Imaging Antenna Array Design Method and System for Lightning VHF Radiation Sources

Abstract

This invention relates to the field of radar equipment and antenna design technology, and in particular to a design method and system for imaging antenna arrays oriented towards VHF lightning radiation sources. The invention uses the coordinate set of each element in the receiving array as a decision vector, and the decision vector as an individual. A genetic optimization algorithm is used for iterative processing. After each generation of the population, the positions are fine-tuned to ensure that all individuals satisfy the set feasible region constraint P. When the population iteration is complete, the broadband directional spectrum of the receiving array is calculated, and the objective function is calculated based on the directional spectrum. The Pareto optimal solution set of the optimization objective minF(p) is obtained as the final decision set. This invention can simultaneously consider multiple indicators such as main lobe width, side lobe suppression, and imaging quality, ensuring the overall performance of the antenna array.

Description

Technical Field

[0001] This invention relates to the field of radar equipment and antenna design technology, and in particular to a design method and system for an imaging antenna array oriented towards lightning VHF radiation sources. Background Technology

[0002] Lightning, a typical product of severe convective weather, is accompanied by strong electric field reconstruction, high-temperature plasma channel formation, and intense electromagnetic radiation during its occurrence. It is one of the major natural disasters threatening power systems, communication systems, space launches, and critical engineering facilities. During lightning discharge, abundant short-pulse radiation signals are generated in the 30–300 MHz Very High Frequency (VHF) band. These signals are highly correlated with microscopic breakdown development, branch channel expansion, and return stroke processes. Numerous studies have shown that imaging and 3D reconstruction of lightning discharges using VHF electromagnetic radiation can acquire the "fine skeleton" of lightning discharge channels with spatial resolution on the order of tens to hundreds of meters and temporal resolution on the order of sub-microseconds to microseconds. This plays an irreplaceable role in the study of lightning physics mechanisms and in refined lightning early warning systems.

[0003] Currently, VHF lightning radiation source imaging has mainly developed two major technical approaches: one is the Time of Arrival (TOA) / Time Difference of Arrival (TDOA) network positioning system, represented by Lightning Mapping Array (LMA). This system deploys a dozen to dozens of receiving stations distributed over a range of tens of kilometers, using the pulse arrival time difference between multiple stations to invert the position of the radiation source in three-dimensional space, thereby obtaining the three-dimensional discharge structure of the entire lightning channel. This type of system has extremely high requirements for time synchronization accuracy, resulting in high hardware and maintenance costs, and its ability to resolve fine near-field structures is limited when the distance between stations is large. The other approach is the imaging method based on VHF broadband interferometer / array direction finding. This method deploys multiple antennas near a single station, using phase difference, cross-correlation, or spatial spectrum estimation algorithms on a baseline scale of several meters to tens of meters to obtain the direction of arrival information (azimuth and elevation angle) of the radiation source. This information is then combined with certain height assumptions or multi-station geometric intersection to achieve two-dimensional or even three-dimensional imaging. Typical examples of this type of system include broadband interferometers based on three-element or four-element arrays and multi-channel VHF direction finding radars.

[0004] With the development of array signal processing and high-performance data acquisition technologies, high-resolution DOA (Direction-of-Arrival) algorithms based on spatial spectrum estimation have been gradually introduced into the field of VHF lightning imaging. In VHF lightning radiation source imaging applications, there is a close relationship between array geometry and imaging quality. The planar distribution of the array determines the sampling structure in the frequency-angle joint space, which in turn determines key characteristics such as beam main lobe width, side lobe structure, radiation pattern null distribution, and spatial spectrum resolution.

[0005] However, array geometry design for specific imaging tasks remains a relatively weak link. Most VHF arrays still follow the "regular geometry + engineering experience" model, lacking clear task-driven indicators. For example, in lightning imaging, the low elevation angle coverage, local spatial resolution, and omnidirectional uniformity that are of concern are rarely systematically optimized through quantitative indicators during the array design stage. Existing array performance evaluations are mostly focused on macroscopic indicators such as overall angular error and spatial position error. There is a lack of systematic and comprehensive quantitative comparison of beam characteristics that directly determine imaging quality, such as peak sidelobe ratio (PSLR) and main lobe width (HPBW). In particular, there is a lack of overall statistical evaluation for a given task ROI under broadband conditions. Although some works have attempted to introduce irregular arrays into VHF positioning systems and combine them with optimization algorithms to improve positioning results, most of them remain at the level of "fine-tuning around a certain geometry" and have not yet formed a complete methodology of "starting from scratch and globally searching for the optimal geometry under a given number of antennas and physical constraints". Summary of the Invention

[0006] To overcome the problems in the existing VHF lightning radiation source imaging system array layout that rely on experience, have an excessively large main lobe width, insufficient side lobe suppression, and significant variations in imaging quality with array geometry, this invention proposes an imaging antenna array design method for lightning VHF radiation sources. This method can take into account multiple indicators such as main lobe width, side lobe suppression, and imaging quality, ensuring the overall performance of the antenna array.

