Zebra optimization-based non-contact measurement method for size of subsurface target in sparse matrix

Abstract

The application provides a sparse array underground target size non-contact measurement method based on zebra optimization, and belongs to the technical field of non-contact size measurement of underground targets. The method can effectively suppress sidelobe levels, and solves the problem that existing methods cannot effectively suppress sidelobe levels. The method comprises the following steps: constructing a measurement signal directivity pattern optimization model of a sparse array; initializing zebra algorithm parameters, and randomly initializing parameter configurations of each individual in a population; updating the parameter configurations of individuals in the population according to zebra foraging behavior; according to zebra anti-predation behavior, when a preset trigger condition is met, the parameter configurations of individuals in the population are updated by jumping; the fitness of the current population is calculated, if a termination condition is met, the optimal array parameter configuration is output, otherwise the position of the predator is updated and the updating step is returned for continuous iteration; the optimal array parameter configuration is used to drive the sparse array to detect the underground target, and the size of the underground target is calculated based on the echo signal obtained after detection. The method is mainly used in the field of nondestructive testing.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of non-contact size measurement of underground targets, and particularly relates to a non-contact size measurement method for underground targets based on zebra optimization. BACKGROUND

[0002] Non-contact size measurement of underground targets refers to a kind of measurement technology for obtaining the shape size, horizontal extension length or spatial interval information of a buried or semi-buried target under the condition that the ground surface is not excavated, the measured object is not contacted, the existing working condition is not interrupted, and the integrity of the underground structure is not damaged. Common implementation approaches are based on electromagnetic wave, ground sound or ultrasonic detection, and array type non-contact measurement devices laid on the ground surface. Compared with traditional measurement methods that need to expose the target or directly contact it, non-contact size measurement of underground targets has the following advantages: no need to excavate and damage the covering layer, and can detect deep-buried or position-limited targets; friendly to the measured objects such as structures, pipelines and cavities, and will not introduce additional stress or deformation; and can complete the measurement in complex underground environment conditions such as non-uniform, layered or water-containing conditions, thus having irreplaceable application value in scenes such as municipal underground facility investigation, underground pipeline and cable orientation detection, hidden structure size verification, and geographic information matching and updating.

[0003] However, the existing non-contact measurement system for the size of underground targets, especially the system using ultra-wideband pulse system and cooperating with multi-channel architecture, still faces severe challenges in actual application, and the measurement accuracy and stability are limited by inherent defects. A core problem is that when the detection signal propagates in a complex underground medium, the non-uniformity of the medium, the existence of multi-interface reflection and multipath scattering, the non-uniformity of the medium, the existence of interlayer interfaces and the scattering of the target itself will cause serious multi-interface reflection and multipath scattering effects. Under this environment, the existing system, especially the system using conventional schemes such as single-transmit-single-receive structure or uniform linear array, will produce adverse phenomena of measurement signal main lobe broadening and high side lobe level due to the inherent array design limitation. Specifically, the main lobe of such a conventional array is relatively wide, which leads to insufficient spatial directivity, making it difficult for the detection energy radiated to the underground medium to form effective focusing in the target direction, and the energy is relatively dispersed.

[0004] The above defects will cause more serious consequences in the signal receiving stage. Due to the wide main lobe and poor directivity, the receiving end is easy to mix up the echoes from the ground reflection, interlayer interface, adjacent target and other non-desired directions while collecting the effective target echo. After the superposition of these interference signals and the weak effective target echo, the signal-to-noise ratio of the measurement is significantly reduced, and the real target boundary information is often covered, thereby introducing the estimation deviation of the length or extension range of the underground target, directly leading to the decrease of the repeatability and accuracy of the measurement results. Even if the conventional beam forming method is used to try to improve the directivity in order to improve the performance, the result is still unsatisfactory, because such method is difficult to effectively suppress the array side lobe. The higher side lobe will "leak" or introduce the scattering energy of the non-target direction into the main lobe measurement channel. This interference makes it extremely difficult to accurately identify the start and end points of the target in the echo signal, and finally causes systematic errors such as overestimation or underestimation of the size, for example, overestimation or underestimation of the length of a pipeline.

