A method, system, device and medium for analyzing frequency characteristics of a grounding grid under lightning impulse

Abstract

The application discloses a lightning impulse grounding grid frequency characteristic analysis method, system, device and medium, including: obtaining initial sample data; using the sample and a preset test frequency set to construct at least two different structure rational function interpolation models, and calculating the output residual thereof in the test frequency band; determining the target frequency point with the maximum modeling uncertainty according to the residual, calling the moment method to supplement high-precision response samples at the point; based on the updated sample set, constructing a diagonal or near-diagonal form rational interpolation model, and judging whether the prediction error of the model at the target frequency point is lower than a preset convergence threshold; if the convergence condition is not met, returning to the multiple model construction step, reiterating using the current sample set until the error meets the standard, and finally outputting the grounding grid frequency response characteristics covering the lightning impulse frequency band. The application realizes efficient analysis of the grounding grid frequency characteristics under lightning impulse, and effectively reduces the time used for analyzing the grounding grid frequency characteristics under lightning impulse.

Description

Technical Field

[0001] This invention relates to the field of lightning protection grounding technology, and in particular to a method, system, equipment and medium for analyzing the frequency characteristics of grounding grids under lightning impulse. Background Technology

[0002] Lightning discharge is a typical source of strong electromagnetic pulse interference, characterized by its extremely high electromagnetic power density. When lightning occurs, it generates a very strong transient electromagnetic field in the surrounding space. This induces a sudden, usually brief, surge in voltage or current in nearby electrical and electronic equipment. This phenomenon often leads to equipment malfunctions, and in severe cases, insulation breakdown or even direct damage to the equipment. To prevent or at least effectively mitigate this well-known hazard, both existing and newly deployed power distribution networks must be effectively electrically isolated from other systems and equipped with a specially designed surge protection system (LPS). Therefore, accurately assessing the actual protective performance of LPS becomes a crucial step in ensuring the safe operation of power facilities.

[0003] A typical lightning protection system (LPS) consists of an underground grounding grid. This grid provides electromagnetic shielding during lightning strikes, significantly suppressing lightning interference within the protected area. However, the suppression effect is not constant but highly dependent on the specific type of LPS used. The selection of the LPS is closely related to the topology of the power distribution system, local soil characteristics, and the intensity of the lightning strike. Although relevant standards (such as the IEC 62305 series) specify lightning protection levels and LPS classifications, the strong high-frequency resonance characteristics of LPS make its response under lightning strikes particularly complex, making system analysis, parameter tuning, and customized design extremely difficult. Therefore, there is an urgent need to establish an analytical method for the frequency characteristics of grounding grids under lightning strikes to fill the gaps in the existing analytical framework. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method, system, equipment, and medium for analyzing the frequency characteristics of grounding grids under lightning impulses, solving the problem that existing technologies make it quite difficult to analyze and customize lightning protection systems (LPS) and that calculating a large number of frequency characteristics is quite time-consuming.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for analyzing the frequency characteristics of a grounding grid under lightning impulse, comprising: Obtain initial sample data; Using the initial sample data and a preset set of test frequencies, at least two rational function interpolation models with different structures are constructed using a rational function interpolation algorithm, and the output residuals of each model are calculated within the preset test frequency range. Based on the residual, determine the target frequency point with the greatest uncertainty in the current modeling, and call the Moment Algorithm to supplement new high-precision response samples at the target frequency point; Based on the updated sample set containing the new high-precision response samples, a higher-precision diagonal and near-diagonal rational interpolation model is constructed, and it is determined whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. If the prediction error is not lower than the convergence threshold, the process returns to the step of constructing multiple interpolation models, and subsequent operations are re-executed using the currently updated sample set. This process is iterated until the convergence condition is met, and finally, the frequency response characteristics of the grounding grid covering the lightning impulse frequency band are output.