[0007] This invention proposes a design method for imaging antenna arrays oriented towards lightning VHF radiation sources. The method uses the coordinate set of each element in the receiving array as the decision vector, and the decision vector as an individual. A genetic optimization algorithm is used for iteration. After each generation of the population is generated, the position is fine-tuned to ensure that the individuals satisfy the set feasible region constraint P. When the population iteration is completed, the broadband directional spectrum of the receiving array is calculated, and the objective function is calculated based on the broadband directional spectrum. The Pareto optimal solution set of the optimization objective minF(p) is obtained as the final decision set.

[0008] The objective functions include F1(p) and F2(p), and the optimization objective minF(p) is a vector composed of F1(p) and F2(p); p represents an individual.

[0009] F1(p) takes into account both the HPBW of the decision vector and the high-frequency beam consistency, aiming to optimize the angular resolution of the receiving array and ensure the consistency of the broadband response.

[0010] F2(p) comprehensively considers the peak sidelobe ratio, aperture utilization, and direction finding error of the decision vector, aiming to improve the sidelobe suppression capability, aperture utilization, and compatibility with the direction finding algorithm of the receiving array.

[0011] Preferred:

[0012] ;

[0013] ;

[0014] Where HPBW(p) is the HPBW corresponding to p. Let p be the high-frequency beam consistency factor. As weight; W high ( p ) represents the main lobe width of the single-frequency radiation pattern of the receiving array corresponding to p at the highest frequency of the radiation source signal. W target The preset physical threshold is 'max', which means taking the maximum value.

[0015] Preferred:

[0016] ;

[0017] PSLR(p) is the peak-to-sidelobe ratio corresponding to p. For aperture utilization factor, Let p be the direction finding error. λ D and As weight.

[0018] Preferably, the pore size utilization factor The method for obtaining the aperture is as follows: First, calculate the actual aperture of the receiving array. When the actual aperture is greater than the effective aperture D... eff Then the aperture utilization factor Set to 0; the actual aperture is less than or equal to the effective aperture D. eff Then the aperture utilization factor Take the actual aperture or a set non-zero value.

[0019] Preferably, based on the correction matrix Constructing a broadband directional spectrum ;

[0020] ;

[0021] in, Frequency point The received signal vector on the frequency point, where K is the total number of frequency points;

[0022] H represents the conjugate operation. for Conjugate;

[0023] For noise power, The diagonal loading coefficient;

[0024] I is the identity matrix.

[0025] Preferably, the feasible domain constraint P of the receiving array includes: minimum spacing constraint, aperture constraint and safe area constraint, wherein the minimum spacing constraint is that the distance between any two array elements is less than or equal to the set minimum distance.

[0026] Preferably, the method for fine-tuning individuals based on the feasible region constraint P is as follows:

[0027] First, for array element pairs that do not meet the minimum spacing constraint, perform a minimum amplitude translation along the connecting line until all array element pairs meet the minimum spacing constraint.

[0028] Then, for array elements that do not meet the aperture constraints, they are translated along the direction from the array element to the set reference point so that all array elements meet the aperture constraints.

[0029] Finally, the installation area constraints are checked by projecting the array elements that fall outside the installation area to the nearest point on the boundary of the installation area.

[0030] Preferably, a binary crossover operator is used for crossover operations during the population iteration process, and the crossover distribution index of the g-th iteration is... and crossover probability The calculation formula is as follows:

[0031] ;

[0032] ;

[0033] ;

[0034] Where tr(.) denotes the trace of the matrix; S (g) For the g-th generation population The covariance matrix, Let S be the i-th individual in the g-th generation of the population, with g initially set to 0, and M being the population size; (0) The covariance matrix of the initial population; Let be the convergence coefficient of the population in the g-th generation. , , and All are given constants.

[0035] Preferably, during population iteration, the variable asynchronous length of the i-th individual... for:

[0036] ;

[0037] in, and The numbers are Gaussian distributed random numbers. , , Let be the sample variance of the g-th generation population. , Both c and c are set constants.

[0038] The present invention proposes an imaging antenna array design system for lightning VHF radiation sources, comprising a memory and a processor. The memory stores a computer program, and the processor is connected to the memory. The processor is used to execute the computer program to implement the imaging antenna array design method for lightning VHF radiation sources.

[0039] The advantages of this invention are:

[0040] (1) This invention proposes an imaging antenna array design method for VHF lightning radiation sources. For the imaging task of VHF lightning radiation sources, a systematic model is performed during the geometric layout stage to model key imaging characteristics such as main lobe width, side lobe structure, and broadband response consistency. The radiation source distribution characteristics and imaging performance requirements are incorporated into a unified design, ensuring that optimal solutions can be found at different azimuth and elevation angles. This invention achieves coordinated optimization of array element layout and radiation pattern performance, improving the accuracy and reliability of VHF lightning radiation source imaging from the source.

[0041] (2) The present invention introduces feasible domain constraints to realize the fine design of VHF array in terms of element spacing, aperture utilization and geometric symmetry, avoids unfavorable structures such as excessive concentration, excessive dispersion or near collinearity of array distribution, improves the resolution of radiation pattern in all angles, and avoids the risk of weak signal loss and angle estimation offset.

