An array unit failure correction method based on an improved teaching and learning optimization algorithm

Abstract

The application discloses an array unit failure correction method based on an improved teaching and learning optimization algorithm, and comprises the following steps: taking a repaired directional diagram radiation characteristic as an optimization target, and recalculating the excitation amplitude of the remaining effective array elements after array unit failure through the improved teaching and learning optimization algorithm. The linear array synthesis method based on the improved teaching and learning optimization algorithm takes the repaired directional diagram radiation characteristic as the optimization target, recalculates the excitation amplitude of the remaining effective array elements after array unit failure through the improved teaching and learning optimization algorithm, corrects the directional diagram after array unit failure, and increases the common excitation constraint condition to improve the stability of an antenna system and reduce the system maintenance cost under the precondition of repairing the directional diagram radiation characteristic.

Description

Technical Field

[0001] This invention relates to a method for correcting array element failures based on an improved teaching and learning optimization algorithm, belonging to the field of linear array antenna pattern synthesis design technology. Background Technology

[0002] Array element failure is equivalent to the absence of an array element at the failure location, meaning that the excitation phase values ​​at the corresponding location are all zero. This leads to phenomena such as widening of the main lobe and raising of the maximum sidelobe level in the radiation pattern, affecting the normal communication function of the array antenna. If the failure array element is replaced or repaired, it has the disadvantages of being very costly or having an excessively long repair cycle in special situations (such as wartime, deep sea or space environments). Therefore, it is possible to optimize the remaining usable array elements to achieve the radiation characteristics of the original array antenna as much as possible. This repair method only requires using optimization algorithms to change the current excitation values ​​of the remaining array elements, which has obvious advantages such as being timely and feasible, simple to operate, and requiring less workload.

[0003] Currently, the main technical means to solve the problem of array element failure is to optimize the remaining array elements. This mainly adopts the improved swarm intelligence optimization algorithm ([1] Wang Zihao, Ma Juntao, Lu Jun, et al. Array element failure correction method based on improved weed invasion algorithm [J]. Computer Simulation, 2021, 38(10). [2] Meng Xianmeng, Cai Cuicui. Array element failure correction based on improved whale optimization algorithm [J]. Journal of Detection and Control, 2020, 42(06).). The optimization goal is to reduce the sidelobe level. The current excitation value of the remaining array elements is adjusted so that the radiation pattern after the array element failure can be corrected, and finally the characteristic index requirements before failure are partially restored.

[0004] The classic teaching and learning optimization algorithm, by simulating a classroom teaching process, achieves a heuristic search of the solution space. It boasts advantages such as simple mathematical principles, few adjustable parameters, and ease of code implementation, and has been successfully applied in industrial fields, such as factory scheduling and logistics route optimization related to knapsack problems, achieving relatively ideal results. However, like other typical swarm intelligence algorithms, the teaching and learning optimization algorithm also suffers from relatively weak mathematical foundations and a tendency to converge prematurely. Existing research has demonstrated that when solving high-dimensional complex nonlinear problems, the algorithm exhibits drawbacks such as premature convergence and insufficient solution accuracy in the later stages of iteration. This, to some extent, limits the theoretical development and application scope of the teaching and learning optimization algorithm.

[0005] Therefore, to address this problem, this invention proposes an array cell failure correction method based on an improved teaching and learning optimization algorithm. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a linear array synthesis method based on an improved teaching and learning optimization algorithm. With the goal of repairing the radiation characteristics of the radiation pattern, the improved teaching and learning optimization algorithm recalculates the excitation amplitude of the remaining effective array elements after the array element failure, so as to correct the radiation pattern after the array element failure. Furthermore, a mechanism for escaping local optima is added to the teaching and learning optimization algorithm to improve the solution accuracy. Thus, under the premise of repairing the radiation characteristics of the radiation pattern, the stability of the antenna system is improved and the system maintenance cost is reduced by adding common excitation constraints.

[0007] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0008] This invention provides a method for array cell failure correction based on an improved teaching and learning optimization algorithm, comprising:

[0009] With the goal of restoring the radiation characteristics of the radiation pattern, an improved teaching and learning optimization algorithm is used to recalculate the excitation amplitude of the remaining effective array elements after array element failure. This improved teaching and learning optimization algorithm includes:

[0010] Step 1: Based on the maximum sidelobe level of the repaired pattern, the preset main lobe width, and the repaired main lobe width, establish the fitness function, the statistical values ​​of the teacher's nearby and same locations, the threshold, the maximum number of iterations, and the size of the teacher-student group, and randomly initialize the teacher-student group;

[0011] Step 2: Determine whether there is a teacher's individual position whose directional pattern satisfies the given radiation characteristics requirement or whether the algorithm has reached the maximum number of iterations. If either condition is met, proceed to step 3; otherwise, proceed to step 4.