[0005] In summary, how to effectively suppress the side lobe level while maintaining the narrow main lobe and high gain of the detection signal, and improve the suppression ability of the complex multipath effect and clutter interference underground, has become a key technical bottleneck restricting the further improvement of the accuracy and reliability of the non-contact measurement of the size of the underground target. SUMMARY

[0006] Therefore, the present application aims to provide a zebra optimization-based sparse array non-contact measurement method for the size of an underground target, so as to solve the problem that the existing method cannot effectively suppress the side lobe level.

[0007] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] The zebra optimization-based sparse array non-contact measurement method for the size of an underground target comprises the following steps:

[0009] Step S1: constructing an optimization model of the measurement signal pattern of the sparse array, wherein the objective function of the optimization model is

[0010]

[0011] wherein d represents the element spacing, a represents the feeding amplitude, φ represents the feeding phase, L represents the maximum side lobe level in the pattern, G represents the maximum gain of the main lobe in the pattern, and w represents the weight of each index.

[0012] ​​Step S2: Initialize the parameters of the Zebra Algorithm, including population size, maximum number of iterations, number of array elements N, foraging intensity, and jump intensity, and randomly initialize the parameter configuration for each individual in the population. ,in, Indicates the first The initial element spacing of each array element. Indicates the first The feed amplitude of each array element, Indicates the first The feed phase of each array element;

[0013] Step S3: Update the parameter configuration of individuals in the population based on the zebras' foraging behavior;

[0014] Step S4: Based on the zebra's anti-predation behavior, when the preset triggering conditions are met, the parameter configuration of individuals in the population is updated in a jump manner to escape the local optimum.

[0015] Step S5: Calculate the fitness of the current population based on the measurement signal pattern optimization model of the sparse array. If the termination condition is met, output the optimal array parameter configuration; otherwise, update the predator position and return to step S3 to continue the iteration.

[0016] Step S6: Use the optimized array parameter configuration to drive the sparse array to detect underground targets, and calculate the size of the underground targets based on the echo signals obtained after detection.

[0017] Furthermore, a preferred embodiment is proposed, wherein the measurement signal pattern of the sparse array in step S1 is represented as follows:

[0018]

[0019] in, This indicates the total number of antenna elements. Indicates the first The feed amplitude of each antenna element, Indicates the first The distance of each antenna element from the reference point Represents the angle on a sparse array in a two-dimensional plane. Indicates the wavelength of the signal. The base of the natural logarithm. j It represents the imaginary unit.

[0020] Furthermore, a preferred method is proposed, wherein the parameter configuration for each individual in step S2 is... The initialization satisfies the following constraints:

[0021] No. Initial element spacing of each element The range of values ​​is , the feeding amplitude of the th array element is in the range of , the feeding phase of the th array element is in the range of .

[0022] Further, it is proposed that in the step S2, the foraging strength and the jumping strength are dynamically adjusted with the iteration number, and the adjustment formulas are respectively:

[0023] ,

[0024] ,

[0025] wherein, represents the foraging strength of the th iteration, represents the maximum iteration number, represents the current iteration number, represents the jumping strength of the th iteration.

[0026] Further, it is proposed that in the step S3, the parameter configuration of the individuals in the population is updated according to the foraging behavior of the zebra, and the update formula is:

[0027] ,

[0028] wherein, represents the parameter configuration of the th array element in the th iteration, represents the parameter configuration of the th array element in the th iteration, represents the global optimal solution in the whole population, represents the foraging strength, represents a random disturbance term.

[0029] Further, it is proposed that the amplitude of the random disturbance term is dynamically attenuated with the iteration process, and is represented as:

[0030] ,

[0031] wherein, represents a disturbance strength factor, represents the maximum value of the variable in the search space, represents the minimum value of the variable in the search space.

[0032] Further, it is proposed that the preset triggering condition in step S4 comprises:

[0033] Condition one: the variation amplitude of the sidelobe level of two consecutive iterations is less than a preset threshold ;

[0034] Condition two: the fitness of the individual is not improved in consecutive iterations:

[0035] Condition three: the distance between the current position of the individual and the position of the predator is less than or equal to a threat threshold.

