Tunnel ground penetrating radar signal denoising analysis method based on wavelet decomposition

Abstract

The invention relates to the technical field of ground penetrating radar detection application, provides a tunnel ground penetrating radar signal denoising analysis method based on wavelet decomposition, and analyzes the local singularity of attenuation speed type measurement signals of local modulus maxima under different scales by using the discontinuity of tunnel ground penetrating radar signals or the discontinuity of derivatives of the tunnel ground penetrating radar signals. The method comprises the following steps: firstly, carrying out wavelet transformation and wavelet decomposition on an obtained signal, calculating a modulus maximum value of a detail coefficient of each wavelet scale, setting a threshold value on the maximum scale, comparing each extreme point with the threshold value to obtain a new modulus maximum value point on the maximum scale, carrying out the calculation on a lower scale, and repeating step by step to obtain a new modulus maximum value point on the maximum scale. And carrying out non-linear interpolation on the modulus maxima of the second scale until reaching the second scale, taking the modulus maxima of the second scale as the modulus maxima of the first scale, and finally reconstructing the signal by adopting the reserved wavelet transform modulus maxima, thereby achieving the purpose of removing the noise of the tunnel ground penetrating radar data signal.

Description

Technical Field

[0001] The present invention relates to the technical field of ground penetrating radar detection applications, and in particular to a tunnel ground penetrating radar signal denoising analysis method based on wavelet decomposition. Background Art

[0002] Ground-penetrating radar (GPR) can conduct exploration without damaging the surface, thus avoiding the potential surface damage and environmental impacts associated with traditional exploration methods. Tunnel construction involves various inspection tasks, and GPR is widely used in tunnels. However, existing applications of GPR in tunnels have been found to suffer from signal interference, resulting in low detection accuracy.

[0003] In the existing technology, the analysis methods for denoising tunnel GPR signals mainly include the following: (1) Wavelet transform: Wavelet transform is a method suitable for processing GPR signals because it can overcome the limitations of Fourier transform in processing non-stationary signals. Wavelet transform can decompose the signal into sub-bands of different frequencies, perform denoising on each sub-band, and then reconstruct the filtered signal. This method performs well in removing high-frequency random noise, and the denoising effect can be optimized by selecting a suitable threshold function. (2) Shearlet transform: Shearlet transform is an advanced signal processing method that is particularly suitable for denoising GPR signals. By calculating the energy difference between the effective signal and the interference signal at different scales and in different directions in the shear domain, random interference can be effectively removed. In addition, combined with wavelet transform, interference signals with similar energy and abnormal frequency can be further suppressed, thereby retaining the effective signal while removing the interference. (3) Deep learning: In recent years, deep learning technology has also been widely used in signal processing. For example, the improved convolutional autoencoder denoising network (MCDAE) is used to denoise GPR signals. This network extracts data features through an encoder, and the decoder reconstructs the compressed data features into the corresponding ground-penetrating radar signal. Experimental results show that this method performs well in suppressing noise and can reconstruct the denoised signal well.

[0004] In some application scenarios, the discontinuity of tunnel ground penetrating radar signals or the discontinuity of their derivatives cannot be completely solved by existing methods. Therefore, it is urgent to develop a new tunnel ground penetrating radar signal denoising analysis method to solve the problems existing in the existing technology. Summary of the Invention

[0005] The present invention aims to provide a tunnel ground penetrating radar signal denoising analysis method based on wavelet decomposition to solve the technical problem of poor noise removal effect of tunnel ground penetrating radar data signal.

[0006] To achieve the above objectives, the present invention discloses a tunnel ground penetrating radar signal denoising and analysis method based on wavelet decomposition. First, the signal acquired by the tunnel ground penetrating radar is subjected to wavelet transform and wavelet decomposition, and the modulus maximum of each wavelet scale detail coefficient is calculated. A threshold is set at the maximum scale, and the size of each extreme point is compared with the threshold to obtain a new modulus maximum point at the maximum scale. The above calculation is carried out at a lower scale and then repeated step by step until the second scale. The modulus maximum of the second scale is nonlinearly interpolated as the modulus maximum of the first scale. Finally, the signal is reconstructed using the retained wavelet transform modulus maximum to achieve the purpose of noise removal of the tunnel ground penetrating radar data signal.

