A Hierarchical Medium Parameter Inversion Method Based on the CMP Model and the Parameter Search OMP Algorithm

Abstract

The present invention relates to a method for inverting layered medium parameters based on the CMP model and the parameter search OMP algorithm, belonging to the technical field of ground penetrating radar, and particularly relates to the inversion of parameters in a layered medium scenario. A sparse solution strategy combining the OMP algorithm and the parameter search cost function is adopted. First, the off-grid medium parameters are estimated based on the OMP algorithm. Then, within the iteration of the OMP algorithm, the dictionary mismatch effect is eliminated based on the parameter search cost function. Then, the channel residual is updated and the dictionary is updated layer by layer to achieve accurate inversion of the medium parameters.

Description

Technical Field

[0001] The present invention relates to a method for inverting layered medium parameters based on the CMP model and the parameter search OMP algorithm, belonging to the technical field of ground penetrating radar, and particularly relating to the parameter inversion of a layered medium scenario. Background Art

[0002] With the rapid development of municipal transportation, the traffic conditions of urban arterial roads are becoming increasingly complex. Road diseases such as road surface collapse and crack hazards are emerging in an endless stream, posing certain safety hazards. This problem has posed challenges to the research on real-time and efficient detection of road surface structures.

[0003] Traditional measurement methods for road surface structures include the core sampling method, that is, drilling core samples from the road to evaluate the structural quality. However, the cost of core sampling is high, the efficiency is low, and the road surface structure is damaged, which is a major drawback of traditional measurement methods. Electromagnetic exploration methods represented by ground penetrating radar (GPR) technology have solved the drawbacks of core sampling and have the characteristics of fast detection speed, strong penetration ability, and high resolution. They are widely used in underground exploration, road detection, building monitoring and other fields. The parameter inversion method based on ground penetrating radar realizes the accurate estimation of structural information such as medium thickness and dielectric constant, provides an efficient detection and prevention means for road diseases and building structure damage, and also provides accurate parameter information for subsequent underground target imaging and recognition detection.

[0004] For the problem of medium parameter estimation in classic layered scenarios such as roads, parameter inversion methods based on Common Middle Point (CMP) data include the common midpoint method, velocity spectrum method, machine learning, etc. The common midpoint method is based on the modeling of underground multi-layer media, constructs the propagation paths of electromagnetic waves in the media layers at different transceiver offsets, establishes the propagation equations of reflected waves in each layer, and solves the equations to estimate the layer parameters. However, in the case of a large number of layers, the solution of the propagation equations is very complex and has a huge amount of calculation. The velocity spectrum method first assumes the propagation speed of electromagnetic waves in the medium, constructs the reflected wave trajectories at different speeds, performs amplitude superposition of the corresponding hyperbolic trajectories in the B-scan, plots the coherence power spectrum diagram of propagation speed and time delay, picks up the layered reflected wave response in the spectrum diagram, and uses the Dix formula to achieve parameter inversion. However, due to the influence of signal oscillation characteristics and multiple reflected waves inside the layered medium, there are many disturbances in the velocity spectrum diagram, and it is difficult to accurately obtain the layered response. The parameter inversion method of machine learning is based on the structure of SVM or neural network, trains and learns the data set, and can achieve accurate inversion results when the test data and the training data belong to similar feature distributions. However, in actual scenarios, the layered medium may be affected by other factors such as surface roughness, medium uniformity, and external object interference, resulting in difficult-to-unify feature distributions, greatly reducing the generalization ability of the neural network, and being unable to be applied to complex engineering scenarios. Summary of the Invention

[0005] To solve the above problems, the present invention proposes a ground penetrating radar layered medium parameter inversion method based on the CMP model and the parameter search OMP algorithm. Aiming at the problems that the traditional time delay estimation signal model is only applicable to one-dimensional A-scan waveforms and the inversion result only contains time delay information, the signal model of common offset is extended to the CMP model, and the joint inversion of reflected wave time delay and layered medium parameters is realized based on the OMP algorithm; aiming at the dictionary mismatch effect existing in OMP, a parameter search cost function with off-grid compensation is constructed, and a parameter search OMP algorithm is established to achieve accurate parameter estimation of the layered medium.

[0006] The technical solution of the present invention is as follows:

[0007] A method for inverting the parameters of a layered medium based on the CMP model and the parameter search OMP algorithm. Aiming at the problems that the traditional time delay estimation signal model is only applicable to one-dimensional A-scan waveforms and the inversion result only contains time delay information, the signal model of common offset is extended to the CMP model, and the joint inversion of reflected wave time delay and layered medium parameters is realized based on the OMP algorithm; aiming at the dictionary mismatch effect existing in OMP, a parameter search cost function with off-grid compensation is constructed, and a parameter search OMP algorithm is established to achieve accurate parameter estimation of the layered medium. This method is based on stepped-frequency echo signals and is realized through the following steps:

[0008] Step 1: Construct the propagation delay of the multi-layer CMP model by:

[0009] (1) Based on the single-layer CMP model, the incident electromagnetic wave is reflected at the bottom of the single-layer medium. The propagation delay of the reflected wave at the first layer interface is expressed as:

[0010]

[0011] Among them, d1,ε r1 They represent the thickness and relative dielectric constant of the first layer of medium, c represents the speed of light, 2L j represents the antenna transmission and reception distance of the jth A-scan, and n represents the number of A-scan channels measured by the ground penetrating radar;

[0012] (2) The single-layer model is derived into a K-layer CMP model, and the propagation delay of the K-th layer interface reflection wave is expressed as:

[0013]

[0014] Among them, d k ,ε rk Represent the thickness and relative dielectric constant of the kth layer, x1, x2, ..., x K represents the lateral offset distance of the electromagnetic wave in the 1st, 2nd, ...Kth layered media;

[0015] The x1,x2,...,x K The method for determining is:

[0016] Assuming that the refraction process satisfies the geometric optics assumption and Snell's law, the refraction point approximation method is used to simplify the solution of the multivariable equations for the refraction point, and a single algebraic operation is used to estimate the position of the refraction point, which is expressed as:

[0017]

[0018] Among them, y b represents the position of the refraction point on the layered interface, y1 represents the intersection of the electromagnetic wave and the layered interface under the assumption of straight-line propagation, y2 represents the position of the electromagnetic wave perpendicularly mapped to the layered interface after refraction, and v1 and v2 represent the propagation speed of the electromagnetic wave in medium 1 and medium 2 respectively;

[0019] Therefore, the lateral offset distance of the electromagnetic wave in the medium is expressed as:

[0020]

[0021] The refraction point position of the K-layer CMP model is derived and expressed as:

[0022]

[0023] Step 2: Based on the propagation delay obtained in Step 1, construct the sparse vector of the multi-layer CMP model. The method is as follows:

[0024] Based on the single-layer CMP model, when k = 1, assume that the medium parameters of the first layer are d = [d 1,1 , d 1,2 ,..., d 1,M1 , where M1 and M2 are the number of grid points of thickness and equivalent dielectric constant respectively, and the discrete intervals are Δd1 and Δε r1 , then the medium parameter combinations are expressed as [(d 1,1 , ε r1,1 ), (d 1,1 , ε r1,2 ),..., (d 1,1 , ε r1,M2 ), (d 1,2 , ε r1,1 )...,(d 1,M1 , ε r1,M2 )], and the reflection wave delay is expressed as:

[0025] F1 = [T1(d 1,1 , ε r1,1 , L j ), T1(d 1,1 , ε r1,2 , L j ),..., T1(d 1,1 , ε r1,M2 , L j ), T1(d 1,2 , ε r1,1 , L j )..., T1(d 1,M1 , ε r1,M2 , L j )]

[0026] Based on the K-layer CMP model, assume that the thickness and relative dielectric constant of the first K - 1 layers of media are known. When k = K, assume that the thickness and relative dielectric constant of the Kth layer of media are d = [d K,1 , d K,2 ,..., d K,M1 , the discrete intervals are Δd K , Δε rK , then the medium parameters are [(d K,1 , ε rK,1 ), (d K,1 , ε rK,2 ),...,(d K,1 , εrK,M2 ),(d K,2 ,ε rK,1 )...,(d K,M1 ,ε rK,M2 )], the reflection wave time delay is expressed as:

[0027] F K = [T K (d K,1 ,ε rK,1 ,L j ), T K (d K,1 ,ε rK,2 ,L j ),..., T K (d K,1 ,ε rK,M2 ,L j ), T K (d K,2 ,ε rK,1 ,L j )..., T K (d K,M1 ,ε rK,M2 ,L j )]

[0028] Among them, the position of the refraction point involved in the reflection time delay is jointly calculated from the medium parameters of the first K - 1 layers and the assumed parameters of the Kth layer;

[0029] The set of reflection wave time delays F K derived from the CMP model, and the sparse vector representation of the K - layer CMP model is:

[0030]

[0031] Among them, N is the number of frequency domain sampling points, f1, f2,..., f N are the frequency domain sampling values, and f i = f1+(i - 1)Δf, f i represents the sampling value of the ith frequency point, and Δf is the frequency domain sampling interval;

[0032] Step 3, establish the sparse dictionary of a single A - scan and construct the CMP sparse model;

[0033] Based on the K - layer CMP model and the reflection wave time delay expression, horizontally splice the sparse vectors of each reflection time delay to construct the sparse dictionary representation A j,K of the jth A - scan:

[0034] A j,K = [a(T K (d K,1 ,ε rK,1 ,Lj )), a(T K (d K,1 , ε rK,2 , L j )),..., a(T K (d K,1 , ε rK,M2 , L j )), a(T K (d K,2 , ε rK,1 , L j )),..., a(T K (d K,M1 , ε rK,M2 , L j ))]

[0035] Thus, the sparsity representation of the j - th A - scan echo signal based on the K - layer CMP model is:

[0036] r j,K = ΛA j,K s + n

[0037] where, r j,K = [r j,K (f1), r j,K (f2),..., r j,K (f N )] T represents the N - frequency - point data vector of the j - th A - scan electromagnetic echo based on the K - layer CMP model with dimension (N, 1), represents the frequency - domain signal pulse matrix with dimension (N, N), A j,K represents the sparse dictionary of the j - th A - scan electromagnetic echo based on the K - layer CMP model with dimension (N, M1M2), s = [s1, s2,..., s K )] T represents the reflection coefficient vector of the layer reflection wave with dimension (M1M2, 1), n = [n(f1), n(f2),..., n(f N )] T represents the frequency - domain Gaussian white noise with dimension (N, 1);

[0038] Therefore, based on the K - layer CMP model, for the echo data r of each trace j,K and the sparse dictionary A j,K adopt a vertical splicing form, and the sparse model based on the stepped - frequency signal and the CMP system is expressed as:

[0039]

[0040] where, r Kis a data vector of dimension (nN, 1) based on the K-layer CMP sparse model, A K is a sparse dictionary of dimension (nN, M1M2) based on the K-layer CMP model;

[0041] Step 4, use the OMP algorithm for parameter inversion according to the K-layer CMP sparse model constructed in Step 3. The specific steps are as follows:

[0042] 1) Initialize the residual component Establish an index set The iteration count k = 1, where the residual component is expressed as

[0043] 2) Calculate the correlation For t ∈ [1, M1M2], solve for the index where θ t represents the t-th column sparse vector of the sparse dictionary A K ;

[0044] 3) According to the parameters [(d k,1 , ε rk,1 ), (d 1,1 , ε rk,2 ),..., (d k,1 , ε rk,M2 ), (d k,2 , ε rk,1 )..., (d k,M1 , ε rk,M2 )] and the index λ k , obtain the out-of-grid parameter (d k , ε rk ) and the propagation delay T k (d k , ε rk , L j ) of the k-th layer;

[0045] 4) According to the out-of-grid parameter range, construct a parameter search cost function and invert the medium parameters;

[0046] 5) According to the medium parameters d k , ε rk , deduce the propagation delay T k (d k , ε rk , L j ) of the reflected wave in the k-th layer, and construct the sparse vector θ k,j = a(T k (d k , ε rk , L j )), j ∈ [1, n], where j is the number of A-scan channels;

[0047] 6) Solve the echo reflection coefficient of each A-scan Update the residual component of each trace Update the total residual component

[0048] 7) Increment k in step 1). If k < K, calculate the propagation delay T of the reflected wave at the k-th stratified interface based on the medium parameters of the first k - 1 layers obtained by inversion and the discretized parameters of the k-th layer assumption k (d k , ε rk , L j ), update the sparse vector a(T k (d k , ε rk , L j )) and the sparse dictionary A K , and return to step 2); if k = K, end;

[0049] The specific method of step 4) is as follows:

[0050] In the k-th iteration of the OMP algorithm, obtain the best matching off-grid parameter d k , ε rk and the corresponding propagation delay T k (d k , ε rk , L j ), with discrete intervals of Δd k , Δε rk , determine the range of off-grid parameters ([d k,min , d k,max , [ε rk,min , ε rk,max ), where:

[0051] d k,min = d k - Δd k / 2, d k,max = d k + Δd k / 2,

[0052]

[0053] Update the range interval Δε of the relative permittivity rk = (ε rk,max - ε rk,min ) / 2. Therefore, the medium parameters of the k-th layer are expressed as:

[0054] d′ k = d k + z1Δd k , |z1| < 0.5 <(

[0055] ε′ rk = ε rk + z2Δε rk , |z2| < 0.5

[0056] Take a random weight vector m = [m1, m2,..., m n , where m1 + m2 +... + m n = 1, and, m j ∈ [0, 1], j ∈ [1, n]. Then the correlation of the sparse vector after parameter search is expressed as:

[0057]

[0058] Therefore, construct the parameter search cost function of the vector [z1, z2]:

[0059]

[0060] Based on the optimization algorithm of global optimization and the parameter search cost function, the reflection wave delay T k (d k + z1Δd k , ε rk + z2Δε rk , L j ) and the medium parameters [d k + z1Δd k , ε rk + z2Δε rk ) are inversely obtained.

[0061] Outside the optimization algorithm, perform Monte Carlo simulation with the number of times P, draw the parameter inversion distribution diagram, and perform an averaging operation on the parameter distribution to obtain the medium parameters:

[0062]

[0063]

[0064] Step 5, perform engineering applications according to the inversion parameters obtained in Step 4:

[0065] In typical layered medium scenarios such as roads and building structures, according to the inversion parameters obtained in Step 4, obtain the change range and trend of the thickness and relative dielectric constant of the layered medium in the detection area, deduce relevant information such as conductivity and moisture content, judge the abnormal areas in the medium structure, and use it to detect diseases such as road surface collapse in complex road structures, providing a reliable method for real-time and efficient monitoring of building structure damage, and also providing accurate background medium parameter information for subsequent target imaging and recognition detection.

