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

Abstract

The invention relates to the technical field of signal processing, and relates to a geological radar de-noising processing method based on particle swarm optimization variational mode decomposition, which comprises the following steps: S1, acquiring and pre-processing original data of a geological radar, and sequentially extracting single-channel radar data as to-be-processed data according to an acquisition sequence; s2, taking the modal number and the penalty factor as a parameter combination, performing optimization on the parameter combination through a particle swarm optimization algorithm, and performing variational modal decomposition on the to-be-processed data based on the optimal parameter combination to obtain a plurality of intrinsic modal components; s3, screening effective signal components based on the validity indexes of the plurality of intrinsic mode components, and reconstructing de-noised single-channel radar data; and S4, repeatedly executing the steps S2 to S3 to obtain all de-noised single-channel radar data, and outputting the de-noised single-channel radar data as a two-dimensional data body or a geological radar profile according to an acquisition sequence. According to the method, signal denoising is carried out based on particle swarm optimization variational mode decomposition, and separation of effective signals and noise interference of the geological radar is realized.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a geological radar denoising method based on particle swarm optimization variational mode decomposition. Background Art

[0002] Engineering defect detection. With environmental changes and structural degradation, various defects are inevitable during construction and after commissioning. To ensure smooth construction and safe operation and maintenance, various technical means are required to accurately detect the defect's location, type, scale, and morphology. This allows for the design of targeted treatment plans based on the specific characteristics of the defect. Currently, commonly used engineering defect detection methods include geological radar, foundation coefficient testing, acoustic wave testing, high-density electrical testing, and borehole imaging. Geological radar has been widely used in engineering defect detection due to its ease of construction, high accuracy, high detection depth, non-destructive testing, and environmental friendliness. Geological radar is a geophysical method that uses antennas to transmit and receive high-frequency electromagnetic waves to detect the internal properties and distribution patterns of materials in a medium. Its basic principle is to transmit high-frequency electromagnetic waves into the ground through a transmitting antenna. As these electromagnetic waves propagate underground, they encounter various interfaces between media, such as rock, soil, karst, and earth caves. When encountering interfaces with different electrical properties, the electromagnetic waves are reflected, with some of the reflected waves returning to the surface and being received by a receiving antenna. By analyzing parameters such as the time difference, amplitude, and waveform of the reflected waves, the structure and properties of the underground medium can be inferred. However, the reflected wave information not only contains effective interface information but also contains a large amount of noise information, which requires specialized denoising processing to highlight the effective interface information.

[0003] The existing geological radar disease detection data processing includes drift removal, static correction, background removal, signal denoising, gain and other processes, among which signal denoising is one of the important steps. Signal denoising needs to be achieved by removing the noise components in the original signal, highlighting the intensity and proportion of the effective signal components, similar to the highlighting of the human voice in call noise reduction, and ultimately achieving the purpose of highlighting abnormal disease signals and improving detection accuracy and precision. At present, geological radar signal denoising is mainly processed by bandpass filtering and Wiener filtering. Wiener filtering is a linear filter based on statistical filtering methods, which is suitable for restoring images contaminated by Gaussian noise. It restores the original signal based on the prior statistical information of the signal (such as autocorrelation function and power spectrum). The design goal of the Wiener filter is to minimize the mean square error. It requires that the observed signal is generalized random and stationary and the statistical characteristics are known. It cannot be applied to situations where the noise is a non-stationary random process.

[0004] There are two problems with the existing geological radar signal denoising technology: (1) Adaptive problem: The types of defects, geological conditions, and interference types are different during the geological radar detection process. It is difficult to fully grasp the underground space structure, medium distribution characteristics, interference information characteristics, and interference degree before detection, and it is impossible to clearly know the statistical characteristics of the radar signal. Due to the inhomogeneity of the medium, the detection signal is not a stable signal. Based on the characteristics of Wiener filtering, it is difficult to achieve good denoising of geological radar signals. Bandpass filtering is simply based on frequency information to directly remove signal information. Not only can it not effectively remove broadband noise residues, but it also causes a large loss of effective abnormal information; (2) Optimal parameter setting problem, that is, parameter setting is too dependent on subjective experience and is often not the optimal solution. In the process of geological radar signal denoising, the setting of technical parameters is crucial. In conventional signal denoising algorithms, the setting of processing parameters is too dependent on human subjective experience. Different people may have different understandings of the same radar data, and people may have different processing experiences. The characteristics of data in different environments are different. It is often difficult to achieve the optimal denoising effect by relying on subjective experience to set filter parameters and debug denoising effects. It is necessary to seek an intelligent optimization algorithm to comprehensively and quickly search and determine the optimal processing parameter settings, so as to achieve the best setting of processing parameters and obtain the best denoising effect at the current level. Summary of the Invention