[0036] Further, it is proposed that the updating method of the position of the predator is:

[0037] ,

[0038] wherein, represents the updated position of the predator, represents the current position of the predator, represents the moving step length of the predator, is a random number.

[0039] Based on the same inventive concept, the present application further proposes a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the zebra optimization-based sparse matrix under-target size non-contact measurement method according to any one of the above.

[0040] Based on the same inventive concept, the present application further proposes a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and when the computer program is run by a processor, the steps of the zebra optimization-based sparse matrix under-target size non-contact measurement method according to any one of the above are executed.

[0041] The present application has the following beneficial effects:

[0042] ​Existing technologies generally employ uniform linear arrays or simple transmit / receive pair structures, with fixed and regular element spacing and excitation methods. Theoretically, this regular structure suffers from an inherent limitation: the main lobe width and sidelobe level are mutually constrained, making it difficult to simultaneously achieve an extremely narrow main lobe and extremely low sidelobes. This invention breaks through this paradigm of regular arrays, introducing a sparse array as the basis for measurement. By breaking the uniformity of element spacing and jointly optimizing the feed amplitude and phase of each element, greater freedom is provided for antenna pattern design. Simultaneously, this invention improves the signal-to-noise ratio of the received signal through targeted suppression of sidelobe energy and optimization combined with a dynamic noise model. Effective target echo energy is enhanced by main lobe focusing, while ineffective interference and noise are suppressed to the greatest extent possible by sidelobe suppression and adaptive mechanisms. This cost-effectiveness allows this invention to maintain excellent detection performance even in harsh underground environments with strong clutter and significant multipath effects.

[0043] This invention does not employ traditional linear optimization or conventional intelligent algorithms. Instead, it introduces a zebra optimization algorithm that simulates the foraging and anti-predation behavior of a zebra herd. The foraging behavior mimics the tendency of zebras to cluster towards food sources (the current optimal solution), guiding parameter configurations to converge towards known favorable regions, achieving rapid local fine-grained search, and ensuring the quality of the solution and the convergence speed. When the algorithm detects that it has fallen into a local optimum (such as fitness stagnation or small sidelobe changes) or is threatened by predators (simulated noise interference), it triggers a jump update, causing some parameter configurations to randomly jump out of the current region and re-explore the global space.

[0044] These two behaviors dynamically switch according to preset conditions during the iteration process, achieving an adaptive balance between global exploration and local development. This ensures that the final array parameter configuration is globally optimal or near-optimal, rather than a locally suboptimal solution that is easily trapped. The method proposed in this invention can still stably find high-performance array configuration schemes even when facing complex conditions such as heterogeneous underground media, layered structures, or random noise. This greatly reduces the sensitivity of measurement results to environmental changes, enabling high consistency and repeatability of results when measuring the same target multiple times under different geological conditions at different times, thus solving the problem of poor measurement stability in existing technologies.

[0045] Through the synergistic effect of sparse array synthesis and zebra optimization, this invention can synthesize a measurement signal pattern with a narrower main lobe and significantly reduced side lobes. A narrower main lobe means stronger angular resolution of underground target boundaries, while lower side lobes greatly reduce the infiltration of stray signals and multiple reflection interference from non-target directions. This makes it clearer and more reliable to accurately identify the start and end points of targets from echo signals, directly translating into a substantial improvement in the accuracy of measuring target length, spacing, and other dimensional parameters, effectively overcoming the systematic errors of overestimating or underestimating dimensions in existing technologies. Attached Figure Description

[0046] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0047] Figure 1 This is a flowchart of the non-contact measurement method for underground target size in sparse arrays based on zebra optimization, as described in this invention.

[0048] Figure 2 This is a schematic diagram of the measurement signal pattern optimization model for the sparse array described in this invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0050] Implementation Method 1: This implementation method proposes a non-contact target size measurement method based on zebra optimization in sparse arrays. The method includes:

[0051] Step S1: Construct an optimization model for the measurement signal pattern of the sparse array, wherein the objective function of the optimization model is... for:

[0052]

[0053] in, This indicates the spacing between array elements. This indicates the power supply amplitude. This indicates the feed phase. HPBW represents the maximum sidelobe level in the radiation pattern, and HPBW represents the width of the main lobe. This represents the maximum gain of the main lobe in the radiation pattern. This indicates the weight of each indicator;