[0007] Preferably, the method comprises the steps of:

[0008] Step S1, performing wavelet decomposition on the signal of the collected tunnel ground penetrating radar data, and calculating the modulus maximum of the wavelet detail coefficient at each scale in the signal;

[0009] Step S2: At the maximum scale, filter out the extreme points generated by noise and calculate a new modulus maximum at the maximum scale;

[0010] Step S3, repeating step S2 at each scale in descending order, and calculating a new modulus maximum at each scale until the second scale is reached;

[0011] Step S4: For the first scale, all modulus maxima at that scale are filtered out, and the modulus maxima at scale 2 are nonlinearly interpolated as new modulus maxima at the first scale;

[0012] Step S5: reconstruct the signal using the retained modulus maximum value, and output the denoised tunnel ground penetrating radar signal.

[0013] Preferably, the specific method of step S2 is: on the maximum scale J, a threshold A is set, if the amplitude of the extreme point is less than the threshold A, it is filtered out, if it is greater than the threshold A, it is retained, and the new modulus maximum point on the maximum scale is calculated, which is expressed as: in is the wavelet decomposition coefficient, J is the maximum scale; if x i In the domain of , any point y has |W f (x0, y)|≤|W(x0, y)|, then (x0, y0) is the maximum point of the wavelet modulus.

[0014] Preferably, the specific method of step S3 is: searching for the propagation position of the modulus maximum point on scale j-1, filtering out the extreme points generated by noise, that is, constructing a neighborhood O(n ji , ε j ), where n ji is the i-th extreme point on scale j, εj is a constant related to scale j; the maximum value of the modulus at scale j-1 is retained in the neighborhood O(n ji , ε j ), calculate the new extreme point on scale j-1, and repeat the above steps scale by scale until scale j=2.

[0015] Preferably, the specific method of step S4 is: for scale j=1, first filter out all the modulus maxima at scale j=1, and perform nonlinear interpolation on the modulus maxima at scale j=2 at the locations where the modulus maxima exist at scale j=2, and use them as the modulus maxima at scale j=1. The calculation process is as follows:

[0016] If the signal is a singular value, then the signal contains a mutation point, that is, there is a constant K, so that the wavelet decomposition of the signal f(x) and the singular value index α satisfy:

[0017]

[0018] Then use: and Calculate the modulus maximum at scale j=1.

[0019] The application of the technical solution of the present invention has the following beneficial effects:

[0020] The present invention utilizes the discontinuity of tunnel GPR signals or their derivatives to analyze the decay rate of local modulus maxima at different scales, thereby measuring the local singularity of the signal. First, the acquired signal is subjected to wavelet transform and wavelet decomposition, and the modulus maxima of the detail coefficients at each wavelet scale are calculated. A threshold is set at the maximum scale, and each extreme point is compared with the threshold to obtain a new modulus maximum point at the maximum scale. The above calculation is then repeated at a lower scale, step by step, until the second scale is reached. The modulus maxima at the second scale are nonlinearly interpolated as the modulus maxima at the first scale. Finally, the signal is reconstructed using the retained wavelet transform modulus maxima, achieving the purpose of removing noise from the tunnel GPR data signal.

[0021] In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail below. DETAILED DESCRIPTION

[0022] The following is a detailed description of embodiments of the present invention, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0023] Example:

[0024] A tunnel ground-penetrating radar signal denoising analysis method based on wavelet decomposition is used for tunnel ground-penetrating radar data analysis and processing. The method is characterized by removing and suppressing noise in tunnel ground-penetrating radar signals by utilizing the local singularity and modulus maximum difference between the signal and the noise, thereby achieving the purpose of gaining deep effective signals. The method comprises the following steps:

[0025] Step 1: Perform wavelet decomposition on the signal of the acquired tunnel ground penetrating radar data and calculate the modulus maximum of the wavelet detail coefficient at each scale in the signal;

[0026] Step 2: Set a threshold A on the maximum scale J. If the amplitude of the extreme point is less than the threshold A, it will be filtered out. If it is greater than the threshold A, it will be retained. Calculate the new modulus maximum point on the maximum scale, expressed as: in is the wavelet decomposition coefficient, J is the maximum scale; if x i In the domain of , any point y has |W f (x0, y)|≤|W(x0, y)|, then (x0, y0) is the wavelet modulus maximum point;

[0027] Step 3: Search for the propagation position of the modulus maximum point on scale j-1, filter out the extreme points generated by noise, that is, construct a neighborhood O(n ji , ε j ), where n ji is the i-th extreme point on scale j, ε j is a constant related to scale j;

[0028] The maximum value of the modulus of scale j-1 is retained in the neighborhood O(n ji , ε j ), calculate the new extreme point on scale j-1, and repeat the above steps on each scale until scale j=2;

[0029] Step 4: For scale j=1, first filter out all the modulus maxima at scale j=1. At the locations where modulus maxima exist at scale j:2, perform nonlinear interpolation using the modulus maxima at scale j=2 as the modulus maxima at scale j=1. The calculation process is as follows:

[0030] If the signal is a singular value, then the signal contains a mutation point, that is, there is a constant K, so that the wavelet decomposition of the signal f(x) and the singular value index α satisfy:

[0031]

[0032] Then use: and Calculate the maximum value of the modulus with scale J = 1;

[0033] Step 5: Reconstruct the signal using the retained wavelet transform modulus maximum.

