Ground penetrating radar medium dielectric property inversion method based on FDTD physical constraint

Abstract

The application discloses a ground penetrating radar medium dielectric property inversion method based on FDTD physical constraint. The method takes ground penetrating radar B-Scan data as input, constructs a unified scale radar data sequence through data preprocessing, and uses a deep inversion network to model the electromagnetic response characteristics of the underground medium in multiple scales to realize preliminary inversion of the dielectric constant and conductivity. On this basis, a time-domain finite difference method-based electromagnetic wave forward propagation model is introduced to numerically simulate the dielectric parameters obtained by inversion and generate corresponding simulated radar data. Meanwhile, a twin neural network is constructed to measure the high-dimensional feature consistency of the simulated data and the original observation data to form a physical constraint signal. Further, an optimization objective function is constructed by combining the data-driven error and the physical consistency constraint to iteratively optimize the inversion network, thereby realizing the collaborative constraint of data driving and physical law. Compared with the traditional method, the application can effectively improve the physical interpretability and generalization ability of the inversion result, realize stable and accurate inversion of the dielectric constant and conductivity of the underground medium in a complex underground environment, and is suitable for high-precision detection and analysis of hidden diseases such as underground cavities of urban roads.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional ground-penetrating radar signal processing technology, and more specifically to a ground-penetrating radar dielectric property inversion method based on FDTD physical constraints. Background Technology

[0002] As a crucial component of urban transportation systems, the structural safety of roads directly impacts the reliability of urban operations. Under the influence of factors such as rainfall erosion, increased traffic loads, and intensive underground development, urban roads are prone to developing cavities, subsidence, and other hidden defects, seriously threatening road structural safety. Ground-penetrating radar (GPR), a highly efficient non-destructive testing technology, transmits high-frequency pulsed electromagnetic waves underground and receives reflected signals from different media interfaces, enabling the analysis of underground structures and media properties. However, due to complex physical phenomena such as reflection, diffraction, scattering, and attenuation during electromagnetic wave propagation underground, relying solely on profile identification is insufficient to accurately reveal the true physical properties of underground cavities and surrounding media. Therefore, it is urgent to establish a mapping relationship between GPR observation data and the electromagnetic parameters of underground media. By combining data-driven methods with the physical constraints of electromagnetic wave propagation, accurate inversion of the dielectric constant and conductivity of underground cavities and surrounding media can be achieved, providing reliable technical support for urban road structural safety assessment and hazard identification. Summary of the Invention

[0003] In view of this, the present invention provides a ground-penetrating radar (GPR) method for inverting the dielectric properties of subsurface media based on FDTD physical constraints. This method first performs scale unification processing on the acquired GPR B-Scan data to construct input data for inverting the electromagnetic parameters of the subsurface media. A nonlinear mapping relationship between radar observation data and the dielectric constant and conductivity of the subsurface media is established through a depth inversion network. After completing the initial data-driven inversion, the obtained medium parameters are simulated using the finite-difference time-domain (FDTD) method to generate simulated radar data corresponding to the inversion results. Furthermore, a Siamese neural network is used to perform high-dimensional feature matching between the simulated data and the original observation data, calculating their similarity to form physical consistency constraints. Based on this, the data-driven inversion results are fused with the physical constraint information. Through iterative optimization of network parameters, the final output distribution of the dielectric constant and conductivity of the subsurface media conforms to both the characteristics of the radar observation data and the laws of electromagnetic wave propagation, achieving stable and accurate inversion of the electromagnetic parameters of subsurface space.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] S1: Data-driven inversion of electrical parameters of underground media, the specific steps are as follows:

[0006] S11: Acquire ground-penetrating radar B-Scan data and perform scale unification processing on the data. The input size is 50*256, where 50 is the data length along the sampling direction and 256 is the number of sampling points. Construct ground-penetrating radar input data for inversion.

[0007] S12: The preprocessed radar data is input into the inversion network. The propagation response of electromagnetic waves in the underground medium is modeled layer by layer through the multi-layer feature extraction module. Residual connections are introduced in the feature extraction process to enhance the deep feature expression capability. An attention mechanism is introduced to strengthen the feature focus on key electromagnetic response areas. An asymmetric downsampling strategy is used to focus on modeling the propagation direction of electromagnetic waves to characterize the propagation time sequence characteristics and energy attenuation law of electromagnetic waves in the underground medium, thereby establishing a nonlinear mapping relationship between radar detection data and electromagnetic parameters of the underground medium.

