Multi-point source antenna parameter analysis method and device based on non-dominated whale algorithm

Abstract

The invention discloses a multi-point source antenna parameter analysis method and device based on a non-dominated whale algorithm. The method comprises the following steps: generating an initial population through a random or heuristic strategy; performing fitness evaluation on the solutions in the initial population to obtain an objective function value corresponding to each solution; performing non-dominated sorting on the solutions in the initial population, and dividing the solutions into a plurality of Pareto leading-edge levels; within a set Pareto leading edge level, obtaining the congestion degree of a solution through calculation; performing adaptive adjustment on the convergence factor and the distance adjustment parameter according to an iteration process; performing target surrounding, spiral search and random search processing on the initial population iteration to generate a filial generation population; combining the initial population with the offspring population to obtain a combined population; a plurality of high-quality solutions are screened out from the combined population, a new generation of population is generated, iterative optimization is carried out, and after iteration is completed, a Pareto leading-edge solution set in the latest iteration population is output. According to the method, the multi-objective optimization problem can be efficiently processed, and the method has relatively high global search capability.

Description

Technical Field

[0001] The present invention relates to the fields of intelligent optimization algorithms and signal technology, and in particular to a multi-point source antenna parameter analysis method and device based on a non-dominated whale algorithm. Background Art

[0002] In multi-point source systems, a significant conflict exists between the control area and interference-to-signal ratio of a three-element antenna array. The control area refers to the area that the three-element antenna array can effectively cover, while the interference-to-signal ratio is the ratio of the maximum amplitude of the signal transmitted by the three-element antenna to the amplitude of the target echo reflected by the target. Typically, increasing the control area requires increasing the distance between antennas or adjusting the array structure, but this often leads to an increase in the interference-to-signal ratio, making the three-element array a beacon. Conversely, reducing the control area to reduce the interference-to-signal ratio may not meet the coverage requirements of practical applications. This conflict is particularly prominent in complex electromagnetic environments, and traditional optimization methods have difficulty finding a balance between the two.

[0003] To address this issue, intelligent optimization algorithms have been widely used in antenna array optimization in recent years. However, traditional single-objective optimization algorithms often only optimize a single performance metric and cannot simultaneously address the multi-objective requirements of control area and interference-to-signal ratio. Furthermore, due to the complex, nonlinear, non-convex, and high-dimensional relationship between control area and interference-to-signal ratio, conventional algorithms are prone to local optimal solutions, making it difficult to find a globally optimal array solution.

[0004] Therefore, how to invent a multi-point source antenna parameter analysis method that can efficiently handle multi-objective optimization problems and has strong global search capabilities has become an urgent problem to be solved. Summary of the Invention

[0005] To this end, the present invention provides a method and apparatus for analyzing the parameters of multi-point source antennas based on the non-dominated whale algorithm. Leveraging the algorithm's global search capabilities and non-dominated sorting mechanism, this method efficiently explores the solution space for multi-objective optimization problems and finds a set of Pareto-optimal solutions. These solutions achieve varying degrees of trade-off between control area and signal-to-interference ratio, providing diverse options for practical applications.

[0006] To achieve the above object, the present invention provides the following technical solution: a multi-point source antenna parameter analysis method based on a non-dominated whale algorithm, comprising:

[0007] Generating an initial population by random or heuristic strategy; randomly selecting a set solution from the initial population as an initial solution; using the initial solution as an optimization starting point, and making the initial solution uniformly distributed in the search space;

[0008] Performing fitness evaluation on the solutions in the initial population based on a multi-objective function to obtain an objective function value corresponding to each solution;

[0009] performing non-dominated sorting on the solutions in the initial population, identifying and obtaining non-dominated solutions, and dividing the solutions in the initial population into a plurality of Pareto frontier levels; determining the dominance relationship of the solutions in the initial population according to the objective function value;

[0010] Within the set Pareto frontier level, the congestion degree of the solution is obtained by calculation; the distribution density of the solution is measured by the congestion degree;

[0011] Adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy;

[0012] Generate a descendant population by iteratively performing surround target, spiral search and random search processing on the initial population;

[0013] Merging the initial population with the offspring population to obtain a joint population; performing non-dominated sorting on the joint population and comparing the congestion degree to screen out several high-quality solutions to generate a new generation population;

[0014] The new generation population is iteratively optimized until the maximum number of iterations is reached or the termination condition is met, the iteration is stopped, and the Pareto front solution set in the latest iterative population is output.