[0012] Step 3: Output the individual teacher's location;

[0013] Step 4: Calculate the fitness function value of individual students and the average fitness value of the group, identify individual teachers, and update the nearby location statistics and same location statistics of individual teachers;

[0014] Step 5: Update the convergence factor;

[0015] Step 6: Compare the individual student fitness score with the average fitness score of the group, and update the individual student position based on the comparison results;

[0016] Step 7: Calculate the Canberra distance between individual students, who then co-evolve according to a homogeneous competition mechanism;

[0017] Step 8: Determine whether the statistical value of the location near the individual teacher has reached the threshold. If so, assign a value to the number in the individual teacher's location.

[0018] Step 9: Determine whether the number of times the teacher appears at the current position has reached the threshold. If so, perturb the teacher's position according to the Bernoulli map and determine whether to retain the perturbed position. Otherwise, proceed to step 10.

[0019] Step 10: Reinitialize the population and proceed to Step 2.

[0020] Furthermore, the far-field radiation pattern of the linear array model in step 1 is represented as follows:

[0021]

[0022] (1) In the formula, the array has M rows of array elements arranged in the same direction, the row spacing is d, and λ is the free space operating wavelength. m It is the excitation amplitude of the m-th array element in the plane, u = sinθ (∈[-1,1]).

[0023] The fitness function established is as follows:

[0024] fit = k1|PSL|-k2|BW-BW d | (2)

[0025] (2) In the formula, k1 and k2 are weighting coefficients, PSL is the maximum sidelobe level obtained after synthesis, and BW d BW is the preset main lobe width, and BW is the main lobe width obtained after synthesis.

[0026] Furthermore, in step 1, the size of the teacher-student group is set to P, where the size of the student group is P-1.

[0027] The average fitness level of the student population is calculated using the following formula:

[0028]

[0029] (3) In the formula, Fit p Let A be the fitness function value of the p-th student (p∈[1,…,P-1]), and let A be the array stimulus corresponding to this student. p It means that A p =[a p、1 ,a p、2 ,…,a p、m ,…,a p、M-1 ,a p、M The statistical value of the location near the individual teacher is j1, and j1 = 0, and the threshold is represented by J1. The statistical value of the same location is j2, and j2 = 0, and the threshold is represented by J2. The maximum number of iterations is set to G, and g is the current number of iterations. P M-dimensional vectors between [0,1] are randomly generated as the initial teacher-student group.

[0030] Furthermore, the specific operation of step 2, determining whether there exists a teacher's individual location whose radiation pattern satisfies the given radiation characteristic requirements and whether the algorithm has reached the maximum number of iterations, is as follows: Determine whether there exists a teacher individual A. best According to equation (1), the maximum sidelobe electrical average of the corresponding radiation pattern is less than the preset threshold PSL and the main lobe width is less than the preset BW. d Determine whether g has reached the maximum number of iterations G.

[0031] Furthermore, the specific operation of outputting the individual teacher position in step 3 is as follows: according to equation (2), the output optimal individual position must satisfy the maximum corresponding Fit value.

[0032] Furthermore, the specific operation of calculating the fitness function value of individual students and the average fitness value of the group in step 4 is as follows: calculate the fitness function value of individual students according to equations (1) and (2), and calculate the average fitness value of the student group according to equation (3).

[0033] Furthermore, the specific operation of determining individual teachers and updating the nearby and same-location statistics of individual teachers in step 4 is as follows: sort all individuals in descending order of fitness value, and then sort individual teacher A... best The optimal solution for the population is defined by the maximum value of the fitness function. If the number in a teacher's position appears consecutively near the original incentive value of the corresponding position, that is, the absolute value of the difference between the two numbers is less than 0.1, then the statistical value j1 is processed as j1 = j1 + 1; otherwise, j1 = 0. If the teacher's position is the same as the previous generation's position, then the statistical value j2 is processed as j2 = j2 + 1; otherwise, j2 = 0.

[0034] Furthermore, the specific operation of updating the convergence factor in step 5 is as follows:

[0035] The update formula for the nonlinear decreasing convergence factor a1 is as follows:

[0036]

[0037] The update formula for the nonlinear decreasing convergence factor a2 is as follows:

[0038]

[0039] Furthermore, the step of updating the individual student's location described in step 6 is as follows:

[0040] If the student's fitness function value is greater than or equal to Fit ave The position update steps are as follows:

[0041]

[0042] In the gth generation, Let m be the m-th dimension component of the p-th student individual. For individual teacher A best The m-th dimension component, Let A be the m-th dimension component of the average position of the student group. mean As determined by equation (7), T F The teaching factor is randomly determined to be 1 or 2, and k3 is a random value that follows a uniform distribution within the range of 0 to 1.