[0008] S13: The feature resolution is restored layer by layer through the decoding module, and multi-scale information is fused by skip connections to output the dielectric constant and conductivity distribution of the subsurface medium retrieved from ground penetrating radar data. The mean square error (MSE) between the retrieved dielectric constant and conductivity and the true values ​​is calculated. p and MSE c This constitutes the data-driven inversion error;

[0009] S2: Construction of physical constraints for electromagnetic propagation and twin consistency determination based on the finite-difference time-domain method, the specific steps of which are as follows:

[0010] S21: Based on the dielectric constant and conductivity distribution of the underground medium obtained by inversion in S1, the propagation of electromagnetic waves in the medium is numerically solved using the finite-difference time-domain method (FDTD) to generate simulated radar B-Scan data corresponding to the inversion parameters;

[0011] S22: The simulated radar data generated by FDTD and the original observed radar data are respectively input into two shared parameter branches of the Siamese neural network. The network performs high-dimensional feature encoding on the two types of data through a multi-layer convolutional feature extraction module. Wavelet transform can be introduced during the feature extraction process to enhance the representation ability of low-frequency global information and high-frequency local detail features. Then, the high-dimensional features of the two branches are mapped to a unified feature space. The consistency between the simulated data and the observed data in the feature space is reflected by the feature similarity measurement, thereby forming a physical law constraint signal.

[0012] S23: Calculate the cosine similarity between the data generated by FDTD and the input data in the high-dimensional feature space. The formula for calculating cosine similarity (Cos_Sim) is as follows:

[0013]

[0014] Where F in F is the high-dimensional feature vector of the input ground-penetrating radar data. sim This is a high-dimensional feature vector of the simulated ground-penetrating radar data calculated based on the inversion results;

[0015] S3: Data-driven inversion and physical constraint fusion optimization, the specific steps are as follows:

[0016] S31: Combine the data-driven and physical consistency constraint errors calculated in S1 and S2 to construct an optimized loss function L. all The calculation formula is as follows:

[0017]

[0018] α, β and γ are the weights of each item, used to balance the influence of data-driven and physical constraints;

[0019] S32: Apply the joint loss function to the training of the S1 inversion network to achieve synergistic optimization of data-driven inversion and FDTD twin physical constraints, thereby obtaining stable and physically interpretable inversion results of the dielectric constant and conductivity of the underground medium. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 The attached figure is a flowchart of a ground-penetrating radar dielectric property inversion method based on FDTD physical constraints provided by the present invention.

[0022] Figure 2 The attached figure shows the structure of the network model for inverting the dielectric properties of ground-penetrating radar media based on FDTD physical constraints. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] See appendix Figure 1 This invention discloses a method for inverting the dielectric properties of a ground-penetrating radar medium based on FDTD physical constraints, comprising:

[0025] S1: Data-driven inversion of electrical parameters of underground media, the specific steps are as follows:

[0026] S11: Acquire ground-penetrating radar B-Scan data and perform scale unification processing on the data. The input size is 50*256, where 50 is the data length along the sampling direction and 256 is the number of sampling points. Construct ground-penetrating radar input data for inversion.

[0027] S12: The preprocessed radar data is input into the inversion network. The propagation response of electromagnetic waves in the underground medium is modeled layer by layer through the multi-layer feature extraction module. Residual connections are introduced in the feature extraction process to enhance the deep feature expression capability. An attention mechanism is introduced to strengthen the feature focus on key electromagnetic response areas. An asymmetric downsampling strategy is used to focus on modeling the propagation direction of electromagnetic waves to characterize the propagation time sequence characteristics and energy attenuation law of electromagnetic waves in the underground medium, thereby establishing a nonlinear mapping relationship between radar detection data and electromagnetic parameters of the underground medium.