[0066] Beneficial effects

[0067] (1) Traditional parameter inversion algorithms cannot adaptively obtain the reflected signal delay. However, the present invention introduces the OMP algorithm in compressed sensing and realizes the adaptive inversion of the reflected signal delay by constructing a signal sparse model.

[0068] (2) Traditional parameter inversion algorithms do not consider the refraction effect between layers and are difficult to apply to multi-layer media inversion. The present invention introduces the refraction point approximation and solves the medium parameters layer by layer iteratively, which greatly reduces the error caused by the refraction effect.

[0069] (3) The signal sparse models in traditional methods are all built in a radar system with integrated transmission and reception. This invention is based on a CMP radar system and proposes a sparse signal model in the CMP system for the first time, thus realizing a sparse solution in the CMP system.

[0070] (4) Traditional compressed sensing greedy algorithms have the problem of dictionary mismatch. The present invention achieves a refined search for off-grid parameters by constructing a parameter search cost function, thereby improving the inversion effect of the algorithm.

[0071] (5) The time delay acquisition and parameter inversion of the traditional parameter inversion algorithm are independent of each other, and the time delay acquisition is judged and extracted only by the time domain signal amplitude, which leads to large errors in the parameter inversion. The present invention designs a special sparse CMP model that uses frequency domain information to achieve the joint inversion of time delay information and medium parameters;

[0072] (6) Compared with the traditional parameter inversion algorithm based on the radar system with integrated transmission and reception, the present invention is based on the CMP system, which realizes the medium parameter inversion by combining different channel data, with high inversion accuracy and little influence from clutter and noise;

[0073] (7) The present invention introduces Monte Carlo simulation to draw a distribution diagram of parameter inversion, performs an average operation on the parameter distribution, prevents the algorithm from falling into the local optimum, and improves the inversion accuracy;

[0074] (8) The present invention uses stepped frequency signals to achieve medium parameter inversion. Compared with pulse radar, it has a larger bandwidth. The range resolution can be improved by adjusting the bandwidth, and accurate inversion of thin layers can be achieved in special scenarios.

[0075] (9) Based on the CMP system, the present invention considers the different attenuation degrees of radar signals under different channel spacings and proposes a channel-by-channel residual update method to avoid the problem of consistent residual component amplitudes when applying the original OMP algorithm to the CMP signal model.

[0076] (10) The present invention constructs a sparse solution strategy combining the OMP algorithm and an optimization algorithm. Based on the OMP algorithm, off-grid medium parameters are estimated. Then, within the iteration of the OMP algorithm, the dictionary mismatch effect is eliminated based on a parameter search cost function, and then the trace residual is updated and the dictionary is updated layer by layer to achieve accurate inversion of the medium parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is the signal processing flowchart of an embodiment of the present invention;

[0078] Figure 2 is the single-layer CMP model established by the method of the present invention;

[0079] Figure 3 is the multi-layer CMP model established by the method of the present invention;

[0080] Figure 4 is the approximate geometric relationship of refraction points based on by the method of the present invention;

[0081] Figure 5 is the discretized parameter grid assumed by the method of the present invention;

[0082] Figure 6 is the three-layer CMP model adopted in the simulation of the method of the present invention;

[0083] Figure 7 is the layered medium model adopted in the actual measurement of the method of the present invention;

[0084] Figure 8 is the asphalt road structure adopted in the actual measurement of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0085] The object of the present invention is to overcome the deficiencies of traditional ground penetrating radar medium parameter inversion methods, and provides a ground penetrating radar layered medium parameter inversion method based on the CMP model and parameter search OMP. The present invention is applicable to multi-layer medium layered models, and is used in various fields such as road detection and building monitoring, and also provides accurate prior structure information for subsequent underground target imaging and recognition detection.

[0086] Figure 1 is the signal processing flowchart of an embodiment of the present invention. The present invention is based on stepped frequency echo signals and is implemented through the following steps:

[0087] Step 1, construct the propagation delay of the multi-layer CMP model, and the method is as follows:

[0088] (1) Based on the single-layer CMP model, as Figure 2 shown, there is a reflection phenomenon of incident electromagnetic waves at the bottom of the single-layer medium, and the propagation delay of the reflected wave at the first layered interface is expressed as:

[0089]

[0090] Among them, d1 and ε r1 respectively represent the thickness and relative dielectric constant of the first-layer medium, c represents the speed of light, and 2L j represents the antenna transceiver spacing of the j-th A-scan, and n represents the number of A-scan channels measured by the ground penetrating radar;

[0091] (2) Deduce the single-layer model to the K-layer CMP model. As Figure 3 shown, the propagation delay of the reflected wave of the K-th layered interface is expressed as:

[0092]

[0093] Among them, d k , ε rk respectively represent the thickness and relative dielectric constant of the k-th layer medium, and x1, x2,..., x K represent the lateral offset distances of the electromagnetic wave in the 1st, 2nd,..., K-th layered media;

[0094] For the above-mentioned x1, x2,..., x K , the determination method is:

[0095] Assume that the refraction process satisfies the geometric optics hypothesis, the refraction process satisfies Snell's law, simplify the solution of the multi-variable equations of the refraction point through the refraction point approximation method, and use a single algebraic operation to estimate the position of the refraction point. As Figure 4 shown, it is expressed as:

[0096]

[0097] Among them, y b represents the position of the refraction point of the layered interface, y1 represents the intersection point of the electromagnetic wave and the layered interface under the straight-line propagation hypothesis, y2 represents the position where the electromagnetic wave is vertically mapped to the layered interface after refraction, and v1 and v2 respectively represent the propagation speeds of the electromagnetic wave in medium 1 and medium 2;

[0098] Therefore, the lateral offset distance of the electromagnetic wave in the medium is expressed as:

[0099]

[0100] Deduce the position of the refraction point of the K-layer CMP model, which is expressed as:

[0101]

[0102] Step 2. According to the propagation delay obtained in Step 1, construct a sparse vector of the multi-layer CMP model. The method is:

[0103] Based on the single-layer CMP model, k = 1. Assume that the thickness and relative permittivity of the first layer of medium are d = [d 1,1 , d 1,2 ,..., d 1,M1 , where M1 and M2 are the number of grid points for thickness and equivalent permittivity respectively, and the discrete intervals are Δd1 and Δε r1 , then the combination of medium parameters is expressed as [(d 1,1 , ε r1,1 ), (d 1,1 , ε r1,2 ),...,(d 1,1 , ε r1,M2 ), (d 1,2 , ε r1,1 )...,(d 1,M1 , ε r1,M2 )], and the delay time of the reflected wave is expressed as:

[0104] F1 = [T1(d 1,1 , ε r1,1 , L j ), T1(d 1,1 , ε r1,2 , L j ),..., T1(d 1,1 , ε r1,M2 , L j ), T1(d 1,2 , ε r1,1 , L j )..., T1(d 1,M1 , ε r1,M2 , L j )]

[0105] Based on the K-layer CMP model, assume that the thickness and relative permittivity of the first K - 1 layers of medium are known, k = K. As Figure 5 shown, assume that the thickness and relative permittivity of the Kth layer of medium are d = [d K,1 , d K,2 ,..., d K,M1 , the discrete intervals are Δd K , Δε rK , then the combination of medium parameters is expressed as [(d K,1 , ε rK,1 ), (d K,1 , ε rK,2 ),...,(d K,1 , ε rK,M2 ), (d K,2 , ε rK,1 )...,(d K,M1 , ε rK,M2), the reflection wave time delay is expressed as:

[0106] F K =[T K (d K,1 ,ε rK,1 ,L j )),T K (d K,1 ,ε rK,2 ,L j )),...,T K (d K,1 ,ε rK,M2 ,L j )),T K (d K,2 ,ε rK,1 ,L j )...,T K (d K,M1 ,ε rK,M2 ,L j )]

[0107] Among them, the position of the refraction point involved in the reflection time delay can be jointly calculated from the medium parameters of the first K - 1 layers and the assumed parameters of the Kth layer;

[0108] The set of reflection wave time delays F derived from the CMP model K , and the sparse vector representation of the K - layer CMP model is:

[0109]

[0110] Among them, N is the number of frequency domain sampling points, f1, f2,..., f N are the frequency domain sampling values, and f i = f1+(i - 1)Δf, f i represents the sampling value of the ith frequency point, and Δf is the frequency domain sampling interval;

[0111] Step 3, establish the sparse dictionary of a single A - scan and construct the CMP sparse model:

[0112] Based on the K - layer CMP model and the reflection wave time delay expression, horizontally splice the sparse vectors of each reflection time delay to construct the sparse dictionary representation A of the jth trace A - scan j,K :

[0113] A j,K =[a(T K (d K,1 ,ε rK,1 ,L j )),a(T K (d K,1 ,ε rK,2 ,L j),...,a(T K (d K,1 ,ε rK,M2 ,L j ),a(T K (d K,2 ,ε rK,1 ,L j ),...,a(T K (d K,M1 ,ε rK,M2 ,L j ))]

[0114] Thus, the sparsity representation of the j-th A-scan echo signal based on the K-layer CMP model is:

[0115] r j,K = ΛA j,K s + n

[0116] where r j,K = [r j,K (f1), r j,K (f2),..., r j,K (f N )] T represents the N-frequency point data vector of the j-th A-scan electromagnetic echo based on the K-layer CMP model with dimension (N,1), represents the frequency domain signal pulse matrix with dimension (N,N), A j,K represents the sparse dictionary of the j-th A-scan electromagnetic echo based on the K-layer CMP model with dimension (N,M1M2), s = [s1, s2,..., s K T represents the reflection coefficient vector of the layer reflection wave with dimension (M1M2,1), n = [n(f1), n(f2),..., n(f N )] T represents the frequency domain Gaussian white noise with dimension (N,1);

[0117] Therefore, based on the K-layer CMP model, for the echo data r of each channel j,K and the sparse dictionary A j,K are concatenated vertically, and the sparse model based on the stepped frequency signal and the CMP system is expressed as:

[0118]

[0119] where r K is the data vector based on the K-layer CMP sparse model with dimension (nN,1), A K is the sparse dictionary based on the K-layer CMP model with dimension (nN,M1M2); ​

[0120] Step 4: Based on the K-layer CMP sparse model constructed in Step 3, use the OMP algorithm for parameter inversion. The specific steps are as follows:

[0121] 1) Initialize the residual component Establish an index set The iteration count k = 1, where the residual component is expressed as

[0122] 2) Calculate the correlation For t ∈ [1, M1M2], solve the index where θ t represents the t-th column sparse vector of the sparse dictionary A K ;

[0123] 3) According to the medium parameter combinations [(d k,1 , ε rk,1 ), (d 1,1 , ε rk,2 ),..., (d k,1 , ε rk,M2 ), (d k,2 , ε rk,1 )..., (d k,M1 , ε rk,M2 )] and the index λ k , obtain the off-grid parameters (d k , ε rk ) of the k-th layer medium and the corresponding propagation time delay T k (d k , ε rk , L j );

[0124] 4) According to the off-grid parameter range, construct a parameter search cost function and invert the medium parameters;

[0125] 5) According to the medium parameters d k , ε rk , deduce the propagation time delay T k (d k , ε rk , L j ) of the k-th layer reflected wave, and construct the sparse vector θ k,j = a(T k (d k , ε rk , L j )), j ∈ [1, n], where j is the number of A-scan channels;

[0126] 6) Solve the echo reflection coefficient of each channel's A-scan Update the residual component of each channel's A-scan Update the total residual component

[0127] 7) Increment k in step 1) by 1. If k < K, calculate the propagation delay T of the reflected wave at the k-th stratified interface based on the medium parameters of the first k - 1 layers obtained by inversion and the discretization parameters assumed for the k-th layer. k (d k , ε rk , L j ), update the sparse vector a(T k (d k , ε rk , L j )) and the sparse dictionary A K , and return to step 2); if k = K, end.

[0128] The specific method for step 4) is as follows:

[0129] In the k-th iteration of the OMP algorithm, based on the correlation calculation, obtain the best-matching off-grid parameter d k , ε rk and the corresponding propagation delay T k (d k , ε rk , L j ). The discrete intervals are Δd k , Δε rk , respectively. Determine the range of the off-grid parameter ([d k,min , d k,max , [ε rk,min , ε rk , max]), where:

[0130] d k,min = d k - Δd k / 2, d k,max = d k + Δd k / 2,

[0131]

[0132] Update the range interval Δε of the relative permittivity rk = (ε rk,max - ε rk,min ) / 2. Therefore, the medium parameters of the k-th layer are expressed as:

[0133] d′ k = d k + z1Δd k , |z1| < 0.5

[0134] ε′ rk = ε rk + z2Δε rk, |z2| < 0.5

[0135] Take a random weight vector m = [m1, m2,..., m n , where m1 + m2 +... + m n = 1, and m j ∈ [0, 1], j ∈ [1, n]. Then the correlation of the sparse vector after parameter search is expressed as:

[0136]

[0137] Therefore, construct the parameter search cost function of the vector [z1, z2]:

[0138]

[0139] Based on the optimization algorithm of global optimization and the parameter search cost function, the reflection wave delay T k (d k + z1Δd k , ε rk + z2Δε rk , L j [[ID=3,3]] of the k-th layer and the medium parameters [d k + z1Δd k , ε rk + z2Δε[[ID=4,0]] rk are inversed;

[0140] Outside the optimization algorithm, perform Monte Carlo simulation with the number of times P, draw the parameter inversion distribution diagram, and perform an averaging operation on the parameter distribution to obtain the medium parameters:

[0141]

[0142]

[0143] Step 5, perform engineering applications according to the inversion parameters obtained in Step 4:

[0144] In typical layered medium scenarios such as roads and building structures, according to the inversion parameters obtained in Step 4, obtain the change range and trend of the thickness and relative dielectric constant of the layered medium in the detection area, deduce relevant information such as conductivity and moisture content, and judge the abnormal areas in the medium structure, so as to detect diseases such as road surface collapses in complex road structures, provide a reliable method for real-time and efficient monitoring of building structure damage, and also provide accurate background medium parameter information for subsequent target imaging and recognition detection.

[0145] Embodiment

[0146] To verify a ground penetrating radar stratified medium parameter inversion method based on the CMP model and parameter search OMP proposed by the present invention, a simulation experiment was designed for analysis. As Figure 6 shown, the simulation uses the gprMax software to construct a three-layer medium model, and the simulation parameters are shown in Table 1.

[0147] Table 1 Simulation parameter settings

[0148]

[0149]

[0150] The simulation results are shown in Table 2. The method proposed by the present invention has achieved excellent inversion accuracy. Based on the three-layer CMP model, the relative error of the layer thickness is controlled within 1%, and the error of the relative dielectric constant is controlled within 4%.