[0043]

[0044] If the student's fitness function value is less than Fit ave Then its position update is determined by equation (8).

[0045]

[0046] Furthermore, the formula for calculating the Canberra distance between individual students mentioned in step 7 is as follows:

[0047]

[0048] Among them, a x、m For the xth student individual A x The m-th dimension component.

[0049] Furthermore, the formula for the collaborative evolution of individual student positions based on the homogeneous competition mechanism mentioned in step 7 is as follows:

[0050]

[0051] in, For the q-th student individual A q The m-th dimension component, A q Distance A p The nearest student to Cambella is k4, which is determined by equation (11), and k5 is determined by equation (12).

[0052]

[0053] Among them, Fit p Let Fit be the fitness function value of the p-th student. q Let q be the fitness function value of the q-th student.

[0054]

[0055] Furthermore, the detailed steps for assigning values ​​to the numbers in the individual teacher positions described in step 8 are as follows:

[0056] Determine whether j1 has reached the maximum threshold J1. If so, the excitation value of the available array element in the failure state is assigned to the number in the corresponding teacher individual.

[0057] Furthermore, the detailed steps for perturbing the teacher's position based on the Bernoulli map in step 9 are as follows:

[0058] Determine whether j2 has reached the maximum threshold J2. If so, perturb the teacher's position according to the Bernoulli mapping, which is equivalent to perturb the teacher's position according to equation (13).

[0059]

[0060] In the formula, Indicates the teacher's position after disturbance The m-th dimension component, ψ is the control parameter.

[0061] Furthermore, the detailed steps for determining whether to retain the disturbed position in step 9 are as follows:

[0062] Based on equation (2), calculate the fitness function values ​​of individual teachers before and after the perturbation. If the fitness function value after the perturbation is greater than the value before the perturbation, then retain the position after the perturbation; otherwise, keep the original position unchanged. That is, the teacher position update formula is equivalent to the following:

[0063]

[0064] In the formula, Let be the fitness function value of an individual teacher in generation g. Let be the fitness function value of an individual teacher after perturbation via Bernoulli mapping.

[0065] Furthermore, the specific operation of re-initializing the population in step 10 is as follows:

[0066] Combine the teacher-student group from step 2 with the new groups obtained from steps 7, 8, and 9. Sort the fitness function values ​​of all teachers-students in the combined group, and retain the top P teachers-students with the largest function values ​​as the new group.

[0067] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0068] The linear array synthesis method based on the improved teaching and learning optimization algorithm provided by this invention aims to repair the radiation characteristics of the radiation pattern. By improving the teaching and learning optimization algorithm, the excitation amplitude of the remaining effective array elements after the array element failure is recalculated to correct the radiation pattern after the array element failure. Furthermore, a mechanism to escape local optima is added to the teaching and learning optimization algorithm to improve the solution accuracy. Thus, under the premise of repairing the radiation characteristics of the radiation pattern, the stability of the antenna system is improved and the system maintenance cost is reduced by adding common excitation constraints.

[0069] This invention provides an array cell failure correction method based on an improved teaching and learning optimization algorithm. It introduces a nonlinear decreasing convergence factor strategy and adds a mechanism to escape local optima on top of the classic teaching and learning optimization algorithm. First, students are divided into high-performing and low-performing students based on their average fitness value. High-performing students, guided by the teacher, update their positions using a nonlinear decreasing convergence factor a1 to improve the algorithm's ability to perform refined searches in specific regions. Low-performing students update their positions using a nonlinear decreasing convergence factor a2 to balance the algorithm's global exploration and local development performance. Second, an escape mechanism is introduced, using a Bernoulli mapping to perturb the individual teacher positions, improving the teacher's local resistance to stagnation. This makes the improved teaching and learning optimization algorithm more advantageous in terms of global search performance and optimization accuracy. Attached Figure Description

[0070] Figure 1 This is a flowchart of the method of the present invention;

[0071] Figure 2 These are the field pattern and a partially enlarged view under normal operating conditions in the embodiments of the present invention;

[0072] Figure 3 These are the field pattern and a partial magnified view of the array element failure state in the embodiments of the present invention;

[0073] Figure 4 These are the repaired field pattern and a partially enlarged view in an embodiment of the present invention;

[0074] Figure 5 These are the array element positions and excitation distributions under three states in the embodiments of the present invention; Detailed Implementation

[0075] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0076] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0077] With the goal of restoring the radiation characteristics of the radiation pattern, an improved teaching and learning optimization algorithm is used to recalculate the excitation amplitude of the remaining effective array elements after array element failure. This improved teaching and learning optimization algorithm includes:

[0078] Step A: Based on the maximum sidelobe level of the repaired pattern, the preset main lobe width, and the repaired main lobe width, establish the fitness function, the statistical values ​​of the teacher's nearby and same locations, the threshold, the maximum number of iterations, and the size of the teacher-student group, and randomly initialize the teacher-student group.

