 As shown, the optimal array element position distribution diagram of 64 grids is as follows Figure 6 As shown, the 64-grid optimal position direction map is as follows Figure 7 shown.

[0125] Experiment 3 further verified the conjecture that a good grid position has continuous concentration in the middle, and it also showed an extremely fast convergence speed in the 64-grid, converging to -20.6836dB in just 17 times. It also performed very well when the grid was fixed. Whether it is optimization speed or optimization ability, the algorithm proposed in this invention has obvious advantages over other algorithms.

[0126] Experiment 4: In this simulation, a linear array with 128 grids was used, and the algorithm proposed in this paper was used to perform an intelligent search for the optimal grid. The lowest sidelobe iterations of 100 iterations of the 128-grid algorithm comparison search are shown in the figure below. Figure 8 As shown, the optimal array element position distribution diagram of 128 grids is as follows Figure 9 As shown, the optimal position direction diagram of 128 grids is as follows Figure 10 shown.

[0127] Experiment 4 further verified the hypothesis that a good grid position has continuous concentration in the middle. Furthermore, the algorithm demonstrated extremely fast convergence speed for a 128-grid grid, converging to -22.6317 dB in just 15 attempts. The proposed algorithm has significant advantages over other algorithms in both optimization speed and optimization capability, particularly when the number of grid cells is very large, enabling it to find the optimal grid element distribution in a relatively short time.

[0128] Simulation experiment 5: In this simulation, the number of iterations is 10,000 to infinite magnification to find the ultimate optimal value of the lowest sidelobe that the algorithm can achieve in 64 grids and 128 grids. The lowest sidelobe iteration graph of 10,000 iterations of the comparison search of each algorithm in 64 grids is shown as follows: Figure 11 As shown in the figure, the lowest sidelobe iteration diagram of 10,000 iterations of the 128-grid algorithm comparison search is as follows Figure 12 shown.

[0129] Through Experiment 5, it can be seen that under the extreme number of iterations, the extreme minimum sidelobe of the 64-grid can reach -21.2305dB, and the extreme minimum sidelobe of the 128-grid can reach -23.4771dB. Compared with the traditional intelligent search algorithm, the intelligent search algorithm of the present invention has better performance in search depth.

[0130] Through the above experiments, the performance comparison between the classic intelligent algorithm and the intelligent algorithm proposed in this invention can be analyzed as shown in Table 2 below:

[0131] Table 2 Comparison of performance of various algorithms

[0132]

[0133] The convergence speed of each algorithm is shown in Table 3 below:

[0134] Table 3 Convergence speed of each algorithm

[0135] The number of iterations required for the 64-grid genetic algorithm to reach the minimum sidelobe level of -18.8dB 22nd generation The number of iterations required for the 64-grid multi-population particle swarm algorithm to reach the minimum sidelobe level of -18.8dB 8th generation The number of iterations required for the algorithm of the present invention to reach the minimum sidelobe level of -20.6dB in 64 grids 3rd generation The number of iterations required for the 128-grid genetic algorithm to reach the minimum sidelobe level of -21.8dB 74th generation The number of iterations required for the 128-grid multi-population particle swarm algorithm to reach the minimum sidelobe level of -21.8dB 83rd generation The number of iterations required for the algorithm of the present invention to reach the minimum sidelobe level of -21.8dB on 128 grids 5th generation

[0136] It can be seen from the above table that the algorithm proposed in the present invention can not only achieve the minimum sidelobe level value that the genetic algorithm and the multi-population particle swarm algorithm cannot achieve, but also can reach a relatively optimal minimum sidelobe level value at an extremely fast convergence speed in the number of iterations.

[0137] In summary, it can be seen that the continuous multi-population particle swarm optimization algorithm based on sparse array grid with adjustable activity has a stronger and faster ability to solve the sparse linear array optimization problem, which is a capability that the traditional genetic algorithm and multi-population particle swarm optimization algorithm do not have.

[0138] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way; any non-essential additions or replacements made by those skilled in the art based on the technical features of the technical solution of the present invention fall within the scope of protection of the present invention.

Claims

1. A sparse array design method for continuous multi-swarm particle swarm collaboration, characterized by: The following steps are involved: Parameter setting steps: Set the total number of grids, the number of particles in the particle swarm X, where each particle is a column in X, representing a sparse array layout, and a row in X corresponds to a grid; the probability that an array element is arranged on the element value grid; set the sparse rate, the total number of iterations, the number of subgroups, and the range of the middle of the grid where the given activity grid is located; Initialization step: Initialize the particle swarm X based on the optimal particle grid concentration principle. The value of each element in the particle swarm velocity V is initially 0. Based on the optimal particle grid concentration principle, set the first row, the last row, and the activity grid of the particle swarm X to 1. Then, randomly assign values ​​between 0 and 1 to each element in the corresponding rows of the remaining grids while meeting the sparsity requirement. Iterative steps: first update the particle swarm velocity V, then update X based on the optimal particle grid concentration principle, X = X + V; based on the optimal particle grid concentration principle, update X as the grid change probability of the reference particle, where, when the grid is an active grid, the closer to the center grid, the smaller the grid change probability; when the grid is an inactive grid, the grid change probability is a fixed value; the adjustable value grid change probability of the active grid is always less than the fixed value grid change probability of the inactive grid; then perform information sharing and collaborative update on X among subgroups; determine whether the current number of iterations reaches the total number of iterations. If so, output X as the optimal sparse array layout; otherwise, return to the iterative step.