[0007] As a preferred embodiment of the method for analyzing the frequency characteristics of grounding grids under lightning impulse as described in this invention, the at least two rational function interpolation models with different structures include: When constructing the first rational function interpolation model, the order of the numerator polynomial is set to be equal to half the current number of samples, rounded down, and the order of the denominator polynomial is equal to the order of the numerator. When constructing the second rational function interpolation model, the order of the numerator polynomial is set to be equal to the order of the denominator polynomial plus one. Both the first and second rational function interpolation models use the same sample data and test frequency set for parameter fitting.

[0008] The beneficial effect of this preferred technical solution is that by constructing two rational function interpolation models whose numerator and denominator orders satisfy diagonal and near-diagonal forms respectively, and fitting them based on the same data, the prediction difference of the model in the uncertainty region can be effectively amplified, thereby accurately identifying the key frequency points that need to be supplemented with sampling.

[0009] As a preferred embodiment of the method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in this invention, the output residual includes: At each test frequency point, the complex response values ​​of the two rational function interpolation models with different structures are calculated respectively; Perform a difference operation on the two complex response values ​​and calculate the magnitude of the difference, which is used as the residual at the corresponding test frequency point; The residuals corresponding to all test frequency points are combined into a residual sequence.

[0010] As a preferred embodiment of the method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in this invention, the target frequency point includes: Iterate through all frequency points in the preset test frequency set; Compare the residual values ​​at each frequency point; The frequency point with the largest residual value is selected as the target frequency point.

[0011] As a preferred embodiment of the method for analyzing the frequency characteristics of grounding grids under lightning impulses described in this invention, the diagonal and near-diagonal rational interpolation models include: When the updated sample set contains an even number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is equal to the order of the denominator polynomial. When the updated sample set contains an odd number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is one greater than the order of the denominator polynomial. The constructed model uses all updated sample data to solve for the coefficients.

[0012] As a preferred embodiment of the method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in this invention, the prediction error includes: Obtain the complex predicted response of the newly constructed rational interpolation model at the target frequency point; Obtain a high-precision response sample calculated at the target frequency point using the Moment algorithm; The difference in magnitude between the complex predicted response and the high-precision response sample is calculated as the prediction error.

[0013] The beneficial effect of this preferred technical solution is that by calculating the modulus difference between the complex predicted response of the newly constructed rational interpolation model at the target frequency point and the high-precision response sample obtained by the moment algorithm, the local approximation accuracy of the model can be accurately quantified, providing a reliable convergence criterion for adaptive iteration.

[0014] As a preferred embodiment of the method for analyzing the frequency characteristics of grounding grids under lightning impulses described in this invention, the step of returning to construct multiple interpolation models includes: The latest high-precision response samples are added to the current sample set to form a new updated sample set. Clear the interpolation model and residual data constructed in the previous round; Based on the updated sample set, the operation of constructing at least two rational function interpolation models with different structures will be re-executed.

[0015] Secondly, the present invention provides a system for analyzing the frequency characteristics of a grounding grid under lightning impulse, comprising: The initial sample acquisition module is used to acquire initial sample data; The residual calculation module is used to construct at least two rational function interpolation models with different structures using the initial sample data and a preset set of test frequencies through a rational function interpolation algorithm, and to calculate the output residual of each model within the preset test frequency range. The uncertainty-driven sampling module is used to determine the target frequency point with the greatest uncertainty in the current modeling based on the residual, and call the moment algorithm to supplement new high-precision response samples at the target frequency point; The convergence judgment module is used to construct a higher-precision diagonal and near-diagonal rational interpolation model based on the updated sample set containing the new high-precision response sample, and to determine whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. An adaptive iterative control module is used to return to the step of constructing multiple interpolation models if the prediction error is not lower than the convergence threshold, and to re-execute subsequent operations using the currently updated sample set. This iterative process continues until the convergence condition is met, and finally outputs the frequency response characteristics of the grounding grid covering the lightning impulse frequency band.