[0005] In view of this, the present invention proposes a geological radar denoising method based on particle swarm optimization variational mode decomposition to solve the problems of unclear statistical characteristics of radar signals and overly subjective setting of signal denoising processing parameters in existing geological radar signal denoising technology.

[0006] The technical solution of the present invention is achieved as follows: The present invention provides a method for denoising geological radar based on particle swarm optimization variational mode decomposition, comprising the following steps:

[0007] S1. Obtain the original geological radar data and pre-process it, extracting single-channel radar data in the order of acquisition as the data to be processed;

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

[0009] S3. Filtering effective signal components based on the effectiveness index of multiple intrinsic mode components and reconstructing the denoised single-channel radar data, wherein the effectiveness index is calculated by integrating the time domain correlation, spectral distribution characteristics, and time decay characteristics of the components;

[0010] S4. Repeat S2 to S3 to obtain all denoised single-channel radar data, and output all denoised single-channel data as a two-dimensional data volume or geological radar profile in the order of acquisition.

[0011] On the basis of the above technical solution, 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 starting position, and obtaining preprocessed radar data.

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

[0013] S21, setting the particle swarm algorithm parameters, initializing the position and velocity of each particle in the particle swarm, where 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, substituting the parameter combination of each particle into the variational mode decomposition algorithm to decompose the single-channel radar data, and calculating the fitness evaluation parameter based on the decomposition result as the fitness value of the particle;

[0015] S23, updating the individual optimal position of each particle and the global optimal position of the particle swarm according to the fitness value;

[0016] S24, updating the particle's speed and position according to the particle's current speed, individual optimal position, and global optimal position;

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

[0018] On the basis of the above technical solution, preferably, the particle swarm algorithm parameters include population size, mode number and penalty factor, the value range of the mode number is [2, 20], and the value range of the penalty factor is [500, 2000].

[0019] On the basis of the above technical solution, preferably, the calculation expression of the fitness evaluation parameter is:

[0020]

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

[0022] Based on the above technical solution, preferably, in step S25, the termination condition is that the maximum number of iterations is reached or the ratio of the maximum fitness to the minimum fitness in the latest four iterations is less than 1.05.

[0023] Based on the above technical solution, preferably, the calculation expression of the effectiveness index is:

[0024]

[0025] x i 、y i are the values of the decomposed components and the original signal at time i, is the mean of the decomposed component and the original signal, B is a weight factor between 0 and 1, which is 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 spectrum points of the decomposed component, and j is the time lag.

[0026] Based on the above technical solution, preferably, in step S3, screening 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. Setting a validity index threshold according to the overall signal situation;

[0028] S32, comparing the validity index of each eigenmode component with a threshold value, and determining the eigenmode component with a validity index greater than or equal to the threshold value as a valid signal component;

[0029] S33. All effective signal components are superimposed and reconstructed to obtain denoised single-channel radar data.

[0030] On the basis of the above technical solution, preferably, the superposition reconstruction calculation formula of the effective signal component is: S n =IMF1+IMF2+...+IMF x , where S n is the reconstructed single-channel radar data, IMF x is the effective eigenmode component.

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

[0032] The geological radar denoising method based on particle swarm optimization variational mode decomposition of the present invention has the following beneficial effects compared with the prior art:

[0033] (1) In order to solve the problem that the filter needs clear statistical characteristics of the radar signal and has poor adaptability to non-stationary random signals during the denoising process of geological radar signals, the present invention introduces variational mode decomposition technology to adaptively match the optimal center frequency and limited bandwidth of each mode in the geological radar signal, and can achieve effective separation of inherent eigenmode components and frequency domain division of the signal, thereby obtaining effective decomposition components of the original signal and finally obtaining the optimal solution to the variational problem;

[0034] (2) To address the problem of strong subjectivity in parameter setting, the present invention uses 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 criterion, and continuously optimizes the particle swarm evolution process to obtain the optimal parameter combination, which greatly reduces the subjectivity of parameter setting.

