A geological radar denoising processing method based on particle swarm optimization variational mode decomposition

Abstract

The present application relates to the technical field of signal processing, and relates to a geological radar denoising method based on particle swarm optimization variational mode decomposition, comprising the following steps: S1, obtaining geological radar original data and performing preprocessing, and sequentially extracting single-channel radar data as to-be-processed data according to the collection sequence; S2, taking the mode number and the penalty factor as a parameter combination, optimizing the parameter combination through a particle swarm optimization algorithm, and performing variational mode decomposition on the to-be-processed data based on the optimal parameter combination to obtain multiple intrinsic mode components; S3, screening effective signal components based on the effectiveness indexes of the multiple intrinsic mode components and reconstructing the denoised single-channel radar data; and S4, repeatedly performing S2 to S3 to obtain all denoised single-channel radar data, and outputting the data as a two-dimensional data body or a geological radar profile according to the collection sequence. The present application realizes the separation of effective signals and noise interference of the geological radar by using signal denoising based on particle swarm optimization variational mode decomposition.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for denoising ground-penetrating radar based on particle swarm optimization variational mode decomposition. Background Technology

[0002] Engineering defect detection is crucial because various defects inevitably appear during construction and after operation due to environmental changes and structural deterioration. Once defects appear, to ensure smooth project progress and safe operation, it is necessary to accurately detect their location, type, scale, and morphology using various technical means. This allows for the design of targeted treatment plans based on the specific characteristics of the defects. Currently, commonly used engineering defect detection methods include ground-penetrating radar (GPR), subgrade coefficient detection, acoustic wave detection, high-density electrical resistivity tomography (EDT), and borehole imaging. Among these, GPR is widely used in engineering defect detection due to its convenient construction, high detection accuracy, large depth, non-destructive testing, and environmental friendliness. GPR is a geophysical method that uses an antenna to transmit and receive high-frequency electromagnetic waves to detect the internal material properties and distribution patterns of a medium. Its basic principle is to transmit high-frequency electromagnetic waves underground using a transmitting antenna. These waves encounter different medium interfaces, such as rocks, soil, karst, and caverns. When encountering geological interfaces with different electrical properties, the electromagnetic waves are reflected, and some of the reflected waves return to the surface and are received by the receiving antenna. By analyzing parameters such as the time difference, amplitude, and waveform of reflected waves, the structure and properties of the underground medium can be inferred. However, reflected wave information not only contains effective interface information but also a large amount of noise information, requiring specialized noise reduction processing to highlight the effective interface information.

[0003] Current ground-penetrating radar (GPR) defect detection data processing includes drift removal, static correction, background removal, signal denoising, and gain adjustment, with signal denoising being a crucial step. Signal denoising aims to eliminate noise components from the original signal, highlighting the intensity and proportion of effective signal components, similar to highlighting human voices in conversation noise reduction. Ultimately, this aims to emphasize abnormal defect signals and improve detection accuracy and precision. Currently, GPR signal denoising primarily utilizes bandpass filtering and Wiener filtering. Wiener filtering is a linear filter based on statistical filtering methods, suitable for restoring images contaminated by Gaussian noise. It recovers the original signal based on prior statistical information (such as autocorrelation function and power spectrum). The design goal of the Wiener filter is to minimize the mean square error, requiring the observed signal to be generally random stationary and its statistical characteristics to be known. Therefore, it cannot be applied to situations where the noise is a non-stationary random process.