[0016] Thirdly, the present invention provides an electronic device, comprising: Memory, used to store programs; A processor is configured to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the method for analyzing the frequency characteristics of the grounding grid under lightning impulse.

[0017] Fourthly, the present invention provides a computer-readable storage medium, comprising: when the program is executed by a processor, the steps of implementing the method for analyzing the frequency characteristics of the grounding grid under lightning impulse.

[0018] The beneficial effects of this invention are as follows: By constructing at least two rational function interpolation models with different structures and calculating their output residuals within the test frequency range, this invention achieves accurate identification of uncertain regions in modeling; by adaptively selecting target frequency points based on the principle of maximizing residuals and calling the moment algorithm to supplement high-precision response samples, it achieves efficient and targeted improvement of model accuracy in key frequency bands, avoiding high-cost simulation across the entire frequency band; by constructing diagonal or near-diagonal rational interpolation models on the updated sample set and using the difference in the modulus of the complex response as the convergence criterion for iterative control, it achieves high-fidelity, wide-band reconstruction of the grounding grid frequency response, significantly improving the computational efficiency and engineering practicality of grounding system analysis under lightning impulse. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a basic flowchart illustrating a method for analyzing the frequency characteristics of a grounding grid under lightning impulse, provided as an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the recursive structure of a rational function interpolation algorithm for a method of analyzing the frequency characteristics of a grounding grid under lightning impulse, provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0022] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for analyzing the frequency characteristics of a grounding grid under lightning impulse is provided, comprising: S100: Obtain initial sample data; S200: Using the initial sample data and a preset set of test frequencies, at least two rational function interpolation models with different structures are constructed using a rational function interpolation algorithm, and the output residuals of each model are calculated within the preset test frequency range; S300: Determine the target frequency point with the greatest uncertainty in the current modeling based on the residual, and call the Moment Algorithm to supplement new high-precision response samples at the target frequency point; S400: Based on the updated sample set containing the new high-precision response samples, construct a higher-precision diagonal and near-diagonal rational interpolation model, and determine whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. S500: If the prediction error is not lower than the convergence threshold, return to the step of constructing multiple interpolation models, re-execute subsequent operations using the currently updated sample set, and iterate in this way until the convergence condition is met, and finally output the grounding grid frequency response characteristics covering the lightning impulse frequency band.

[0023] It should be noted that existing technologies face a series of challenges in analyzing the frequency characteristics of grounding grids under lightning impulses. These include: traditional full-band frequency sweep methods relying heavily on electromagnetic numerical algorithms (such as the method of moments), resulting in extremely high computational costs and difficulty in meeting the timeliness requirements of engineering projects; secondly, grounding grids exhibit strong resonance and nonlinear characteristics under high-frequency lightning excitation, making it difficult for conventional polynomial interpolation or low-order fitting models to accurately characterize their complex frequency response, easily leading to insufficient accuracy; existing modeling methods often employ uniform or empirical sampling strategies, failing to identify key frequency bands with drastic response changes, resulting in sample redundancy or missing information; furthermore, the lack of effective adaptive mechanisms makes it difficult to achieve a dynamic balance between computational resources and approximation accuracy, leading to either overcomputation or unreliable convergence. These problems collectively restrict the efficient and high-precision simulation application of grounding systems in lightning transient analysis.

[0024] Therefore, in response to the aforementioned problems of the difficulty in analyzing and customizing existing lightning protection systems (LPS) and the time-consuming calculation of a large number of frequency characteristics, the steps of S100-S500 introduce an adaptive rational function interpolation algorithm based on dual-model residual driving, which significantly reduces the number of costly electromagnetic calculations and efficiently reconstructs the broadband frequency response characteristics of the grounding grid under lightning impact while ensuring accuracy.