[0054] Step S2: Initialize the parameters of the Zebra Algorithm, including population size, maximum number of iterations, number of array elements N, foraging intensity, and jump intensity, and randomly initialize the parameter configuration for each individual in the population. ,in, Indicates the first The initial element spacing of each array element. Indicates the first The feed amplitude of each array element, Indicates the first The feed phase of each array element;

[0055] Step S3: Update the parameter configuration of individuals in the population based on the zebras' foraging behavior;

[0056] Step S4: Based on the zebra's anti-predation behavior, when the preset triggering conditions are met, the parameter configuration of individuals in the population is updated in a jump manner to escape the local optimum.

[0057] Step S5: Calculate the fitness of the current population based on the measurement signal pattern optimization model of the sparse array. If the termination condition is met, output the optimal array parameter configuration; otherwise, update the predator position and return to step S3 to continue the iteration.

[0058] Step S6: Use the optimized array parameter configuration to drive the sparse array to detect underground targets, and calculate the size of the underground targets based on the echo signals obtained after detection.

[0059] Implementation Method 2, see below Figure 1 and Figure 2 This embodiment describes a complete implementation of the non-contact measurement method for underground target size based on zebra optimization described in Embodiment 1, including:

[0060] A non-contact measurement method for target size in sparse arrays based on zebra optimization, the method comprising:

[0061] Step S1: Construct an optimization model for the measurement signal pattern of the sparse array;

[0062] In this embodiment, to address the problem that the non-contact measurement system for underground targets is susceptible to various noise and scattering interferences during signal transmission and echo acquisition in complex environments, an optimization model for the measurement signal pattern of a sparse array is constructed. The optimization model for the measurement signal pattern of a sparse array is as follows: Figure 2 As shown, the measurement signal pattern of its sparse array is represented as follows:

[0063]

[0064] in, This indicates the total number of antenna elements. Indicates the first The distance of each antenna element from the reference point Represents the angle on a sparse array in a two-dimensional plane. Indicates the wavelength of the signal. The base of the natural logarithm. j Represents the imaginary unit;

[0065] To ensure that the measurement signal has lower sidelobe energy, narrower main lobe width, and higher main lobe gain, thereby improving ranging resolution and anti-interference performance, this embodiment constructs an objective function for the measurement signal pattern optimization model of a sparse array. As shown below:

[0066]

[0067] in, Indicates the spacing between array elements. Indicates the power supply amplitude. Indicates the feed phase, This represents the maximum sidelobe level in the radiation pattern. This represents the maximum sidelobe level in the radiation pattern. For the angle The operator that retrieves the maximum value. Here, HPBW represents the array directional gain function, and HPBW represents the width of the main lobe, which indicates the angular range covered when the radiation intensity of the main lobe decreases by 3 dB. This represents the maximum gain of the main lobe in the radiation pattern. These represent the weights of each indicator, used to measure the importance of each indicator to the optimization model of the measured signal pattern.

[0068] Step S2: Initialize the parameters of the Zebra Algorithm, including population size, maximum number of iterations, number of array elements N, foraging intensity, and jump intensity, and randomly initialize the parameter configuration for each individual in the population. ,in, Indicates the first The initial element spacing of each array element. Indicates the first The feed amplitude of each array element, Indicates the first The feed phase of each array element;

[0069] The Zebra Optimization Algorithm described in this embodiment is a novel intelligent optimization algorithm inspired by the group foraging and anti-predation behaviors of zebras in nature. The foraging behavior improves the efficiency of food acquisition through group cooperation, while the anti-predation behavior is that the group uses the randomness of movement and distribution to confuse predators. The combination of these two behavioral patterns provides a natural balance mechanism for exploration and development in the optimization algorithm. The Zebra Algorithm has the ability to escape local optima and search for the global optimum.

[0070] Initialize the parameters of the Zebra Optimization Algorithm by randomly initializing N array elements, each representing a possible solution. For the nth array element... The initial values ​​of each array element can be expressed as:

[0071]

[0072] in Indicates the first The initial element spacing of each array element. The initial element spacing for the first element. This is the initial element spacing for the second element. Let N be the initial element spacing of the Nth element. Indicates the first The feed amplitude of each array element, The feed amplitude of the first array element. The feed amplitude for the second array element. The feed amplitude of the Nth array element. Indicates the first The feed phase of each array element The feed phase of the first array element, The feed phase for the second array element, This represents the feed phase of the Nth array element.