2. The method according to claim 1, wherein: The grid positions of each subgroup in X are updated by sharing information and collaborating among subgroups based on the leadership group discussion mechanism, which includes: Mechanism a. Distinguish between good particles and poor particles, and replace poor particles with good particles in the sub-group according to the set probability; Mechanism b. triggering mechanism a according to conditional probability, where the greater the number of iterations the conditional probability satisfies, the smaller the probability of triggering mechanism a; Mechanism c. Particles in the subgroup undergo mutation updates with a preset low probability; Mechanism d. Randomly exchange particles in a sub-population with a preset low probability.

3. The method according to claim 2, wherein: The parameter setting steps are as follows: given the total number of grids is M, the number of particles in the particle group X is N, Represents the real number field, sets the total number of iterations to G and the number of subgroups to N s , the range of the activity grid is determined by giving the starting position coefficient qp and the ending position coefficient zp of the activity grid; In the initialization step, all grid cells where the particle is located in the position interval (M*qp, M*zp) are set to 1.

4. The method according to claim 3, wherein: The iterative steps specifically include: The grid position of the best historical performance pbest i Calculation steps: Take X as the grid position pbest of the best historical performance i ; Based on the result of the particle swarm X rounding function, the sparse array layout is obtained, and then the peak sidelobe level value psll_vec of all particles is obtained according to the directional pattern i ; Optimal grid position gbest i Calculation steps: Divide the particle swarm X evenly into N s subgroups, psll_vec i Divided into N s The peak sidelobe level value s_psll_vec of the subgroup i,l , l is the subgroup number variable, l=0,1,…N s ; Take each subgroup s_psll_vec i,l The minimum value is taken as the optimal peak sidelobe level sbest_psll of each subgroup i (l); optimal position of subgroup sbest_pos i is sbest_psll i (l) The corresponding particle position; combined with N s sbest_pos i,l Get the optimal grid position gbest of all particles in the current iteration i ; The steps to update X and X's velocity V based on the optimal particle grid concentration principle are: using X and the best historical performance grid position pbest i and the optimal grid position gbest of the current iteration i Update the particle swarm velocity V; then update X with reference to the particle grid change probability; The steps of sharing information and collaborating among subgroups in X to update the grid positions of each subgroup are implemented based on the leadership group discussion mechanism; Update the peak sidelobe level value psll_vec of all particles according to X i Steps; Output judgment step: judge whether the number of iterations i reaches the total number of iterations G. If so, take the current X as the optimal sparse array layout; otherwise, return to the iteration step.

5. The method according to claim 3, wherein: The qp is set to 25%, the zp is set to 70%, and the grid located in the middle 45% of the entire grid area is the activity grid.

6. The method according to claim 5, wherein: The probability of grid change P(x) is calculated as: x is the xth grid in X, and P(x) represents the probability of the xth grid changing.

7. The method according to claim 5, wherein: The specific method of updating the grid change probability P(x) of the reference particle is: A judgment parameter sj1 with a value between (0,1) is randomly generated. If the x-th grid satisfies P(x)>sj1, X will use the latest element in V at row x and column j to update the element in X at row x and column j. If a negative value appears in X, it will be updated to 0, and if a value greater than 1 appears, it will be updated to 1. When the grid in X is traversed, the update of X for the i-th iteration is completed.

8. The method according to claim 4, wherein: Use X and the grid position pbest with the best historical performance i and the optimal grid position gbest of the current iteration i The method to update the particle swarm velocity V is: Among them, V(:,j) represents the jth row in X, that is, the velocity of the jth particle, w represents the dynamically updated inertia weight parameter, c1, c2 represent the first and second parameter learning factors, r1, r2 represent the first and second random vectors, pbest i (:,j) represents pbest i The jth row in the middle; The dynamically updated inertia weight parameter w=w_max-((w_max-w_min)*i / G); w_min and w_max are the preset minimum and maximum inertia weight parameters respectively.

9. The method according to claim 4, wherein: The method of distinguishing good particles from poor particles in mechanism a is; The standardized fitness is used as an indicator to distinguish excellent particles from poor particles. In the i-th iteration, the peak sidelobe level values ​​of all particle groups are normalized to obtain the calculated standardized fitness norm_fitness. i , Among them, eps is the anti-zero factor; norm_fitness i Synchronize to each subgroup to obtain the fitness of each subgroup particle sb_norm_fitness i ; Find the standardized fitness sb_norm_fitness in the subgroup i Particles with a value below 0.5 are considered poor particles, and the rest are considered excellent particles.

10. The method according to claim 9, wherein: Mechanism b is specifically as follows: randomly set a random number sj2 between 0 and 1, and trigger mechanism a only when sj2≤(1-i / G).

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