[0004] There are two problems with existing ground-penetrating radar signal denoising technology: (1) Adaptability problem: During the ground-penetrating radar detection process, the types of defects, geological conditions, and interference types are different. It is difficult to fully grasp the underground spatial structure, medium distribution characteristics, interference information characteristics and interference degree before detection, and it is impossible to clearly know the statistical characteristics of radar signals. Due to the inhomogeneity of the medium, the detection signal is not a stationary signal. Based on the characteristics of Wiener filtering, it is difficult to achieve good denoising of ground-penetrating radar signals. Bandpass filtering simply removes signal information directly based on frequency information, which not only fails to remove broadband noise residue well, but also causes a large loss of effective abnormal information; (2) Optimal parameter setting problem, that is, the parameter setting relies too much on subjective experience and is often not the optimal solution. In the process of ground-penetrating radar signal denoising, the setting of technical parameters is crucial. In conventional signal denoising algorithms, the setting of processing parameters relies too much on human subjective experience. Different people may have different understandings of the same radar data, different people may have different processing experiences, and different environmental data characteristics are different. Relying on subjective experience to set filter parameters and adjust the denoising effect often makes it difficult to achieve the optimal denoising effect. There is a need to find an intelligent optimization algorithm that can comprehensively and quickly search for and determine the optimal processing parameter settings, in order to achieve the best setting of processing parameters and obtain the best denoising effect under the current level. Summary of the Invention

[0005] In view of this, the present invention proposes a ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition, in order to solve the problems of unclear radar signal statistical characteristics and overly subjective signal denoising processing parameter settings in existing ground-penetrating radar signal denoising technologies.

[0006] The technical solution of this invention is implemented as follows: This invention provides a ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition, comprising the following steps:

[0007] S1. Acquire raw data from the ground-penetrating radar and preprocess it. Extract single-channel radar data in sequence according to the acquisition order as data to be processed.

[0008] S2. Using the number of modes and the penalty factor as a parameter combination, the particle swarm optimization algorithm is used to optimize the parameter combination, and variational mode decomposition is performed on the data to be processed based on the optimal parameter combination to obtain multiple intrinsic mode components.

[0009] S3. Based on the effectiveness index of multiple intrinsic mode components, effective signal components are screened and the denoised single-channel radar data is reconstructed. The effectiveness index is calculated by comprehensively considering the temporal correlation, spectral distribution characteristics and time decay characteristics of the components.

[0010] S4. Repeat steps S2 to S3 to obtain all denoised single-channel radar data. Output all denoised single-channel data as two-dimensional data volumes or ground-penetrating radar profiles in the order of acquisition.

[0011] Based on the above technical solutions, preferably, the preprocessing in step S1 includes: storing the original data as structured data, performing zero-point correction on the structured data according to the data jump position, and obtaining the preprocessed radar data.

[0012] Based on the above technical solutions, preferably, in step S2, optimizing the parameter combination using the particle swarm optimization algorithm specifically includes:

[0013] S21. Set the particle swarm algorithm parameters and initialize the position and velocity of each particle in the particle swarm. The particle position represents the parameter combination consisting of the mode number and the penalty factor, and the velocity represents the parameter search direction.

[0014] S22. Substitute the parameter combination of each particle into the variational mode decomposition algorithm to decompose the single-channel radar data, and calculate the fitness evaluation parameters based on the decomposition results as the fitness value of the particle.

[0015] S23. Update the individual optimal position of each particle and the global optimal position of the particle swarm based on the fitness value;

[0016] S24. Update the particle's velocity and position based on the particle's current velocity, individual optimal position, and global optimal position;

[0017] S25. Repeat steps S22-S24 until the termination condition is met; output the globally optimal parameter combination as the optimal parameters for variational mode decomposition.

[0018] Based on the above technical solutions, preferably, the particle swarm optimization algorithm parameters include population size, number of modes, and penalty factor, with the number of modes ranging from [2, 20] and the penalty factor ranging from [500, 2000].

[0019] Based on the above technical solutions, preferably, the calculation expression for the fitness evaluation parameter is as follows:

[0020]

[0021] K is the number of modes, N is the number of spectral points of the nth component, and P is the number of modes. n (f i ) represents the power spectral density at the i-th frequency point of the n-th component, and m is the median value of the power spectral density of that component.