[0015] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, the expression of the initial population is:

[0016] P0={x1,x2,...x i ,...x N},i=1,...,N

[0017]

[0018] Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

[0019] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, in the process of performing fitness evaluation on the solutions in the initial population based on the multi-objective function and obtaining the objective function value corresponding to each solution, the expression of the multi-objective function is:

[0020]

[0021] Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are:

[0022]

[0023] Where, δ ab is the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna;

[0024] The calculation formula of the objective function value is:

[0025] F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]}

[0026] Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

[0027] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, in the process of determining the dominance relationship of the solutions in the initial population by the objective function value, when the solution x i Dominant solution x j When x i and solution x j The conditional expressions satisfied are:

[0028]

[0029] In the formula, k is the serial number of the function; l is the serial number of the function; f k (x i ),f k (x j ) are the solutions for x i Settlement jThe objective function value of the kth function; f l (x i ),f l (x j ) are the solutions for x i Settlement j The objective function value about the lth function.

[0030] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, in the process of calculating the congestion degree, the congestion degree of adjacent solutions is calculated according to the difference in the objective function values of adjacent solutions:

[0031]

[0032] Where, d i is the degree of congestion; and are the maximum and minimum values of the kth objective function at this layer, respectively.

[0033] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, the expression for dynamically adjusting the convergence factor and the distance adjustment parameter is:

[0034] A=2a·rand-a

[0035] C=2·rand

[0036] a=(2-2t / T max )

[0037] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; T max is the maximum number of iterations; t is the current number of iterations.

[0038] As a preferred solution of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, in the process of iteratively performing target encirclement, spiral search and random search processing on the initial population, target encirclement processing is the process of moving other solutions in the population to the position of the target solution; the solution position update formula is:

[0039]

[0040] Where t is the current iteration number; is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the position of the optimal solution at the tth iteration; is the distance between the optimal solution and the general solution;

[0041] The mathematical model expression of spiral search processing is:

[0042]

[0043] Where, is the distance between the whale and the current global optimal solution; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1]; P is a random number in [0, 1];

[0044] The mathematical model expression of random search processing is:

[0045]

[0046] Where, The distance between the random solution and the general solution; is a randomly selected whale position vector.

[0047] The present invention also provides a multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, based on the above multi-point source antenna parameter analysis method based on the non-dominated whale algorithm, including:

[0048] An initialization module is used to generate an initial population through random or heuristic strategies; randomly select a set solution from the initial population as an initial solution; use the initial solution as an optimization starting point, and evenly distribute the initial solution in the search space;

[0049] A fitness module is used to evaluate the fitness of the solutions in the initial population based on a multi-objective function to obtain an objective function value corresponding to each solution;

[0050] a non-dominated sorting module, configured to perform non-dominated sorting on the solutions in the initial population, identify non-dominated solutions, and divide the solutions in the initial population into a plurality of Pareto frontier levels; and determine the dominance relationship of the solutions in the initial population by using the objective function value;

[0051] A congestion calculation module is used to obtain the congestion of the solution by calculation within a set Pareto front level; and measure the distribution density of the solution by the congestion;

[0052] The parameter update module is used to adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy;

[0053] A three-stage iteration module is used to generate a descendant population by iteratively performing surround target, spiral search and random search on the initial population;

[0054] An elite retention module is used to merge the initial population with the offspring population to obtain a joint population; by performing non-dominated sorting on the joint population and comparing the congestion degree, a number of high-quality solutions are screened out to generate a new generation population;

[0055] The optimization output module is used to iteratively optimize the new generation population until a maximum number of iterations is reached or a termination condition is satisfied, stop the iteration, and output the Pareto frontier solution set in the latest iterative population.

[0056] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the initialization module, the expression of the initial population is:

[0057] P0={x1,x2,...x i ,...x N},i=1,...,N

[0058]

[0059] Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

[0060] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the fitness module, in the process of performing fitness evaluation on the solutions in the initial population based on the multi-objective function and obtaining the objective function value corresponding to each solution, the expression of the multi-objective function is:

[0061]

[0062] Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are:

[0063]

[0064] Where, δ abis the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna.

[0065] The calculation formula of the objective function value is:

[0066] F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]}

[0067] Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

[0068] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the non-dominated sorting module, in the process of determining the dominance relationship of the solutions in the initial population by the objective function value, the solution x i Dominant solution x j When x i and solution x j The conditional expressions satisfied are:

[0069]

[0070] In the formula, k is the serial number of the function; l is the serial number of the function; f k (x i ),f k (x j ) are the solutions for x i Settlement j The objective function value of the kth function; f l (x i ),f l (x j ) are the solutions for x i Settlement j The objective function value about the lth function.

[0071] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the congestion calculation module, in the process of calculating the congestion, the congestion of adjacent solutions is calculated according to the difference in the objective function values of adjacent solutions:

[0072]

[0073] Where, d i is the degree of congestion; and are the maximum and minimum values of the kth objective function at this layer, respectively.