[0151] Table 2 Simulation inversion results

[0152]

[0153] Table 3 Measured parameter settings

[0154]

[0155] Furthermore, the stratified medium scenarios and the measured scenarios of asphalt roads shown in Figure 7 、 Figure 8 are adopted, as well as the experimental parameters in Table 3 and Table 4. The radar system consists of a vector network analyzer and an array antenna, and the antenna is placed on a slidable guide rail. As shown in Table 4, the inversion error of the layer thickness in the stratified medium experiment is within 7 mm, and the inversion error of the layer thickness in the measured asphalt road is within 1.5 cm. The relative dielectric constant of each layer is also controlled within a reasonable range.

[0156] Table 4 Measured inversion results

[0157]

[0158] In summary, the above is only the preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A layered medium parameter inversion method based on the CMP model and parameter search OMP algorithm, characterized in that The steps of the method include: Step 1, construct the propagation delay of the multi-layer CMP model; Step 2: construct a sparse vector of the multi-layer CMP model based on the propagation delay constructed in step 1; Step 3, constructing a multi-layer CMP sparse model based on the sparse vector of the multi-layer CMP model obtained in step 2; Step 4, performing parameter inversion using the OMP algorithm based on the multi-layer CMP sparse model constructed in step 3 to obtain inversion parameters; Step 5, guiding the detection of the road structure according to the inversion parameters obtained in step 4; In step 1, the method for constructing the propagation delay of the multi-layer CMP model is: The propagation delay of the first layered interface reflection wave is: Among them, d1,ε r1 They represent the thickness and relative dielectric constant of the first layer of medium, c represents the speed of light, 2L j represents the antenna transmission and reception distance of the jth A-scan, and n represents the number of A-scan channels measured by the ground penetrating radar; The propagation delay of the Kth layered interface reflection wave is expressed as: Among them, d k ,ε rk Represent the thickness and relative dielectric constant of the kth layer, x1, x2, ..., x K represents the lateral offset distance of the electromagnetic wave in the 1st, 2nd, ...Kth layered media; The x1,x2,...,x K The method for determining is: In step 2, the method for constructing the sparse vector of the multi-layer CMP model is: Based on the single-layer CMP model, k = 1, assuming that the first layer medium parameters are d = [d 1,1 ,d 1,2 ,...,d 1,M1 ], Where M1 and M2 are the grid points of thickness and equivalent dielectric constant respectively, and the discrete intervals are Δd1 and Δε respectively. r1 , then the medium parameter combination is expressed as [(d 1,1 ,ε r1,1 ),(d 1,1 ,ε r1,2 ),...,(d 1,1 ,ε r1,M2 ),(d 1,2 ,ε r1,1 )...,(d 1,M1 ,ε r1,M2 )], the reflected wave delay is expressed as: F1=[T1(d 1,1 ,e r1,1 ,L j ),T1(d 1,1 ,e r1,2 ,L j ),...,T1(d 1,1 ,e r1,M2 ,L j ), T1(d 1,2 ,e r1,1 ,L j )...,T1(d 1,M1 ,e r1,M2 ,L j )] Based on the K-layer CMP model, assuming that the thickness and relative dielectric constant of the first K-1 layers are known, where k = K, the thickness and relative dielectric constant of the Kth layer are d = [d K,1 ,d K,2 ,...,d K,M1 ], The discrete intervals are Δd K ,Δε rK , then the medium parameter is [(d K,1 ,ε rK,1 ),(d K,1 ,ε rK,2 ),...,(d K,1 ,ε rK,M2 ),(d K,2 ,ε rK,1 )...,(d K,M1 ,ε rK,M2 )], the reflected wave delay is expressed as: F K =[T K (d K,1 ,ε rK,1 ,L j ),T K (d K,1 ,ε rK,2 ,L j ),...,T K (d K,1 ,ε rK,M2 ,L j ), T K (d K,2 ,ε rK,1 ,L j )...,T K (d K,M1 ,ε rK,M2 ,L j )] The refraction point position involved in the reflection delay is calculated by combining the parameters of the first K-1 layers of media and the assumed parameters of the Kth layer. The reflected wave delay set F derived from the CMP model K , the sparse vector representation of the K-layer CMP model is: Where N is the number of frequency domain sampling points, f1,f2,...,f N is the frequency domain sampling value, and f i =f1+(i-1)Δf,f i represents the sampling value of the i-th frequency point, Δf is the frequency domain sampling interval; In step 3, the method for constructing a multi-layer CMP sparse model is: Based on the K-layer CMP model and the reflection wave delay expression, the sparse vectors of each reflection delay are horizontally spliced to construct the sparse dictionary representation A of the j-th A-scan. j,K : A j,K =[a(T K (d K,1 ,ε rK,1 ,L j )),a(T K (d K,1 ,ε rK,2 ,L j )),..., a(T K (d K,1 ,ε rK,M2 ,L j )),a(T K (d K,2 ,ε rK,1 ,L j )),...,a(T K (d K,M1 ,ε rK,M2 ,L j ))] The sparsity of the j-th A-scan echo signal based on the K-layer CMP model is expressed as: r j,K =ΛA j,K s+n Among them, r j,K =[r j,K (f1),r j,K (f2),...,r j,K (f N )] T Represents the N frequency point data vector of the j-th A-scan electromagnetic echo based on the K-layer CMP model of dimension (N,1), A represents the frequency domain signal pulse matrix of dimension (N,N), j,K represents the sparse dictionary of the j-th A-scan electromagnetic echo based on the K-layer CMP model of dimension (N, M1M2), s=[s1,s2,...,s K ] T Reflection coefficient vector representing the layer reflection wave of dimension (M1M2,1), n=[n(f1),n(f2),...,n(f N )] T represents frequency domain Gaussian white noise of dimension (N,1); Based on the K-layer CMP model, the echo data of each channel r j,K With the sparse dictionary A j,K In the form of vertical splicing, the sparse model based on the stepped frequency signal and the CMP system is expressed as: Among them, r K is a data vector of dimension (nN, 1) based on the K-layer CMP sparse model, A K It is a sparse dictionary based on the K-layer CMP model of dimension (nN,M1M2); In step 4, the steps of performing parameter inversion are: 1) Initialize the residual component Create an index collection Iteration count k = 1, where the residual component is expressed as 2) Calculate the correlation Solving Index where θ t Represents the sparse dictionary A K The t-th column sparse vector of 3) According to the parameter [(d k,1 ,ε rk,1 ),(d 1,1 ,ε rk,2 ),...,(d k,1 ,ε rk,M2 ),(d k,2 ,ε rk,1 )...,(d k,M1 ,ε rk,M2 )] with index λ k , get the k-th layer off-grid parameter (d k ,ε rk ) and propagation delay T k (d k ,ε rk ,L j ); 4) According to the off-grid parameter range, a parameter search cost function is constructed to invert the medium parameters; 5) According to the medium parameter d k ,ε rk , derive the propagation delay T of the kth layer reflected wave k (d k ,ε rk ,L j ), construct a sparse vector θ k,j =a(T k (d k ,ε rk ,L j )),j∈[1,n], where j is the number of A-scan channels; 6) Calculate the echo reflection coefficient of each A-scan Update each residual component Update the total residual component 7) Increment k in step 1) by 1. If k < K, calculate the propagation delay T of the reflected wave at the k-th stratified interface based on the medium parameters of the first k - 1 layers obtained by inversion and the discretization parameters assumed for the k-th layer. k (d k ,ε rk ,L j ), update the sparse vector a(T k (d k ,ε rk ,L j )) and the sparse dictionary A K , and return to step 2); if k = K, end.