[0028] S13: The feature resolution is restored layer by layer through the decoding module, and multi-scale information is fused by skip connections to output the dielectric constant and conductivity distribution of the subsurface medium retrieved from ground penetrating radar data. The mean square error (MSE) between the retrieved dielectric constant and conductivity and the true values ​​is calculated. p and MSE c This constitutes the data-driven inversion error;

[0029] S2: Construction of physical constraints for electromagnetic propagation and twin consistency determination based on the finite-difference time-domain method, the specific steps of which are as follows:

[0030] S21: Based on the dielectric constant and conductivity distribution of the underground medium obtained by inversion in S1, the propagation of electromagnetic waves in the medium is numerically solved using the finite-difference time-domain method (FDTD) to generate simulated radar B-Scan data corresponding to the inversion parameters;

[0031] S22: The simulated radar data generated by FDTD and the original observed radar data are respectively input into two shared parameter branches of the Siamese neural network. The network performs high-dimensional feature encoding on the two types of data through a multi-layer convolutional feature extraction module. Wavelet transform can be introduced during the feature extraction process to enhance the representation ability of low-frequency global information and high-frequency local detail features. Then, the high-dimensional features of the two branches are mapped to a unified feature space. The consistency between the simulated data and the observed data in the feature space is reflected by the feature similarity measurement, thereby forming a physical law constraint signal.

[0032] S23: Calculate the cosine similarity between the data generated by FDTD and the input data in the high-dimensional feature space. The formula for calculating cosine similarity (Cos_Sim) is as follows:

[0033]

[0034] Where F in F is the high-dimensional feature vector of the input ground-penetrating radar data. sim This is a high-dimensional feature vector of the simulated ground-penetrating radar data calculated based on the inversion results;

[0035] S3: Data-driven inversion and physical constraint fusion optimization, the specific steps are as follows:

[0036] S31: Combine the data-driven and physical consistency constraint errors calculated in S1 and S2 to construct an optimized loss function L. all The calculation formula is as follows:

[0037]

[0038] α, β and γ are the weights of each item, used to balance the influence of data-driven and physical constraints;

[0039] S32: Apply the joint loss function to the training of the S1 inversion network to achieve synergistic optimization of data-driven inversion and FDTD twin physical constraints, thereby obtaining stable and physically interpretable inversion results of the dielectric constant and conductivity of the underground medium.

[0040] Figure 2The diagram shows the network structure for inverting the dielectric properties of a ground-penetrating radar (GPR) medium based on FDTD physical constraints. This network structure mainly includes a data-driven inversion module for the electromagnetic parameters of the subsurface medium and an electromagnetic propagation physical constraint module based on the finite-difference time-domain (FDTD) method. Accurate reconstruction of the inversion results is achieved through joint optimization. First, in the data-driven inversion process, GPR B-Scan data is acquired and scaled to construct input data of size 50*256, where 50 represents the data length along the sampling direction and 256 represents the number of sampling points. Then, the preprocessed radar data is input into the inversion network. A multi-layer feature extraction module models the propagation response of electromagnetic waves in the subsurface medium layer by layer. Residual connections are introduced during feature extraction to enhance the expression of deep features, an attention mechanism is introduced to strengthen the focus on key electromagnetic response regions, and an asymmetric downsampling strategy is used to focus on modeling the propagation direction of electromagnetic waves, thereby characterizing the propagation time-series characteristics and energy attenuation laws of electromagnetic waves in the subsurface medium. Based on this, the feature resolution is restored layer by layer through the decoding module, and multi-scale feature fusion is achieved by combining skip connections. Finally, the dielectric constant distribution and conductivity distribution of the underground medium are output, and the mean square error between the inversion result and the true value is calculated to constitute the data-driven inversion error.

[0041] To improve the physical consistency of the inversion results, electromagnetic propagation physical constraints are introduced based on the data-driven inversion described above. Specifically, based on the dielectric constant and conductivity distribution of the subsurface medium obtained from the inversion, the finite-difference time-domain method is used to numerically solve the propagation process of electromagnetic waves in the medium, generating simulated ground-penetrating radar B-Scan data corresponding to the inversion parameters. Subsequently, the simulated data and the original observation data are respectively input into two shared parameter branches of a Siamese neural network. High-dimensional feature encoding is performed on the two types of data through a multi-layer convolutional feature extraction module, and wavelet decomposition is introduced during the feature extraction process to enhance the joint representation ability of low-frequency overall structural information and high-frequency detailed features. Then, the features extracted from the two branches are mapped to a unified feature space. By calculating the cosine similarity between the high-dimensional feature vectors, the consistency between the simulated data and the observation data in the feature space is measured, thereby constructing physical consistency constraints between the inversion results and the laws of electromagnetic propagation.