[0035] (3) The present invention proposes a fitness evaluation parameter E and provides a calculation method for it. The absolute mean error is used in the calculation formula 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 versatility and adaptability of the formula.

[0036] (4) The present invention proposes an effectiveness index C and its calculation formula, which comprehensively considers time delay, mean difference of the sequence, weighting and frequency characteristics (through the power spectrum integral term). Compared with the simple correlation coefficient calculation method, it can reflect the relationship between sequences more comprehensively and meticulously. It has obvious advantages in processing complex actual 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 This is a flow chart of the geological radar denoising method based on particle swarm optimization variational mode decomposition of the present invention;

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

[0040] Figure 3 A simulated radar signal diagram according to an embodiment of the present invention;

[0041] Figure 4 Schematic diagram of optimal variational mode decomposition components of an embodiment of the present invention;

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

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

[0044] Figure 7 These are diagrams showing the effects of different noise levels being improved after noise reduction processing according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

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

[0047] S1. Obtain the original geological radar data and pre-process it, extracting single-channel radar data in the order of acquisition as the data to be processed;

[0048] S2, using the modal number K and penalty factor α as parameter combinations, the particle swarm optimization algorithm is used to optimize the parameter combination, and variational modal decomposition is performed on the processed data based on the optimal parameter combination to obtain multiple intrinsic mode components;

[0049] S3. Filtering effective signal components based on the effectiveness index of multiple intrinsic mode components and reconstructing the denoised single-channel radar data, wherein the effectiveness index is calculated by integrating the time domain correlation, spectral distribution characteristics, and time decay characteristics of the components;

[0050] S4. Repeat S2 to S3 to obtain all denoised single-channel radar data, and output all denoised single-channel data as a two-dimensional data volume or geological radar profile in the order of acquisition.

[0051] The present invention adaptively determines the optimal parameter combination of variational mode decomposition through the particle swarm optimization algorithm, solving the problems of strong subjectivity in parameter setting and unstable denoising effect caused by traditional methods relying on manual experience. The decomposition components are accurately screened in combination with the effectiveness index (comprehensive time domain correlation, spectral distribution and time attenuation characteristics), effectively distinguishing non-stationary noise from effective signals, and achieving an improvement in the signal-to-noise ratio under complex geological conditions. The process of channel-by-channel processing-overall reconstruction is adopted, taking into account both algorithm efficiency and signal detail retention, significantly improving the detection accuracy and reliability of geological radar in engineering disease detection (such as karst and soil cave identification).

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

[0053] S11. Data Import and Storage: Read raw detection data from the geological radar device, including the number of radar channels (N), sampling rate (M), the time-domain waveform value of each channel, and observation parameters (such as antenna frequency and sampling interval). Store the data in the order of acquisition as a two-dimensional data matrix data[n,m], where the row (n) represents the channel sequence (n = 1, 2, ..., N) and the column (m) represents the sampling point sequence of each channel (m = 1, 2, ..., M). This structure facilitates the extraction and processing of single-channel radar data.

[0054] The horizontal interval between adjacent single-channel radar data (i.e., fixed point spacing) is set according to on-site detection requirements and is usually no more than 0.5 m to ensure uniformity in the spatial distribution of the data and avoid missing effective signals or reducing resolution due to excessive spacing.

[0055] S12. Preprocess the original data of the geological radar: determine the zero point of the time axis by detecting the starting point of the initial reflection wave of the radar signal (that is, the starting time point when the electromagnetic wave is first received after being emitted); perform time shift correction on the data of all channels according to the starting position to eliminate the time offset caused by equipment startup 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 radar signal take-off position is identified and the geological radar data is zero-point corrected without performing any gain adjustment or filtering operations to prevent artificial introduction of signal distortion or noise amplification.

[0057] S13, single channel data extraction: extract the nth channel radar data S in the order of acquisition n As data to be processed,

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

[0059] S21. Set the parameters of the particle swarm algorithm. The parameters of the particle swarm algorithm include the population size, the maximum number of iterations, the number of modes, and the penalty factor. The value range of the mode number is [2, 20] to avoid over-decomposition (generating false modes) or under-decomposition (omitting valid features). The value range of the penalty factor is [500, 2000] and is used to control the bandwidth of the intrinsic mode component. A penalty factor that is too small will lead to modal aliasing, while a penalty factor that is too large will lead to local information loss.

