Array unit failure correction method based on improved dogvessel swarm optimization algorithm

Abstract

The invention discloses an array unit failure correction method based on an improved doliolaria group optimization algorithm, and the method specifically comprises the steps: randomly selecting a suboptimal individual as a population leader from an adjacent region of a population optimal individual, guiding the population to carry out the search in a global range, combining with a mechanism based on a discovery probability, removing a disadvantage solution, and carrying out the optimization of the population leader. A mutation strategy based on adaptive elite guidance is integrated to enhance the diversity level of the population, the population is endowed with strong global search ability in the initial stage of iteration, the algorithm is prompted to quickly position a potential high-quality solution in a wide search space, and the population is enabled to have excellent local mining ability by adjusting the discovery probability, so that the precision of the solution is improved; meanwhile, a variable-scale reverse learning strategy fused with a dynamic step length is also introduced, so that the capability of the algorithm for getting rid of the constraint of a local extreme value is enhanced. According to the invention, the stability performance of the antenna system is greatly enhanced, and the maintenance cost expenditure of the system is effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the field of array antenna pattern synthesis design, and particularly relates to an array element failure correction method based on an improved salp swarm optimization algorithm. Background Art

[0002] In practical applications, a single antenna element is difficult to meet performance indicators, so it is necessary to construct an antenna array, which is composed of several similar array elements arranged in different spatial positions and is mainly divided into a linear array, a planar array and a conformal array. The array uses the interference superposition principle to radiate signals in a specific direction to achieve high gain, narrow beam or radiation beams with specific shapes and angles, and is widely used in sonar, smart antennas, radar electronic countermeasures, wireless communication and other fields. To improve the performance of the array, it is necessary to process and analyze the array signals, and intelligent optimization algorithms are often used to solve such signal processing synthesis problems. For example, in an early warning radar, it is required that the main lobe width of the array pattern be as narrow as possible and the maximum sidelobe level be as low as possible to facilitate target detection and reduce the influence of interference. Array signal analysis involves multiple indicators such as sidelobe level, pattern gain, main lobe width and null angle, which are collectively called pattern synthesis. The core is to optimize the objective function, that is, to determine the optimal array element arrangement, amplitude and phase, etc., to balance the sidelobe level and the main lobe width. However, in practical applications, even if the algorithm obtains the optimal parameters and applies them to the element excitation and position, there may still be element failures or damages due to environmental or physical factors, which will then cause the problem of missing elements and affect the normal operation of the array antenna. To address this problem, there are mainly two strategies for pattern repair: one is to perform sparse processing by adjusting the positions of the remaining available elements; the other is to repair the pattern shape by changing the excitation amplitude or phase. Compared with other methods, optimizing the excitation amplitude is more convenient and feasible in practical applications and programming, without the need to repair damaged elements or move the positions of the remaining available elements, especially in the case of large array antennas or fixed element positions.

[0003] The salp swarm algorithm, as a new type of heuristic intelligent optimization technology with certain influence, its core idea is derived from the accurate simulation of the chain foraging behavior of the salp swarm. This algorithm is famous for its transparent mechanism, simple parameter configuration and remarkable optimization efficiency, and has occupied an important position in the field of intelligent computing and become the focus of common concern in academia and industry. Its application scope is extensive, covering many key fields such as the optimization of photovoltaic system efficiency, the improvement of image processing technology, and the efficient processing of biomedical signals, demonstrating excellent problem-solving capabilities. However, although the salp swarm algorithm performs excellently in many aspects, like many meta-heuristic swarm intelligent optimization algorithms, it also faces certain limitations. Specifically, there is still room for improvement in its global search ability, the stability of the optimization results needs to be enhanced, and it is prone to falling into local optimal solutions in specific situations. Summary of the Invention

[0004] Objective of the Invention: To solve the problems existing in the above-mentioned existing foundation, the present invention provides an array unit failure correction method based on an improved salp swarm optimization algorithm.