[0074] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the parameter updating module, the expression for dynamically adjusting the convergence factor and the distance adjustment parameter is:

[0075] A=2a·rand-a

[0076] C=2·rand

[0077] a=(2-2t / T max )

[0078] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; T max is the maximum number of iterations; t is the current number of iterations.

[0079] As a preferred solution of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm, in the three-stage iterative module, during the process of iteratively performing target encirclement, spiral search, and random search processing on the initial population, target encirclement processing is the process of moving other solutions in the population to the position of the target solution; the solution position update formula is:

[0080]

[0081]

[0082] Where t is the current iteration number; is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the position of the optimal solution at the tth iteration; is the distance between the optimal solution and the general solution;

[0083] The mathematical model expression of spiral search processing is:

[0084]

[0085] Where, is the distance between the whale and the current global optimal solution; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1]; P is a random number in [0, 1];

[0086] The mathematical model expression of random search processing is:

[0087]

[0088] Where, The distance between the random solution and the general solution; is a randomly selected whale position vector.

[0089] The present invention has the following advantages: the present invention generates an initial population through a random or heuristic strategy; randomly selects a set solution from the initial population as an initial solution; uses the initial solution as an optimization starting point, and makes the initial solution uniformly distributed in the search space; performs fitness evaluation on the solutions in the initial population based on a multi-objective function, and obtains the objective function value corresponding to each solution; performs non-dominated sorting on the solutions in the initial population, identifies and obtains non-dominated solutions, and divides the solutions in the initial population into several Pareto front levels; determines the dominance relationship of the solutions in the initial population through the objective function value; obtains the solution by calculating the Pareto front level within the set Pareto front level. The algorithm uses the crowding degree to measure the density of solutions; adaptively adjusts the convergence factor and distance adjustment parameter based on the iterative process to balance search efficiency and accuracy; generates a child population by iteratively performing surround target, spiral search, and random search on the initial population; merges the initial population with the child population to obtain a merged population; selects several high-quality solutions by performing non-dominated sorting on the merged population and comparing the crowding degree to generate a new generation population; iteratively optimizes the new generation population until the maximum number of iterations is reached or a termination condition is met, at which point the iterations cease and the Pareto frontier solution set in the latest iterative population is output. Leveraging the global search capability and non-dominated sorting mechanism of the non-dominated whale algorithm, the present invention efficiently explores the solution space for multi-objective optimization problems and finds a set of Pareto-optimal solutions. These solution sets achieve varying degrees of trade-off between control area and interference-to-signal ratio, providing diverse options for practical applications. The present invention resolves the conflict between control area and interference-to-signal ratio for triples, effectively balancing their performance requirements and providing an efficient and reliable solution for antenna array optimization in complex electromagnetic environments. The present invention has broad application prospects in fields such as multi-point source system array methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0091] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0092] Figure 1 Schematic diagram of the flow of the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm provided in Example 1 of the present invention;

[0093] Figure 2 Schematic diagram of the distribution of equivalent radiation centers of triples in the case of target echoes in the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm provided in Example 1 of the present invention;

[0094] Figure 3 A schematic diagram of a curve corresponding to a Pareto front solution set in a multi-point source antenna parameter analysis method based on a non-dominated whale algorithm provided in Example 1 of the present invention;

[0095] Figure 4 This is a schematic diagram of the distribution of equivalent radiation centers of triples corresponding to key balance points in the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm provided in Example 1 of the present invention;

[0096] Figure 5 Schematic diagram of the architecture of a multi-point source antenna parameter analysis device based on the non-dominated whale algorithm provided in Example 2 of the present invention;

[0097] Figure 6 Schematic diagram of the specific framework of the multi-point source antenna parameter analysis device based on the non-dominated whale algorithm provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0098] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0099] Example 1

[0100] See also Figure 1 Embodiment 1 of the present invention provides a multi-point source antenna parameter analysis method based on a non-dominated whale algorithm, comprising the following steps:

[0101] S1. Generate an initial population by random or heuristic strategy; randomly select a set solution from the initial population as an initial solution; use the initial solution as the optimization starting point, and make the initial solution uniformly distributed in the search space;

[0102] S2. Perform fitness evaluation on the solutions in the initial population based on a multi-objective function to obtain an objective function value corresponding to each solution;

[0103] S3. performing non-dominated sorting on the solutions in the initial population, identifying non-dominated solutions, and dividing the solutions in the initial population into a plurality of Pareto frontier levels; determining the dominance relationship of the solutions in the initial population by using the objective function value;

[0104] S4. Within the set Pareto frontier level, obtain the congestion degree of the solution by calculation; and measure the distribution density of the solution by the congestion degree;

[0105] S5. Adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy;

[0106] S6. Generate a descendant population by iteratively performing surround target, spiral search, and random search on the initial population;

[0107] S7. Merge the initial population with the offspring population to obtain a joint population; perform non-dominated sorting on the joint population and compare the congestion degree to select several high-quality solutions to generate a new generation population;

[0108] S8. Iteratively optimize the new generation population until the maximum number of iterations is reached or the termination condition is met, stop the iteration, and output the Pareto frontier solution set in the latest iterative population.