[0042] (3) The present invention considers the balance mechanism of interference-sensitive indicators such as sidelobe energy and peak sidelobe ratio, and is suitable for multi-source and strong-weak source mixed scenarios. It can reduce sidelobe interference and avoid the image quality from fluctuating with the position of the radiation source.

[0043] (4) This invention models the task requirements of lightning imaging, calculates key performance indicators such as main lobe width and peak-to-side lobe ratio using a broadband (30–60 MHz) spatial spectrum, and establishes a multi-objective optimization model based on these indicators. Combining an improved global evolutionary algorithm and array geometric feasibility constraints, this invention can automatically search for the optimal planar layout scheme within the limited physical dimensions of the antenna array. Experimental results show that this method can significantly reduce the main lobe width, improve side lobe suppression, and enhance overall imaging resolution while maintaining the hardware structure, providing an efficient and engineerable array design approach for constructing a high-precision VHF lightning radiation source imaging system.

[0044] (5) Experimental results verified the applicability and effectiveness of the method in complex lightning radiation source imaging scenarios. It can maintain stable spatial resolution performance under different elevation and azimuth angles, providing key technical support for building a higher precision and more robust lightning VHF radiation source imaging and positioning system. Attached Figure Description

[0045] Figure 1 This is a flowchart of an imaging antenna array design method for lightning VHF radiation sources proposed in this invention.

[0046] Figure 2(a) Optimal array layout of uniform circular array;

[0047] Figure 2(b) shows the optimal layout of a non-uniform L-shaped array.

[0048] Figure 2(c) Optimal uniform L-shaped array layout;

[0049] Figure 3(a) PSLR iteration curves for three optimal arrays;

[0050] Figure 3(b) shows the HPSW iteration curves for the three optimal arrays;

[0051] Figure 4 MUSIC power spectrum of the elevation angle section. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0053] Reference Figure 1 The present embodiment proposes an imaging antenna array design method for lightning VHF radiation sources, which includes the following steps.

[0054] S1. Initialize the radiation source location and population; the individuals in the population represent the receiving array implementation scheme, specifically the decision vector formed by concatenating the coordinates of all array elements in the receiving array; the formula for individual p is expressed as:

[0055] (1)

[0056] Where, p n Let p1, p2, and p3 represent the coordinates of the nth receiving element (i.e., the nth element of the receiving array); N is the number of elements in the receiving array, 1 ≤ n ≤ N; p1, p2, and p3 represent the coordinates of the nth receiving element (i.e., the nth element of the receiving array); p4 is the number of elements in the receiving array, 1 ≤ n ≤ N; p5, p6, and p7 are the coordinates of the nth N The coordinates of the 1st, 2nd and Nth receiving array elements respectively.

[0057] S2, perform crossover operations on the population.

[0058] This step specifically involves performing crossover on the population using the binary crossover (SBX) operator, with the crossover distribution index... and crossover probability The calculation formula is as follows:

[0059] (2)

[0060] (3)

[0061] (4)

[0062] (5)

[0063] Where tr(.) denotes the trace of the matrix; S (g) and These are the g-th generation populations. The covariance matrix and mean, Let be the i-th individual in the g-th generation population, M be the population size, T be the superscript indicating transpose, and F be the Fourier transform. S is the convergence coefficient of the g-th generation population. (0) Let g be the covariance matrix of the initial population, with an initial value of 0.

[0064] , , and All are given constants.

[0065] When the population is relatively dispersed in the target space Larger crossover probability Higher and distribution index Smaller populations result in offspring that differ significantly from their parents in geometric space, which is beneficial for exploring different array geometries; as the population gradually concentrates near the Pareto front... Reduce, crossover probability Decrease and distribution index Increase the number of offspring, which are generated near the parent, thus enhancing the local fine-grained search of candidate geometries.

[0066] Through cross-distribution index and crossover probability The iteration of the crossover operator achieves the adaptiveness of the crossover operator by explicitly coupling the target statistic with the array performance, which is different from the conventional adaptive strategy that only relies on algebra or parameter variance.

[0067] S3. Introduce mutations into the population.

[0068] This step specifically employs a multi-scale hybrid mutation strategy for mutation, as shown in Formula 6; for example, if the number of population iterations g is less than the threshold T0, then Cauchy distribution is used for mutation, with a mutation probability of P1; if g is greater than or equal to T0, Gaussian distribution is used for mutation, with a mutation probability of P2; P2 is less than P1; T0 is a set value.

[0069] During the mutation process, the variable length is calculated using the following formula:

[0070] (6)

[0071] , ;

[0072] in, Let be the variable asynchronous length of the i-th individual in the population. and The numbers are Gaussian distributed random numbers. Let be the sample variance of the g-th generation population. , Both c and c are set constants. This indicates that the mean is 0 and the variance is... The Gaussian normal distribution; This indicates that the mean is 0 and the variance is... It follows a Gaussian normal distribution.