[0005] Technical Solution: The present invention discloses an array unit failure correction method based on an improved salp swarm optimization algorithm, which specifically includes the following steps:

[0006] Step 1: Establish a fitness function by combining the maximum sidelobe level of the repaired radiation pattern, the preset main lobe width BW d and the repaired main lobe width; set the population size P, randomly initialize the population, and initialize and set the maximum number of iterations G; represents the number of times that the absolute value of the difference between the m-th dimension value of the historical best individual of the salp and the m-th dimension value of the excitation in the normal working state before failure is less than the preset threshold, represents the number of times that the absolute value of the difference between the value of the m-th dimension in the position of the historical best individual of the salp and the value of the m-th dimension in the position of the historical best individual of the salp in the previous iteration process is less than the preset threshold; and the initial values of both are 0;

[0007] Step 2: Determine the historical best individual X g、best of the g-th iteration of the salp, and update and

[0008] Step 3: Update the discovery probability P g ;

[0009] Step 4: Calculate the similarity between all populations of the current iteration and the historical best individual X g、best , select candidate solutions, randomly select an individual from the candidate solutions as X g、Approx·best , and update the population individuals based on the guiding strategy of the optimal solution neighborhood information based on X g、Approx·best ;

[0010] Step 5: Determine whether to perturb individuals according to the discovery probability. If so, execute Step 6; otherwise, execute Step 7;

[0011] Step 6: Implement an adaptive elite-guided mutation strategy to perturb individuals, and determine whether to retain the perturbed individuals;

[0012] Step 7: Determine whether reaches the preset threshold If so, assign values to the elements in the position of the optimal individual, and go to Step 8; otherwise, directly go to Step 8;

[0013] Step 8: Determine whether it reaches a preset value If so, perturb the historical optimal individual position according to the variable-scale reverse learning strategy with a fused dynamic step size, and determine whether to retain the perturbed historical optimal individual, then go to Step 9; otherwise, directly go to Step 9;

[0014] Step 9: Determine whether the iteration stop condition is satisfied. If so, terminate the iteration and output the historical optimal individual of the salp swarm; otherwise, increment the iteration count by 1 and go to Step 2.

[0015] Furthermore, the expression of the adaptive fitness function in Step 1 is:

[0016] fit = k1|PSL - k2|BW - BW d |

[0017] where k1 and k2 are weight coefficients, PSL is the maximum sidelobe level obtained after synthesis, and BW is the main lobe width obtained after synthesis.

[0018] Furthermore, the specific update of the discovery probability in Step 3 is:

[0019]

[0020] where rand(.) is a function for generating pseudo-random numbers, is the floor function, and P1 and P2 are respectively the preset lower and upper limit values of the discovery probability when; P3 and P4 are respectively the preset lower and upper limit values of the discovery probability when.

[0021] Furthermore, the selection of individual X in Step 4 g、Approx·best is specifically: Calculate the similarity between the current iteration's population individuals and X g、best :

[0022]

[0023] where sim(.) is the similarity function, represents the p-th individual in the g-th iteration, p = 1, 2,..., P; M represents the total number of array elements arranged in the same direction, represents the m-th element of the p-th individual in the g-th iteration, w m is the element similarity weight, and the expression of w m is:

[0024]

[0025] where, is the m-th dimensional element in X g、best ;

[0026] Arrange the individuals in the population of the current iteration in descending order of similarity, and form candidate solutions with the positions of the individuals within the top H%.

[0027] Furthermore, the update of the positions of the individuals in the population in step 4 is specifically as follows

[0028] When p = 1, 2, …, P - 1, update the position of the p-th individual according to the following formula:

[0029]

[0030] where new represents after update, old represents before update, p represents the p-th individual, m represents the m-th dimension of the p-th individual, and X represents an element;

[0031] When p = P, update the position of the P-th individual according to the following formula:

[0032]

[0033] where The expression of is:

[0034]

[0035] where and are random numbers with a value range between [0, 1], is X g 、Approx·best The m-th dimension element in.