[0109] In this embodiment, in step S1, an initial population is generated by a random or heuristic strategy; a setting solution is randomly selected from the initial population as an initial solution; the initial solution is used as an optimization starting point, and the initial solution is evenly distributed in the search space;

[0110] Specifically, in the case of a target, the equivalent radiation center distribution of the triplet is as follows Figure 3 As shown, it exhibits hexagonal geometry. Therefore, the triplet baseline length x, the triplet triangle height y, and the JSR are used as input. The baseline length x is empirically bounded to 0.2 and to 0. The JSR is also bounded to 30 and to 10. The initial population P0 is then randomly generated.

[0111] Among them, the expression of the initial population is:

[0112] P0={x1,x2,...x i,...x N},i=1,...,N

[0113]

[0114] Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

[0115] In this embodiment, a set of feasible parameter solutions is selected from the initial population as the optimization starting point to ensure that the initial solutions are evenly distributed in the search space, so as to fully explore the diversity of the solution space and lay the foundation for subsequent optimization.

[0116] In this embodiment, in step S2, the fitness of the solutions in the initial population is evaluated based on a multi-objective function to obtain the objective function value corresponding to each solution;

[0117] Specifically, the spatial array model of the triplet is to select the appropriate triplet baseline length and JSR to make the triplet's control area as large as possible to protect the target's safety, while keeping the JSR as small as possible to prevent the triplet from becoming a beacon. Therefore, the mathematical model of the spatial array model of the triplet in the case of target echo is:

[0118]

[0119] Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are:

[0120]

[0121] Where, δ ab is the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna.

[0122] The calculation formula of the objective function value is:

[0123] F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]}

[0124] Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

[0125] In this embodiment, in step S3, non-dominated sorting is performed on the solutions in the initial population to identify non-dominated solutions, and the solutions in the initial population are divided into a number of Pareto frontier levels; the dominance relationship of the solutions in the initial population is determined by the objective function value;

[0126] Specifically, let the population be P, which contains N individuals. For each individual x in the population i , calculate its number of dominant individuals n i and the set of individuals S dominated by it i .

[0127] If the solution x for two individuals i Dominant solution x j When x i and solution x j The conditional expressions satisfied are:

[0128]

[0129] In the formula, k is the serial number of the function; l is the serial number of the function; f k (x i ),f k (x j ) are the solutions for x i Settlement j The objective function value of the kth function; f l (x i ),f l (x j ) are the solutions for x i Settlement j The objective function value about the lth function.

[0130] Number of dominant individuals n i :x i Dominated by many individuals.

[0131] Dominated set S i :x i Which individuals are controlled?

[0132] In this embodiment, the process of non-dominated sorting is:

[0133] T1. Initialize n for each individual i =0 and

[0134] T2, for each individual x i , traverse all individuals x in the population j ;

[0135] Among them, if x i Dominate x j , then S i =S i ∪{x j};

[0136] If x j Dominate x i , then n i =n i +1;

[0137] T3, all n i = 0 as the first non-dominated layer F1;

[0138] T4. For each individual x in the first layer F1 i , update the set of individuals S dominated by it i The n of each individual j ; If n j =0, then add it to the next non-dominated layer F2;

[0139] T5. Repeat step T4 until all individuals are sorted into the corresponding levels.

[0140] In this embodiment, in step S4, within the set Pareto front level, the congestion degree of the solution is obtained by calculation; the distribution density of the solution is measured by the congestion degree;

[0141] Specifically, crowding distance is used to measure the density of each individual in its non-dominated layer. Individuals with greater crowding distance are more sparsely populated with individuals around them, and are more likely to be selected into the next generation.

[0142] Let F i is the i-th non-dominated layer, and its congestion calculation steps are as follows:

[0143] M1. Initialize the crowding degree d of each individual i =0;

[0144] M2, for each objective function f k :

[0145] Among them, the individuals in this layer are calculated according to the objective function value f k Sorting;

[0146] For the sorted individuals, let the crowding degree of the boundary individuals be infinite;

[0147] For non-boundary individuals, their crowding degree is calculated based on the difference in the objective function values of adjacent individuals:

[0148]

[0149] Where, d i is the degree of congestion; and are the maximum and minimum values of the kth objective function at this layer, respectively.