[0079] Step B: Determine whether there is a teacher's individual position whose radiation pattern satisfies the given radiation characteristics requirement or whether the algorithm has reached the maximum number of iterations. If either condition is met, proceed to step C; otherwise, proceed to step D.

[0080] Step C: Output the individual teacher's location.

[0081] Step D: Calculate the fitness function value of individual students and the average fitness value of the group, identify individual teachers, and update the nearby location statistics and same location statistics of individual teachers.

[0082] Step E: Update the convergence factor.

[0083] Step F: Compare the individual student fitness value with the average fitness value of the group, and update the individual student position based on the comparison results.

[0084] Step G: Calculate the Campbell's distance between individual students, who then co-evolve according to a homogeneous competition mechanism.

[0085] Step H: Determine whether the statistical value of the location near the individual teacher has reached the threshold. If so, assign a value to the number in the individual teacher's location.

[0086] Step 1: Determine whether the number of times the teacher appears at the current position has reached the threshold. If so, perturb the teacher's position according to the Bernoulli mapping and determine whether to retain the perturbed position.

[0087] Step J: Reinitialize the population. Proceed to Step B.

[0088] Step Aa: The far-field radiation pattern of the linear array model is represented as follows:

[0089]

[0090] (1) In the formula, the array has M rows of array elements arranged in the same direction, the row spacing is d, and λ is the free space operating wavelength. m It is the excitation amplitude of the m-th array element in the plane, u = sinθ (∈[-1,1]).

[0091] The fitness function established is as follows:

[0092] fit = k1|PSL|-k2|BW-BW d | (2)

[0093] (2) In the formula, k1 and k2 are weighting coefficients, PSL is the maximum sidelobe level obtained after synthesis, and BW d BW is the preset main lobe width, and BW is the main lobe width obtained after synthesis.

[0094] The size of the teacher-student group is set to P, where the size of the student group is P-1. The average fitness of the student group is calculated as follows:

[0095]

[0096] (3) In the formula, Fit p Let A be the fitness function value of the p-th student (p∈[1,...,P-1]), and the array stimulus corresponding to this student is A. p It means that A p =[a p、1 ,a p、2 ,…,a p、m ,...,a p、M-1 ,a p、M ].

[0097] Step Ab: The statistical value of the location near the individual teacher is j1, and j1 = 0, the threshold is represented by J1, the statistical value of the same location is j2, and j2 = 0, the threshold is represented by J2, set the maximum number of iterations as G, g is the current number of iterations, and randomly generate P M-dimensional vectors between [0,1] as the initial teacher-student group.

[0098] Step B: Determine if there is an individual teacher A. best According to equation (1), the maximum sidelobe electrical average of the corresponding radiation pattern is less than the preset threshold PSL and the main lobe width is less than the preset BW. d Determine whether g has reached the maximum number of iterations G.

[0099] Step C: According to equation (2), the optimal individual position output must satisfy the maximum corresponding Fit value.

[0100] Step Da: Calculate the fitness function value of an individual student according to equations (1) and (2), and calculate the average fitness value of the student group according to equation (3).

[0101] Step Db: Sort all individuals in descending order of fitness value, starting with teacher individual A. best The optimal solution for the population is defined by the maximum value of the fitness function. If the number in a teacher's position appears consecutively near the original incentive value of the corresponding position, that is, the absolute value of the difference between the two numbers is less than 0.1, then the statistical value j1 is processed as j1 = j1 + 1; otherwise, j1 = 0. If the teacher's position is the same as the previous generation's position, then the statistical value j2 is processed as j2 = j2 + 1; otherwise, j2 = 0.

[0102] Step E: The specific operation for updating the convergence factor is as follows:

[0103] The update formula for the nonlinear decreasing convergence factor a1 is as follows:

[0104]

[0105] The update formula for the nonlinear decreasing convergence factor a2 is as follows:

[0106]

[0107] Step F: The steps to update the individual student's location are as follows:

[0108] If the student's fitness function value is greater than or equal to Fit ave The position update steps are as follows:

[0109]

[0110] In the gth generation, Let m be the m-th dimension component of the p-th student individual. For individual teacher A best The m-th dimension component, Let A be the m-th dimension component of the average position of the student group. mean As determined by equation (7), T F The teaching factor is randomly determined to be 1 or 2, and k3 is a random value that follows a uniform distribution within the range of 0 to 1.