[0073] This demonstrates that the magnitude of variation automatically adjusts with the dispersion of the variation dimension (i.e., the mutated element coordinate components) within the population, and simultaneously provides large-scale jumps and small-scale corrections through the superposition of Gaussian kernels at two scales. When the element coordinates have not yet formed a significant cluster within the feasible region P, The larger the variable asynchronous length, the more the algorithm can jump between different geometric topologies of the array (such as L-shaped, uniform L-shaped, non-uniform L-shaped, circular, etc.); near convergence, The reduced, variable-asynchronous length automatically shrinks, making it easier to fine-tune the position of array elements in the local neighborhood to improve the radiation pattern index.

[0074] S4. Perform feasible region projection and environment selection to optimize each individual in the population so that each individual satisfies the feasible region constraint P.

[0075] Specifically, this step involves traversing all individuals in the population and performing projection optimization:

[0076] First, all pairs of array elements that violate the minimum spacing constraint are translated along the connecting line with the minimum amplitude to satisfy the lower bound of the distance, that is, the distance between any pair of array elements satisfies the minimum spacing constraint.

[0077] Then, the distance between each array element and the reference point is detected, and the array elements that exceed the upper limit of the aperture are radially projected back to the aperture boundary.

[0078] Finally, the installation area constraints are checked, and array elements falling outside the installation area are projected to the nearest point on the boundary of the installation area.

[0079] After optimizing each individual in the population one by one, all individuals in the population satisfy the feasible region constraint P (including minimum spacing constraint, aperture constraint and installation area constraint).

[0080] Minimum spacing constraint:

[0081] The Euclidean distance between any two array elements (the nth receiving array element and the mth receiving array element) is defined as d. nm The minimum spacing constraint formula is expressed as:

[0082] (7)

[0083] (8)

[0084] Where, p n Let p be the coordinate vector of the nth receiving element. m Let be the coordinate vector of the m-th receiving array element; The wavelength is determined by the shortest wavelength corresponding to the upper limit of the operating frequency band and the physical dimensions of the antenna, in accordance with current relevant standards.

[0085] Aperture constraints:

[0086] Limiting the array's geometric aperture can prevent high-frequency gate lobes and aliasing issues caused by excessively long baselines. Selecting an array reference point... (Specifically, the array's geometric center or a fixed array element can be chosen); the aperture constraint can be expressed by the formula:

[0087] (9)

[0088] D max is the set distance threshold; N is the number of elements in the receiving array.

[0089] Installation area constraints:

[0090] Receiver array deployment is typically limited by the actual installation area, i.e., the available installation plane area. The region D is a two-dimensional plane defined by the platform dimensions, surrounding obstacles, and safety boundaries. Thus, the installation area constraints are denoted as... .

[0091] In summary, the array geometry set that satisfies all constraints can be obtained. P (i.e., feasible region) is represented as:

[0092] (10)

[0093] S5. Determine if the population has converged;

[0094] If not, update g to g+1 and then return to step S2;

[0095] If yes, then proceed to step S6.

[0096] Specifically, the number of population iterations can be used as the convergence condition for this step.

[0097] S6. Calculate the broadband directional spectrum of each receiver array (i.e., individual) in the population. Then, normalization is performed to obtain the normalized directional spectrum. .

[0098] Traditional broadband directional spectrum The construction method is as follows: for the receiving array at each frequency point covariance matrix on Perform eigenvalue decomposition to extract the signal subspace. and noise subspace Then, a narrowband music spatial spectrum is constructed based on the noise subspace. Then, for each frequency point... On The broadband directional spectrum is obtained by averaging the values. : and These are the elevation and azimuth angles of the received signal from the receiving array, respectively; since the position of the receiving array remains unchanged, the elevation angle... and azimuth It changes as the location of the radiation source changes.

[0099] covariance matrix The eigenvalue decomposition formula is:

[0100] (11)

[0101] in, It is by A diagonal matrix composed of the first G largest eigenvalues, It is a diagonal matrix composed of the remaining eigenvalues, where G is a set value; For the signal subspace, Let H be the noise subspace, and H denotes conjugation.

[0102] The narrowband music spatial spectrum is:

[0103] (12)

[0104] in, For the corresponding frequency point Angle of elevation and azimuth The guiding vector; the guiding vector lies entirely within the signal subspace at the true incident direction, and is therefore orthogonal to the noise subspace, as expressed by the formula:

[0105] (13)

[0106] in, , , and These are the signal propagation delays from the 1st, 2nd, nth, and Nth array elements in the receiving array to the specified array reference point, respectively; 1 ≤ n ≤ N.

[0107] (14)

[0108] Where K is the total number of frequency points.

[0109] It is worth noting that in this application, based on the correction matrix Constructing a broadband directional spectrum Soon As the covariance matrix Substituting into Formula 11, extract the noise subspace. Then execute formulas 12-13 to obtain the calculated narrowband MUSIC spatial spectrum. and broadband directional spectrum .

[0110] Correction matrix for:

[0111] (15)

[0112] in Frequency point The received signal vector on the frequency spectrum, where K is the total number of frequency points; H represents the conjugate operation. for Conjugate; For noise power, is the diagonal loading coefficient; I is the identity matrix.

[0113] Broadband directional spectrum The normalization formula is:

[0114] (16)

[0115] S7, Based on Normalized Directional Spectrum Calculate the peak sidelobe ratio (PSLR) and broadband beamwidth (HPBW) of the receiver array based on the broadband directional spectrum. Calculate the direction finding error of the receiving array .