[0036] Furthermore, step 5 is specifically: Generate random numbers with a value range between [0, 1] for all individuals in this iteration. If the random number is less than the discovery probability, then perturb the individual.

[0037] Furthermore, step 6 is specifically:

[0038] Use the following formula to update the position of the individual that needs to be perturbed:

[0039]

[0040] where represents the m-th element of the p-th individual in the g-th iteration, AEGU represents after perturbation, is a random number with a value range between [0, 1];

[0041] Calculate the fitness value of the perturbed individual after perturbation. If the fitness value of the individual after perturbation is greater than that before perturbation, retain the position after perturbation; otherwise, keep the original position unchanged.

[0042] Further, the specific process of assigning values to the elements in the optimal individual position in step 7 is as follows: Assign the excitation value of the available array elements in the failure state to the corresponding elements in the historical optimal individual position.

[0043] Further, in step 8, the following formula is used to perturb the optimal individual position:

[0044]

[0045] where, is the m-th dimensional element of the perturbed historical optimal individual, is the m-th dimensional element of the array element excitation A Chebyshev obtained by synthesizing the Chebyshev method, is the m-th dimensional element of X g、best in, is the maximum value of the m-th dimension of the population composed of the historical optimal individual and the candidate solution group, is the minimum value of the m-th dimension of the population composed of the historical optimal individual and the candidate solution group;

[0046] Calculate the fitness value of the perturbed historical optimal individual. If the fitness value after perturbation is greater than that before perturbation, retain the position after perturbation; otherwise, keep the original position unchanged.

[0047] Further, the iteration stop condition in step 9 is to satisfy the maximum number of iterations or the maximum sidelobe level of the radiation pattern corresponding to X g、best is less than the preset threshold PSL and the main lobe width is less than BW d .

[0048] Beneficial effects: The present invention introduces a strategy based on an improved comprehensive similarity calculation method. This strategy randomly selects sub-optimal individuals within the neighboring region of the population's optimal individual as the population leader to guide the population to conduct a global search. This strategy makes full use of the information differences of different dominant solutions, significantly enhancing the diversity of the algorithm's search path and search efficiency. To further improve the optimization performance of the algorithm, the present invention combines a mechanism based on discovery probability to eliminate inferior solutions and enhance the diversity level of the population. Specifically, an adaptive elite-guided mutation strategy is incorporated into the invention. This strategy endows the population with strong global search ability at the initial stage of iteration, enabling the algorithm to quickly locate potential high-quality solutions within a wide search space; while at the later stage of iteration, by adjusting the discovery probability, the population is enabled to have better local mining ability, thereby improving the accuracy of the solution. In addition, to significantly enhance the anti-stagnation characteristics of the algorithm, the present invention introduces a variable-scale reverse learning strategy integrating dynamic step size, which aims to strengthen the algorithm's ability to break free from the bondage of local extrema. During the process of generating reverse solutions, this strategy comprehensively considers the dynamic global information of the population, effectively widening the distribution range of the population within the search space by combining the random step size strategy and adaptively adjusting the generation mode of reverse solutions, thereby significantly enhancing the optimization efficiency and robustness of the algorithm. The experimental simulation results show that, on the premise of maintaining the stable radiation characteristics of the array antenna pattern before repair, by introducing common excitation constraint conditions, the present invention significantly improves the stability of the antenna system and effectively reduces the system maintenance cost. This research provides a new solution for the field of array antenna pattern synthesis technology and explores a practical and feasible implementation path. Brief Description of the Drawings

[0049] Figure 1 is the flow chart of the present invention;

[0050] Figure 2 are the patterns of the array in normal and failure states;

[0051] Figure 3 is the pattern of the array in the calibrated state;

[0052] Figure 4 are the excitation diagrams of the array in normal and calibrated states;

[0053] Figure 5 is the comparison of the array performance after calibration using the traditional method and the method of the present invention. Detailed Embodiment

