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

Abstract

This invention relates to the field of phased array technology, and particularly to a large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization. The method includes: establishing a task set based on the satellite requirements for telemetry and control; for different tasks within the task set, statistically analyzing visible time windows based on task execution interval sets to generate an initial solution set; calculating the objective function for each set of phased array scheduling solutions to construct an initial solution set matrix; reducing the dimensionality of the initial solution set matrix; establishing a probabilistic surrogate model between the dimensionality-reduced solution set and the corresponding objective function value; using simulated annealing to search for updated solutions and calculating the objective function value; and appending the updated solutions to the initial solution set. This invention employs a high-dimensional combinatorial Bayesian optimization algorithm to solve the phased array element scheduling problem. Compared to traditional optimization methods relying on a large number of samples, such as solution swarm optimization and genetic algorithms, high-dimensional combinatorial Bayesian optimization significantly improves optimization efficiency by reducing the number of times the objective function must be evaluated and effectively utilizing existing information.

Description

Technical Field

[0001] This invention relates to the field of phased array technology, and in particular to a method for scheduling elements of a large-scale phased array based on high-dimensional combined Bayesian optimization. Background Technology

[0002] Phased array technology is widely used in radar, communications, electronic warfare, and imaging. It utilizes multiple antenna elements, controlling the amplitude and phase of each element to precisely adjust the direction and shape of the beam, achieving rapid beam steering and multi-target tracking. The key to phased arrays lies in the scheduling and phase control of their elements, ensuring the beam has good gain and resolution in the desired direction.

[0003] In phased array applications, the element scheduling problem can be viewed as a high-dimensional combinatorial optimization problem. Specifically, with multiple elements available, different scheduling methods and control strategies directly affect system performance metrics, such as signal gain, resolution, and anti-interference capability. As the number of elements increases, the scheduling space grows exponentially, making it difficult for traditional optimization methods to find the optimal solution within a reasonable timeframe. Summary of the Invention

[0004] This invention discloses a large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization, the specific method of which is as follows:

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

[0006] Establish a mission set based on the satellite's tracking and control requirements;

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

[0008] The initial solution set matrix is ​​reduced in dimension to obtain the reduced-dimensional solution set;

[0009] A probabilistic proxy model is established between the dimensionality-reduced solution set and the corresponding objective function value.

[0010] The simulated annealing algorithm is used to search for an updated solution, and the objective function value is calculated.

[0011] The updated solution is appended to the initial solution set;

[0012] The process of repeatedly updating and adding the initial solution set and calculating the objective function value continues until the number of iterations reaches the preset target. Then, the loop exits, and the optimal objective function value is selected as the final phased array element scheduling scheme.

[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 for each phased array scheduling solution is calculated using the following method:

[0016] For task i, a number x is randomly generated between 0 and the maximum visible time window number. i A solution generated by a random method is denoted as:

[0017] X = [x1, x2, ..., x M ]

[0018] N sets of solutions are generated using a random method and placed in a matrix, denoted as:

[0019]

[0020] Based on the task requirements, the objective function formula is defined, and the objective function values ​​of the N sets of solutions are denoted as:

[0021]

[0022] In the formula, O is the objective function matrix composed of the objective function values ​​of N sets of solutions, where f i This represents the objective function value corresponding to the i-th solution.

[0023] Furthermore, the initial solution set matrix is ​​reduced in dimensionality using the following method:

[0024] Let the dimension of the reduced dimension be R, and generate an R-row, M-column reduced dimension matrix A, where each element is an independent Bernoulli distributed random variable;

[0025] Multiplying the initial solution set matrix by the transpose of the dimension-reduced matrix yields the dimension-reduced solution set F:

[0026] F = S × A T

[0027] Where S is the initial solution set matrix of the N sets of solutions generated from the M tasks.

[0028] Furthermore, a probabilistic proxy model is established based on the dimensionality-reduced 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 as follows:

[0031]

[0032]

[0033] Where, n f and n F These are the maximum lags affecting the current output and input, respectively, ξ. k It is output noise;

[0034] Given that the input and output data are known and the structure g is fixed, the identification is transformed into the estimation of the parameter vector θ.

[0035] Where the noise ξ k It follows a zero-mean Gaussian distribution, i.e.

[0036]

[0037] The precision parameter τ follows a gamma distribution, i.e.

[0038]

[0039] In the formula, a0 and b0 are constant parameters;

[0040] Assuming 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 represented as:

[0043] p(θ,α,τ)=p(θ|α,τ)p(α)p(τ)

[0044] The new objective function value y * The probability distribution for a specific combination of tasks is as follows:

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

[0046] Where θ and α are vectors, and θ, α, and τ all have variance and expectation: θ i The variance and expectation are respectively expressed as μ(θ) i ),∑(θ i );α i The variance and expectation are respectively expressed as μ(α) i ),∑(α i); the variance and expectation of τ are represented as μ(μ) and ∑(τ), respectively; θ, α, and τ are optimized using variational Bayesian algorithms.

