Multi-point source antenna arraying method and device based on whale optimization algorithm

Abstract

The invention discloses a multi-point source antenna arraying method and device based on a whale optimization algorithm, and the method comprises the steps: taking a triple baseline length as an input, determining an upper bound and a lower bound of the triple baseline length according to an actual condition, and randomly generating an initial scheme population; constructing a mathematical model of a triple arrangement mode, calculating the fitness of a length selection scheme, and evaluating the performance of the length selection scheme according to the fitness; the fitness serves as the search basis of the whale optimization algorithm, set parameters of the whale optimization algorithm are dynamically adjusted, and the global exploration and local development capacity of the whale optimization algorithm is balanced; and solving the mathematical model of the triple arrangement mode through a whale optimization algorithm, and outputting an optimal scheme. According to the method, the model can be solved through the whale optimization algorithm, and the optimal arraying mode of the triple antenna under the condition of no target echo is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna array and optimization algorithm, and in particular to a multi-point source antenna array method and device based on a whale optimization algorithm. Background Art

[0002] The design and optimization of multi-point source systems has long been a hot topic in antenna systems. By leveraging the coordinated operation of multiple antenna elements, multi-point source systems can achieve complex beamforming and signal processing, thereby improving overall system performance. However, system performance does not rely solely on advanced hardware; more critically, it relies on leveraging the system's potential through appropriate array configuration and signal parameter optimization.

[0003] The spatial layout of antennas is a key factor influencing the performance of multi-point source systems. Different antenna arrays directly affect signal propagation characteristics, beam directivity, and system capabilities. Research has shown that a reasonable antenna array not only optimizes signal coverage but also, by adjusting the relative positions of antenna elements, positions the equivalent composite scattering point farther from the antenna center. This optimization not only effectively expands the system's protection area but also significantly improves overall system performance.

[0004] Therefore, how to achieve the optimal layout of the multi-point source system through optimization algorithms has become an urgent problem to be solved. Summary of the Invention

[0005] To this end, the present invention provides a multi-point source antenna array method and device based on the whale optimization algorithm. By constructing a mathematical model of the array of triple antennas in the absence of target echoes and solving the model using the whale optimization algorithm, the optimal array method of the triple antenna in the absence of target echoes is obtained.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a multi-point source antenna array method based on a whale optimization algorithm, comprising:

[0007] Taking the triplet baseline length as input, determining the upper bound and lower bound of the triplet baseline length according to actual conditions; randomly generating an initial solution population based on the upper bound and the lower bound;

[0008] Constructing a mathematical model of the triplet array mode; calculating the fitness of each length selection scheme in the initial scheme population through the mathematical model; and evaluating the performance of the length selection scheme according to the fitness;

[0009] Using the fitness as a search basis of the whale optimization algorithm, dynamically adjusting the setting parameters of the whale optimization algorithm to balance the global exploration and local development capabilities of the whale optimization algorithm;

[0010] The whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population;

[0011] The whale optimization algorithm performs a surround search on the refined search solution population through a surround search strategy to obtain the optimal solution population;

[0012] The whale optimization algorithm obtains a population of supplementary solutions by performing extensive searches by randomly selecting directions and positions;

[0013] The optimal solution population and the supplementary solution population are merged to obtain a target solution population; the target solution population is iteratively optimized and selected using the whale optimization algorithm to output the optimal solution.

[0014] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, the expression of the initial solution population is:

[0015] P0={x1,x2,...x i ,...x N},i=1,...,N

[0016] x i =(x max -x min )*rand(·)+x min

[0017] Where P0 is the initial solution 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.

[0018] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, the mathematical model expression of the triple array method is:

[0019]

[0020] Where S is the objective function; 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.

[0021] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, in the process of dynamically adjusting the setting parameters of the whale optimization algorithm, the dynamic adjustment expression of the setting parameters is:

[0022] A=2a·rand-a

[0023] C=2·rand

[0024] a=(2-2t / T max )

[0025] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor; T max is the maximum number of iterations; t is the current number of iterations.

[0026] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, in the process of the whale optimization algorithm performing a fine search on the initial solution population through the spiral path, the mathematical model expression of the spiral path search is:

[0027]

[0028]

[0029] Where, is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the current optimal position of the whale; is the distance between the whale and the current global optimal individual; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1].

[0030] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, in the process of the whale optimization algorithm performing a surround search on the fine search solution population through the surround search strategy, the mathematical model expression of the surround search is:

[0031]

[0032]

[0033] Where, is the distance between the current whale position and the optimal position.