[0073] To ensure the optimization proceeds smoothly, this implementation method limits the first... Initial element spacing of each element The range of values ​​is To prevent the occurrence of the grid lobe phenomenon, the first Feed amplitude of each element The range of values ​​is , No. Feed phase of each element The range of values ​​is .

[0074] In this implementation, the number of array elements N is set to 8, which is considered a small-scale problem. Therefore, the population size P is set to 20, and the maximum number of iterations is set to 100. The foraging intensity is initially set to 0.3, as a higher foraging intensity helps accelerate optimization convergence. In the later stages of optimization, the foraging intensity is gradually reduced to 0.1 to ensure population diversity and to discover the global optimum. This process can be represented as:

[0075]

[0076] in, It indicates the first Foraging intensity in the next iteration This represents the maximum number of iterations. This indicates the current iteration number.

[0077] Jump intensity Setting the jump strength to 0.2 in the initial stage is beneficial for escaping local optima and can better resist the influence of noise interference. The jump strength is adjusted as iterations progress. The jump intensity decreases continuously as the objective function approaches the optimal solution. Taking 0.05, this process can be represented as:

[0078]

[0079] in, The first The jump strength of the next iteration This represents the maximum number of iterations. This indicates the current iteration number.

[0080] In summary, the parameter settings for Zebra Optimization are shown in Table 1:

[0081] Table 1. Parameter settings for the Zebra optimization algorithm

[0082]

[0083] Step S3: Update the parameter configuration of individuals in the population based on the zebras' foraging behavior;

[0084] The foraging behavior simulates the tendency of a zebra herd to move towards the current optimal location when searching for food, while retaining a certain degree of randomness to explore local areas. The purpose of this step is to search for the optimal value in a local area, simulating foraging behavior to update the parameter configuration of individuals in the population. The update process can be represented as:

[0085]

[0086] in, It indicates the first The array element in the first The parameter configuration in the next iteration represents the current solution, while This represents the globally optimal solution within the entire population, indicating the currently known optimal parameter configuration. During foraging, all individuals tend to move towards... This is to search for local optima. This represents the foraging intensity, a parameter used to control the foraging intensity. It is set to a relatively large value of 0.3 at the beginning of optimization, allowing individuals to quickly approach the global optimum, which helps accelerate convergence. As iterations progress, the foraging intensity gradually decreases, facilitating finer searching in the later stages of iteration. This represents the random perturbation term, which is a random variable. Its purpose is to maintain population diversity and prevent individuals from prematurely concentrating near local optima. It can be expressed as:

[0087]

[0088] Among them, the amplitude of the disturbance Related to the size of the solution space, it can be expressed as:

[0089]

[0090]

[0091] in, This represents the maximum value of the variable in the search space. This represents the minimum value of the variable in the search space.

[0092] Larger perturbation amplitudes in the initial stage are beneficial for exploration; moderate perturbation amplitudes in the middle stage are beneficial for balancing exploration and development; and smaller perturbation amplitudes in the later stage are beneficial for refining the capture of the optimal value. Dynamically adjusting the perturbation amplitude helps to balance global exploration capability with local convergence accuracy.

[0093] Step S4: Based on the zebra's anti-predation behavior, when the preset triggering conditions are met, the parameter configuration of individuals in the population is updated in a jump manner to escape the local optimum.

[0094] Anti-predation behavior is used to enhance the global search capability of an algorithm. Its purpose is to increase the probability of finding the global optimum by jumping to a new parameter configuration when the optimization process gets stuck in a local optimum, thus escaping the local optimum. Anti-predation behavior is triggered during the optimization process when any one of the following three conditions is met.

[0095] Condition 1: The sidelobe level decreases only slightly. Specifically, this means that when the parameters are configured in two consecutive iterations, the change in the sidelobe level is less than the set threshold. This process can be represented as:

[0096]

[0097] in, It indicates the first Sidelobe level of the next iteration. It is a pre-set threshold.