[0047] Furthermore, the simulated annealing algorithm is used to search for the updated solution and 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.

[0049]

[0050] Sampling is performed at the point of maximum expectation, and the sampling function is designed as follows:

[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 of the sample, with the best known value being y. * ;

[0053] Based on the optimization algorithm and the acquisition function, n new solutions are found, represented as follows:

[0054]

[0055] The objective function values ​​of the n solutions are denoted as:

[0056]

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

[0060]

[0061] Furthermore, the objective function is constructed based on the measurement and control task satisfaction rate η1, the array element resource utilization rate η2, and the array element resource conflict rate η3, and 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 follows:

[0065]

[0066] Where M′ represents the number of tasks completed, the difference between the task end time and the start time is calculated, and 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 |Z| represents the total number of array elements used;

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

[0071]

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

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

[0074] This invention employs a high-dimensional combinatorial Bayesian optimization method for scheduling phased array elements, reducing the number of evaluations of the objective function while effectively utilizing existing information, thus significantly improving optimization efficiency. Furthermore, dimensionality reduction of decision variables can reduce the computational load during model training and prediction, thereby increasing processing speed.

[0075] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0076] The accompanying drawings of this invention are described below.

[0077] Figure 1 The following is a simulation result diagram for an example.

[0078] Figure 2 The simulation results are shown in the Bayesian optimization diagram without dimensionality reduction.

[0079] Figure 3 This is a schematic diagram of the overall process of the present invention. Detailed Implementation

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

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

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

[0083] Secondly, establish the given task set: create a list including four variables: task sequence number, satellite ID, task duration, and task execution status, and represent 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 cylinder, with 26,469 points representing phased array elements, one point coordinate representing one array element, and the activation angle is 60 degrees.

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

[0086] During the scheduling process, the evaluation can be based on the telemetry and control task fulfillment rate η1, array element resource utilization rate η2, and array element resource conflict rate η3. The objective function is:

[0087] f = w1η1 + w2η2 - w3η3

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

[0089]

[0090] Where M′ represents the number of tasks to be completed. The difference between the task end time and the start time is calculated, and if it is greater than the duration, the task is considered complete.

[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 This represents the total number of array elements used, where |Z| represents the total number of array elements.

[0094] The element resource conflict rate η3 represents the ratio of the number of conflicting elements to the number of elements used, 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, and w3 = 0.2;

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

[0099] x i ∈[0,cos(i)],x i ∈Z

[0100] For 20 tasks, 20 solutions are generated using a random method. The solution set is placed in the following matrix:

[0101]

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

[0103] O = [f1…f 20 ] T

[0104] S3. Dimensionality reduction matrix A reduces the dimension of the solution. Dimensionality reduction matrix A is a 10x20 random matrix, where each element is an independent Bernoulli distributed random variable. Multiplying the initial solution set matrix by the transpose of the dimension reduction matrix yields the dimension-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 dimensionality-reduced solution and its corresponding objective function is established as follows:

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

[0109] Assume the model is as follows:

[0110]

[0111] Since the structure of the model is unknown in the prior information, the identification process pre-assumes the output y. k It is related to the input and output values ​​of the past 4 times, that is

[0112] Furthermore, the model structure is a polynomial combination of the highest 3rd degree of the input-output values ​​over the past 4 iterations, i.e.:

[0113]

[0114] Where the noise ξ k It follows a zero-mean Gaussian distribution, i.e.

[0115]

[0116] The precision parameter τ follows a gamma distribution, i.e.

[0117]

[0118] In the formula, a0 and b0 are constant parameters;

[0119] Assuming 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 represented as:

[0122] p(θ,α,τ)=p(θ|α,τ)p(α)p(τ)

[0123] θ i The expected value and variance are respectively:

[0124]

[0125] α i The expected value and variance are respectively:

[0126]

[0127] The expected value and variance of τ are respectively:

[0128]

[0129] The model parameters were optimized using an adaptive stochastic variational Bayesian algorithm.

[0130] The new objective function value y * The probability distribution for a specific combination of tasks is as follows:

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

[0132] S5. Five new solutions are found by using the simulated annealing algorithm in parallel for five runs. 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, the selected solution is perturbed to generate a neighborhood solution, that is, one element in the current set of solutions is randomly changed.

[0136] S53. Calculate the expected improvement of the neighborhood solution. The acquisition function is designed as follows:

[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 of the sample, with the best known value being y. * .

[0139] S54. If the new solution offers a better expected improvement, then accept the new solution directly; if the new solution offers a worse expected improvement, accept the new solution with probability P.

[0140] Let the previous state be x(n) with energy E(n); and the next state be x(n+1) with energy E(n+1). Define the 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] Five new solutions were found based on the simulated annealing algorithm and the acquisition function, as follows:

[0144]

[0145] The objective function values ​​of the 5 solutions are denoted 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, denoted as:

[0150]

[0151] Let the current optimal 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 table below:

[0153]

[0154]

[0155] Table 1 shows the total number of visible time windows (cos) for 20 tasks and the solutions (x) given by the high-dimensional combined Bayesian algorithm and the non-dimensional Bayesian optimization algorithm (x′) in this invention. The table above shows that the large-scale phased array element scheduling method based on high-dimensional combined Bayesian optimization used in this invention is feasible.

