Ground penetrating radar forward physical equivalent method, device and equipment and storage medium

Abstract

The application discloses a ground penetrating radar forward physical equivalent method, device and equipment and a storage medium. The method comprises the following steps: simulating a boundary domain where a PML layer is located, and degrading a calculation formula of the PML layer into a calculation formula of a calculation domain; vectorizing the calculation formula of the PML layer and the calculation domain to obtain a vector calculation formula, and realizing degradation of the PML layer to the calculation domain by controlling variable parameter values in the vector calculation formula; reconstructing the vector calculation formula into an RNN model, inputting a point source, an initial field and electrical parameters into the RNN model, and obtaining field components at a specified time sequence; expanding dimensions of input parameters and the field components of the RNN model, inputting the expanded three-dimensional field components and parameter tensors into the RNN model, constructing a plurality of ground penetrating radar physical models, simulating the ground penetrating radar, and obtaining a simulation B-Scan image. The application greatly improves simulation efficiency, guarantees the accuracy of simulation results, and improves the utilization rate of a calculation device.

Description

Technical Field

[0001] This invention relates to the field of electromagnetics, and in particular to a method, apparatus, device, and storage medium for forward modeling physical equivalence of ground penetrating radar. Background Technology

[0002] Ground-penetrating radar (GPR) is a non-invasive detection technology that uses an antenna to emit electromagnetic pulses towards targets in the underlying medium to detect and locate anomalies and structural characteristics underground or inside objects. Currently, this technology is widely used in civil engineering, geological disaster prevention, military, and archaeology. Electromagnetic wave simulation is the most important topic in GPR technology research and is the foundation for applications such as anomaly detection and target inversion.

[0003] In electromagnetic wave forward modeling, commonly used methods include the FDTD (Finite Difference Time Domain) method, parallel methods, and deep learning-based methods. However, these methods result in huge simulation time consumption, low computational efficiency, complex custom operations, and the inability to achieve parallel simulation of multiple physical models. They also fail to balance generalization, efficiency, and accuracy, making them difficult to apply to practical problems. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to overcome the shortcomings of the prior art and provide a ground-penetrating radar forward modeling physical equivalence method, apparatus, equipment and storage medium.

[0005] This invention provides the following technical solution:

[0006] In a first aspect, this disclosure provides a ground-penetrating radar forward modeling physical equivalence method, the method comprising:

[0007] Simulation calculations are performed on the boundary domain where the PML layer is located. By truncating the computational domain in the boundary domain, the computational formula of the PML layer is degenerated into the computational formula of the computational domain.

[0008] The computation formulas of the PML layer and the computation domain are vectorized to obtain vector computation formulas. By controlling the variable parameter values ​​in the vector computation formulas, the degradation of the PML layer to the computation domain is achieved.

[0009] The vector calculation formula is reconstructed into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components at a specified time. The field components include electric field components and magnetic field components.

[0010] The dimensions of the input parameters and field components of the RNN model are expanded to obtain the expanded three-dimensional field components and parameter tensors.

[0011] By inputting the three-dimensional field components and the parameter tensor into the RNN model, multiple different ground-penetrating radar physical models are constructed. The ground-penetrating radar is then simulated and calculated using each of the ground-penetrating radar physical models to obtain simulated B-Scan images.

[0012] Furthermore, simulation calculations are performed on the boundary domain where the PML layer is located. By truncating the computational domain within the boundary domain, the computational formula of the PML layer is degenerated into the computational formula of the computational domain, including:

[0013] The boundary domain is simulated using the FDTD method, and the PML layer is used as the boundary condition in the boundary domain to construct the step formula of the PML layer.

[0014] By adjusting the correlation coefficient in the step formula, the calculation formula of the PML layer is degenerated into the calculation formula in the calculation domain.

[0015] Further, the vector computation formula includes a first sub-vector matrix and a second sub-vector matrix. The computation formulas of the PML layer and the computation domain are vectorized to obtain the vector computation formula, which includes:

[0016] The computational formulas of the PML layer and the computational domain are vectorized to obtain two first sub-vector matrices;

[0017] Based on the difference direction, the field components of the computational domain are zero-filled with one layer, and the difference calculation is performed on the two first sub-vector matrices to obtain two second sub-vector matrices.

[0018] Furthermore, the variable parameter values ​​include electrical conductivity and magnetic loss. By controlling the variable parameter values ​​in the vector calculation formula, the degradation of the PML layer to the computational domain is achieved, including:

[0019] In the computational domain, the position of the conductivity in the computational domain is set to the same position as the position of the magnetic loss in the computational domain;

[0020] In the computational domain, both the conductivity and the magnetic loss are set to be equal to the conductivity value in the ground-penetrating radar physical model, so as to unify the formulas of the PML layer and the computational domain.