[0034] As a preferred solution of the multi-point source antenna array method based on the whale optimization algorithm, in the process of the whale optimization algorithm performing a wide search by randomly selecting directions and positions, the mathematical model expression of the wide search is:

[0035]

[0036]

[0037] Where, is the distance between the current whale position and the random position; is a randomly selected whale position vector.

[0038] The present invention also provides a multi-point source antenna array device based on the whale optimization algorithm, based on the above multi-point source antenna array method based on the whale optimization algorithm, including:

[0039] An initialization module is configured to take a triplet baseline length as input, determine an upper bound and a lower bound of the triplet baseline length according to actual conditions, and randomly generate an initial solution population based on the upper bound and the lower bound;

[0040] A fitness module is used to construct a mathematical model of the triplet array mode; calculate the fitness of each length selection scheme in the initial scheme population through the mathematical model; and evaluate the performance of the length selection scheme based on the fitness;

[0041] A parameter updating module is used to use the fitness as the search basis of the whale optimization algorithm, dynamically adjust the setting parameters of the whale optimization algorithm, and balance the global exploration and local development capabilities of the whale optimization algorithm;

[0042] A spiral attack module, used for the whale optimization algorithm to perform a fine search on the initial solution population through a spiral path to obtain a fine search solution population;

[0043] The encirclement module is used for the whale optimization algorithm to perform encirclement search on the refined search solution population through an encirclement search strategy to obtain the optimal solution population;

[0044] A random search module, used in the whale optimization algorithm to conduct a wide search by randomly selecting directions and positions to obtain a population of supplementary solutions;

[0045] The optimization output module is used to merge the optimal solution population and the supplementary solution population to obtain a target solution population; iteratively optimize and select the target solution population through the whale optimization algorithm to output the optimal solution.

[0046] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the initialization module, the expression of the initial solution population is:

[0047] P0={x1,x2,...x i ,...x N},i=1,...,N

[0048] x i =(x max -x min )*rand(·)+x min

[0049] Where P0 is the initial solution population; xi 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.

[0050] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the fitness module, the mathematical model expression of the triple array mode is:

[0051]

[0052] Where S is the objective function; 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.

[0053] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the parameter updating module, in the process of dynamically adjusting the setting parameters of the whale optimization algorithm, the dynamic adjustment expression of the setting parameters is:

[0054] A=2a·rand-a

[0055] C=2·rand

[0056] a=(2-2t / T max )

[0057] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor; T max is the maximum number of iterations; t is the current number of iterations.

[0058] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the spiral attack module, during the process of the whale optimization algorithm performing a fine search on the initial solution population through the spiral path, the mathematical model expression of the spiral path search is:

[0059]

[0060]

[0061] Where, is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the current optimal position of the whale; is the distance between the whale and the current global optimal individual; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1].

[0062] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the encirclement module, during the process in which the whale optimization algorithm performs encirclement search on the fine search solution population through the encirclement search strategy, the mathematical model expression of the encirclement search is:

[0063]

[0064] Where, is the distance between the current whale position and the optimal position.

[0065] As a preferred solution of the multi-point source antenna array device based on the whale optimization algorithm, in the random search module, during the process of the whale optimization algorithm performing a wide search by randomly selecting directions and positions, the mathematical model expression of the wide search is:

[0066]

[0067]

[0068] Where, is the distance between the current whale position and the random position; is a randomly selected whale position vector.

[0069] The present invention has the following advantages: the present invention takes the triple baseline length as input, determines the upper and lower bounds of the triple baseline length according to actual conditions; randomly generates an initial solution population according to the upper and lower bounds; constructs a mathematical model of the triple array method; calculates the fitness of each length selection solution in the initial solution population through the mathematical model; evaluates the performance of the length selection solution according to the fitness; uses the fitness as the search basis of the whale optimization algorithm, dynamically adjusts the setting parameters of the whale optimization algorithm, and balances the global exploration and local development capabilities of the whale optimization algorithm; the whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population; the whale optimization algorithm performs a surround search on the fine search solution population through a surround search strategy to obtain an optimal solution population; the whale optimization algorithm performs an extensive search by randomly selecting directions and positions to obtain a supplementary solution population; the optimal solution population and the supplementary solution population are merged to obtain a target solution population; the target solution population is iteratively optimized and selected by the whale optimization algorithm to output the optimal solution. The present invention constructs a mathematical model of the arrangement of triple antennas in the absence of target echoes and solves the model using the whale optimization algorithm, thereby obtaining the optimal arrangement of the triple antennas in the absence of target echoes. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] 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.