[0116] (17)

[0117] in, To set the elevation angle of the receiving array corresponding to the radiation source, To obtain the broadband directional spectrum corresponding to this set radiation source The elevation angle estimate obtained by direction finding.

[0118] S8. Construct and solve the optimization objective minF(p) to obtain its Pareto optimal solution set as the final decision set. After obtaining the final decision set, the optimal array can be further selected based on antenna performance indicators. For example, first select the optimal PSLR array from the final decision set, and then further select the optimal HPBW array as the final optimal array. The specific selection principle can be set according to the scenario requirements. For example, if the scenario requirements place more emphasis on HPBW, then the optimal HPBW array can be selected first, and then the optimal PSLR array can be selected.

[0119] (18)

[0120] Where F1(p) and F2(p) are both objective function terms; P is the feasible region constraint P of the decision vector p, which includes the constraints of minimum spacing between receiving array elements, maximum aperture and installation area boundary.

[0121] The objective function F1(p) aims to optimize the angular resolution of the receiver array and ensure the consistency of the broadband response. This function is determined by the broadband main lobe half-power beamwidth (HPBW) and the high-frequency beam consistency factor. Weighted composition:

[0122] (19)

[0123] Wherein, HPBW(p) is the HPBW corresponding to the decision vector (i.e., individual) p, which directly reflects the detail resolution capability of the imaging system; high-frequency beam consistency factor The introduction of this is to suppress the non-uniform sparse array at the upper limit of the operating frequency band. f max The grid lobe phenomenon may occur at this location; The set high-frequency beam consistency penalty weight.

[0124] High-frequency beam consistency factor The main lobe width of the array's single-frequency radiation pattern at the highest frequency of the radiation source signal was calculated. W high To quantify, when W high Exceeding the preset physical threshold W target hour, This will exhibit linear growth, thus forcing the algorithm to eliminate geometric structures that perform well at low frequencies but exhibit spurious peaks at high frequencies. The calculation formula is as follows:

[0125] (20)

[0126] in, W high ( p ) represents the receiving array corresponding to decision vector p in f max The main lobe width of the single-frequency pattern at that location W high .

[0127] The objective function F2(p) is used to improve the sidelobe suppression capability, aperture utilization, and compatibility with the direction-finding algorithm of the receiving array. Its mathematical form is expressed as:

[0128] (twenty one)

[0129] In the formula, PSLR(p) is the peak sidelobe ratio corresponding to the decision vector p. Taking a negative value aims to transform it into a minimization problem. λ D Apply penalty weights to the aperture. For direction finding error, This is the weighting of the direction finding error;

[0130] This is the aperture utilization factor, used to prevent aperture waste caused by excessive clustering of array elements. Define the effective aperture D. eff The maximum span of the current geometry on the receiving array geometry plane, where the actual aperture of the receiving array is greater than the effective aperture D. eff Then the aperture utilization factor Set to 0; if the actual aperture of the receiving array is less than or equal to the effective aperture D. eff Then the aperture utilization factor A value greater than 0 forces array elements to spread toward the physical boundary to increase the baseline length.

[0131] Since there is no explicit linear or convex relationship between the two objective functions F1(p) and F2(p), and different objectives are physically constrained by each other, this invention does not adopt a weighted summation form with preset weights, but retains an unweighted multi-objective structure. By solving the Pareto optimal solution set of the above problem, a set of array layouts with different trade-off characteristics is obtained.

[0132] The above method is verified in conjunction with specific embodiments below.

[0133] This embodiment constructs a high-fidelity VHF lightning interferometer array design scenario. The experimental parameters are set by comprehensively considering the physical characteristics of lightning, electromagnetic wave propagation characteristics, array physical constraints, and the convergence requirements of the stochastic optimization algorithm. The specific configuration is as follows. In terms of physical scenario and array geometry configuration, the lightning physical model sets the discharge channel base height to 5000m and the fractal dimension to 1.3 to simulate the spatial morphology of typical cloud-to-ground lightning.

[0134] The simulation operates within a frequency band ranging from 27.5 MHz to 60 MHz, covering typical high-frequency communication bandwidth. To balance computational efficiency with frequency domain resolution, this band is discretized into 11 equally spaced frequency sampling points. During evaluation, the algorithm coherently accumulates or statistically averages the array responses of all sampling points. The receiver array to be optimized comprises seven omnidirectional elements and is strictly constrained within a side length L. max Within a two-dimensional rectangular planar area of ​​20 meters, to prevent physical overlap of array elements and excessive mutual coupling effects, a lower limit d is set for the Euclidean distance between array elements. min =1.5m. In addition, to ensure the accuracy of the index calculation, the high-precision angle grid step size used in the radiation pattern evaluation is set to 0.1°, covering the hemispherical airspace from -90° to +90°.

