Large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization

Abstract

The invention relates to the technical field of phased arrays, in particular to a large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization. Comprising the steps of establishing a task set according to satellite requirements needing measurement and control; for different tasks in the task set, counting visible time windows according to the task execution interval set, generating an initial solution set, calculating an objective function of each group of phased array scheduling solutions, and constructing an initial solution set matrix; performing dimension reduction on the initial solution set matrix; establishing a probability agent model with a corresponding objective function value according to the dimensionality reduction solution set; searching an update solution by using a simulated annealing algorithm, and calculating a target function value; and appending the updated solution to the initial solution set. According to the invention, a high-dimensional combined Bayesian combination optimization algorithm is adopted, and the array element scheduling problem of the phased array is solved. Compared with a traditional optimization method depending on a large number of samples, such as group solving, genetic algorithm and high-dimensional combined Bayesian, the optimization efficiency is remarkably improved by reducing the number of times that the target function must be evaluated and effectively utilizing existing information at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of phased arrays, and in particular to a large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization. Background Art

[0002] Phased array technology is widely used in radar, communications, electronic countermeasures, imaging and other fields. It uses multiple antenna elements to accurately adjust the direction and shape of the beam by controlling the amplitude and phase of each element, achieving rapid beam steering and multi-target tracking. The key to phased array is the scheduling and phase control of its elements to ensure that the beam has good gain and resolution in the desired direction.

[0003] In phased array applications, the scheduling problem of array elements can be viewed as a high-dimensional combinatorial optimization problem. Specifically, there are multiple array elements to choose from, and different scheduling methods and control strategies will directly affect the performance indicators of the system, such as signal gain, resolution, and anti-interference ability. As the number of array elements increases, the scheduling space grows exponentially, making it difficult for traditional optimization methods to find the optimal solution within a reasonable time. Summary of the invention

[0004] The present invention discloses a large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization, and the specific method is as follows:

[0005] Collect historical information of phased array satellites to establish a mission execution interval set;

[0006] Establish mission sets based on satellite requirements for measurement and control;

[0007] For different tasks in the task set, the visible time window is counted according to the task execution interval set, and the initial solution set is generated accordingly. The objective function of each set of phased array scheduling solutions is calculated, and the initial solution set matrix is ​​constructed.

[0008] Reduce the dimension of the initial solution set matrix to obtain a reduced-dimensional solution set;

[0009] A probability proxy model between the corresponding objective function value is established according to the dimension reduction solution set;

[0010] Use the simulated annealing algorithm to search for the updated solution and calculate the objective function value;

[0011] Append the updated solution to the initial solution set;

[0012] Repeat the updating, appending of the initial solution set and calculation of the objective function value until the number of iterations reaches the preset target, exit the loop, and select the optimal objective function value as the final phased array element scheduling solution.

[0013] Furthermore, the task execution interval set includes: satellite ID, satellite model, execution interval, start time, end time and duration.

[0014] Furthermore, the task set includes: task sequence number, satellite ID, task duration and task execution status.

[0015] Furthermore, the objective function of each phased array scheduling solution is calculated. The specific method is as follows:

[0016] For task i, a number x is randomly generated between 0 and the maximum visible time window number. i , then a set of solutions generated by random method is recorded as:

[0017] X=[x1,x2,…,x M ]

[0018] Generate N sets of solutions using a random method and put them in a matrix, recorded as:

[0019]

[0020] The objective function formula is set according to the task requirements, and the objective function value of N groups of solutions is recorded as:

[0021]

[0022] Where O is the objective function matrix composed of the objective function values ​​of N sets of solutions, where f i Represents the objective function value corresponding to the i-th group of solutions.