[0098] Condition 2: Fitness has not improved; when an individual's fitness is continuously... If there is no improvement in the next iteration, anti-predation behavior is triggered. This process can be represented as:

[0099]

[0100] in, It indicates the first The fitness value of the next iteration. It is a pre-set threshold. It is the number of consecutive iterations without improvement. It indicates the first - The fitness value of the next iteration.

[0101] Condition 3: Being within a predator's threat zone. Because an individual is within a predator's threat zone, it needs to move away from the predator. This process can be represented as:

[0102]

[0103] in, This indicates the current parameter combination. This indicates the location of the predator. The distance threshold is represented.

[0104] Step S5: Calculate the fitness of the current population based on the measurement signal pattern optimization model of the sparse array. If the termination condition is met, output the optimal array parameter configuration; otherwise, update the predator position and return to step S3 to continue the iteration.

[0105] In this embodiment, predator position updates are represented as noise and multipath scene parameter updates. Predators are used in the Zebra Optimization algorithm to simulate the impact of noise interference. By updating the predator positions, the parameter configuration in the population is adjusted, enabling the synthesized sparse array to possess noise resistance performance. The process of noise and multipath scene parameter updates can be represented as follows:

[0106]

[0107] in, This indicates the current position of the predator, and the direction angle of the noise. This indicates the predator's stride length and controls the direction of the noise. It is a random number, used to introduce randomness into noise.

[0108] Step S6: Use the optimized array parameter configuration to drive the sparse array to detect underground targets, and calculate the size of the underground targets based on the echo signals obtained after detection.

[0109] The dimensions of the underground target described in this embodiment include the target's length, horizontal extension length, spatial spacing, or outline dimensions.

[0110] This embodiment proposes a non-contact measurement method for underground target dimensions based on zebra optimization and sparse arrays. It optimizes the traditional measurement array structure into a sparse linear array. Existing non-contact measurement systems for underground target dimensions often employ a single-transmitter-single-receiver structure or a uniform linear array. The resulting radiation main lobe is wide and lacks directivity, making it difficult to effectively focus the transmitted energy. Furthermore, the received signal is easily contaminated with scattering and noise interference from undesired directions, leading to length estimation errors and measurement instability. To address this issue, this embodiment introduces sparse array synthesis technology, jointly optimizing the array spacing, feed amplitude, and phase. This achieves main lobe energy concentration and beam narrowing while significantly reducing sidelobe energy, effectively suppressing noise and multipath reflection interference from undesired directions, and improving the signal-to-noise ratio and length measurement accuracy of non-contact underground target dimension measurement.

[0111] This implementation proposes a non-contact measurement method for sparse array subsurface target dimensions based on zebra optimization. The zebra optimization algorithm is introduced to achieve global optimization of array parameters: it simulates the foraging and anti-predation behavior of zebras in nature. Foraging behavior corresponds to a local optimization process, where cooperative search gradually converges the solution space to a favorable region; anti-predation behavior corresponds to a global jump search, used to re-explore new regions when trapped in local optima. This mechanism achieves an adaptive balance between global search and refined local search, significantly improving the convergence speed and global optimality of array parameter optimization, thus maintaining high resolution and stability of the non-contact measurement system under complex subsurface conditions.

[0112] This implementation proposes a non-contact measurement method for underground target dimensions using a sparse array based on zebra optimization, and designs a dynamic parameter adjustment mechanism: In the zebra optimization algorithm of this implementation, parameters such as foraging intensity, jumping intensity, and random perturbation amplitude dynamically change during the iteration process. Larger values ​​are used in the early stages to enhance global search capability and avoid getting trapped in local extrema; in the later stages, parameter values ​​are gradually reduced to improve local search accuracy, achieving a dynamic balance between global search and local exploitation. This mechanism ensures that the measurement system can still obtain an optimal array configuration with high stability and high repeatability under complex underground noise and multipath scattering environments, thereby significantly improving the overall accuracy and reliability of non-contact measurement of underground target dimensions.

[0113] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0114] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit its protection scope. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading this disclosure, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the published pending claims.