[0135] Regarding the parameter settings for the physics-driven evolutionary algorithm, the population size is set to N. pop =120, maximum number of iterations G max =50. To achieve a dynamic balance between exploration and development, the basic crossover probability of the adaptive simulated binary crossover (SBX) operator is set to p. c =0.8, its distribution index It is not a fixed value, but follows a linear growth function. This allows the distribution range of offspring to gradually converge from a wide area to the neighborhood of the parent generation as the iteration progresses. In the first 50% of the evolutionary process, Cauchy mutation is used with the dominant probability, and its scale parameter is set to 10% of the range of the decision variable values, utilizing the long-tail effect to maintain population diversity. In the latter 50% of the process, a smooth transition to Gaussian mutation is adopted, with its standard deviation decreasing from 20% of the range to 1% with each generation, to perform a local fine-grained search. Simultaneously, an amplitude weight threshold is set in the feasible region projection mechanism. Any weight below this value will be forced to zero in order to obtain a sparse solution.

[0136] Regarding the penalty factor setting for multi-objective optimization, the weight coefficients of each physical factor were rigorously tuned to guide the population towards a physically realizable Pareto front. The high-frequency beam consistency penalty weight was set as follows: =5.0, and a penalty is triggered only when the high-frequency (60MHz) beamwidth exceeds the target value by 15°; the aperture is set using a penalty weight of . λ D =10, its higher weight is intended to force the effective aperture of the array to reach at least 80% of the maximum aperture, preventing aperture waste caused by element clustering; the weight of the MUSIC direction finding error is set to This serves as a soft constraint-assisted optimization.

[0137] In terms of setting up the spatial spectrum estimation and verification environment, in order to test the array's resolution performance under non-ideal conditions, the radiation source was placed at a non-grid point location. To verify the algorithm's estimation accuracy for off-axis targets, the channel environment signal-to-noise ratio (SNR) was set to 10 dB to simulate moderate noise interference. To address the numerical stability issue of covariance matrix inversion, diagonal loading of coefficients was employed. Precisely set to noise power 5%. The MUSIC spectral peak search adopts a three-level cascade strategy: first, a coarse scan of the entire domain with a step size of 0.5° is performed, then a fine scan is performed within ±5° of the peak value, and finally, a super-fine spectrum with a resolution of 0.01° is reconstructed using cubic spline interpolation, thereby achieving high-precision estimation of the direction of arrival.

[0138] In summary, in this embodiment, the array size is 7 elements, the array installation area is limited to a 20m × 20m planar region, and the minimum spacing between elements is constrained to 1.5m. The simulated lightning radiation source has a height of 10km and a frequency band set from 27.5MHz to 60MHz. Discrete frequency points are selected at equal intervals within this frequency band for broadband synthetic radiation pattern and broadband MUSIC spectrum calculation. The layout optimization of the seven-antenna array elements is performed within the region for non-uniform L-shaped, uniform L-shaped, and uniform circular arrays.

[0139] The relevant parameter settings for the method of this invention are as follows: the initial population size is set to 120, the initial crossover probability is 0.8, the variable dimension is 15, and the maximum number of iterations is 50. After obtaining the Pareto solution, PSLR≤-13dB is set as a constraint, and the individual with the smallest HPBW satisfying the constraint in the solution set is selected as the optimal array. The optimal array layout and performance optimization iteration curves of non-uniform L-shaped, uniform L-shaped, and uniform circular arrays are shown in Figures 2(a), 2(b), 2(c), 3(a), and 3(b).

[0140] As shown in Figures 3(a) and 3(b), all three types of array topologies exhibit a typical evolutionary characteristic of "rapid optimization in the early stage and slow convergence in the later stage" during the multi-objective evolutionary search process. With the iteration number as the horizontal axis, the "maximum value - average value" statistical curves of sidelobe level (PSLR) and half-power beamwidth (HPBW) show the most significant decrease in the first 5-10 generations, entering a stable range after the 20th-25th generations, and remaining at a low level until the 50th generation. This phenomenon indicates that, under a given population size and operator parameter settings, the evolutionary population has basically completed the transition from global solution space exploration to fine-grained optimization of the local solution domain. The overall distribution of the non-dominated solution set tends to stabilize, and the optimization process enters the convergence stage.

[0141] The PSLR iteration curves in Figure 3(a) reflect the evolutionary convergence process of the array's sidelobe suppression capability. The uniform circular array maintains the optimal sidelobe suppression level throughout the entire iteration cycle. Its maximum and average PSLR values ​​decrease rapidly and tend to stabilize in the first 10 to 15 generations, eventually stabilizing at around -3.56 dB, with a very small numerical gap between them. This indicates that the topology has low population dispersion in the sidelobe index dimension, strong solution set consistency, and good repeatability of the optimization results.

[0142] The PSLR convergence rate of the uniform L-shaped array is also relatively fast. Its maximum value drops from about -3.2dB initially to the range of -3.35 to -3.36dB and then remains stable. The average value is slightly higher than the level corresponding to the maximum value and tends to level off in the later stage. This indicates that the topology can stably achieve a certain degree of sidelobe suppression, but the optimal suppression level is significantly weaker than that of the uniform circular array.