[0054] The accompanying drawings that form a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0055] The core objective of the present invention is to effectively address and overcome the technical problems existing in the field of array antenna pattern synthesis research by introducing a series of algorithm optimization techniques, especially aiming at the key technical challenge of quickly and accurately repairing the pattern in the case of element failure. To this end, the present invention is committed to constructing a set of efficient and accurate improved salp swarm optimization algorithm. By adjusting the excitation weights of the remaining elements, this algorithm can ensure that the radiation characteristics of the pattern are comprehensively and effectively restored, thereby restoring the performance indicators of the antenna to the level before failure. The results of the present invention not only provide a new technical solution and practical exploration path for the field of array antenna synthesis, but also have important theoretical value and practical application significance, making a positive contribution to promoting the technological progress and development of this field.

[0056] As Figure 1 shown, the specific process of the present invention is as follows:

[0057] Step A: Establish a fitness function, the statistical value of the proximity of the historical best individual of the salp to the original excitation, and the reproduction statistical value threshold, the maximum number of iterations, the population size, and randomly initialize the population;

[0058] Step B: Determine the historical best individual of the salp and update the statistical value of the proximity of the historical best individual of the salp to the original excitation and the reproduction statistical value

[0059] Step C: Update the discovery probability;

[0060] Step D: Implement a guiding strategy based on the neighborhood information of the optimal solution to update the population individuals;

[0061] Step E: Judge whether to perturb the individual according to the discovery probability. If so, execute Step F; otherwise, execute Step G;

[0062] Step F: Implement an adaptive elite-guided mutation strategy to perturb the individual and judge whether to retain the perturbed individual;

[0063] Step G: Judge whether the statistical value near the original excitation of the historical best individual reaches the threshold. If so, assign values to the numbers in the position of the best individual and execute Step H; otherwise, execute Step H;

[0064] Step H: Judge whether the number of times the historical best individual appears at the current position reaches the threshold. If so, perturb the position of the best individual according to the variable-scale reverse learning strategy integrating the dynamic step size and judge whether to retain the perturbed position, and execute Step I; otherwise, execute Step I;

[0065] Step I: Determine whether the radiation pattern corresponding to the position of the historical optimal individual meets the given radiation characteristic requirements or whether the algorithm has reached the maximum number of iterations. If either of these conditions is met, execute Step J; otherwise, increment the iteration count by 1 and execute Step B.

[0066] Step J: Output the historical optimal individual of the salp swarm.

[0067] Step Aa: The far-field radiation pattern of the linear array model is expressed as:

[0068]

[0069] where M elements are arranged in the same direction in the array, the row spacing is d, and λ is the operating wavelength in free space. In the formula, a m is the excitation amplitude of the m-th element, u = sinθ, and θ ∈ [0°, 180°].

[0070] The established fitness function is:

[0071] fit = k1|PSL| - k2|BW - BW d | (2)

[0072] where k1 and k2 are weight coefficients, PSL is the maximum sidelobe level obtained after synthesis, BW d is the preset main lobe width, and BW is the main lobe width obtained after synthesis.

[0073] Step Ab: Set the salp swarm size to P. The array excitation corresponding to the p-th (p = 1,..., P) salp individual is represented by A p where A p = [a p、1 , a p、2 ,..., a p、m ,..., a p、M-1 , a p、M , and a p、m is the excitation of the m-th element in the p-th vector. fit p is the fitness function value of the p-th salp individual. represents the number of times the m-th dimension value of the historical optimal individual of the salp is close to the excitation m-th dimension value in the normal working state before approaching failure, that is, the absolute value difference between the two values is less than δ1. The initial value of is 0, and the threshold is set to is the number of times the m-th dimension value in the position of the historical optimal individual of the salp is close to the m-th dimension value in the position of the historical optimal individual of the salp in the previous iteration process, that is, the absolute value difference between the two values is less than δ2; The initial value of is 0, and the threshold is set to Set the maximum number of iterations to G, where g is the current iteration number, and randomly generate M-dimensional vectors within [0,1] for P individuals as the initial salp swarm population.