[0111]

[0112] If the student's fitness function value is less than Fit ave Then its position update is determined by equation (8).

[0113]

[0114] Step Ga: The formula for calculating the Canberra distance between individual students is as follows:

[0115]

[0116] Among them, a x、m For the xth student individual A x The m-th dimension component.

[0117] Step Gb: The formula for the co-evolution of individual student positions based on the homogeneous competition mechanism is as follows:

[0118]

[0119] in, For the q-th student individual A q The m-th dimension component, A q Distance A p The nearest student to Cambella, k4 is determined by equation (11), and k5 is determined by equation (12).

[0120]

[0121] Among them, Fit p Let Fit be the fitness function value of the p-th student. q Let q be the fitness function value of the q-th student.

[0122]

[0123] Step H: The detailed steps for assigning values ​​to the numbers in the individual teacher positions are as follows:

[0124] Determine whether j1 has reached the maximum threshold J1. If so, the excitation value of the available array element in the failure state is assigned to the number in the corresponding teacher individual.

[0125] Step Ia: The detailed steps for perturbing the teacher's position based on the Bernoulli map are as follows:

[0126] Determine whether j2 has reached the maximum threshold J2. If so, perturb the teacher's position according to the Bernoulli mapping, which is equivalent to perturb the teacher's position according to equation (13).

[0127]

[0128] In the formula, Indicates the teacher's position after disturbance The m-th dimension component, where ψ is the control parameter.

[0129] Step Ib: The detailed steps for perturbing the teacher's position based on the Bernoulli map are as follows:

[0130] Based on equation (2), calculate the fitness function values ​​of individual teachers before and after the perturbation. If the fitness function value after the perturbation is greater than the value before the perturbation, then retain the position after the perturbation; otherwise, keep the original position unchanged. That is, the teacher position update formula is equivalent to the following:

[0131]

[0132] In the formula, Let be the fitness function value of an individual teacher in generation g. Let be the fitness function value of an individual teacher after perturbation via Bernoulli mapping.

[0133] Step J: The detailed steps for re-initializing the population are as follows:

[0134] Combine the teacher-student group from step B with the new group obtained from steps G, H, and I. Sort the fitness function values ​​of all teachers-students in the combined group, and retain the top P teachers-students with the largest function values ​​as the new group.

[0135] S10: Establish the fitness function and set the size of the teacher and student group.

[0136] The far-field radiation pattern of the linear array model is represented as follows:

[0137]

[0138] (1) In the formula, the array has M rows of array elements arranged in the same direction, the row spacing is d, and λ is the free space operating wavelength. m It is the excitation amplitude of the m-th array element in the plane, u = sinθ (∈[-1,1]).

[0139] The fitness function established is as follows:

[0140] fit = k1|PSL|-k2|BW-BW d | (2)

[0141] (2) In the formula, k1 and k2 are weighting coefficients, PSL is the maximum sidelobe level obtained after synthesis, and BW d BW is the preset main lobe width, and BW is the main lobe width obtained after synthesis.

[0142] Furthermore, in step 1, the size of the teacher-student group is set to P, where the size of the student group is P-1.

[0143] The average fitness level of the student population is calculated using the following formula:

[0144]

[0145] (3) In the formula, Fit pLet A be the fitness function value of the p-th student (p∈[1,...,P-1]), and the array stimulus corresponding to this student is A. p It means that A p =[a p、1 ,a p、2 ,...,a p、m ,...,a p、M-1 ,a p、M ].

[0146] S11: Set the statistics of teachers' nearby and same-location locations, thresholds, maximum number of algorithm iterations, and randomly initialize the teacher and student population.

[0147] The statistical value of the location near the individual teacher is j1, and j1 = 0, and the threshold is represented by J1. The statistical value of the same location is j2, and j2 = 0, and the threshold is represented by J2. The maximum number of iterations is set to G, and g is the current number of iterations. P M-dimensional vectors between [0,1] are randomly generated as the initial teacher-student group.

[0148] S12: Determine whether the radiation pattern satisfies the radiation characteristics or whether the maximum number of iterations has been reached.