[0071] 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.

[0072] Figure 1 This is a flow chart of a multi-point source antenna array method based on a whale optimization algorithm provided in Example 1 of the present invention;

[0073] Figure 2 Schematic diagram of the composite coordinates of triplet vectors in the multi-point source antenna array method based on the whale optimization algorithm provided in Example 1 of the present invention;

[0074] Figure 3 This is a complete planar distribution diagram of the triplet equivalent scattering points in the multi-point source antenna array method based on the whale optimization algorithm provided in Example 1 of the present invention;

[0075] Figure 4 Schematic diagram of the mathematical model of the triplet array method in the multi-point source antenna array method based on the whale optimization algorithm provided in Example 1 of the present invention;

[0076] Figure 5 A schematic diagram of an iteration curve for solving the whale optimization algorithm in a possible embodiment provided in Example 1 of the present invention;

[0077] Figure 6 This is a schematic diagram of the architecture of a multi-point source antenna array device based on the whale optimization algorithm provided in Example 2 of the present invention;

[0078] Figure 7 This is a schematic diagram of the logical structure of a multi-point source antenna array device based on the whale optimization algorithm provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0079] 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.

[0080] Example 1

[0081] See also Figure 1 Embodiment 1 of the present invention provides a multi-point source antenna array method based on a whale optimization algorithm, comprising the following steps:

[0082] S1. Taking the triplet baseline length as input, determining the upper and lower bounds of the triplet baseline length according to actual conditions; and randomly generating an initial solution population based on the upper and lower bounds.

[0083] S2. Constructing a mathematical model of the triplet array method; calculating the fitness of each length selection scheme in the initial scheme population using the mathematical model; and evaluating the performance of the length selection scheme based on the fitness;

[0084] S3. Using the fitness as a search basis for the whale optimization algorithm, dynamically adjusting the set parameters of the whale optimization algorithm to balance the global exploration and local development capabilities of the whale optimization algorithm;

[0085] S4, the whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population;

[0086] S5, the whale optimization algorithm performs a surround search on the refined search solution population through a surround search strategy to obtain the optimal solution population;

[0087] S6. The whale optimization algorithm performs a wide search by randomly selecting directions and positions to obtain a population of supplementary solutions;

[0088] S7. Merge the optimal solution population and the supplementary solution population to obtain a target solution population; perform iterative optimization selection on the target solution population using the whale optimization algorithm to output the optimal solution.

[0089] In this embodiment, in step S1, the triplet baseline length is used as input, and the upper and lower bounds of the triplet baseline length are determined according to actual conditions; an initial solution population is randomly generated based on the upper and lower bounds;

[0090] Specifically, the triplet baseline length l is used as input, and the upper bound of the triplet baseline length l is determined to be 0.2 km and the lower bound is 0 km according to the actual situation. Then, the initial population is randomly generated based on the upper and lower bounds of the triplet baseline length l.

[0091] Among them, the expression of the initial solution population is:

[0092]

[0093] Where P0 is the initial solution 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.

[0094] In this embodiment, in step S2, a mathematical model of the triplet array is constructed; the fitness of each length selection scheme in the initial scheme population is calculated using the mathematical model; and the performance of the length selection scheme is evaluated based on the fitness;

[0095] Specifically, first establish the coordinate system of the triple antenna, the coordinate system is as follows Figure 2 The position of the equivalent synthetic scattering point of the triplet is shown as follows:

[0096]

[0097] Where X, Y, and Z are the three vector directions of the three-dimensional coordinate system; E a 、E b 、E c are the amplitudes of antennas A, B, and C respectively; δ ab and δ ac are the phase differences between the interference signals transmitted by the triplet antennas B and C and the interference signal transmitted by antenna A; δ bc is the phase difference between the interference signals emitted by the triplet antenna B and antenna C; γ is the free space impedance; θ max is the maximum pitch angle of the triplet array element; is the maximum azimuth.

[0098] The formula for converting rectangular coordinates into spherical coordinates is:

[0099]

[0100] Where, is the azimuth angle; θ is the elevation angle of the triplet array element.