[0074] Step Ba: According to Equation (2), sort all individuals in the current generation and the historical best individual of the previous generation in ascending order of fitness function values. The individual corresponding to the maximum fitness value is the historical best individual X of the salps g、best , is the m-th dimension data of X g、best of.

[0075] Step Bb: If the m-th dimension value in the position of the historical best individual of the salps is close to the m-th dimension value of the normal excitation, then perform processing on the statistical value , otherwise If the m-th dimension value in the position of the historical best individual of the salps is close to the m-th dimension value in the position of the historical best individual of the salps during the previous iteration process, that is, the absolute difference between the two values is less than δ2, then perform processing on the statistical value , otherwise

[0076] Step C: Update the discovery probability according to the following formula:

[0077]

[0078] In the first stage of the iteration process, P g is a random number within the range [P1, P2], where P1 and P2 are the lower and upper limits of the discovery probability in this stage. In the second stage of the iteration process, P g is a random number within the range [P3, P4], where P3 and P4 are the lower and upper limits of the discovery probability in this stage. is the floor function.

[0079] Step Da: Randomly select an individual with a relatively high comprehensive similarity to X g、best as X g、Approx·best . The formula for calculating the comprehensive similarity between an individual in the population and the historical best individual is as follows:

[0080]

[0081] where, is the m-th element in the position vector of the p-th salp individual, are the upper and lower extreme values of the m-th element in all individual positions, and w m is the element similarity weight. The update formula is as follows:

[0082]

[0083] Calculate the comprehensive similarity value between the individuals in the population and the historical optimal individual according to Equation (4), sort the similarity values from small to large, select the positions of the top H% of the individuals as candidate solutions, and randomly select one solution from the candidate solutions as X g 、Approx·best .

[0084] Step Db: The position update formula for the individuals in the population is as follows:

[0085]

[0086] where and are random numbers with values in the range [0, 1].

[0087]

[0088] where, new represents after update, old represents before update, where p ∈ [1, P). If p = P, the position update formula for the individual is as follows:

[0089]

[0090] Step E: Randomly generate Judge whether it is less than the discovery probability P g . If so, perturb the individual in the population.

[0091] Step Fa: The formula for perturbing the individual position is as follows:

[0092]

[0093] where is a random number with a value in the range [0, 1], AEGU represents after perturbation.

[0094] Step Fb: Calculate the fitness function value of the individual after perturbation. If the fitness function value of the individual after perturbation is greater than the value before perturbation, retain the position after perturbation; otherwise, keep the original position unchanged, that is, judge whether the position of the individual is updated according to the following formula:

[0095]

[0096] In the formula, is the position of the individual after perturbation.

[0097] Step G: Judge whether it reaches the threshold If so, assign the excitation value of the available array elements in the failure state to the corresponding elements in the historical optimal individual position.

[0098] Step Ha: Judge whether it reaches the threshold If so, perturb the optimal individual position according to the variable-scale reverse learning strategy that combines the fusion dynamic step size.

[0099] Step Hb: Perturb the historical optimal individual position according to the following formula:

[0100]

[0101] where, is the m-th dimension element of the perturbed historical optimal individual, is the m-th dimension element of the array element excitation A obtained by synthesizing by the Chebyshev method Chebyshev in, is the m-th dimension element of X g、best in, is the maximum value of the m-th dimension of the group composed of the historical optimal individual and the candidate solution group, is the minimum value of the m-th dimension of the group composed of the historical optimal individual and the candidate solution group.

[0102] Step Hc: Calculate the fitness function values of the historical optimal individual before and after perturbation. If the fitness function value after perturbation is greater than the value before perturbation, keep the position after perturbation; otherwise, keep the original position unchanged, that is, judge whether the position of the historical optimal individual is updated according to the following formula:

[0103]

[0104] Step I: Judge whether the maximum sidelobe level of the radiation pattern corresponding to the historical optimal individual X g、best of the salp swarm is less than the preset threshold PSL and the main lobe width is less than the preset BW d or judge whether g reaches the maximum number of iterations G.