[0149] The specific steps to determine whether there exists a teacher's location whose radiation pattern satisfies the given radiation characteristics and whether the algorithm has reached its maximum number of iterations are as follows: Determine whether there exists a teacher A. best According to equation (1), the maximum sidelobe electrical average of the corresponding radiation pattern is less than the preset threshold PSL and the main lobe width is less than the preset BW. d Determine whether g has reached the maximum number of iterations G.

[0150] S13: Output the individual teacher's location

[0151] According to equation (2), the optimal individual position output must satisfy the condition that the corresponding Fit value is maximized.

[0152] S14: Calculate the fitness function value of individual students and the average fitness value of the group.

[0153] The fitness function value of an individual student is calculated based on equations (1) and (2), and the average fitness value of the student group is calculated based on equation (3).

[0154] S15: Identify individual teachers and update their nearby location statistics and same-location statistics.

[0155] Sort all individuals by fitness value from largest to smallest, teacher individual A bestThe optimal solution for the population is defined by the maximum value of the fitness function. If the number in a teacher's position appears consecutively near the original incentive value of the corresponding position, that is, the absolute value of the difference between the two numbers is less than 0.1, then the statistical value j1 is processed as j1 = j1 + 1; otherwise, j1 = 0. If the teacher's position is the same as the previous generation's position, then the statistical value j2 is processed as j2 = j2 + 1; otherwise, j2 = 0.

[0156] S16: Update convergence factor

[0157] The update formula for the nonlinear decreasing convergence factor a1 is as follows:

[0158]

[0159] The update formula for the nonlinear decreasing convergence factor a2 is as follows:

[0160]

[0161] S17: Determine whether an individual student's fitness value is less than the group's average fitness value.

[0162] If the student's fitness function value is greater than or equal to Fit ave Then proceed to step S18. If the student's fitness function value is less than Fit... ave Then proceed to step S19.

[0163] S18: High-performing students update their positions based on the convergence factor a1.

[0164] The steps for updating the position of high-performing students are as follows:

[0165]

[0166] In the gth generation, Let m be the m-th dimension component of the p-th student individual. For individual teacher A best The m-th dimension component, Let A be the m-th dimension component of the average position of the student group. mean As determined by equation (7), T F The teaching factor is randomly determined to be 1 or 2, and k3 is a random value that follows a uniform distribution within the range of 0 to 1.

[0167]

[0168] S19: Regular students update their positions based on the convergence factor a2.

[0169] The steps for updating the location of an individual student are as follows:

[0170]

[0171] S20: Calculate the Cambera distance between individual students.

[0172] The formula for calculating the Canberra distance between individual students is as follows:

[0173]

[0174] Among them, a x、m For the xth student individual A x The m-th dimension component.

[0175] S21: Individual students evolve collaboratively based on a homogeneous competition mechanism.

[0176] The formula for the co-evolution of individual student positions based on a homogeneous competition mechanism is as follows:

[0177]

[0178] in, For the q-th student individual A q The m-th dimension component, A q Distance A p The nearest student to Cambella, k4 is determined by equation (11), and k5 is determined by equation (12).

[0179]

[0180] Among them, Fit p Let Fit be the fitness function value of the p-th student. q Let q be the fitness function value of the q-th student.

[0181]

[0182] S22: Determine whether the statistical value of the location near an individual teacher has reached a threshold.

[0183] If j1 reaches the maximum threshold J1, then proceed to step S23; otherwise, proceed to step S24.

[0184] S23: Assign values ​​to the numbers in the teacher's individual position.

[0185] Assign the excitation value of the available array element in the failed state to the number in the corresponding teacher individual.

[0186] S24: Determine whether the statistical value of individual teachers at the same location has reached the threshold.

[0187] If j2 reaches the maximum threshold J2, then proceed to step S25; otherwise, proceed to step S29.

[0188] S25: Perturbation of individual teacher positions based on Bernoulli mapping

[0189] Perturbing the teacher's position according to the Bernoulli mapping is equivalent to perturbing the teacher's position according to equation (13).

[0190]

[0191] In the formula, Indicates the teacher's position after disturbance The m-th dimension component, where ψ is the control parameter.

[0192] S26: Determine whether the fitness value decreases after being disturbed.

[0193] If the teacher's position fitness function value after being perturbed by the Levy flight strategy is less than the fitness value before the perturbation, then execute S27; otherwise, execute S28.

[0194] S27: Preserve the position after disturbance

[0195] The teacher retains the position after the disturbance, which is equivalent to updating the teacher's position according to formula (14).

[0196]

[0197] S28: The individual teacher's position remains unchanged.

[0198] Equivalent to equation (18), the teacher remains in the same position as before the disturbance.