[0060] Initialize the position and velocity of each particle in the particle swarm. The "position" of each particle is represented by a two-dimensional vector, where the first component represents the modal 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, the population size is preferably set to 20, and the maximum number of iterations is set to 20.

[0061] S22. Substituting the parameter combination of each particle into the variational mode decomposition algorithm to decompose the data to be processed, obtaining a number of intrinsic mode components, and calculating the fitness evaluation parameter based on the decomposition result as the fitness value of the particle.

[0062] One of the approximate entropy, fuzzy entropy, envelope entropy, envelope spectrum peak factor, etc. can be selected as the parameter optimization fitness evaluation standard. Here, the fitness evaluation parameter E is proposed as the fitness evaluation standard. The calculation expression of the fitness evaluation parameter is:

[0063]

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

[0065] In the present 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 ensure the comparability of different data scales through standardization.

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

[0067] In each iteration, each particle is evaluated based on its calculated fitness value. If the current particle's fitness is higher than its historical record, its individual optimal position is updated. Simultaneously, the particle with the best fitness is selected from the entire population and its position is designated as the global optimal position. This updating process ensures that the entire particle swarm continuously evolves toward lowering the E value and improving decomposition performance.

[0068] S24. Update the particle's velocity and position based on the particle's current velocity, individual optimal position, and global optimal position. The standard PSO velocity update formula is used to update each particle's velocity based on the particle's current velocity, individual optimal position, and global optimal position. The updated velocity is then used to correct the particle's position. Through this process, the particle searches for a better solution within the parameter space, gradually approaching the global optimal parameter region.

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

[0070] The iteration termination condition is set as:

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

[0072] The fitness of each particle, E, calculated based on its position information (x, y), is used as the particle's fitness. The particle position is iteratively updated until the maximum number of iterations or the local fitness ratio threshold is reached, resulting in the optimal parameter combination. Reaching the local fitness ratio threshold indicates that the iterations have stabilized the fitness improvement and reached a local optimal solution. Setting the maximum number of iterations and the local fitness ratio threshold effectively reduces the number of invalid iterations and the computational overhead. Through these steps, key parameters in the variational mode decomposition process can be automatically searched and optimized, significantly reducing the uncertainty caused by subjective parameter settings. Using a particle swarm optimization algorithm to perform a global parameter search, the particle's intrinsic mode components (IMCs) in the variational mode decomposition process more closely reflect the true characteristics of the signal, thereby accurately separating the effective signal from noise in the ground-penetrating radar signal. In particular, the fitness evaluation parameter E, introduced by the algorithm, comprehensively considers the power spectrum characteristics of the decomposed IMCs in a standardized manner, ensuring robustness to outliers and promoting efficient convergence of the entire algorithm, providing a solid parameter foundation 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. It is a key technical step to ensure high-quality reconstruction of geological radar signals.

[0073] Under normal circumstances, radar signal fluctuations caused by changes in the shallow propagation medium are far stronger than random environmental noise. Without adding gain, the original signal is strongly correlated with the theoretical signal, approximating a noise-free theoretical signal. Correlation with the original signal is an important indicator for evaluating the effectiveness of modal decomposition components. Furthermore, since signal fluctuations caused by geological structures, diseases, and other factors are generally low-frequency, the frequency distribution of the component signals is also a key indicator for evaluating signal effectiveness. Initially, radar signals exhibit minimal attenuation, a high signal-to-noise ratio, and high reliability. However, as travel time increases, the effective signal attenuates significantly, reducing its reliability. Therefore, effectiveness should gradually decay over time. By comprehensively considering correlation, spectral characteristics, and time decay, an effectiveness index has been proposed to evaluate component signal effectiveness.

[0074] Furthermore, in the present invention, after obtaining multiple intrinsic modal components of the variational modal decomposition of the single-channel geological radar signal in step S2, each intrinsic modal component is evaluated using a predefined validity index in step S3. The validity index comprehensively considers the correlation between the intrinsic modal component and the original signal in the time domain, the spectral distribution of the component, and the attenuation characteristics over time. The calculation formula of the validity index is:

[0075]

[0076] x i 、y i are the values of the decomposed components and the original signal at time i, is the mean of the decomposed component and the original signal, B is a weight factor between 0 and 1, which is used to control the weight attenuation 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 spectrum points of the decomposed component, which is generally taken as 500 according to the characteristics of radar data, and j is the time lag.