[0022] Based on the above technical solutions, preferably, in step S25, the termination condition is reaching the maximum number of iterations or the ratio of the maximum fitness to the minimum fitness in the last 4 iterations is less than 1.05.

[0023] Based on the above technical solutions, preferably, the calculation expression for the effectiveness index is as follows:

[0024]

[0025] x i y i Let i be the values ​​of the decomposed components and the original signal at time i, respectively. B is the mean of the decomposed component and the original signal, and is a weighting factor between 0 and 1 used to control the weight decay rate of the signal as time increases. P(f) is the power spectral density function of the decomposed component, a is the number of signal sampling points, b is the number of spectral points of the decomposed component, and j is the time lag.

[0026] Based on the above technical solutions, preferably, step S3, which involves filtering effective signal components based on the effectiveness index of each intrinsic mode component and reconstructing the denoised single-channel radar data, specifically includes:

[0027] S31. Set the effectiveness index threshold according to the overall signal condition;

[0028] S32. Compare the effectiveness index of each intrinsic mode component with the threshold. Intrinsic mode components with an effectiveness index greater than or equal to the threshold are determined as effective signal components.

[0029] S33. Superimpose and reconstruct all effective signal components to obtain denoised single-channel radar data.

[0030] Based on the above technical solutions, preferably, the formula for calculating the superposition and reconstruction of the effective signal components is: S n =IMF1 + IMF2 + ... + IMF x S n For the reconstructed single-channel radar data, the IMF x For effective intrinsic mode components.

[0031] Based on the above technical solutions, preferably, the fixed point distance between adjacent single-channel radar data in step S1 is no greater than 0.5m.

[0032] The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition of the present invention has the following advantages over the prior art:

[0033] (1) In the process of denoising ground-penetrating radar signals, the filter needs to have clear statistical characteristics of the radar signal and has poor adaptability to non-stationary random signals. This invention introduces variational mode decomposition technology, which can adaptively match the optimal center frequency and limited bandwidth of each mode in the ground-penetrating radar signal. It can also achieve effective separation of intrinsic mode components, frequency domain division of the signal, and thus obtain the effective decomposition components of the original signal, and finally obtain the optimal solution of the variational problem.

[0034] (2) To address the problem of excessive subjectivity in parameter setting, this invention utilizes the particle swarm optimization algorithm to search for the optimal parameter combination of variational mode decomposition. The particle swarm optimization algorithm is a classic swarm intelligence algorithm. It uses the variational mode decomposition parameter combination as the particle position and the fitness evaluation parameter as the evaluation standard to continuously optimize the particle swarm evolution process, thereby obtaining the optimal parameter combination and greatly reducing the subjectivity of parameter setting.

[0035] (3) This invention proposes a fitness evaluation parameter E and gives its calculation method. The calculation formula uses the absolute mean error for standardization, which makes the formula more robust to outliers in the data and more accurately reflects the true distribution of the data and the accuracy of the prediction. Through standardization, data of different scales or magnitudes can be compared and evaluated under the same standard, which enhances the universality and adaptability of the formula.

[0036] (4) This invention proposes an effectiveness index C and its calculation formula. The formula comprehensively considers time delay, mean difference of the sequence, weighting and frequency characteristics (through power spectrum integral term). Compared with the simple correlation coefficient calculation method, it can more comprehensively and meticulously reflect the relationship between sequences. It has obvious advantages in processing complex real data, such as non-stationary time series and signals with specific frequency components. The introduction of weighting factors allows the formula to be flexibly adjusted according to different application scenarios and data characteristics to better adapt to various complex analysis needs. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. 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.

[0038] Figure 1 The flowchart shows the denoising method for ground-penetrating radar based on particle swarm optimization variational mode decomposition according to the present invention.