[0143] The maximum PSLR value of the non-uniform L-shaped array is close to that of the uniform L-shaped array, and it stabilizes at around -3.37dB in the later stage, indicating that it can search for the best sidelobe individuals with performance comparable to that of the uniform L-shaped array. However, its average PSLR curve shows a significant rebound in the 8th to 15th generations, and stabilizes at around -3.11dB in the later stage, resulting in a large difference between the maximum value and the average value.

[0144] Under the multi-objective trade-off criteria and constraints set in the embodiments, the feasible solution space of the non-uniform L-shaped topology is more dispersed. A considerable proportion of individuals in the population tend to sacrifice sidelobe suppression performance for optimization of other objectives such as main lobe width reduction, thereby increasing the population average PSLR. At the same time, the evolutionary algorithm can still retain a small number of individuals with excellent sidelobe performance in the solution set of this topology, keeping their maximum PSLR value within a relatively optimal range. In summary, the uniform circular array has the best sidelobe suppression capability and stability.

[0145] The HPBW iteration curves in Figure 3(b) characterize the convergence evolution process of the array's angular resolution capability. The uniform circular array exhibits a significant advantage in the main lobe width index. Its maximum and average HPBW values ​​rapidly decrease in the first 5-8 generations and stabilize around 7.2 dB. Moreover, the two statistical curves almost overlap, indicating that the main lobe width of the population solution under this topology is well consistent. The optimization process has a stable effect on improving HPBW, and the variance of the solution is small, demonstrating excellent angular resolution performance and robustness.

[0146] Both uniform and non-uniform L-shaped arrays exhibited a rapid decrease in HPBW from an initial high level of 14-19, stabilizing in the 10.6-10.8 dB range after generations 20-25. Comparison reveals that the maximum HPBW curve of the non-uniform L-shaped array is generally slightly lower than that of the uniform L-shaped array, stabilizing at 10.3-10.5 dB in the later stages. This indicates that introducing additional geometric degrees of freedom through non-uniform spacing allows for further optimization of the array's main lobe width. However, the gap between the average and maximum values ​​remains significant in the early evolutionary stages, reflecting a higher dispersion of solutions within the population. The uniform L-shaped array shows a relatively smaller "maximum-average" HPBW gap and a smoother convergence curve, indicating a more concentrated distribution of feasible solutions and making it easier for the evolutionary search to achieve a consistent main lobe width optimization level.

[0147] Combining PSLR and HPBW metrics, under the given parameters and constraints, the uniform circular array simultaneously achieves minimum HPBW and minimum PSLR, with its maximum and average values ​​closely matching, indicating that this receiver array possesses outstanding overall performance and superior stability and repeatability at the population statistical level. The uniform L-shaped array exhibits moderate PSLR and HPBW, with a smooth convergence curve and relatively fast convergence rate, making it suitable for engineering scenarios with limited design freedom and the need to obtain stable multi-objective compromise solutions. The non-uniform L-shaped array shows weaker average performance: its optimal HPBW is slightly better than the uniform L-shaped array, and its optimal PSLR is comparable, but the population average PSLR is significantly higher, indicating that this topology is more likely to produce solutions that "achieve main lobe contraction at the expense of sidelobe elevation."

[0148] This embodiment also verifies the effectiveness of the method of the present invention through broadband signal imaging simulation. The simulation environment is set in the frequency band of 30 MHz to 60 MHz, the frequency step is set to 2 MHz, the incident signal-to-noise ratio is 0 dB, and the incident angle is (azimuth -120°, elevation 0°). Analysis is performed on a sparse array structure containing 7 elements. To comprehensively evaluate the imaging performance of different topologies, four arrays were compared experimentally: the optimal non-uniform L-shaped array obtained by algorithm optimization, the optimal uniform L-shaped array, the optimal uniform circular array, and the unoptimized random L-shaped array. The spatial spectrum calculation uses a broadband conventional beamforming algorithm. Its normalized power spectrum is obtained by coherently accumulating the steering vector and array manifold at each frequency point. The specific broadband beamforming power output can be expressed as the incoherent superposition of the signal power at each frequency point, thereby simulating the detection scenario of a real broadband lightning radiation source. Figure 4 The MUSIC power spectrum is shown for the elevation cross-section of the four arrays.

[0149] Figure 4 The horizontal axis represents the elevation angle (the angle between the incident direction of the radiation source and the horizon; the azimuth angle is the angle required for the antenna array to rotate clockwise to true north), and the vertical axis represents the normalized power amplitude. A magnified view further illustrates the detailed features of the main lobe region at -3dB. For the unoptimized random L-shaped array shown by the yellow dashed line, its main lobe width is significantly wider than the other three array configurations. It is evident that without an optimization algorithm, randomly distributed array elements struggle to achieve effective aperture expansion, resulting not only in a low angular resolution but also insufficient energy focusing capability, failing to meet the application requirements of high-precision detection.

[0150] Uniform and non-uniform L-shaped arrays exhibit balanced performance characteristics, with both main lobe width and side lobe level indicators at moderate levels, showing relatively stable overall performance. However, limited by the geometric constraints of fixed element spacing, the aperture expansion potential of this topology is limited, and there is a clear upper limit to the improvement of angular resolution, making it difficult to adapt to higher precision detection tasks.