[0025] Example 2, refer to Figure 2 Table 1 illustrates one embodiment of the present invention, providing a method for analyzing the frequency characteristics of a grounding grid under lightning impulse based on the previous embodiment, comprising: In this embodiment of the application, the initial sample selection strategy in step S100 includes selecting two endpoint frequencies (one low and one high) within the lightning impulse frequency band in the initial stage, calling the moment algorithm to calculate the corresponding electromagnetic response, and using them as initial sample data to start the adaptive modeling process.

[0026] In an optional implementation, the initial sample selection strategy in step S100 can also uniformly select multiple (e.g., 3 to 5) frequency points within the main frequency band of lightning impact, call the moment algorithm to obtain the corresponding high-precision response as initial sample data, so as to start the subsequent adaptive modeling process.

[0027] In an optional implementation, the initial sample selection strategy in step S100 can also estimate the main resonant frequency of the grounding grid based on its geometric dimensions, and call the moment algorithm at that frequency and its adjacent high and low frequency points to obtain a high-precision response as initial sample data to start the adaptive modeling process.

[0028] It should be noted that the rational function interpolation algorithm in this invention refers to a type of numerical method that approximates discrete frequency domain samples using rational functions (i.e., rational functions where both the numerator and denominator are polynomials); its output is a specific "rational function interpolation model".

[0029] In this embodiment of the application, step S200 includes at least two rational function interpolation models with different structures, including: When constructing the first rational function interpolation model, the order of the numerator polynomial is set to be equal to half the current number of samples, rounded down, and the order of the denominator polynomial is equal to the order of the numerator. When constructing the second rational function interpolation model, the order of the numerator polynomial is set to be equal to the order of the denominator polynomial plus one. Both the first and second rational function interpolation models use the same sample data and test frequency set for parameter fitting.

[0030] It should be noted that the rational function interpolation algorithm used in this invention approximates the frequency response of the grounding grid by constructing at least two rational function interpolation models with different structures.

[0031] In this embodiment, the rational function interpolation model is based on the LPS frequency response. The rational approximation form is constructed, where: in, Indicates the frequency response of LPS. and These are the L-order numerator polynomial and the M-order denominator polynomial, respectively. and For undetermined coefficients, For frequency.

[0032] In this embodiment of the application, for the first rational function interpolation model ( When the total order L+M is odd, we take L=M+3; when L+M is even, we take L=M+2. For the second rational function interpolation model ( When L+M is odd, take L=M+4; when L+M is even, take L=M+3.

[0033] In this embodiment of the application, the output of the residual in step S200 includes: At each test frequency point, the complex response values ​​of the two rational function interpolation models with different structures are calculated respectively; Perform a difference operation on the two complex response values ​​and calculate the magnitude of the difference, which is used as the residual at the corresponding test frequency point; The residuals corresponding to all test frequency points are combined into a residual sequence.

[0034] In this embodiment of the application, the uncertainty assessment method in step S200 involves constructing two rational function interpolation models with different structures, calculating the normalized residuals of their complex responses on a preset set of test frequencies, and selecting the frequency point corresponding to the largest residual as the target frequency point with the greatest modeling uncertainty.

[0035] In an optional implementation, the uncertainty assessment method in step S200 can also construct a rational function interpolation model based on the current sample in each iteration, use leave-one-out cross-validation to calculate the prediction error at each test frequency point, and select the frequency point corresponding to the maximum error as the target frequency point to supplement the high-precision sample.

[0036] In an optional implementation, the uncertainty assessment method in step S200 can also construct a Gaussian process regression model based on the current high-precision sample in each iteration, use the predicted variance of its output to quantify the modeling uncertainty of each test frequency point, and select the frequency point corresponding to the largest variance as the target frequency point to call the moment algorithm to supplement new samples.

[0037] In this embodiment of the application, the residuals are calculated in a normalized form, specifically as follows: in, , For the first Each test frequency, and These are the complex response values ​​of the two interpolation models at this frequency point. For normalized residuals.

[0038] In this embodiment of the application, the target frequency point in step S300 includes: Iterate through all frequency points in the preset test frequency set; Compare the residual values ​​at each frequency point; The frequency point with the largest residual value is selected as the target frequency point.