[0077] Step S3 specifically includes the following steps:

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

[0079] S32. Compare the validity index of each eigenmode component with a threshold value. Eigenmode components with a validity index greater than or equal to the threshold value are determined to be valid signal components. For each eigenmode component obtained in step S2, a validity index C is calculated according to the validity index calculation formula. The calculated C value of each eigenmode component is compared with the set threshold value T. When the validity index C of a particular eigenmode component is greater than or equal to the threshold value T, the component is determined to be a valid signal component; otherwise, the component is determined to be a noise component or an irrelevant component and will be eliminated in subsequent processing.

[0080] S33, all effective signal components are superimposed and reconstructed to obtain the denoised single-channel radar data. The superimposition and reconstruction calculation formula of the effective signal components is: S n =IMF1+IMF2+...+IMF x , where S n is the reconstructed single-channel radar data, IMF x is the xth effective intrinsic mode component screened out. Through this superposition method, the main information and key features in the original signal can be retained, while the noise interference can be effectively removed, and the signal-to-noise ratio and data quality of the final signal can be improved.

[0081] Single-channel radar data are processed sequentially and output as a two-dimensional N×M data volume data[n,m] or a geological radar profile in the order of acquisition.

[0082] By utilizing the aforementioned steps, the effectiveness index can be fully utilized to quantitatively evaluate each intrinsic mode component, thereby enabling intelligent differentiation between effective signal and noise components within each decomposition result. This method not only considers time-domain correlation but also incorporates spectral distribution and time decay characteristics, making the entire component screening process more comprehensive and accurate. Ultimately, by superimposing and reconstructing 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 noise reduction process, providing important technical support for subsequent data analysis and geological radar imaging.

[0083] Example

[0084] Since it is impossible to obtain a completely noise-free geological radar signal with a completely uniform medium under natural conditions, in this embodiment, a theoretical noise-free signal is simulated through a simulation experiment, and the actual acquisition signal is simulated by adding random noise data.

[0085] (1) Simulation data preparation

[0086] Based on GprMax, a geological radar disease detection simulation was conducted, such as Figure 2 As shown, the thickness of the water-bearing strata 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 with a burial depth of 7.5m.

[0087] The simulation results are as follows Figure 3 As shown in the figure, when the aquifer thickness reaches 1m, the radar reflection signal from the dry-wet interface is clearly visible, while the radar reflection signal intensity caused by voids is greatly weakened. Using exponential gain, the void anomaly can still be identified. When the aquifer thickness reaches 2m, the radar reflection signal from the dry-wet interface is still visible, but the radar reflection signal anomaly caused by voids cannot be accurately identified even with exponential gain. When the aquifer thickness reaches 3m, the radar reflection signal from the dry-wet interface is visible, but the void radar reflection signal anomaly is completely unrecognizable. Simulation results show that as the aquifer thickness increases, the radar reflection signal attenuates rapidly, and the effective signal is gradually lost in the ambient noise.

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

[0089] The simulation results of the radar signal from model c were selected for variational mode denoising optimized by a particle swarm optimization algorithm. First, random Gaussian white noise was added to the theoretical signal of model c to simulate a signal containing environmental noise. The noisy signal was then fed into the particle swarm optimization variational mode decomposition algorithm. The particle swarm algorithm was used to determine the optimal VMD (VD) parameters (K, α). The population size was set to 20, the maximum number of iterations was 20, the K value iteration range was (2, 20), and the α value iteration range 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 particle swarm algorithm was 6, and the optimal α value was 1592.

[0090] The analog signal is decomposed by VMD based on the optimal parameters (K, α) to obtain 6 IMF (intrinsic mode function) components, such as Figure 4 As shown in , the spectrum distribution of the six IMF components is calculated at the same time, as shown in Figure 5 As shown in Figure 2, according to the calculation formula of the effectiveness index C, the effectiveness index of the IMF1 component is the largest, which is 6.47×10 -4 According to the maximum threshold method, this component is used as the denoising result. By comparing the signals before and after denoising, such as Figure 6 As shown in the figure, the denoised signal has a smooth surface and rich details, and is essentially consistent with the original signal in terms of overall shape and oscillation amplitude. Calculations show that the SNR (signal-to-noise ratio) is 15.025dB after adding noise and 25.8093dB after denoising, representing a 10.7842dB improvement in signal quality.