[0039] Figure 2This is a simulation diagram of the GprMax model according to an embodiment of the present invention;

[0040] Figure 3 This is a simulated radar signal diagram of an embodiment of the present invention;

[0041] Figure 4 This is a schematic diagram of the optimal variational mode decomposition components in an embodiment of the present invention;

[0042] Figure 5 This is a decomposed component spectrum diagram of an embodiment of the present invention;

[0043] Figure 6 This is a comparison diagram of noise reduction before and after an embodiment of the present invention;

[0044] Figure 7 The diagram shows the effect of noise reduction processing on different noise levels in an embodiment of the present invention. Detailed Implementation

[0045] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the 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.

[0046] like Figure 1 As shown, this invention provides a ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition, comprising the following steps:

[0047] S1. Acquire raw data from the ground-penetrating radar and preprocess it. Extract single-channel radar data in sequence according to the acquisition order as data to be processed.

[0048] S2. Using the mode number K and penalty factor α as a parameter combination, the parameter combination is optimized by the particle swarm optimization algorithm, and variational mode decomposition is performed on the data to be processed based on the optimal parameter combination to obtain multiple intrinsic mode components.

[0049] S3. Based on the effectiveness index of multiple intrinsic mode components, effective signal components are screened and the denoised single-channel radar data is reconstructed. The effectiveness index is calculated by comprehensively considering the temporal correlation, spectral distribution characteristics and time decay characteristics of the components.

[0050] S4. Repeat steps S2 to S3 to obtain all denoised single-channel radar data. Output all denoised single-channel data as two-dimensional data volumes or ground-penetrating radar profiles in the order of acquisition.

[0051] This invention adaptively determines the optimal parameter combination for variational mode decomposition using a particle swarm optimization algorithm, solving the problems of subjective parameter setting and unstable denoising effects caused by reliance on human experience in traditional methods. It combines an effectiveness index to accurately screen decomposed components (considering temporal correlation, spectral distribution, and time decay characteristics), effectively distinguishing non-stationary noise from valid signals and improving the signal-to-noise ratio under complex geological conditions. Employing a channel-by-channel processing-overall reconstruction process balances algorithm efficiency with signal detail preservation, significantly improving the detection accuracy and reliability of ground-penetrating radar in engineering defect detection (such as karst and soil cave identification).

[0052] Furthermore, step S1 specifically includes the following steps:

[0053] S11. Data Import and Storage: Read the raw detection data from the ground-penetrating radar equipment, including the number of radar channels (N), sampling rate (M), time-domain waveform values ​​of each channel signal, and observation parameters (such as antenna frequency and sampling interval). Store the data in a two-dimensional data matrix data[n,m] according to the acquisition order, where rows (n) represent the channel order (n = 1, 2, ..., N), and columns (m) represent the sampling point number of each channel signal (m = 1, 2, ..., M). This structure facilitates the extraction and processing of single-channel radar data channel by channel.

[0054] The horizontal spacing (i.e., fixed point distance) between adjacent single-channel radar data is set according to the field detection requirements, usually not exceeding 0.5m, in order to ensure the uniformity of data distribution in space and avoid the loss of effective signals or the reduction of resolution due to excessive spacing.

[0055] S12. Preprocess the raw data of the ground-penetrating radar: Determine the zero point of the time axis by detecting the starting point of the initial reflected wave of the radar signal (i.e., the starting time point when the electromagnetic wave is first received after it is emitted); perform time shift correction on the data of all channels according to the starting position to eliminate the time offset caused by equipment start-up delay or environmental interference, and ensure that the signals of each channel are strictly aligned in the time dimension.

[0056] During the data preprocessing stage, only the starting position of the radar signal is identified, and zero-point correction is performed on the ground radar data. No gain adjustment or filtering operation is performed to prevent artificially introduced signal distortion or noise amplification.

[0057] S13, Single-channel data extraction: Extract the nth radar data channel S sequentially according to the acquisition order. n As data to be processed,

[0058] Furthermore, the specific implementation steps of step S2 include:

[0059] S21. Set the particle swarm optimization (PSO) algorithm parameters, including population size, maximum number of iterations, number of modes, and penalty factor. The number of modes ranges from [2, 20] to avoid over-decomposition (generating false modes) or under-decomposition (missing effective features). The penalty factor ranges from [500, 2000] to control the bandwidth of intrinsic mode components. A penalty factor that is too small will lead to mode aliasing, while a penalty factor that is too large will lead to the loss of local information.