[0023] Furthermore, the initial solution set matrix is ​​reduced in dimension. The specific method is as follows:

[0024] Set the dimension after dimensionality reduction to R, and generate a reduced dimension matrix A with R rows and M columns, where each element is an independent Bernoulli distribution random variable;

[0025] Multiply the initial solution set matrix by the transpose of the dimension reduction matrix to obtain the reduced dimension solution set F:

[0026] F=S×A T

[0027] Among them, S is the initial solution set matrix of the N groups of solution sets generated for the M tasks mentioned above.

[0028] Furthermore, a probabilistic proxy model is established between the dimensionality reduction solution set and the corresponding objective function value. The specific method is as follows:

[0029] D t ={(F1,f1),(F2,f2)…(F N ,f N )}

[0030] Assume the model is:

[0031]

[0032]

[0033] Among them, n f and n F are the maximum lags that affect the output and input at the current moment, ξ k is the output noise;

[0034] When the input and output data are known and the structure g is fixed, the identification is transformed into an estimation of the parameter vector θ;

[0035] The noise ξ k It obeys a zero-mean Gaussian distribution, that is,

[0036]

[0037] The precision parameter τ follows the gamma distribution, that is

[0038]

[0039] Where a0 and b0 are constant parameters;

[0040] Assume that the parameter θ follows a Gaussian distribution with respect to parameters α and τ, and α follows a gamma distribution with respect to constants c0 and d0, then

[0041]

[0042] The joint prior distribution is expressed as:

[0043] p(θ,α,τ)=p(θ|α,τ)p(α)p(τ)

[0044] The new objective function value y * The probability distribution on a specific task combination is:

[0045] p(y(x k+1 )|D t )=∫θ T g(x k+1 )q(θ,α,τ)dθdαdτ

[0046] Among them, θ and α are vectors, and θ, α, and τ all have variance and expectation: θ i The variance and expectation of i ),∑(θ i ); α i The variance and expectation of i ),∑(α i); the variance and expectation of τ are expressed as μ(μ) and ∑(τ) respectively; the variational Bayes algorithm is used to optimize θ, α, and τ.

[0047] Furthermore, the simulated annealing algorithm is used to search for an updated solution to calculate the objective function value. The specific method is as follows:

[0048] The optimization algorithm uses the solution with the largest objective function value as the initial solution of the algorithm:

[0049]

[0050] Sampling is performed at the expected maximum, and the acquisition function is designed as:

[0051] EI(x k+1 )=∫max[y sample -y * ,0]p(y sample |D t )dy sample

[0052] where y sample Represents x k+1 The posterior distribution sample of the current best known value is y * ;

[0053] According to the optimization algorithm combined with the acquisition function, n groups of new solutions are found, which can be expressed as:

[0054]

[0055] The objective function value of n groups of solutions is recorded as:

[0056]

[0057] The solution set that combines the new solution s with the original solution set S replaces the original solution set S, which is recorded as:

[0058]

[0059] The objective function value o corresponding to the new solution is combined with the objective function value O corresponding to the original solution set to replace the objective function value corresponding to the original solution set, which is recorded as:

[0060]

[0061] Furthermore, the objective function is constructed according to the measurement and control task satisfaction rate η1, the array resource utilization rate η2, and the array resource conflict rate η3. The specific formula is as follows:

[0062] f=w1η1+w2η2-w3η3

[0063] Among them, w1, w2 and w3 are weights;

[0064] The measurement and control task satisfaction rate η1 is calculated as:

[0065]

[0066] Where M′ is the number of completed tasks. The difference between the task end time and the start time is calculated. If it is greater than the duration, the task is completed.

[0067] The array element resource utilization rate η2 represents the ratio of all used array elements to the total number of array elements, expressed as:

[0068]

[0069] in represents the total number of array elements used, and |Z| represents the total number of array elements;

[0070] The array element resource conflict rate η3 represents the ratio of the number of conflicting array elements to the number of used array elements, which is expressed as:

[0071]

[0072] in, Indicates the number of conflicting elements.