[0151] The uniform circular array, represented by the blue solid line, achieves a narrower main lobe width. As clearly observed in the magnified view, the main lobe width of this array is significantly narrower than that of the uniform L-shaped array. This indicates that the non-uniform sparse arrangement achieved by optimizing the element spacing can effectively expand the equivalent aperture while maintaining the same number of elements, thereby significantly improving angular resolution. Simultaneously, compared to uniform and non-uniform L-shaped arrays, the optimized uniform circular array significantly reduces sidelobe levels, completely avoiding the generation of high-level grating lobes and ensuring the reliability of single main peak identification during target detection.

[0152] In summary, the simulation results verify that the method of this invention can effectively mine the optimal solution of the Pareto front between the main lobe width (angular resolution) and the peak-to-side lobe ratio. Furthermore, it verifies the engineering practical value and promotion potential of uniform circular arrays in improving the spatial resolution and anti-interference performance of lightning detection systems.

[0153] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0154] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0155] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A method for designing an imaging antenna array for a lightning VHF radiation source, characterized in that, Using the coordinate set of each element in the receiving array as the decision vector, and the decision vector as the individual, a genetic optimization algorithm is used for iteration. After each generation of the population is generated, the position is fine-tuned to ensure that the individuals satisfy the set feasible region constraint P. When the population iteration is completed, the broadband directional spectrum of the receiving array is calculated, and the objective function is calculated based on the broadband directional spectrum. The Pareto optimal solution set of the optimization objective minF(p) is obtained as the final decision set. The objective functions include F1(p) and F2(p), and the optimization objective minF(p) is a vector composed of F1(p) and F2(p); p represents an individual. F1(p) takes into account both the main lobe width of the decision vector and the high-frequency beam consistency, aiming to optimize the angular resolution of the receiving array and ensure the consistency of the broadband response; F2(p) comprehensively considers the peak sidelobe ratio, aperture utilization, and direction finding error of the decision vector, aiming to improve the sidelobe suppression capability, aperture utilization, and compatibility with the direction finding algorithm of the receiving array. Where HPBW(p) is the main lobe width corresponding to p. Let p be the high-frequency beam consistency factor. As weight; W high ( p ) represents the main lobe width of the single-frequency radiation pattern of the receiving array corresponding to p at the highest frequency of the radiation source signal. W target This is a preset physical threshold; max indicates taking the maximum value. PSLR(p) is the peak-to-sidelobe ratio corresponding to p. For aperture utilization factor, Let p be the direction finding error. λ D and As weight; The feasible region constraints P of the receiving array include: minimum spacing constraint, aperture constraint and safe area constraint. The minimum spacing constraint is that the distance between any two array elements is less than or equal to the set minimum distance.

2. The imaging antenna array design method for lightning VHF radiation sources as described in claim 1, characterized in that, Aperture utilization factor The method for obtaining the aperture is as follows: First, calculate the actual aperture of the receiving array. When the actual aperture is greater than the effective aperture D... eff Then the aperture utilization factor Set to 0; the actual aperture is less than or equal to the effective aperture D. eff Then the aperture utilization factor Take the actual aperture or a set non-zero value.

3. The imaging antenna array design method for lightning VHF radiation sources as described in claim 1, characterized in that, Based on the correction matrix Constructing a broadband directional spectrum ; in, Frequency point The received signal vector on the frequency spectrum, where K is the total number of frequency points; H represents the conjugate operation. for Conjugate; For noise power, is the diagonal loading coefficient; I is the identity matrix.

4. The imaging antenna array design method for lightning VHF radiation sources as described in claim 1, characterized in that, The method for fine-tuning an individual based on the feasible region constraint P is as follows: First, for array element pairs that do not meet the minimum spacing constraint, perform a minimum amplitude translation along the connecting line until all array element pairs meet the minimum spacing constraint. Then, for array elements that do not meet the aperture constraints, they are translated along the direction from the array element to the set reference point so that all array elements meet the aperture constraints. Finally, the installation area constraints are checked by projecting the array elements that fall outside the installation area to the nearest point on the boundary of the installation area.

5. The imaging antenna array design method for a lightning VHF radiation source as described in any one of claims 1-4, characterized in that, The binary crossover operator is used for crossover operations during the population iteration process. The crossover distribution index of the g-th iteration is... and crossover probability The calculation formula is as follows: Where tr(.) denotes the trace of the matrix; S (g) For the g-th generation population The covariance matrix, Let S be the i-th individual in the g-th generation of the population, with g initially set to 0, and M being the population size; (0) The covariance matrix of the initial population; For the first g The convergence coefficient of the generation population. , , and All are given constants.

6. The imaging antenna array design method for lightning VHF radiation sources as described in claim 5, characterized in that, During population iteration, the variable length of the i-th individual for: in, and The numbers are Gaussian distributed random numbers. , , Let be the sample variance of the g-th generation population. , Both c and c are set constants.

7. A design system for an imaging antenna array oriented towards a lightning VHF radiation source, characterized in that, It includes a memory and a processor. The memory stores a computer program, and the processor is connected to the memory. The processor is used to execute the computer program to implement the imaging antenna array design method for lightning VHF radiation sources as described in any one of claims 1-6.

Images