[0105] Step J: Output the position of the historical optimal individual of the salp swarm as the excitation of the array antenna.

[0106] For comparison, the results of Case 3 in the reference (Qi Z, Gao G, Xie X, et al. FAILED ELEMENTSCORRECTION METHOD BASED ON MULTI-STRATEGY GREY WOLF OPTIMIZER[J]. 10thInternational Symposium on TestAutomation&Instrumentation(ISTAI 2024), 2024) are selected in this embodiment. The initial parameters are shown in Table 1.

[0107] Table 1

[0108]

[0109] As shown in Table 2, the preset number of failed array elements under the condition of a 150-element array is 6, 12, and 18 respectively. The radiation patterns in the normal, failed, and corrected states are as Figure 2 and Figure 3 shown. The technology involved in the present invention has an obvious effect on repairing the radiation pattern with deteriorated radiation characteristics. Comparing with the results in the reference literature, the repaired radiation pattern in the present invention achieves a similar main lobe broadening (under any array element failure ratio condition, BW ∈ {1.80, 1.88, 1.92}° compared with BW MGOW = {1.79, 1.82, 1.98}°) and a consistent maximum side lobe level. The array excitations in different states are as Figure 4 shown. Under the condition of a 4% array element failure ratio, only 2 out of 144 available array elements need to adjust the excitation during the repair process. As the array element failure ratio increases, the adjustment ratio of available array elements also increases significantly. When the array element failure ratio increases to 12%, the number of available array elements that need to adjust the excitation increases to 5. As Figure 5 described, compared with the results of the comparative literature, the number of available array element adjustments obtained by the technology of the present invention after repairing the radiation pattern is reduced by 17% - 33%. The research content of the above comparative literature emphasizes that under the condition of meeting the radiation characteristics of the repaired radiation pattern, the excitation adjustment amount of available array elements should be reduced as much as possible, and the excitation adjustment amount obtained by the technology of the present invention is further reduced, which proves the superiority of the technology of the present invention.

[0110] Table 2

[0111]

[0112] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0113] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks

[0114] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device that implements the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks

[0115] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks

[0116] The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. An array unit failure correction method based on an improved salp swarm optimization algorithm, characterized in that Specifically, it includes the following steps: Step 1: Combine the maximum sidelobe level of the repaired radiation pattern, the preset main lobe width BW d and the repaired main lobe width to establish a fitness function; Set the population size P and randomly initialize the population. Initialize and Set the maximum number of iterations G; Denote the number of times that the absolute value of the difference between the m-th dimension value of the historical best individual of salps and the m-th dimension value of the excitation in the normal working state before failure is less than the preset threshold. Denote the number of times that the absolute value of the difference between the m-th dimension value in the position of the historical best individual of salps and the m-th dimension value in the position of the historical best individual of salps in the previous iteration process is less than the preset threshold; and The initial values of both are 0; Step 2: Determine the historical optimal individual X of the salp swarm algorithm in the g-th iteration g、best , and update and Step 3: Update the discovery probability P g ; Step 4: Calculate the similarity between all populations in this iteration and the historical optimal individual X g、best , select candidate solutions, randomly select an individual from the candidate solutions as X g、Approx·best , and based on X g、Approx·best , implement a guiding strategy based on the neighborhood information of the optimal solution to update the population individuals; Step 5: Determine whether to perturb an individual according to the discovery probability. If so, execute Step 6; otherwise, execute Step 7. Step 6: Implement an adaptive elite-guided mutation strategy to perturb the individual, and determine whether to retain the perturbed individual. Step 7: Determine whether the preset threshold is reached If yes, assign values to the elements in the optimal individual position and go to Step 8; otherwise, directly go to Step 8; Step 8: Determine whether the preset value is reached If so, perturb the position of the historical optimal individual according to the variable-scale reverse learning strategy with a fused dynamic step size, determine whether to retain the perturbed historical optimal individual, and go to Step 9; Otherwise, directly go to Step 9. Step 9: Determine whether the iteration stop condition is met. If so, terminate the iteration and output the historical optimal individual of Salp Swarm Algorithm; otherwise, increment the iteration count by 1 and go to Step 2.