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

[0157]

[0158] like Figure 1 As shown, the method used in this invention can achieve an optimization result of 0.6 for the objective function of 20 measurement and control tasks, with a time of 913.45s; Figure 2 The result shown is that the Bayesian optimization method without dimensionality reduction achieves an optimization time of approximately 0.579 for the objective function of 20 measurement and control tasks, with a time of 2197.6 seconds. This demonstrates the effectiveness of the method presented in this invention. Compared with Bayesian optimization without dimensionality reduction, the method used in this invention has a shorter optimization time, higher efficiency, and yields 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 and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do 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 method for scheduling elements of a large-scale phased array based on high-dimensional combinatorial Bayesian optimization, characterized in that, The specific method is as follows: Collect historical information from phased array satellites to establish a task execution interval set; Establish a mission set based on the satellite's tracking and control requirements; For different tasks in the task set, the visible time window is statistically analyzed based on the task execution interval set, and an initial solution set is generated accordingly. The objective function of each group of phased array scheduling solutions is calculated, and the initial solution set matrix is ​​constructed. The initial solution set matrix is ​​reduced in dimension to obtain the reduced-dimensional solution set; A probabilistic proxy model is established between the dimensionality-reduced solution set and the corresponding objective function value. The simulated annealing algorithm is used to search for an updated solution, and the objective function value is calculated. The updated solution is appended to the initial solution set; The process of repeatedly updating and adding the initial solution set and calculating the objective function value continues until the number of iterations reaches the preset target. Then, the loop exits, and the optimal objective function value is selected as the final phased array element scheduling scheme.

2. The large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization as described in 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 combinatorial Bayesian optimization as described in 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 combinatorial Bayesian optimization as described in claim 1, characterized in that, The objective function for each phased array scheduling solution is calculated using the following method: For task i, a number x is randomly generated between 0 and the maximum visible time window number. i Let the set of solutions generated by the random method be denoted as the initial solution set: X=[x1,x2,…,x M ] N sets of solutions are generated using a random method and placed in a matrix, denoted as the initial solution set matrix: Based on the task requirements, the objective function formula is defined, and the objective function values ​​of the N sets of solutions are denoted as: In the formula, O is the objective function matrix composed of the objective function values ​​of N sets of solutions, where f i This represents the objective function value corresponding to the i-th solution.

5. The large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization as described in claim 4, characterized in that, The dimensionality reduction of the initial solution set matrix is ​​performed as follows: Let the dimension of the reduced dimension be R, and generate an R-row, M-column reduced dimension matrix A, where each element is an independent Bernoulli distributed random variable; Multiplying the initial solution set matrix by the transpose of the dimension-reduced matrix yields the dimension-reduced solution set F: F=S×A T 。 6. The large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization as described in claim 5, characterized in that, A probabilistic proxy model is established based on the dimensionality-reduced solution set and the corresponding objective function value. The specific method is as follows: The sample set of the dimensionality-reduced solution and its corresponding objective function is established as follows: D t ={(F1,f1),(F2,f2)…(F N ,f N )} Assume the model is as follows: Where, n f and n F These are the maximum lags affecting the current output and input, respectively, ξ. k It is output noise; Given that the input and output data are known and the structure g is fixed, the identification is transformed into the estimation of the parameter vector θ. Where the noise ξ k It follows a zero-mean Gaussian distribution, i.e. The precision parameter τ follows a gamma distribution, i.e. In the formula, a0 and b0 are constant parameters; Assuming 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 represented as: p(θ,α,τ)=p(θ|α,τ)p(α)p(τ) The new objective function value y * The probability distribution for a specific combination of tasks is as follows: p(y(x k+1 )|D t )=∫θ T g(x k+1 )q(θ,α,τ)dθdαdτ Where θ and α are vectors, and θ, α, and τ all have variance and expectation: θ i The variance and expectation are respectively expressed as μ(θ) i ),∑(θ i );α i The variance and expectation are respectively expressed as μ(α) i ),∑(α i The variance and expectation of τ are represented as μ(τ) and ∑(τ), respectively; the model parameters are optimized using an adaptive stochastic variational Bayesian algorithm.

7. The large-scale phased array element scheduling method based on high-dimensional combinatorial Bayesian optimization as described in claim 6, characterized in that, The simulated annealing algorithm is used to search for updated solutions 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. Sampling is performed at the point of maximum expectation, and the sampling function is designed as follows: EI(x k+1 )=∫max[y sample -the * ,0]p(y sample |D t )of sample Where y sample Represents x k+1 The posterior distribution of the sample, with the best known value being y. * ; Based on the optimization algorithm and the acquisition function, n new solutions are found, represented as follows: The objective function values ​​of the n solutions are denoted as: The solution set that combines the new solution s with the original solution set S replaces the original solution set S, and is denoted 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, denoted as:

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