[0101] According to equations (2) and (3), by controlling the values of the six variables of triplet amplitude and phase, the complete plane distribution diagram of the triplet equivalent scattering points under different array arrangements can be simulated, as shown in Figure 3 As shown. The amplitude of the triplet is set to be free within the range of 0 to 1 with a step size of 0.1 (E a =0:0.1:1, E b =0:0.1:1, E c =0:0.1:1), the phase is free to take values within 0~π with a step size of 0.1π(δ a =0:0.1π:π,δ b =0:0.1π:π,δ c =0:0.1π:π). Set the regular triangle array Isosceles triangle array θ max =d, in the isosceles right triangle array θ max =d. Figure 3 It can be seen that the maximum control area of the two arrays of equilateral triangle and isosceles right triangle in the omnidirectional case is 75πl 2 and 50πl 2 In practice, the baseline length l of the triplet is generally no more than 200m. Therefore, in the omnidirectional case, the maximum control area of the two arrays, the equilateral triangle and the isosceles right triangle, is 3πkm respectively. 2 and 2πkm 2 For the isosceles triangle array, such as Figure 4 As shown, the corresponding mathematical model is:

[0102]

[0103] Where S is the objective function; 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.

[0104] Formula (4) is used as the objective function of the whale optimization algorithm to calculate the fitness of each triplet baseline length selection scheme and evaluate the performance according to the size.

[0105] In this embodiment, in step S3, the fitness is used as the search basis of the whale optimization algorithm, and the setting parameters of the whale optimization algorithm are dynamically adjusted to balance the global exploration and local development capabilities of the whale optimization algorithm;

[0106] Specifically, the dynamic adjustment expression of the setting parameters is:

[0107] A=2a·rand-a

[0108] C=2·rand (5)

[0109] a=(2-2t / T max )

[0110] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor; T max is the maximum number of iterations; t is the current number of iterations.

[0111] In this embodiment, in step S4, the whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population;

[0112] Specifically, in the whale optimization algorithm, the whale attacks its prey by moving in an upward spiral and continuously shrinking the encirclement. Its mathematical model is shown in formula (6):

[0113]

[0114]

[0115] Where, is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the current optimal position of the whale; is the distance between the whale and the current global optimal individual; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1].

[0116] In this embodiment, in step S5, the whale optimization algorithm performs a surround search on the fine search solution population using a surround search strategy to obtain the optimal solution population;

[0117] Specifically, in the whale optimization algorithm, whales exchange information with each other and randomly wander around to search for 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 move to the optimal position and update their positions using formula (8):

[0118]

[0119] Where, is the distance between the current whale position and the optimal position.

[0120] In this embodiment, in step S6, the whale optimization algorithm performs a wide search by randomly selecting directions and positions to obtain a population of supplementary solutions;

[0121] Specifically, when |A| ≥ 1, it means that the whales are swimming outside the shrinking circle and performing random searches based on each other's positions. Its mathematical model is expressed as shown in formula (9):

[0122]

[0123] Where, is the distance between the current whale position and the random position; is a randomly selected whale position vector.

[0124] In this embodiment, in step S7, the optimal solution population and the supplementary solution population are merged to obtain a target solution population; the target solution population is iteratively optimized and selected using the whale optimization algorithm to output the optimal solution.

[0125] Specifically, all possible solutions are iteratively optimized through the whale optimization algorithm to output the optimal solution.

[0126] In a possible embodiment, a specific simulation example is provided as follows:

[0127] In the simulation experiment, the process of solving the spatial array model of triples using the whale optimization algorithm is as follows: Figure 5 As shown in the figure, the Whale Optimization algorithm converged after 17 iterations and reached the optimal value of 9.4242. The corresponding optimal solution is [0.2, 0.17321], which is an equilateral triangle array. Therefore, in the omnidirectional case, the equilateral triangle array is the optimal one, and the optimal baseline length is 0.2 km.

[0128] In summary, the present invention takes the triple baseline length as input, determines the upper and lower bounds of the triple baseline length according to actual conditions; randomly generates an initial solution population based on the upper and lower bounds; constructs a mathematical model of the triple array method; calculates the fitness of each length selection scheme in the initial solution population through the mathematical model; evaluates the performance of the length selection scheme based on the fitness; uses the fitness as the search basis of the whale optimization algorithm, dynamically adjusts the setting parameters of the whale optimization algorithm, and balances the global exploration and local development capabilities of the whale optimization algorithm; the whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population; the whale optimization algorithm performs an encirclement search on the fine search solution population through an encirclement search strategy to obtain an optimal solution population; the whale optimization algorithm performs an extensive search by randomly selecting directions and positions to obtain a supplementary solution population; the optimal solution population and the supplementary solution population are merged to obtain a target solution population; the target solution population is iteratively optimized and selected by the whale optimization algorithm to output the optimal solution. The present invention constructs a mathematical model of the arrangement of triple antennas in the absence of target echoes and solves the model using the whale optimization algorithm, thereby obtaining the optimal arrangement of the triple antennas in the absence of target echoes.