Claims

1. A non-contact measurement method for target size in sparse arrays based on zebra optimization, characterized in that, The method includes: Step S1: Construct an optimization model for the measurement signal pattern of the sparse array, wherein the objective function of the optimization model is... for: in, Indicates the spacing between array elements. Indicates the power supply amplitude. Indicates the feed phase, HPBW represents the maximum sidelobe level in the radiation pattern, and HPBW represents the width of the main lobe. This represents the maximum gain of the main lobe in the radiation pattern. This indicates the weight of each indicator; Step S2: Initialize the parameters of the Zebra Algorithm, including population size, maximum number of iterations, number of array elements N, foraging intensity, and jump intensity, and randomly initialize the parameter configuration for each individual in the population. ,in, Indicates the first The initial element spacing of each array element. Indicates the first The feed amplitude of each array element, Indicates the first The feed phase of each array element; Step S3: Update the parameter configuration of individuals in the population based on the zebras' foraging behavior; Step S4: Based on the zebra's anti-predation behavior, when the preset triggering conditions are met, the parameter configuration of individuals in the population is updated in a jump manner to escape the local optimum. Step S5: Calculate the fitness of the current population based on the measurement signal pattern optimization model of the sparse array. If the termination condition is met, output the optimal array parameter configuration; otherwise, update the predator position and return to step S3 to continue the iteration. Step S6: Use the optimized array parameter configuration to drive the sparse array to detect underground targets, and calculate the size of the underground targets based on the echo signals obtained after detection.

2. The non-contact measurement method for target size in sparse arrays based on zebra optimization according to claim 1, characterized in that, The measurement signal pattern of the sparse array in step S1 is represented as follows: in, This indicates the total number of antenna elements. Indicates the first The distance of each antenna element from the reference point Represents the angle on a sparse array in a two-dimensional plane. Indicates the wavelength of the signal. The base of the natural logarithm. j It represents the imaginary unit.

3. The non-contact measurement method for target size in sparse arrays based on zebra optimization according to claim 2, characterized in that, The parameter configuration for each individual in step S2 The initialization satisfies the following constraints: No. Initial element spacing of each element The range of values ​​is , No. Feed amplitude of each element The range of values ​​is , No. Feed phase of each element The range of values ​​is .

4. The non-contact measurement method for underground target size in sparse arrays based on zebra optimization according to claim 1, characterized in that, In step S2, the foraging intensity and jumping intensity are dynamically adjusted with the number of iterations, and the adjustment formulas are as follows: ， ， in, Indicates the first Foraging intensity in the next iteration Indicates the maximum number of iterations. Indicates the current iteration number. Indicates the first The jump strength of the next iteration.

5. The non-contact measurement method for target size in sparse arrays based on zebra optimization according to claim 4, characterized in that, In step S3, the parameter configuration of individuals in the population is updated based on the zebras' foraging behavior. The update formula is as follows: , in, Indicates the first The array element in the first Parameter configuration in the next iteration. Indicates the first The array element in the first Parameter configuration in the next iteration. This represents the globally optimal solution in the entire population. Indicates foraging intensity, This represents a random disturbance term.

6. The non-contact measurement method for underground target size in sparse arrays based on zebra optimization according to claim 5, characterized in that, The random disturbance term amplitude The decay occurs dynamically as the iteration progresses, and is represented as: ， in, , This represents the maximum value of the variable in the search space. This represents the minimum value of the variable in the search space.

7. The non-contact measurement method for target size in sparse arrays based on zebra optimization according to claim 1, characterized in that, The preset triggering conditions in step S4 include: Condition 1: The change in sidelobe level between two consecutive iterations is less than a pre-set threshold. ; Condition 2: The fitness of an individual is continuous No improvement was achieved in the next iteration: Condition 3: The distance between the individual's current location and the predator's location is less than or equal to the threat threshold.

8. The non-contact measurement method for target size in sparse arrays based on zebra optimization according to claim 1, characterized in that, The predator's location is updated as follows: ， in, This indicates the updated predator location. Indicates the current location of the predator. Indicates the predator's stride length. It is a random number.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the non-contact measurement method for the size of underground targets in sparse arrays based on zebra optimization as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the non-contact measurement method for target size in sparse arrays based on zebra optimization as described in any one of claims 1-8.

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