[0150] In this embodiment, in step S5, the convergence factor and the distance adjustment parameter are adaptively adjusted according to the iterative process to balance the search efficiency and accuracy;

[0151] Specifically, the expression for dynamically adjusting the convergence factor and the distance adjustment parameter is:

[0152] A=2a·rand-a

[0153] C=2·rand

[0154] a=(2-2t / T max )

[0155] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; T max is the maximum number of iterations; t is the current number of iterations.

[0156] In this embodiment, in step S6, the initial population is iteratively subjected to target encirclement, spiral search, and random search processes to generate a descendant population;

[0157] Specifically, surrounding the target is to surround the prey: In WOA, whale groups exchange information with each other and randomly walk to search for the location of prey. Each whale represents an individual, and the position of each individual in the search space represents a solution. Assuming that the current optimal position is the target prey, let The other individuals in the group all move to the optimal position, and the formula for their position update is:

[0158]

[0159]

[0160] Where t is the current iteration number; is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the position of the optimal solution at the tth iteration; is the distance between the optimal solution and the general solution.

[0161] In this embodiment, bubble net predation: In WOA, whales attack prey by moving in an upward spiral and continuously shrinking the encirclement. There are two methods to describe the whale's predation behavior, namely the shrinking encirclement mechanism and the spiral position update.

[0162] Among them, the shrinkage and encirclement mechanism is realized through the convergence factor a.

[0163] Spiral update position: Whales swim towards their prey in a spiral motion trajectory, and its mathematical model expression is:

[0164]

[0165] Where, represents the distance between the whale and the current global optimal individual; b is a constant that limits the logarithmic spiral form; δ represents a random number in [-1, 1].

[0166] The whale swims along a spiral path around the prey's shrinking circle, selecting the same probability P for the shrinking and surrounding mechanism and the spiral position update. The mathematical model expression is:

[0167]

[0168] Where P is a random number in [0, 1].

[0169] Random search: When |A| ≥ 1, it means that the whales are swimming outside the shrinking circle and performing random search based on their positions. The mathematical model expression is:

[0170]

[0171]

[0172] Where, is the distance between the random solution and the general solution; is a randomly selected whale position vector.

[0173] Then Add to the offspring population Q t middle.

[0174] In this embodiment, in step S7, the initial population and the offspring population are merged to obtain a joint population; a number of high-quality solutions are screened out by performing non-dominated sorting and comparing the congestion degree on the joint population to generate a new generation population;

[0175] Specifically, the current population P t and the offspring population Q t Merge to form a joint population R t . t Perform non-dominated sorting and select the first N individuals according to the non-dominated level and crowding degree to form a new generation of population P t+1 .

[0176] In this embodiment, in step S8, the new generation population is iteratively optimized until the maximum number of iterations is reached or the termination condition is satisfied, the iteration is stopped, and the Pareto front solution set in the latest iterative population is output.

[0177] Specifically, the new generation population is iteratively optimized until the maximum number of iterations or other termination conditions are reached, then the iteration is stopped and the Pareto front solution set in the current population is output; otherwise, the process goes to step S3 to continue the iteration.

[0178] In this embodiment, according to general conclusions, the equilateral triangle array has significant advantages in performance. Therefore, the present invention adopts the equilateral triangle array as the basic configuration. In addition, from the perspective of the triplet parameter tolerance, the present invention conducts an in-depth study on the relationship between total gain and JSR, and finally selects α = 0.5dB, δ ab =115°, β=0.5dB, δ ac =230°relationship curve is used as the basis for optimization.

[0179] On the basis of completing the array mode and parameter selection, the present invention further adopts NSGWOA to solve the proposed mathematical model. Through algorithm optimization, the relationship curve between JSR and protected area is obtained, as shown in the figure below: Figure 3 As shown. According to the principle of protection radius of three times the baseline length, the present invention selects a key balance point from the curve. The corresponding protection area radius of this point is 0.6125km, which is exactly three times the triplet baseline length. At the same time, the JSR value of this point is 14.2818dB, and the corresponding triplet equivalent radiation center distribution diagram is shown as follows: Figure 4 This result ensures adequate target protection while avoiding the problem of the ternary group becoming a beacon due to excessively high JSR. Therefore, this balance point achieves an optimal trade-off between protection effectiveness and signal power, providing a reliable theoretical basis for practical engineering applications.