[0034] The present invention calculates the position and amplitude of the modulus maximum of the wavelet transform coefficient corresponding to the signal, and utilizes the local singularity of the signal and the difference analysis results of the modulus maximum to remove and suppress the noise in the tunnel ground penetrating radar signal, realize filtering, and achieve the purpose of gaining the deep effective signal.

[0035] This paper uses two improved fixed threshold soft and hard threshold function methods for evaluation. The evaluation process of soft and hard thresholds is more comprehensive and objective, and can more conveniently match the ground penetrating radar wavelet signal. The present invention adopts the db4 wavelet basis threshold that better matches the radar wavelet signal, and provides the calculation method and implementation process of the fixed threshold and soft and hard threshold functions:

[0036] Fixed threshold: Where σ is the standard deviation of each scale coefficient.

[0037] Hard threshold function:

[0038] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A tunnel ground penetrating radar signal denoising analysis method based on wavelet decomposition, characterized in that: Firstly, the signal acquired by the tunnel ground penetrating radar is subjected to wavelet transform and wavelet decomposition, and the modulus maximum of each wavelet scale detail coefficient is calculated. A threshold is set at the maximum scale, and the size of each extreme point is compared with the threshold to obtain a new modulus maximum point at the maximum scale. The above calculation is carried out at a lower scale and then repeated step by step until the second scale. The modulus maximum of the second scale is nonlinearly interpolated as the modulus maximum of the first scale. Finally, the signal is reconstructed using the retained wavelet transform modulus maximum to achieve the purpose of noise removal of the tunnel ground penetrating radar data signal.

2. The tunnel ground penetrating radar signal denoising analysis method according to claim 1, characterized in that: Includes steps: Step S1, performing wavelet decomposition on the signal of the collected tunnel ground penetrating radar data, and calculating the modulus maximum of the wavelet detail coefficient of each scale in the signal; Step S2: On the maximum scale, filter out the extreme points generated by the noise, and calculate a new modulus maximum on the maximum scale; Step S3, repeating step S2 in order of decreasing scale, and calculating a new modulus maximum value at each scale until the second scale; Step S4: for the first scale, all modulus maxima at the scale are filtered out, and nonlinear interpolation is performed on the modulus maxima at scale 2 as new modulus maxima at the first scale; Step S5: reconstruct the signal using the retained modulus maximum value, and output the denoised tunnel ground penetrating radar signal.

3. The tunnel ground penetrating radar signal denoising analysis method according to claim 2 is characterized in that: The specific method of step S2 is: on the maximum scale J, a threshold A is set, if the amplitude of the extreme point is less than the threshold A, it is filtered out, if it is greater than the threshold A, it is retained, and the new modulus maximum point on the maximum scale is calculated, which is expressed as: in is the wavelet decomposition coefficient, J is the maximum scale; if x i In the domain of , any point y has |W f (x0, y)|≤|W(x0, y)|, then (x0, y0) is the wavelet modulus maximum point.

4. The tunnel ground penetrating radar signal denoising analysis method according to claim 2, characterized in that: The specific method of step S3 is: search for the propagation position of the modulus maximum point on the scale j-1, filter out the extreme points generated by noise, that is, construct a neighborhood O(n) at the modulus maximum point on the scale j-1. ji , ε j ), where n ji is the i-th extreme point on scale j, ε j is a constant related to scale j; the modulus maximum point of scale j-1 is retained in the neighborhood O(n ji , ε j ), calculate the new extreme point on scale j-1, and repeat the above steps scale by scale until scale j=2.

5. The tunnel ground penetrating radar signal denoising analysis method according to claim 2, characterized in that: The specific method of step S4 is: for scale j=1, first filter out all the modulus maxima at scale j=1, and perform nonlinear interpolation on the modulus maxima at scale j=2 as the modulus maxima at scale j=1. The calculation process is as follows: If the signal is a singular value, then the signal contains a mutation point, that is, there is a constant K, so that the wavelet decomposition of the signal f(x) and the singular value index α satisfy: Then use: and Compute the modulus maximum for scale j=1.

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