[0073] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0074] The present invention adopts a high-dimensional combined Bayesian optimization method to schedule phased array elements, which reduces the number of evaluations of the objective function and effectively utilizes existing information, significantly improving the efficiency of optimization. At the same time, dimensionality reduction of decision variables can reduce the amount of calculation during model training and prediction, thereby improving processing speed.

[0075] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The accompanying drawings of the present invention are as follows.

[0077] Figure 1 Graph showing simulation results of the embodiment.

[0078] Figure 2 This is a diagram of the simulation results of Bayesian optimization without dimensionality reduction.

[0079] Figure 3 It is a schematic diagram of the overall process of the present invention. DETAILED DESCRIPTION

[0080] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0081] A large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization, such as Figure 3 As shown, the specific steps are as follows:

[0082] S1. Establish all task execution interval sets based on the collected information: establish a list including satellite ID, satellite model, execution interval, start time, end time and duration variables;

[0083] Secondly, establish a given task set: establish a list of four variables including task sequence number, satellite ID, task duration and task execution status, and indicate the specific information of each task in the corresponding position of the list;

[0084] In this embodiment, the phased array configuration adopts a hemisphere plus a cylinder, 26469 points are used to represent the phased array elements, one point coordinate represents one element, and the activation angle is 60 degrees.

[0085] S2, the number of measurement and control tasks M = 20, the dimension of dimensionality reduction is set to R = 10, and the number of initial samples N = 20;

[0086] During the scheduling process, the objective function can be evaluated based on the measurement and control task satisfaction rate η1, array resource utilization rate η2, and array resource conflict rate η3.

[0087] f=w1η1+w2η2-w3η3

[0088] The measurement and control task satisfaction rate η1 is calculated as:

[0089]

[0090] Where M′ is the number of completed tasks. The difference between the task end time and the start time is calculated. If it is greater than the duration, the task is completed.

[0091] The array element resource utilization rate η2 represents the ratio of all used array elements to the total number of array elements, expressed as:

[0092]

[0093] in represents the total number of array elements used, and |Z| represents the total number of array elements.

[0094] The array element resource conflict rate η3 represents the ratio of the number of conflicting array elements to the number of used array elements, which is expressed as:

[0095]

[0096] in Indicates the number of conflicting array elements;

[0097] Set the weights in the objective function to w1=0.2, w2=0.4, w3=0.2;

[0098] For task i, count the number of visible time windows, denoted as cos(i), and randomly generate the solution:

[0099] x i ∈[0,cos(i)],x i ∈Z

[0100] Generate 20 sets of solutions for 20 tasks using a random method, and put the solution set in the following matrix:

[0101]

[0102] Set the number of iterations to 20 and calculate the objective function for each set of solutions:

[0103] O=[f1…f 20 ] T

[0104] S3, the dimension reduction matrix A reduces the dimension of the solution. The dimension reduction matrix A is a random matrix with 10 rows and 20 columns, in which each element is an independent Bernoulli distribution random variable. Multiply the initial solution set matrix and the transpose of the dimension reduction matrix to obtain the reduced solution set F:

[0105] F=S×A T

[0106] S4. Establish a probabilistic proxy model. The specific method is as follows:

[0107] The sample set of the solution after dimensionality reduction and the corresponding objective function is established as follows:

[0108] D t ={(F1,f1),(F2,f2)…(F 20 ,f 20 )}

[0109] Assume the model is:

[0110]

[0111] Since the structure of the model is unknown in the prior information, the identification process presupposes that the output y k Related to the input and output values ​​of the past 4 times, that is

[0112] And the model structure is the highest third-order polynomial combination of the past four input and output values, that is:

[0113]

[0114] The noise ξ k It obeys a zero-mean Gaussian distribution, that is,

[0115]

[0116] The precision parameter τ follows the gamma distribution, that is

[0117]

[0118] Where a0 and b0 are constant parameters;