2. The array element failure correction method based on the improved salp swarm optimization algorithm according to claim 1, wherein, The expression of the adaptation function in Step 1 is: fit = k1|PSL| - k2|BW - BW d | where k1 and k2 are weight coefficients, PSL is the maximum sidelobe level obtained after synthesis, and BW is the main lobe width obtained after synthesis.

3. The array unit failure correction method based on an improved salp swarm optimization algorithm according to claim 1, characterized in that The specific update of the discovery probability in Step 3 is: where rand(.) is a function used to generate pseudo-random numbers, is the floor function, and P1 and P2 are respectively when, the lower and upper limit values of the preset discovery probability; P3 and P4 are respectively when, the lower and upper limit values of the preset discovery probability.

4. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that Select individual X in step 4 g、Approx·best Specifically: calculate the similarity between the population individuals at the current iteration and X g、best as follows: where sim(.) is the similarity function, represents the p-th individual in the g-th iteration, p = 1, 2, …, P; M represents the total number of array elements arranged in the same direction, represents the m-th element of the p-th individual in the g-th iteration, w m is the element similarity weight, w m has the following expression: Among them, is the m-th dimensional element of X g、best in Arrange the population individuals of the current iteration in descending order of similarity, and form candidate solutions with the positions of individuals within the range of the top H%.

5. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that, The specific update of the positions of individuals in the population in Step 4 is When p = 1, 2, …, P - 1, update the position of the p-th individual according to the following formula: where new represents after update, old represents before update, p represents the p-th individual, m represents the m-th dimension of the p-th individual, and X represents an element; When p = P, update the position of the P-th individual according to the following formula: Among them The expression of is: Among them, and are random numbers within the range of [0, 1], is X g 、Approx·best the m-th dimensional element in 6. The array element failure correction method based on an improved salp swarm optimization algorithm according to claim 1, wherein Step 5 is specifically: Generate a random number in the range of [0, 1] for all individuals in this iteration. If the random number is less than the discovery probability, perturb the individual.

7. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that Step 6 is specifically: Use the following formula to update the position of the individual to be perturbed: Among them, represents the m-th element of the p-th individual in the g-th iteration, AEGU after perturbation, is a random number with a value range between [0, 1]; Calculate the fitness value of the perturbed individual. If the fitness value of the perturbed individual is greater than the fitness value before perturbation, retain the perturbed position; otherwise, keep the original position unchanged.

8. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that The specific assignment process for the elements in the position of the optimal individual in Step 7 is: Assign the excitation value of the available array elements in the failure state to the corresponding elements in the position of the historical optimal individual.

9. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that In Step 8, use the following formula to perturb the position of the optimal individual: Among them, is the m-th dimension element of the historical optimal individual after perturbation, is the m-th dimension element of the array element excitation A Chebyshev synthesized by the Chebyshev method, is the m-th dimension element of X g、best and is the maximum value of the m-th dimension of the population composed of the historical optimal individual and the candidate solution group, is the minimum value of the m-th dimension of the population composed of the historical optimal individual and the candidate solution group;​ Calculate the fitness value of the perturbed historical optimal individual. If the fitness value after perturbation is greater than the fitness value before perturbation, retain the perturbed position; otherwise, keep the original position unchanged.

10. A method for correcting the failure of array units based on an improved salp swarm optimization algorithm according to claim 1, characterized in that The iteration stop condition in step 9 is to satisfy the maximum number of iterations or X g、best The maximum sidelobe level of the corresponding radiation pattern is less than the preset threshold PSL and the main lobe width is less than BW d .

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