[0199]

[0200] S29: Reinitialize the population

[0201] Combine the teacher-student group from step S12 with the new groups obtained from steps S18, S19, S23, and S25. Sort the fitness function values ​​of all teacher-student individuals in the combined group, and retain the top P teacher-student individuals with the largest function values ​​as the new group.

[0202] Experiment: For comparison, Example 1 from the reference (Qi Z, Bai Y, Zhang X. Synthesis of Linear and Planar Arrays Via Sequential Convex Optimizations[J].2019.DOI:10.1109 / ACCESS.2019.2962998.) was selected. Figure 4 The results are shown in Table 1.

[0203] Table 1. Parameter settings of the improved Bluebottle Bowerbird algorithm in this invention.

[0204]

[0205] In the simulation experiments compared with the literature, the half-power beamwidth of the designed radiation pattern was 0.4°, the ideal radiation pattern PSL was limited to -38.3208dB, the corresponding array aperture was 182.7440λ, the element spacing was 0.9669λ, and it contained 190 array elements. After the multi-convex optimization method in the comparison literature was used, 6.8% of the array elements were sparsed. The repaired PSL was limited to -33.0495dB, the aperture was 179.8433λ, and after the preset failure handling and passive sparsification, 14.4% of the excitation of the 187 array elements was set to zero. The specific zeroing positions are shown in Table 2.

[0206] Table 2. Distribution of Incentive Zeroing and Common Incentive Array Elements

[0207]

[0208] The simulation conditions are set as follows: the initial array configuration is consistent with the corrected array in the comparative example above. Before obtaining the ideal and repaired radiation patterns, the excitation of the array elements at the positions in Table 2 is set to zero. It is worth noting that, compared with the examples in the literature, the array configuration processed by this invention is more stringent before obtaining the ideal radiation pattern (the aperture is reduced from 182.7440λ to 179.8433λ, the position of the failed array element is consistent with the comparative example, and the proportion of pre-set zero array elements is increased). After synthesis by the algorithm of this invention, Figure 2 This is an ideal radiation pattern and a magnified view under normal operating conditions. Figure 3 The images show the field pattern and a magnified view of a portion of the array under element failure conditions. The repaired field pattern and a magnified view of a portion of the array are shown below. Figure 4 A comparison in Table 3 reveals that the radiation characteristics (half-power beamwidth, PSL) of the radiation pattern under normal operating and repair states are consistent with the results in the literature. In the design obtained in this invention, 5% of the array elements do not need to adjust their excitation amplitude to participate in the correction. In contrast, the design in the references requires the entire array to participate in the radiation pattern correction. This invention overcomes the shortcomings of the multi-convex optimization method in handling the array element failure correction problem by failing to achieve common excitation constraints, thereby improving the stability of the antenna system and reducing the system maintenance cost.

[0209] Table 3 Comparison of correction results between the present invention and the multiconvex optimization methods in the prior art.

[0210]

[0211]

[0212] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0213] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0214] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0215] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0216] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for array cell failure correction based on an improved teaching and learning optimization algorithm, characterized in that, include: With the goal of restoring the radiation characteristics of the radiation pattern, an improved teaching and learning optimization algorithm is used to recalculate the excitation amplitude of the remaining effective array elements after array element failure. This improved teaching and learning optimization algorithm includes: A fitness function was established by combining the maximum sidelobe level of the repaired pattern, the preset main lobe width, and the repaired main lobe width, and the teacher and student population was randomly initialized. Determine whether there is a radiation pattern corresponding to the individual teacher's location that satisfies the given radiation characteristics requirement or whether the algorithm has reached the maximum number of iterations. If either condition is met, output the individual teacher's location as the optimization result; otherwise, repeat the optimization steps until either of the aforementioned conditions is met. The optimization steps include: Calculate the fitness function value of individual students and the average fitness value of the group, identify individual teachers, and update the nearby location statistics and same location statistics of individual teachers; Update the convergence factor; Compare individual student fitness scores with the group fitness average, and update individual student positions based on the comparison results; Calculate the Campbell's distance between individual students, who then co-evolve based on a homogeneous competition mechanism. Determine whether the statistical value of the location near an individual teacher has reached a threshold. If so, assign a value to the number in the individual teacher's location. Determine if the number of times a teacher appears at the current position has reached a threshold. If so, perturb the teacher's position according to the Bernoulli map and determine whether to retain the perturbed position; otherwise, reinitialize the group. The updated convergence factor includes: Nonlinear decreasing convergence factor The update formula is as follows: (4)； Nonlinear decreasing convergence factor The updated formula is as follows: (5)； The steps to update an individual student's location are as follows: If the student's fitness function value is greater than or equal to The position update steps are as follows: (6)； in, The maximum number of iterations, For the current iteration number, the th iteration... generation, For the first The first student individual dimensional components, For individual teachers The dimensional components, The first position of the average position of the student group dimensional components, average location Determined by equation (7), As a teaching factor, it is randomly assigned to be 1 or 2. These are random values ​​that follow a uniform distribution within the range of 0 to 1; (7)； If the student's fitness function value is less than Then its position update is determined by equation (8); (8)； The size of the teacher and student group is The student population is [size missing]. ; The average fitness level of the student population includes: (3)； (3) In the formula, For the first The fitness function value of each student, and the array stimulus corresponding to that student is determined by... express, The statistical value of the location near the individual teacher is ,and Threshold is expressed as The statistical value at the same position is ,and Threshold is expressed as Set the maximum number of iterations to , The current iteration number is randomly generated. Between [0,1] The dimensional vector serves as the initial group of teachers and students.