[0060] The position and velocity of each particle in the particle swarm are initialized, where the "position" of each particle is represented by a two-dimensional vector, where the first component represents the mode number K, the second component represents the penalty factor α, and the velocity represents the parameter search direction. The initial position and velocity are randomly generated within a defined range. In one embodiment, more preferably, the population size is set to 20, and the maximum number of iterations is set to 20.

[0061] S22. Substitute the parameter combination of each particle into the variational mode decomposition algorithm to decompose the data to be processed, obtain several intrinsic mode components, and calculate the fitness evaluation parameters based on the decomposition results as the fitness value of the particle.

[0062] One of the following can be chosen as the fitness evaluation criterion for parameter optimization: approximate entropy, fuzzy entropy, envelope entropy, or envelope spectrum peak factor. Here, fitness evaluation parameter E is proposed as the fitness evaluation criterion, and the calculation expression for the fitness evaluation parameter is as follows:

[0063]

[0064] K is the number of modes, N is the number of spectral points of the nth component, and P is the number of modes. n (f i Let be the power spectral density at the i-th frequency point of the n-th component, and m be the median of the power spectral density of that component. The above fitness evaluation parameter expression uses absolute error for standardization, making the expression more robust to outliers in the data and more accurately reflecting the true distribution of the data and the accuracy of predictions. The median of the power spectral density is used as the criterion for judging data discrepancy.

[0065] In this invention, the fitness of each particle is calculated to reflect the quality of the parameter combination on the decomposition effect. The fitness evaluation parameter E can effectively eliminate the influence of outliers, and the comparability of different data scales is ensured through standardization.

[0066] S23. Update the individual optimal position of each particle and the global optimal position of the particle swarm based on the fitness value.

[0067] In each iteration, based on the calculated fitness value, each particle is evaluated: if the current particle's fitness is higher than its historical record, the particle's individual optimal position is updated; simultaneously, the particle with the best fitness is selected from all particles, and its position is taken as the global optimal position. This update process ensures that the entire particle swarm continuously evolves in the direction of reducing the E value and improving the decomposition effect.

[0068] S24. Update the particle's velocity and position based on its current velocity, individual optimal position, and global optimal position. Using the standard PSO velocity update formula, update the velocity of each particle based on its current velocity, individual optimal position, and global optimal position, and then use the updated velocity to correct its position. Through this process, the particles search for better solutions in the parameter space, and each particle gradually moves closer to the globally optimal parameter region.

[0069] S25. Repeat steps S22-S24 until the termination condition is met; output the globally optimal parameter combination as the optimal parameters for variational mode decomposition.

[0070] The iteration termination condition is set as follows:

[0071] The system is considered to have converged when either the preset maximum number of iterations is reached, or the ratio of the global best fitness to the worst fitness in the last four consecutive iterations is less than 1.05. At this point, the globally optimal parameter combination, i.e., the optimal number of modes K and the penalty factor α, is output. This combination will be used subsequently for the final variational mode decomposition of the single-channel radar data.