[0039] In this embodiment of the application, the diagonal and near-diagonal rational interpolation models in step S400 include: When the updated sample set contains an even number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is equal to the order of the denominator polynomial. When the updated sample set contains an odd number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is one greater than the order of the denominator polynomial. The constructed model uses all updated sample data to solve for the coefficients.

[0040] In this embodiment of the application, the construction method of the interpolation model structural difference in step S400 is to construct the first and second rational function interpolation models along the horizontal expansion path (fixed denominator order, increasing numerator order) and the vertical expansion path (fixed numerator order, increasing denominator order), respectively, and set the specific order relationship between the numerator and denominator polynomials according to the parity of the current total number of samples, thereby forming the structural difference.

[0041] In an optional implementation, the construction method of the interpolation model structure difference in step S400 can also be to construct two rational function interpolation models along the same diagonal or zigzag path in each iteration, respectively using asymmetric order combinations such as [L / M] and [L+1 / M−1], and generate model divergence by different allocation of numerator and denominator orders while keeping the total order consistent.

[0042] In an optional implementation, the construction method of the interpolation model structure difference in step S400 can also be to use standard Padé-type rational functions and continued fraction expansions (or Chebyshev rational approximations) as the basis function forms of the two interpolation models in each iteration, so that the output difference is generated due to the different function spaces under the same sample set, which is used to drive uncertainty assessment.

[0043] In the embodiments of this application, the newly constructed rational interpolation model ( The order of L+M satisfies the following: when the total order L+M corresponding to the total number of samples is even, take L=M (diagonal form); when L+M is odd, take L=M+1 (near diagonal form).

[0044] In this embodiment of the application, the prediction error in step S400 includes: Obtain the complex predicted response of the newly constructed rational interpolation model at the target frequency point; Obtain a high-precision response sample calculated at the target frequency point using the Moment algorithm; The difference in magnitude between the complex predicted response and the high-precision response sample is calculated as the prediction error.

[0045] In this embodiment of the application, the convergence criterion in step S400 is defined by calculating the relative error between the complex predicted response of the newly constructed rational interpolation model at the target frequency point and the high-precision response sample obtained by the method of moments in each iteration, and determining whether the relative error is less than a preset convergence threshold in order to decide whether to terminate the adaptive iteration process.

[0046] In an optional implementation, the convergence criterion in step S400 can also be defined by constructing a new rational interpolation model based on the updated sample set in each iteration, and calculating the L² norm difference between the model output of the previous round and the model output at all preset test frequency points. If the global difference is less than a preset threshold, the iteration is terminated.

[0047] In an optional implementation, the convergence criterion in step S400 can also be defined by determining whether the current iteration number has reached a preset maximum value or whether the total number of samples has exceeded the allowed upper limit after each new sample is added. If either condition is met, the adaptive iteration process is forcibly terminated.

[0048] In this embodiment of the application, the prediction error is used to determine convergence in the form of relative error, specifically as follows: in, Method of Moments at the target frequency point High-precision response samples obtained at the location. The new interpolation model predicts the value at this point. This is a preset convergence threshold. If the inequality is satisfied, the iteration terminates; otherwise, the loop continues.

[0049] In this embodiment of the application, step S500, which involves constructing multiple interpolation models, includes: The latest high-precision response samples are added to the current sample set to form a new updated sample set. Clear the interpolation model and residual data constructed in the previous round; Based on the updated sample set, the operation of constructing at least two rational function interpolation models with different structures will be re-executed.