[0042] Building upon this foundation, data-driven inversion errors are jointly modeled with physical consistency constraints based on Siamese networks, constructing a unified optimized loss function. By assigning weight coefficients to various errors, the synergistic fusion of data-driven information and physical constraint information is achieved. This joint loss function is then applied to the training process of the inversion network. Through continuous iterative optimization of network parameters, the inversion results are made to fit the observed data while satisfying the laws of electromagnetic wave propagation. This results in a stable, accurate, and physically interpretable distribution of the dielectric constant and conductivity of the subsurface medium, achieving a highly reliable inversion of the dielectric properties of the subsurface medium.

[0043] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for inverting the dielectric properties of a ground-penetrating radar medium based on FDTD physical constraints, characterized in that, include: S1: Data-driven inversion of electrical parameters of underground media, the specific steps are as follows: S11: Acquire ground-penetrating radar B-Scan data and perform scale unification processing on the data. The input size is 50*256, where 50 is the data length along the sampling direction and 256 is the number of sampling points. Construct ground-penetrating radar input data for inversion. S12: The preprocessed radar data is input into the inversion network. The propagation response of electromagnetic waves in the underground medium is modeled layer by layer through the multi-layer feature extraction module. Residual connections are introduced in the feature extraction process to enhance the deep feature expression capability. An attention mechanism is introduced to strengthen the feature focus on key electromagnetic response areas. An asymmetric downsampling strategy is used to focus on modeling the propagation direction of electromagnetic waves to characterize the propagation time sequence characteristics and energy attenuation law of electromagnetic waves in the underground medium, thereby establishing a nonlinear mapping relationship between radar detection data and electromagnetic parameters of the underground medium. S13: The feature resolution is restored layer by layer through the decoding module, and multi-scale information is fused by skip connections to output the dielectric constant and conductivity distribution of the subsurface medium retrieved from ground penetrating radar data. The mean square error (MSE) between the retrieved dielectric constant and conductivity and the true values ​​is calculated. p and MSE c This constitutes the data-driven inversion error; S2: Construction of physical constraints for electromagnetic propagation and twin consistency determination based on the finite-difference time-domain method, the specific steps of which are as follows: S21: Based on the dielectric constant and conductivity distribution of the underground medium obtained by inversion in S1, the propagation of electromagnetic waves in the medium is numerically solved using the finite-difference time-domain method (FDTD) to generate simulated radar B-Scan data corresponding to the inversion parameters; S22: The simulated radar data generated by FDTD and the original observed radar data are respectively input into two shared parameter branches of the Siamese neural network. The network performs high-dimensional feature encoding on the two types of data through a multi-layer convolutional feature extraction module. Wavelet transform can be introduced during the feature extraction process to enhance the representation ability of low-frequency global information and high-frequency local detail features. Then, the high-dimensional features of the two branches are mapped to a unified feature space. The consistency between the simulated data and the observed data in the feature space is reflected by the feature similarity measurement, thereby forming a physical law constraint signal. S23: Calculate the cosine similarity between the data generated by FDTD and the input data in the high-dimensional feature space. The formula for calculating cosine similarity (Cos_Sim) is as follows: Where F in F is the high-dimensional feature vector of the input ground-penetrating radar data. sim This is a high-dimensional feature vector of the simulated ground-penetrating radar data calculated based on the inversion results; S3: Data-driven inversion and physical constraint fusion optimization, the specific steps are as follows: S31: Combine the data-driven and physical consistency constraint errors calculated in S1 and S2 to construct an optimized loss function L. all The calculation formula is as follows: α, β and γ are the weights of each item, used to balance the influence of data-driven and physical constraints; S32: Apply the joint loss function to the training of the S1 inversion network to achieve synergistic optimization of data-driven inversion and FDTD twin physical constraints, thereby obtaining stable and physically interpretable inversion results of the dielectric constant and conductivity of the underground medium.

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