[0072] The fitness of each particle is calculated based on its position information (x, y). The particle positions are iteratively updated until the maximum number of iterations or a local fitness ratio threshold is reached, yielding the optimal parameter combination. Reaching the local fitness ratio threshold indicates that the iteration's improvement on fitness has stabilized, reaching a local optimum. Setting a maximum number of iterations and a local fitness ratio threshold effectively reduces unnecessary iterations and computational steps. Through these steps, key parameters in the variational mode decomposition process can be automatically searched and optimized, significantly reducing uncertainties caused by subjective parameter settings. Using a particle swarm optimization algorithm for global parameter search ensures that each intrinsic mode component in the variational mode decomposition process better matches the true characteristics of the signal, thereby achieving accurate separation of effective signal and noise in ground-penetrating radar signals. In particular, the introduced fitness evaluation parameter E, which comprehensively considers the power spectrum characteristics of the decomposed intrinsic mode components in a standardized manner, ensures robustness against outliers and promotes efficient convergence of the entire algorithm, providing solid parameter support for subsequent signal reconstruction. This implementation method not only reduces manual intervention in parameter setting, but also improves the adaptability and denoising effect of non-stationary random signal processing, which is a key technical step to ensure high-quality reconstruction of ground-penetrating radar signals.

[0073] Under normal circumstances, radar signal variations caused by changes in the shallow propagation medium are much stronger than environmental random noise. Without gain adjustment, the original signal is strongly correlated with the theoretical signal, approximating a noise-free theoretical signal. The correlation with the original signal is an important basis for evaluating the effectiveness of mode decomposition components. Meanwhile, signal fluctuations caused by geological structures and defects are generally low-frequency signals, so the frequency distribution of component signals is also a key indicator for evaluating signal effectiveness. Radar signals exhibit low attenuation and high signal-to-noise ratio in the initial stage, resulting in high reliability. However, as travel time increases, the effective signal attenuates significantly, reducing reliability. Therefore, effectiveness should gradually decrease over time. Considering correlation, spectral characteristics, and time attenuation, an effectiveness index is proposed to evaluate the effectiveness of component signals.

[0074] Furthermore, in this invention, after obtaining multiple intrinsic mode components from variational mode decomposition of a single-channel ground-penetrating radar signal in step S2, step S3 evaluates each intrinsic mode component using a predefined effectiveness index. This effectiveness index comprehensively considers the correlation between the intrinsic mode component and the original signal in the time domain, the component's spectral distribution, and its attenuation characteristics over time. The formula for calculating the effectiveness index is:

[0075]

[0076] x i y i Let i be the values ​​of the decomposed components and the original signal at time i, respectively. B is the mean of the decomposed component and the original signal. B is a weighting factor between 0 and 1, used to control the weight decay rate of the signal as time increases. P(f) is the power spectral density function of the decomposed component. a is the number of signal sampling points. b is the number of spectral points of the decomposed component, which is generally taken as 500 according to the characteristics of radar data. j is the time lag.

[0077] Step S3 specifically includes the following steps:

[0078] S31. Set an effectiveness index threshold based on the overall signal characteristics. Based on the overall characteristics of the radar signal and experimental statistical results, firstly, based on the signal's noise level and expected characteristics, set an effectiveness index threshold T. This threshold can be determined experimentally or obtained through historical data analysis. Its purpose is to distinguish between truly effective signal components and components containing high noise interference. Preferably, the maximum effectiveness index value of each component is set as the effectiveness index threshold.

[0079] S32. Compare the validity index of each intrinsic mode component with a threshold. Intrinsic mode components with a validity index greater than or equal to the threshold are determined as valid signal components. For each intrinsic mode component obtained in step S2, calculate the validity index C according to the formula for calculating the validity index. Compare the calculated C value of each intrinsic mode component with the set threshold T. When the validity index C of an intrinsic mode component is greater than or equal to the threshold T, the component is determined as a valid signal component; otherwise, the component is judged as a noise component or an irrelevant component and will be removed in subsequent processing.

[0080] S33. All effective signal components are superimposed and reconstructed to obtain the denoised single-channel radar data. The formula for calculating the superposition and reconstruction of effective signal components is: S n =IMF1 + IMF2 + ... + IMF x S n For the reconstructed single-channel radar data, the IMF x The xth effective intrinsic mode component is selected. By superimposing the components in this way, the main information and key features of the original signal can be preserved, while noise interference can be effectively removed, thus improving the signal-to-noise ratio and data quality of the final signal.