[0180] In summary, the present invention has the following advantages: the present invention generates an initial population through a random or heuristic strategy; randomly selects a set solution from the initial population as an initial solution; uses the initial solution as the optimization starting point, and makes the initial solution uniformly distributed in the search space; performs fitness evaluation on the solutions in the initial population based on a multi-objective function, and obtains the objective function value corresponding to each solution; performs non-dominated sorting on the solutions in the initial population, identifies and obtains non-dominated solutions, and divides the solutions in the initial population into several Pareto front levels; determines the dominance relationship of the solutions in the initial population through the objective function value; obtains the optimal solution by calculating the optimal solution within the set Pareto front level; The method comprises the following steps: determining the congestion of solutions; measuring the density of solutions using the congestion; adaptively adjusting the convergence factor and distance adjustment parameter according to the iterative process to balance search efficiency and accuracy; iteratively performing surround target, spiral search, and random search on the initial population to generate a descendant population; merging the initial population with the descendant population to obtain a merged population; screening out several high-quality solutions by performing non-dominated sorting on the merged population and comparing the congestion degree to generate a new generation population; iteratively optimizing the new generation population until the maximum number of iterations is reached or a termination condition is met, at which point the iterations are terminated and the Pareto frontier solution set in the latest iterative population is output. Leveraging the global search capability and non-dominated sorting mechanism of the non-dominated whale algorithm, the present invention can efficiently explore the solution space for multi-objective optimization problems and find a set of Pareto optimal solutions. These solution sets can achieve varying degrees of trade-offs between control area and interference-to-signal ratio, providing diverse options for practical applications. This invention resolves the conflict between the triplet control area and the signal-to-interference ratio, effectively balancing the performance requirements of both. It also provides an efficient and reliable solution for optimizing antenna arrays in complex electromagnetic environments. The invention has broad application prospects in fields such as multi-point source system array methods.

[0181] It should be noted that the method of the embodiments of the present disclosure can be performed by a single device, such as a computer or server. The method of the embodiments of the present disclosure can also be applied in a distributed scenario, where multiple devices cooperate to perform the method. In such a distributed scenario, one of the multiple devices may only perform one or more steps of the method of the embodiments of the present disclosure, and the multiple devices will interact with each other to complete the method.

[0182] It should be noted that the above description is limited to some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in an order different from that described in the above embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0183] Example 2

[0184] See also Figure 5 and Figure 6 Embodiment 2 of the present invention further provides a multi-point source antenna parameter analysis device based on a non-dominated whale algorithm, comprising:

[0185] Initialization module 001 is used to generate an initial population through random or heuristic strategies; randomly select a set solution from the initial population as an initial solution; use the initial solution as the optimization starting point, and make the initial solution uniformly distributed in the search space;

[0186] Fitness module 002, used to evaluate the fitness of the solutions in the initial population based on a multi-objective function to obtain the objective function value corresponding to each solution;

[0187] The non-dominated sorting module 003 is used to perform non-dominated sorting on the solutions in the initial population, identify non-dominated solutions, and divide the solutions in the initial population into a number of Pareto frontier levels; determine the dominance relationship of the solutions in the initial population according to the objective function value;

[0188] The congestion calculation module 004 is used to obtain the congestion of the solution by calculation within the set Pareto front level; the distribution density of the solution is measured by the congestion;

[0189] Parameter update module 005, used to adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy;

[0190] The three-stage iteration module 006 is used to generate a descendant population by iteratively performing surround target, spiral search and random search on the initial population;

[0191] The elite retention module 007 is used to merge the initial population with the offspring population to obtain a joint population; by performing non-dominated sorting and comparing the congestion degree on the joint population, a number of high-quality solutions are screened out to generate a new generation population;

[0192] The optimization output module 008 is used to iteratively optimize the new generation population until the maximum number of iterations is reached or the termination condition is met, stop the iteration, and output the Pareto frontier solution set in the latest iterative population.

[0193] In this embodiment, in the initialization module 001, the expression of the initial population is:

[0194] P0={x1,x2,...x i ,...x N},i=1,...,N

[0195]

[0196] Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

[0197] In this embodiment, in the fitness module 002, in the process of performing fitness evaluation on the solutions in the initial population based on the multi-objective function and obtaining the objective function value corresponding to each solution, the expression of the multi-objective function is:

[0198]

[0199] Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are:

[0200]

[0201] Where, δ ab is the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna.