[0129] 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.

[0130] 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.

[0131] Example 2

[0132] See also Figure 6 and Figure 7 Embodiment 2 of the present invention further provides a multi-point source antenna array device based on a whale optimization algorithm, including:

[0133] Initialization module 001 is used to take the triplet baseline length as input, determine the upper and lower bounds of the triplet baseline length according to actual conditions; and randomly generate an initial solution population based on the upper and lower bounds;

[0134] Fitness module 002 is used to construct a mathematical model of the triplet array mode; calculate the fitness of each length selection scheme in the initial scheme population through the mathematical model; and evaluate the performance of the length selection scheme based on the fitness;

[0135] Parameter updating module 003, used to use the fitness as the search basis of the whale optimization algorithm, dynamically adjust the setting parameters of the whale optimization algorithm, and balance the global exploration and local development capabilities of the whale optimization algorithm;

[0136] Spiral attack module 004, used for the whale optimization algorithm to perform a fine search on the initial solution population through a spiral path to obtain a fine search solution population;

[0137] Surrounding module 005, used for the whale optimization algorithm to perform a surround search on the refined search solution population through a surround search strategy to obtain the optimal solution population;

[0138] Random search module 006, used for the whale optimization algorithm to conduct extensive searches by randomly selecting directions and positions to obtain a population of supplementary solutions;

[0139] The optimization output module 007 is used to merge the optimal solution population and the supplementary solution population to obtain a target solution population; iteratively optimize and select the target solution population through the whale optimization algorithm to output the optimal solution.

[0140] In this embodiment, in the initialization module 001, the expression of the initial solution population is:

[0141] P0={x1,x2,...x i ,...x N},i=1,...,N

[0142] x i =(x max -x min )*rand(·)+x min

[0143] Where P0 is the initial solution 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.

[0144] In this embodiment, in the fitness module 002, the mathematical model expression of the triplet array is:

[0145]

[0146] Where S is the objective function; 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.

[0147] In this embodiment, in the parameter updating module 003, during the process of dynamically adjusting the setting parameters of the whale optimization algorithm, the dynamic adjustment expression of the setting parameters is:

[0148] A=2a·rand-a

[0149] C=2·rand

[0150] a=(2-2t / T max )

[0151] Where A and C are distance adjustment parameters; rand is a random number uniformly distributed in [0, 1]; a is the convergence factor; T max is the maximum number of iterations; t is the current number of iterations.

[0152] In this embodiment, in the spiral attack module 004, during the process of the whale optimization algorithm performing a fine search on the initial solution population through the spiral path, the mathematical model expression of the spiral path search is:

[0153]

[0154]

[0155] Where, is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the current optimal position of the whale; is the distance between the whale and the current global optimal individual; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1].

[0156] In this embodiment, in the encirclement module 005, during the process of the whale optimization algorithm performing an encirclement search on the refined search solution population using the encirclement search strategy, the mathematical model expression of the encirclement search is:

[0157]

[0158]

[0159] Where, is the distance between the current whale position and the optimal position.

[0160] In this embodiment, in the random search module 006, during the process of performing a wide search by randomly selecting directions and positions in the whale optimization algorithm, the mathematical model expression of the wide search is:

[0161]

[0162]

[0163] Where, is the distance between the current whale position and the random position; is a randomly selected whale position vector.

[0164] 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.

[0165] Example 3

[0166] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code for a multi-point source antenna array method based on a whale optimization algorithm is stored. The program code includes instructions for executing the multi-point source antenna array method based on a whale optimization algorithm of embodiment 1 or any possible implementation thereof.

[0167] 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)).

[0168] Example 4

[0169] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0170] 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 array method based on the whale optimization algorithm of Example 1 or any possible implementation thereof.

[0171] 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.

[0172] 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.

[0173] 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.