[0081] The single-channel radar data is processed sequentially, and the processed single-channel data is output as a two-dimensional N×M data volume data[n,m] or a ground-penetrating radar profile according to the acquisition order.

[0082] By employing the above steps, the effectiveness index can be fully utilized to quantitatively evaluate each intrinsic mode component, thereby achieving intelligent differentiation between effective signal and noise components in each decomposition result. This method not only considers time-domain correlation but also integrates spectral distribution and time decay characteristics, making the entire component selection process more comprehensive and accurate. Finally, through the superposition and reconstruction of the effective components, single-channel radar data with excellent denoising effects can be obtained, ensuring that the signal still fully reflects geological information during the denoising process. This provides crucial technical support for subsequent data analysis and ground-penetrating radar imaging.

[0083] Example

[0084] Since it is impossible to obtain completely noise-free and uniformly homogeneous ground-penetrating radar signals under natural conditions, this embodiment simulates theoretically noise-free signals through simulation experiments and simulates actual acquired signals by adding random noise data.

[0085] (1) Simulation data preparation

[0086] A simulation of ground-penetrating radar defect detection was performed based on GprMax, such as... Figure 2 As shown, the thicknesses of the aquifer in the four models a, b, c, and d are 0m, 1m, 2m, and 3m, respectively, and the simulated detection target is a 1m diameter soil hole buried at a depth of 7.5m.

[0087] Simulation results are as follows Figure 3 As shown, when the aquifer thickness reaches 1m, the radar reflection signal at the wet-dry interface of the soil layer is clearly visible. The radar reflection signal intensity caused by cavities is greatly reduced, and the cavity anomaly can still be identified through exponential gain. When the aquifer thickness reaches 2m, the radar reflection signal at the wet-dry interface of the soil layer is still visible, but the radar reflection signal anomaly caused by cavities cannot be accurately identified even through exponential gain. When the aquifer thickness reaches 3m, the radar reflection signal at the wet-dry interface of the soil layer is visible, but the cavity radar reflection signal anomaly is completely undetectable. Simulation results show that with the increase of aquifer thickness, the radar reflection signal attenuates rapidly, and the effective signal is gradually buried in environmental noise.

[0088] (2) Single-channel signal decomposition and evaluation

[0089] Variational mode denoising (VMD) was performed using particle swarm optimization (PSO) based on simulation results of radar signals from model c. First, random Gaussian white noise was added to the theoretical signal of model c to simulate a noise-laden signal. This noisy signal was then input into the PSO-optimized variational mode decomposition algorithm. The optimal VMD parameters (K, α) were determined using the PSO algorithm. The population size was set to 20, the maximum number of iterations was 20, the iteration range of K was (2, 20), and the iteration range of α was (800, 2000). After four iterations, the fitness curve stabilized, indicating that the optimal VMD parameters (K, α) had been found. The optimal K value calculated by the PSO algorithm was 6, and the optimal α value was 1592.