[0202] The calculation formula of the objective function value is:

[0203] F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]}

[0204] Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

[0205] In this embodiment, in the non-dominated sorting module 003, in the process of determining the dominance relationship of the solutions in the initial population by using the objective function value, when the solution x i Dominant solution x j When x i and solution x j The conditional expressions satisfied are:

[0206]

[0207] In the formula, k is the serial number of the function; l is the serial number of the function; f k (x i ),f k (x j ) are the solutions for x i Settlement j The objective function value of the kth function; f l (x i ),f l (x j ) are the solutions for x i Settlement j The objective function value about the lth function.

[0208] In this embodiment, in the congestion degree calculation module 004, in the process of calculating the congestion degree, the congestion degree of adjacent solutions is calculated according to the difference in the objective function values of adjacent solutions:

[0209]

[0210] Where, d i is the degree of congestion; and are the maximum and minimum values of the kth objective function at this layer, respectively.

[0211] In this embodiment, in the parameter updating module 005, the expression for dynamically adjusting the convergence factor and the distance adjustment parameter is:

[0212] A=2a·rand-a

[0213] C=2·rand

[0214] a=(2-2t / T max )

[0215] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; T max is the maximum number of iterations; t is the current number of iterations.

[0216] In this embodiment, in the three-stage iterative module 006, during the process of iteratively performing the target surround, spiral search, and random search processing on the initial population, the target surround processing is the process of moving other solutions in the population toward the position of the target solution; the solution position update formula is:

[0217]

[0218]

[0219] Where t is the current iteration number; is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the position of the optimal solution at the tth iteration; is the distance between the optimal solution and the general solution;

[0220] The mathematical model expression of spiral search processing is:

[0221]

[0222] Where, is the distance between the whale and the current global optimal solution; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1]; P is a random number in [0, 1];

[0223] The mathematical model expression of random search processing is:

[0224]

[0225]

[0226] Where, is the distance between the random solution and the general solution; is a randomly selected whale position vector.

[0227] It should be noted that the information interaction, execution process, etc. between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and no further details will be given here.

[0228] Example 3

[0229] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code of a multi-point source antenna parameter analysis method based on a non-dominated whale algorithm is stored. The program code includes instructions for executing the multi-point source antenna parameter analysis method based on a non-dominated whale algorithm of embodiment 1 or any possible implementation thereof.

[0230] Computer-readable storage media can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0231] Example 4

[0232] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0233] The processor and the memory communicate with each other through a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the multi-point source antenna parameter analysis method based on the non-dominated whale algorithm of Example 1 or any possible implementation thereof.

[0234] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor, which is implemented by reading software code stored in a memory. The memory can be integrated into the processor or located outside the processor and exist independently.

[0235] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from a website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode.

[0236] Obviously, those skilled in the art will appreciate that the various modules or steps of the present invention described above can be implemented using a general-purpose computing system. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Alternatively, they can be implemented using program code executable by a computing system, and thus, they can be stored in a storage system and executed by the computing system. In some cases, the steps shown or described herein can be performed in a different order than that shown, or they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0237] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A multi-point source antenna parameter analysis method based on the non-dominated whale algorithm is characterized by: include: Generate the initial population through random or heuristic strategies; Randomly select a setting solution from the initial population as an initial solution; Using the initial solution as an optimization starting point and making the initial solution uniformly distributed in the search space; Performing fitness evaluation on the solutions in the initial population based on a multi-objective function to obtain an objective function value corresponding to each solution; performing non-dominated sorting on the solutions in the initial population, identifying and obtaining non-dominated solutions, and dividing the solutions in the initial population into a plurality of Pareto frontier levels; determining the dominance relationship of the solutions in the initial population according to the objective function value; Within the set Pareto frontier level, the congestion degree of the solution is obtained by calculation; the distribution density of the solution is measured by the congestion degree; Adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy; Generate a descendant population by iteratively performing surround target, spiral search and random search processing on the initial population; Merging the initial population with the offspring population to obtain a joint population; performing non-dominated sorting on the joint population and comparing the congestion degree to screen out several high-quality solutions to generate a new generation population; The new generation population is iteratively optimized until the maximum number of iterations is reached or the termination condition is met, the iteration is stopped, and the Pareto front solution set in the latest iterative population is output.

2. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 1 is characterized in that: The expression of the initial population is: P0={x1,x2,...x i ,...x N },i=1,...,N Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

3. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 2 is characterized in that: In the process of performing fitness evaluation on the solutions in the initial population based on the multi-objective function and obtaining the objective function value corresponding to each solution, the expression of the multi-objective function is: Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are: Where, δ ab is the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna; The calculation formula of the objective function value is: F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]} Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

4. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 3 is characterized in that: In the process of determining the dominance relationship of the solutions in the initial population by the objective function value, when the solution x i Dominant solution x j When x i and solution x j The conditional expressions satisfied are: In the formula, k is the serial number of the function; l is the serial number of the function; f k (x i ),f k (x j ) are the solutions for x i Settlement j The objective function value of the kth function; f l (x i ),f l (x j ) are the solutions for x i Settlement j The objective function value about the lth function.

5. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 4 is characterized in that: In the process of calculating the congestion degree, the congestion degree of adjacent solutions is calculated according to the difference in the objective function values of adjacent solutions: Where, d i is the degree of congestion; and are the maximum and minimum values of the kth objective function at this layer, respectively.

6. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 5, characterized in that: The expression for dynamically adjusting the convergence factor and the distance adjustment parameter is: A=2a·rand-a C=2·rand a=(2-2t / T max ) Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases; T max is the maximum number of iterations; t is the current iteration number.

7. The multi-point source antenna parameter analysis method based on the non-dominated whale algorithm according to claim 6, characterized in that: In the process of iteratively performing surround target, spiral search and random search on the initial population, surround target processing is the process of moving other solutions in the population to the position of the target solution; the solution position update formula is: Where t is the current iteration number; is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the position of the optimal solution at the tth iteration; is the distance between the optimal solution and the general solution; The mathematical model expression of spiral search processing is: Where, is the distance between the whale and the current global optimal solution; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1]; P is a random number in [0, 1]; The mathematical model expression of random search processing is: Where, The distance between the random solution and the general solution; is a randomly selected whale position vector.

8. A multi-point source antenna parameter analysis device based on a non-dominated whale algorithm, using the multi-point source antenna parameter analysis method based on a non-dominated whale algorithm according to any one of claims 1 to 7, characterized in that: include: Initialization module, used to generate the initial population through random or heuristic strategies; Randomly select a setting solution from the initial population as an initial solution; Using the initial solution as an optimization starting point and making the initial solution uniformly distributed in the search space; A fitness module is used to evaluate the fitness of the solutions in the initial population based on a multi-objective function to obtain an objective function value corresponding to each solution; a non-dominated sorting module, configured to perform non-dominated sorting on the solutions in the initial population, identify non-dominated solutions, and divide the solutions in the initial population into a plurality of Pareto frontier levels; and determine the dominance relationship of the solutions in the initial population by using the objective function value; A congestion calculation module is used to obtain the congestion of the solution by calculation within a set Pareto front level; and measure the distribution density of the solution by the congestion; The parameter update module is used to adaptively adjust the convergence factor and distance adjustment parameters according to the iterative process to balance the search efficiency and accuracy; A three-stage iteration module is used to generate a descendant population by iteratively performing surround target, spiral search and random search on the initial population; An elite retention module is used to merge the initial population with the offspring population to obtain a joint population; by performing non-dominated sorting on the joint population and comparing the congestion degree, a number of high-quality solutions are screened out to generate a new generation population; The optimization output module is used to iteratively optimize the new generation population until a maximum number of iterations is reached or a termination condition is satisfied, stop the iteration, and output the Pareto frontier solution set in the latest iterative population.

9. The multi-point source antenna parameter analysis device based on the non-dominated whale algorithm according to claim 8, characterized in that: In the initialization module, the expression of the initial population is: P0={x1,x2,...x i ,...x N },i=1,...,N Where P0 is the initial population; x i is the individual in the population; N is the population size; x max and x min are the upper and lower bounds of the population respectively; rand(·) is the (0,1) uniform distribution function.

10. The multi-point source antenna parameter analysis device based on the non-dominated whale algorithm according to claim 9, characterized in that: In the fitness module, in the process of performing fitness evaluation on the solutions in the initial population based on the multi-objective function and obtaining the objective function value corresponding to each solution, the expression of the multi-objective function is: Where x is the baseline length of the triplet; y is the height of the triangle of the triplet; l is the maximum baseline length of the triplet; AF T is the total angle factor; G mt is the total gain; is the azimuth gain; G mθ is the pitch gain; jsr is the interference-to-signal ratio; is the azimuth coordinate of the triplet antenna; θ i is the elevation coordinate of the triplet antenna; α is the amplitude ratio of antenna B relative to antenna A in the triplet antenna; β is the amplitude ratio of antenna C relative to antenna A in the triplet antenna; a, b, c, d are: Where, δ ab is the phase difference between antenna B and antenna A in the triplet antenna; δ ac is the phase difference between antenna C and antenna A in the triplet antenna; The calculation formula of the objective function value is: F={[f1(x1),f2(x1)],...,[f1(x i ),f2(x i )],...,[f1(x N ),f2(x N )]} Where F is the objective function value; f1(x i ) is the objective function for maximizing the control area of the triplet; f2(jsr) is the objective function for minimizing jsr.

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