[0119] Assume that the parameter θ follows a Gaussian distribution with respect to parameters α and τ, and α follows a gamma distribution with respect to constants c0 and d0, then

[0120]

[0121] The joint prior distribution is expressed as:

[0122] p(θ,α,τ)=p(θ|α,τ)p(α)p(τ)

[0123] θ i The expectation and variance of are:

[0124]

[0125] α i The expectation and variance of are:

[0126]

[0127] The expectation and variance of τ are:

[0128]

[0129] Optimize model parameters using adaptive stochastic variational Bayes algorithm;

[0130] The new objective function value y * The probability distribution on a specific task combination is:

[0131] p(y(x k+1 )|D t )=∫θ T g(x k+1 )q(θ,α,τ)dθdαdτ

[0132] S5. Use the simulated annealing algorithm five times in parallel to search for five new solutions. The specific steps are as follows:

[0133] S51. Use the solution with the largest objective function value as the initial solution of the algorithm:

[0134]

[0135] S52. In the simulated annealing algorithm, a neighborhood solution is generated by perturbation for each selected solution, that is, an element in the current set of solutions is randomly changed.

[0136] S53, calculating the expected improvement of the neighborhood solution, the acquisition function is designed as:

[0137] EI(x k+1 )=∫max[y sample -y * ,0]p(y sample |D t )dy sample

[0138] where y sample Represents x k+1 The posterior distribution sample of the current best known value is y * .

[0139] S54. If the expected improvement of the new solution is better, then the new solution is directly accepted; if the expected improvement of the new solution is worse, then the new solution is accepted with probability P.

[0140] Let the previous state be x(n) and the energy be E(n); the next state be x(n+1) and the energy be E(n+1), and define the acceptance probability P of the system changing from x(n) to x(n+1) as:

[0141]

[0142] S6. Add the five new solutions generated by the simulated annealing algorithm to the initial solution and calculate their objective function values.

[0143] According to the simulated annealing algorithm combined with the acquisition function, 5 new solutions are found, which are expressed as:

[0144]

[0145] The objective function values ​​of the 5 sets of solutions are recorded as:

[0146]

[0147] Replace the original solution set S with the solution set that combines the new solution s with the original solution set S:

[0148]

[0149] The objective function value o corresponding to the new solution is combined with the objective function value O corresponding to the original solution set to replace the objective function value corresponding to the original solution set, which is recorded as:

[0150]

[0151] Let the current best objective function be f * , if f * If -0.6<0.001 or the set number of iterations is reached, exit the loop; otherwise, repeat S3 to S6.

[0152] The simulation results are shown in the following table:

[0153]

[0154]

[0155] As shown in Table 1, the total number of visible time windows (cos) of 20 tasks and the solution (x) given by the high-dimensional combined Bayesian algorithm of the present invention and the solution (x′) given by the Bayesian optimization algorithm without dimensionality reduction are shown in Table 1. The above table shows that the large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization used in the present invention is feasible.

[0156] The final results of the algorithm are shown in the following table, including the objective function and optimization time.

[0157]

[0158] like Figure 1 As shown in FIG. 1 , the objective function optimization result of the method used in the present invention for 20 measurement and control tasks can reach 0.6, and the time is 913.45s; Figure 2 The result of the Bayesian optimization method without dimensionality reduction on the objective function of 20 measurement and control tasks is about 0.579, and the time is 2197.6s. This shows the effectiveness of the method of the present invention. Compared with the Bayesian optimization without dimensionality reduction, the method used in the present invention has a shorter optimization time, higher efficiency, and a better objective function.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization, characterized in that: The specific method is as follows: Collect historical information of phased array satellites to establish a mission execution interval set; Establish mission sets based on satellite requirements for measurement and control; For different tasks in the task set, the visible time window is counted according to the task execution interval set, and the initial solution set is generated accordingly. The objective function of each set of phased array scheduling solutions is calculated, and the initial solution set matrix is ​​constructed. Reduce the dimension of the initial solution set matrix to obtain a reduced-dimensional solution set; A probability proxy model between the corresponding objective function value is established according to the dimension reduction solution set; Use the simulated annealing algorithm to search for the updated solution and calculate the objective function value; Append the updated solution to the initial solution set; Repeat the updating, appending of the initial solution set and calculation of the objective function value until the number of iterations reaches the preset target, exit the loop, and select the optimal objective function value as the final phased array element scheduling solution.

2. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 1, characterized in that: The task execution interval set includes: satellite ID, satellite model, execution interval, start time, end time and duration.

3. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 1, characterized in that: The task set includes: task sequence number, satellite ID, task duration and task execution status.

4. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 1, characterized in that: Calculate the objective function of each phased array scheduling solution. The specific method is as follows: For task i, a number x is randomly generated between 0 and the maximum visible time window number. i , then a set of solutions generated by random method is recorded as: X=[x1,x2,…,x M ] Generate N sets of solutions using a random method and put them in a matrix, recorded as: The objective function formula is set according to the task requirements, and the objective function value of N groups of solutions is recorded as: Where O is the objective function matrix composed of the objective function values ​​of N sets of solutions, where f i Represents the objective function value corresponding to the i-th group of solutions.

5. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 4, characterized in that: The initial solution set matrix is ​​reduced in dimension. The specific method is as follows: Set the dimension after dimensionality reduction to R, and generate a reduced dimension matrix A with R rows and M columns, where each element is an independent Bernoulli distribution random variable; Multiply the initial solution set matrix by the transpose of the dimension reduction matrix to obtain the reduced dimension solution set F: F=S×A T Among them, S is the initial solution set matrix of the N groups of solution sets generated for the M tasks mentioned above.

6. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 5, characterized in that: According to the dimension reduction solution set, a probabilistic proxy model is established between the corresponding objective function value. The specific method is as follows: D t ={(F1,f1),(F2,f2)…(F N ,f N )} Assume the model is: Among them, n f and n F are the maximum lags that affect the output and input at the current moment, ξ k is the output noise; When the input and output data are known and the structure g is fixed, the identification is transformed into an estimation of the parameter vector θ; The noise ξ k It obeys a zero-mean Gaussian distribution, that is, The precision parameter τ follows the gamma distribution, that is Where a0 and b0 are constant parameters; Assume that the parameter θ follows a Gaussian distribution with respect to parameters α and τ, and α follows a gamma distribution with respect to constants c0 and d0, then The joint prior distribution is expressed as: p(θ,α,τ)=p(θ|α,τ)p(α)p(τ) The new objective function value y * The probability distribution on a specific task combination is: p(y(x k+1 )|D t )=∫θ T g(x k+1 )q(θ,α,τ)dθdαdτ Among them, θ and α are vectors, and θ, α, and τ all have variance and expectation: θ i The variance and expectation of i ),∑(θ i ); α i The variance and expectation of i ),∑(α i ); the variance and expectation of τ are expressed as μ(τ) and ∑(τ) respectively; the variational Bayesian algorithm is used to optimize θ, α, and τ.

7. The large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization according to claim 6, characterized in that: Use the simulated annealing algorithm to search for the updated solution and calculate the objective function value. The specific method is as follows: The optimization algorithm uses the solution with the largest objective function value as the initial solution of the algorithm: Sampling is performed at the expected maximum, and the acquisition function is designed as: where y sample Represents x k+1 The posterior distribution sample of the current best known value is y * ; According to the optimization algorithm combined with the acquisition function, n groups of new solutions are found, which can be expressed as: The objective function value of n groups of solutions is recorded as: The solution set that combines the new solution s with the original solution set S replaces the original solution set S, which is recorded as: The objective function value o corresponding to the new solution is combined with the objective function value O corresponding to the original solution set to replace the objective function value corresponding to the original solution set, which is recorded as:

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