[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 in the scope of protection of the present invention.

Claims

1. A method for denoising geological radar based on particle swarm optimization variational mode decomposition, characterized in that: The following steps are involved: S1. Obtain the original geological radar data and pre-process it, extracting single-channel radar data in the order of acquisition as the data to be processed; S2. Using the modal number and penalty factor as parameter combinations, the particle swarm optimization algorithm is used to optimize the parameter combination. Based on the optimal parameter combination, variational modal decomposition is performed on the processed data to obtain multiple intrinsic mode components. S3. Filtering effective signal components based on the effectiveness index of multiple intrinsic mode components and reconstructing the denoised single-channel radar data, wherein the effectiveness index is calculated by integrating the time domain correlation, spectral distribution characteristics, and time decay characteristics of the components; S4. Repeat S2 to S3 to obtain all denoised single-channel radar data, and output all denoised single-channel data as a two-dimensional data volume or geological radar profile in the order of acquisition.

2. The method for denoising geological radar data based on particle swarm optimization variational mode decomposition according to claim 1, wherein: 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 starting position, and obtaining preprocessed radar data.

3. The method for denoising geological radar data based on particle swarm optimization variational mode decomposition according to claim 1, wherein: In step S2, optimizing the parameter combination by the particle swarm optimization algorithm specifically includes: S21, setting the particle swarm algorithm parameters, initializing the position and velocity of each particle in the particle swarm, where 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, substituting the parameter combination of each particle into the variational mode decomposition algorithm to decompose the single-channel radar data, and calculating the fitness evaluation parameter based on the decomposition result as the fitness value of the particle; S23, updating the individual optimal position of each particle and the global optimal position of the particle swarm according to the fitness value; S24, updating the particle's speed and position according to the particle's current speed, individual optimal position, and global optimal position; S25. Repeat steps S22-S24 until the termination condition is met; output the global optimal parameter combination as the optimal parameters of variational mode decomposition.

4. The method for denoising geological radar data based on particle swarm optimization variational mode decomposition according to claim 3, wherein: The particle swarm algorithm parameters include population size, mode number and penalty factor. The value range of the mode number is [2, 20], and the value range of the penalty factor is [500, 2000].

5. The method for denoising geological radar data based on particle swarm optimization variational mode decomposition according to claim 3, wherein: The calculation expression of the fitness evaluation parameter is: K is the number of modes, N is the number of spectrum points of the nth component, P n (f i ) is the power spectral density of the nth component at the ith frequency point, and m is the median value of the power spectral density of this component.

6. The method for denoising geological radar based on particle swarm optimization variational mode decomposition according to claim 3, characterized in that: In step S25, the termination condition is that the maximum number of iterations is reached or the ratio of the maximum fitness to the minimum fitness in the last four iterations is less than 1.

05.

7. The method for denoising geological radar based on particle swarm optimization variational mode decomposition according to claim 1, characterized in that: The calculation expression of the effectiveness index is: x i 、y i are the values of the decomposed components and the original signal at time i, is the mean of the decomposed component and the original signal, B is a weight factor between 0 and 1, which is 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 spectrum points of the decomposed component, and j is the time lag.

8. The method for denoising geological radar based on particle swarm optimization variational mode decomposition according to claim 7, characterized in that: In step S3, the effective signal components are screened based on the effectiveness index of each eigenmode component and the denoised single-channel radar data is reconstructed, specifically including: S31. Setting a validity index threshold according to the overall signal situation; S32, comparing the validity index of each eigenmode component with a threshold value, and determining the eigenmode component with a validity index greater than or equal to the threshold value as a valid signal component; S33. All effective signal components are superimposed and reconstructed to obtain denoised single-channel radar data.

9. The method for denoising geological radar data based on particle swarm optimization variational mode decomposition according to claim 8, wherein: The superposition and reconstruction calculation formula of the effective signal components is: n =IMF1+IMF2+...+IMF x , where S n is the reconstructed single-channel radar data, IMF x is the effective eigenmode component.

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

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