[0050] In this embodiment, the rational function interpolation model is generated using a recursive algorithm, with the initial condition being... , ( Subsequent items are calculated according to the following rules: For the new interpolation model ( Using a zigzag path (e.g., [0 / 0]→[0 / 1]→[1 / 1]→[1 / 2]→[2 / 2] …), the formula is: For the first interpolation model ( The first three columns are interpolated using a polynomial formula along the horizontal path ([0 / 0] → [1 / 0] → [2 / 0] → [3 / 0]): Subsequent columns are converted to the above zigzag formula; For the second interpolation model ( The first three columns are interpolated using the inverse polynomial interpolation formula along the vertical path ([0 / 0]→[0 / 1]→[0 / 2]→[0 / 3]): Subsequent columns are also converted to zigzag formulas.

[0051] The aforementioned recursive mechanism ensures that different structural models are constructed efficiently within a unified framework, while also reflecting their path differences.

[0052] In the embodiments of this application, the rational function interpolation algorithm used in this invention is based on a Thiele-type recursive structure (see Table 1), and its basic form is as follows: Figure 2 As shown. The innovation of this invention lies in using different paths (horizontal, vertical, and diagonal) of the table to construct two interpolation models with different structures, and using the output residuals of the two models to drive adaptive sampling, thereby achieving efficient modeling of the grounding grid frequency response.

[0053] Table 1 Thiele-type interpolation table

[0054] Example 3 is an embodiment of the present invention. This embodiment differs from the first embodiment in that it provides a system for analyzing the frequency characteristics of a grounding grid under lightning impulse.

[0055] It should be noted that the technical solution of the grounding grid frequency characteristic analysis system under lightning impulse is based on the same concept as the technical solution of the grounding grid frequency characteristic analysis method under lightning impulse described above. For details not described in detail in the technical solution of the grounding grid frequency characteristic analysis system under lightning impulse in this embodiment, please refer to the description of the technical solution of the grounding grid frequency characteristic analysis method under lightning impulse described above.

[0056] This embodiment provides a system for analyzing the frequency characteristics of a grounding grid under lightning impulse, comprising: The initial sample acquisition module is used to acquire initial sample data; The residual calculation module is used to construct at least two rational function interpolation models with different structures using the initial sample data and a preset set of test frequencies through a rational function interpolation algorithm, and to calculate the output residual of each model within the preset test frequency range. The uncertainty-driven sampling module is used to determine the target frequency point with the greatest uncertainty in the current modeling based on the residual, and call the moment algorithm to supplement new high-precision response samples at the target frequency point; The convergence judgment module is used to construct a higher-precision diagonal and near-diagonal rational interpolation model based on the updated sample set containing the new high-precision response sample, and to determine whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. An adaptive iterative control module is used to return to the step of constructing multiple interpolation models if the prediction error is not lower than the convergence threshold, and to re-execute subsequent operations using the currently updated sample set. This iterative process continues until the convergence condition is met, and finally outputs the frequency response characteristics of the grounding grid covering the lightning impulse frequency band.

[0057] This embodiment also provides an electronic device applicable to a method for analyzing the frequency characteristics of a grounding grid under lightning impulse, including: The system includes a memory and a processor. The memory stores computer-executable instructions, and the processor executes these instructions to implement a method for analyzing the frequency characteristics of a grounding grid under lightning impulse, as proposed in the above embodiments.

[0058] This embodiment also provides a storage medium storing a computer program, which, when executed by a processor, implements a method for analyzing the frequency characteristics of a grounding grid under lightning impulse as proposed in the above embodiments.

[0059] The storage medium proposed in this embodiment belongs to the same inventive concept as the method for analyzing the frequency characteristics of a grounding grid under lightning impact proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0060] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0061] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for analyzing the frequency characteristics of a grounding grid under lightning impulse, characterized in that, include: Obtain initial sample data; Using the initial sample data and a preset set of test frequencies, at least two rational function interpolation models with different structures are constructed using a rational function interpolation algorithm, and the output residuals of each model are calculated within the preset test frequency range. Based on the residual, determine the target frequency point with the greatest uncertainty in the current modeling, and call the Moment Algorithm to supplement new high-precision response samples at the target frequency point; Based on the updated sample set containing the new high-precision response samples, a higher-precision diagonal and near-diagonal rational interpolation model is constructed, and it is determined whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. If the prediction error is not lower than the convergence threshold, the process returns to the step of constructing multiple interpolation models, and subsequent operations are re-executed using the currently updated sample set. This process is iterated until the convergence condition is met, and finally, the frequency response characteristics of the grounding grid covering the lightning impulse frequency band are output.

2. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 1, characterized in that: The at least two rational function interpolation models with different structures include: When constructing the first rational function interpolation model, the order of the numerator polynomial is set to be equal to half the current number of samples, rounded down, and the order of the denominator polynomial is equal to the order of the numerator. When constructing the second rational function interpolation model, the order of the numerator polynomial is set to be equal to the order of the denominator polynomial plus one. Both the first and second rational function interpolation models use the same sample data and test frequency set for parameter fitting.

3. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 1 or 2, characterized in that: The output residual includes: At each test frequency point, the complex response values ​​of the two rational function interpolation models with different structures are calculated respectively; Perform a difference operation on the two complex response values ​​and calculate the magnitude of the difference, which is used as the residual at the corresponding test frequency point; The residuals corresponding to all test frequency points are combined into a residual sequence.

4. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 3, characterized in that: The target frequency point includes: Iterate through all frequency points in the preset test frequency set; Compare the residual values ​​at each frequency point; The frequency point with the largest residual value is selected as the target frequency point.

5. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 4, characterized in that: The diagonal and near-diagonal rational interpolation models include: When the updated sample set contains an even number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is equal to the order of the denominator polynomial. When the updated sample set contains an odd number of samples, construct a rational function interpolation model in which the order of the numerator polynomial is one greater than the order of the denominator polynomial. The constructed model uses all updated sample data to solve for the coefficients.

6. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 5, characterized in that: The prediction error includes: Obtain the complex predicted response of the newly constructed rational interpolation model at the target frequency point; Obtain a high-precision response sample calculated at the target frequency point using the Moment algorithm; The difference in magnitude between the complex predicted response and the high-precision response sample is calculated as the prediction error.

7. The method for analyzing the frequency characteristics of a grounding grid under lightning impulse as described in claim 6, characterized in that: The steps for returning to construct multiple interpolation models include: The latest high-precision response samples are added to the current sample set to form a new updated sample set. Clear the interpolation model and residual data constructed in the previous round; Based on the updated sample set, the operation of constructing at least two rational function interpolation models with different structures will be re-executed.

8. A system for analyzing the frequency characteristics of a grounding grid under lightning impulse, comprising the method described in any one of claims 1-7, characterized in that, include: The initial sample acquisition module is used to acquire initial sample data; The residual calculation module is used to construct at least two rational function interpolation models with different structures using the initial sample data and a preset set of test frequencies through a rational function interpolation algorithm, and to calculate the output residual of each model within the preset test frequency range. The uncertainty-driven sampling module is used to determine the target frequency point with the greatest uncertainty in the current modeling based on the residual, and call the moment algorithm to supplement new high-precision response samples at the target frequency point; The convergence judgment module is used to construct a higher-precision diagonal and near-diagonal rational interpolation model based on the updated sample set containing the new high-precision response sample, and to determine whether the prediction error of the newly constructed rational interpolation model at the target frequency point is lower than a preset convergence threshold. An adaptive iterative control module is used to return to the step of constructing multiple interpolation models if the prediction error is not lower than the convergence threshold, and to re-execute subsequent operations using the currently updated sample set. This iterative process continues until the convergence condition is met, and finally outputs the frequency response characteristics of the grounding grid covering the lightning impulse frequency band.

9. An electronic device, characterized in that, include: Memory, used to store programs; A processor for loading the program to perform the steps of the method as claimed in any one of claims 1-7.

10. A computer-readable storage medium storing a program, characterized in that, When the program is executed by a processor, it implements the steps of the method as described in any one of claims 1-7.

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