2. The array cell failure correction method based on the improved teaching and learning optimization algorithm according to claim 1, characterized in that, The far-field radiation pattern of the array cell model includes: (1)； (1) In the formula, the array is arranged along the same direction. Row array elements, row spacing is , It is the free space operating wavelength, where It is located in the plane of the first The incentive range of each array element ; The fitness function includes: (2)； (2) In the formula, , These are the weighting coefficients. This represents the maximum sidelobe level obtained after synthesis. The preset main lobe width, This represents the width of the main lobe after synthesis.

3. The array element failure correction method based on the improved teaching and learning optimization algorithm according to claim 1, characterized in that, The determination of whether there exists a radiation pattern corresponding to an individual teacher's location that satisfies the given radiation characteristics and whether the algorithm has reached the maximum number of iterations includes: Determine whether individual teachers exist According to equation (1), the maximum sidelobe electrical average of the corresponding radiation pattern is less than the preset threshold. And the width of the main lobe is smaller than the preset value. ,judge Has the maximum number of iterations been reached? ; The output teacher individual position includes: according to equation (2), the optimal output individual position must satisfy the corresponding... Maximum value; The calculation of the fitness function value of an individual student and the average fitness value of the group includes: calculating the fitness function value of an individual student according to equations (1) and (2), and calculating the average fitness value of the student group according to equation (3).

4. The array element failure correction method based on the improved teaching and learning optimization algorithm according to claim 3, characterized in that, The process of identifying individual teachers and updating their nearby and same-location statistics includes: Sort all individuals by fitness value from largest to smallest, then sort the individual teachers... Defined by the population optimal solution corresponding to the maximum value of the fitness function, if the numbers in a teacher's individual position continuously appear near the original incentive value of the corresponding position, that is, the absolute value of the difference between the two numbers is less than 0.1, then the statistical value is considered optimal. Do Handle it, otherwise If the teacher's position is the same as the previous generation's, then the statistical value... Do Handle it, otherwise .

5. The array cell failure correction method based on the improved teaching and learning optimization algorithm according to claim 4, characterized in that, The formula for calculating the Cambera distance between individual students includes: (9)； in, For the first individual students The Dimensional components; The formula for the collaborative evolution of individual student positions based on a homogeneous competition mechanism includes: (10)； in, For the first individual students The dimensional components, Distance The nearest student to Canberra Determined by equation (11), Determined by equation (12); (11)； in, For the first The fitness function value of each student. For the first The fitness function value of each student; (12)。 6. The array cell failure correction method based on the improved teaching and learning optimization algorithm according to claim 5, characterized in that, The process of assigning values ​​to the numbers in the individual teacher positions includes: judge Has the maximum threshold been reached? If so, the excitation value of the array element in the failure state can be assigned to the number in the corresponding teacher individual; The perturbation of the teacher's position based on the Bernoulli map includes: judge Has the maximum threshold been reached? If so, then perturb the teacher's position according to the Bernoulli mapping, which is equivalent to perturb the teacher's position according to equation (13); (13)； In the formula, Indicates the teacher's position after disturbance The dimensional components, These are control parameters.

7. The array element failure correction method based on the improved teaching and learning optimization algorithm according to claim 6, characterized in that, The determination of whether to retain the perturbated position includes: Based on equation (2), calculate the fitness function values ​​of individual teachers before and after the perturbation. If the fitness function value after the perturbation is greater than the value before the perturbation, then retain the position after the perturbation; otherwise, keep the original position unchanged. That is, the teacher position update formula is equivalent to the following: (14)； In the formula, For the first The fitness function value of individual teachers in the middle school. Let be the fitness function value of an individual teacher after perturbation via Bernoulli mapping.

Images