[0174] 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 array method based on the whale optimization algorithm is characterized by: include: Taking the triplet baseline length as input, determining the upper bound and the lower bound of the triplet baseline length according to actual conditions; Randomly generate an initial solution population according to the upper bound and the lower bound; Constructing a mathematical model of the triplet array mode; calculating the fitness of each length selection scheme in the initial scheme population using the mathematical model; and evaluating the performance of the length selection scheme based on the fitness; Using the fitness as a search basis of the whale optimization algorithm, dynamically adjusting the setting parameters of the whale optimization algorithm to balance the global exploration and local development capabilities of the whale optimization algorithm; The whale optimization algorithm performs a fine search on the initial solution population through a spiral path to obtain a fine search solution population; The whale optimization algorithm performs a surround search on the refined search solution population through a surround search strategy to obtain the optimal solution population; The whale optimization algorithm obtains a population of supplementary solutions by performing extensive searches by randomly selecting directions and positions; The optimal solution population and the supplementary solution population are merged to obtain a target solution population; the target solution population is iteratively optimized and selected using the whale optimization algorithm to output the optimal solution.

2. The multi-point source antenna array method based on the whale optimization algorithm according to claim 1 is characterized in that: The expression of the initial solution population is: P0={x1,x2,...x i ,...x N },i=1,...,N x i =(x max -x min )*rand(·)+x min Where P0 is the initial solution 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 array method based on the whale optimization algorithm according to claim 2 is characterized in that: The mathematical model expression of the triple array is: Where S is the objective function; 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.

4. The multi-point source antenna array method based on the whale optimization algorithm according to claim 3 is characterized in that: In the process of dynamically adjusting the setting parameters of the whale optimization algorithm, the dynamic adjustment expression of the setting parameters 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; T max is the maximum number of iterations; t is the current number of iterations.

5. The multi-point source antenna array method based on the whale optimization algorithm according to claim 4 is characterized in that: In the process of the whale optimization algorithm performing a fine search on the initial solution population through the spiral path, the mathematical model expression of the spiral path search is: Where, is the position of the i-th whale in the d-dimensional space during the t-th iteration; is the current optimal position of the whale; is the distance between the whale and the current global optimal individual; e is the natural base; b is a constant that limits the logarithmic spiral form; δ is a random number in [-1, 1].

6. The multi-point source antenna array method based on the whale optimization algorithm according to claim 5, characterized in that: In the process of the whale optimization algorithm performing a surround search on the refined search solution population through the surround search strategy, the mathematical model expression of the surround search is: Where, is the distance between the current whale position and the optimal position.

7. The multi-point source antenna array method based on the whale optimization algorithm according to claim 6, characterized in that: In the process of performing extensive search by randomly selecting directions and positions in the whale optimization algorithm, the mathematical model expression of the extensive search is: Where, is the distance between the current whale position and the random position; is a randomly selected whale position vector.

8. A multi-point source antenna array device based on a whale optimization algorithm, adopting the multi-point source antenna array method based on a whale optimization algorithm according to any one of claims 1 to 7, characterized in that: include: an initialization module, configured to take the triplet baseline length as input and determine the upper and lower bounds of the triplet baseline length according to actual conditions; Randomly generate an initial solution population according to the upper bound and the lower bound; A fitness module is used to construct a mathematical model of the triplet array mode; calculate the fitness of each length selection scheme in the initial scheme population through the mathematical model; and evaluate the performance of the length selection scheme based on the fitness; A parameter updating module is used to use the fitness as the search basis of the whale optimization algorithm, dynamically adjust the setting parameters of the whale optimization algorithm, and balance the global exploration and local development capabilities of the whale optimization algorithm; A spiral attack module, used for the whale optimization algorithm to perform a fine search on the initial solution population through a spiral path to obtain a fine search solution population; The encirclement module is used for the whale optimization algorithm to perform encirclement search on the fine search solution population through the encirclement search strategy to obtain the optimal solution population; A random search module, used in the whale optimization algorithm to conduct a wide search by randomly selecting directions and positions to obtain a population of supplementary solutions; An optimization output module, configured to merge the optimal solution population and the supplementary solution population to obtain a target solution population; The target solution population is iteratively optimized and selected using the whale optimization algorithm to output the optimal solution.

9. The multi-point source antenna array device based on the whale optimization algorithm according to claim 8, characterized in that: In the initialization module, the expression of the initial solution population is: P0={x1,x2,...x i ,...x N },i=1,...,N x i =(x max -x min )*rand(·)+x min Where P0 is the initial solution 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 array device based on the whale optimization algorithm according to claim 9, characterized in that: In the fitness module, the mathematical model expression of the triple array is: Where S is the objective function; 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.

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