2. The layered medium parameter inversion method based on the CMP model and the parameter search OMP algorithm according to claim 1, characterized in that: The specific method of step 4) is: In the kth iteration of the OMP algorithm, the best matching off-grid parameter d is obtained according to the correlation calculation. k ,ε rk and the corresponding propagation delay T k (d k ,ε rk ,L j ), the discrete intervals are Δd k ,Δε rk , determine the range of the off-grid parameter ([d k,min ,d k,max ],[ε rk,min ,ε rk,max ]),in: d k,min =d k -Δd k / 2,d k,max =d k +Δd k / 2, Update the range interval Δε of the relative dielectric constant rk =(ε rk,max -ε rk,min ) / 2, so the k-th layer medium parameter is expressed as: d′ k =d k +z1Δd k ,|z1|<0.5 e' rk =e rk +z2No rk ,|z2|<0.5 Take a random weight vector m=[m1,m2,...,m n ], where m1+m2+...+m n =1, and m j ∈[0,1],j∈[1,n], the correlation of the sparse vector after parameter search is expressed as:

3. The layered medium parameter inversion method based on the CMP model and the parameter search OMP algorithm according to claim 2, characterized in that: The method to construct the parameter search cost function of the vector [z1,z2] is: Based on the global optimization algorithm and parameter search cost function, the reflection wave delay T of the kth layer is obtained by inversion. k (d k +z1Δd k ,ε rk +z2Δε rk ,L j ) and medium parameters [d k +z1Δd k ,ε rk +z2Δε rk ].

4. The layered medium parameter inversion method based on the CMP model and the parameter search OMP algorithm according to claim 3, characterized in that: The method for inverting medium parameters is: outside the optimization algorithm, Monte Carlo simulation is performed with a number of P times, the parameter inversion distribution diagram is drawn, and the parameter distribution is averaged to obtain the medium parameters:

5. The layered medium parameter inversion method based on the CMP model and the parameter search OMP algorithm according to claim 1, characterized in that: In step 5, the method for guiding the detection of road structures based on the obtained inversion parameters is as follows: in a layered medium scenario of roads and building structures, based on the inversion parameters, the variation range and trend of the layered medium thickness and relative dielectric constant in the detection area are obtained, and relevant information such as conductivity and moisture content is derived to determine abnormal areas in the medium structure, detect pavement defects in the road structure, and monitor damage to the building structure.

Images