[0090] The analog signal was decomposed using VMD based on the optimal parameters (K, α), yielding six IMF (Intrinsic Mode Function) components, such as... Figure 4 As shown, the spectral distributions of the six IMF components were calculated simultaneously, as follows: Figure 5 As shown, according to the formula for calculating the effectiveness index C, the IMF1 component has the highest effectiveness index, which is 6.47 × 10⁻⁶. -4 The component is used as the denoising result based on the maximum threshold method. By comparing the signals before and after denoising, such as... Figure 6 As shown, the denoised signal has a smooth surface and rich details, and its overall shape and oscillation amplitude are basically consistent with the original signal. Calculations show that the SNR (signal-to-noise ratio) after adding noise is 15.025 dB, while the SNR after denoising is 25.8093 dB, representing a signal quality improvement of 10.7842 dB.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for denoising ground-penetrating radar based on particle swarm optimization variational mode decomposition, characterized in that, Includes the following steps: S1. Acquire raw data from the ground-penetrating radar and preprocess it. Extract single-channel radar data in sequence according to the acquisition order as data to be processed. S2. Using the number of modes and the penalty factor as a parameter combination, the particle swarm optimization algorithm is used to optimize the parameter combination, and variational mode decomposition is performed on the data to be processed based on the optimal parameter combination to obtain multiple intrinsic mode components. S3. Based on the effectiveness index of multiple intrinsic mode components, effective signal components are screened and the denoised single-channel radar data is reconstructed. The effectiveness index is calculated by comprehensively considering the temporal correlation, spectral distribution characteristics and time decay characteristics of the components. S4. Repeat S2 to S3 to obtain all denoised single-channel radar data. Output all denoised single-channel data as two-dimensional data volumes or ground-penetrating radar profiles in the order of acquisition. The formula for calculating the effectiveness index is as follows: ; , Let i be the values ​​of the decomposed components and the original signal at time i, respectively. , These are the mean values ​​of the decomposed components and the original signal, respectively. It is a weighting factor between 0 and 1, used to control the rate at which the weights decay as the signal increases over time. Let be the power spectral density function of the decomposed component, a be the number of signal sampling points, b be the number of spectral points of the decomposed component, and j be the time lag.

2. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 1, characterized in that, The preprocessing in step S1 includes: storing the raw data as structured data, performing zero-point correction on the structured data according to the data jump position, and obtaining the preprocessed radar data.

3. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 1, characterized in that, In step S2, the optimization of parameter combinations using the particle swarm optimization algorithm specifically includes: S21. Set the particle swarm algorithm parameters and initialize the position and velocity of each particle in the particle swarm. The particle position represents the parameter combination consisting of the mode number and the penalty factor, and the velocity represents the parameter search direction. S22. Substitute the parameter combination of each particle into the variational mode decomposition algorithm to decompose the single-channel radar data, and calculate the fitness evaluation parameters based on the decomposition results as the fitness value of the particle. S23. Update the individual optimal position of each particle and the global optimal position of the particle swarm based on the fitness value; S24. Update the particle's velocity and position based on the particle's current velocity, individual optimal position, and global optimal position; S25. Repeat steps S22-S24 until the termination condition is met; output the globally optimal parameter combination as the optimal parameters for variational mode decomposition.

4. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 3, characterized in that, The particle swarm optimization (PSO) parameters include population size, number of modes, and penalty factor. The number of modes ranges from [2, 20], and the penalty factor ranges from [500, 2000].

5. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 3, characterized in that, The calculation expression for the fitness evaluation parameters is as follows: ; 6. K is the number of modes, and N is the number of spectral points of the nth component. Let m be the power spectral density at the i-th frequency point of the n-th component, and m be the median value of the power spectral density of that component.

7. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 3, characterized in that, In step S25, the termination condition is reaching the maximum number of iterations or the ratio of the maximum fitness to the minimum fitness in the last 4 iterations being less than 1.

05.

8. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 1, characterized in that, Step S3, which involves filtering effective signal components based on the effectiveness index of each intrinsic mode component and reconstructing the denoised single-channel radar data, specifically includes: S31. Set the effectiveness index threshold according to the overall signal condition; S32. Compare the effectiveness index of each intrinsic mode component with the threshold. Intrinsic mode components with an effectiveness index greater than or equal to the threshold are determined as effective signal components. S33. All effective signal components are superimposed and reconstructed to obtain the denoised single-channel radar data.

9. The ground-penetrating radar denoising method based on particle swarm optimization variational mode decomposition as described in claim 7, characterized in that, The formula for calculating the superposition and reconstruction of the effective signal components is: S n =IMF1+IMF2+...+IMF x S n For the reconstructed single-channel radar data, the IMF x For effective intrinsic mode components.

10. The method for denoising ground-penetrating radar based on particle swarm optimization variational mode decomposition as described in claim 1, characterized in that, In step S1, the fixed point distance between adjacent single-channel radar data is no greater than 0.5m.

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