[0021] Furthermore, the vector calculation formula also includes four sub-vector calculation formulas. These formulas are reconstructed into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components at a specified time sequence. These field components include electric field components and magnetic field components, including:

[0022] The vector calculation formula is reconstructed into the RNN model, which contains multiple RNN layers. In each RNN layer, the electric field component and magnetic field component of the previous time series are input.

[0023] The sub-vector calculation formula is used as the parameter matrix of the RNN model, and the point source, initial field, and electrical parameters are input into each RNN layer to obtain the electric field component and magnetic field component of the specified time sequence.

[0024] Furthermore, the dimensions of the input parameters and field components of the RNN model are expanded to obtain the expanded three-dimensional field components and parameter tensors, including:

[0025] By expanding the dimensions of each of the sub-vector calculation formulas, the electric field components, and the magnetic field components, we obtain three-dimensional sub-vector calculation formulas and three-dimensional field components.

[0026] The point source is expanded into a point source matrix. The dimensions of the three-dimensional sub-vector calculation formula, the three-dimensional field components, the parameter tensor, and the point source matrix include the height, width, and number of ground-penetrating radar physical models to be constructed.

[0027] Furthermore, by inputting the three-dimensional field components and the parameter tensor into the RNN model, multiple different ground-penetrating radar physical models are constructed, including:

[0028] The three-dimensional field components, the parameter tensor, and the point source matrix are input into the corresponding RNN layers, and the RNN layers are stacked a preset number of times to construct multiple ground-penetrating radar physical models.

[0029] Secondly, this disclosure provides a ground-penetrating radar forward modeling physical equivalent device, the device comprising:

[0030] The degradation module is used to perform simulation calculations on the boundary domain where the PML layer is located. By truncating the computational domain in the boundary domain, the calculation formula of the PML layer is degenerated into the calculation formula of the computational domain.

[0031] The simulation module is used to vectorize the computation formulas of the PML layer and the computation domain to obtain vector computation formulas. By controlling the variable parameter values ​​in the vector computation formulas, the degradation of the PML layer to the computation domain is realized.

[0032] The reconstruction module is used to reconstruct the vector calculation formula into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components with a specified time sequence. The field components include electric field components and magnetic field components.

[0033] An extension module is used to extend the dimensions of the input parameters and field components of the RNN model to obtain extended three-dimensional field components and parameter tensors.

[0034] The module is used to construct multiple different ground-penetrating radar physical models by inputting the three-dimensional field components and the parameter tensor into the RNN model, and to perform simulation calculations on the ground-penetrating radar through each of the ground-penetrating radar physical models to obtain simulated B-Scan images.

[0035] Thirdly, this disclosure provides a computer device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the ground-penetrating radar forward modeling physical equivalence method described in the first aspect.

[0036] Fourthly, this disclosure provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the ground-penetrating radar forward modeling physical equivalence method described in the first aspect.

[0037] The embodiments of this application have the following advantages:

[0038] The ground-penetrating radar forward modeling physical equivalence method provided in this application includes: performing simulation calculations on the boundary domain where the PML layer is located; degenerating the calculation formula of the PML layer into the calculation formula of the calculation domain by truncating the calculation domain in the boundary domain; vectorizing the calculation formulas of the PML layer and the calculation domain to obtain vector calculation formulas; achieving the degeneration of the PML layer to the calculation domain by controlling the variable parameter values ​​in the vector calculation formulas; reconstructing the vector calculation formulas into an RNN model; inputting point source, initial field, and electrical parameters into the RNN model to obtain field components of a specified time sequence, wherein the field components include electric field components and magnetic field components; expanding the dimensions of the input parameters and field components of the RNN model to obtain expanded three-dimensional field components and parameter tensors; constructing multiple different ground-penetrating radar physical models by inputting the three-dimensional field components and the parameter tensors into the RNN model; and performing simulation calculations on the ground-penetrating radar using each of the ground-penetrating radar physical models to obtain simulated B-Scan images. The ground-penetrating radar forward modeling physical equivalent method proposed in this application integrates a perfectly matched layer and a computational domain. Compared with traditional simulation methods, it significantly improves simulation efficiency while ensuring the accuracy of simulation results. It can also perform forward modeling of multiple different physical models simultaneously, thereby improving the utilization rate of computing equipment.

[0039] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the various drawings, similar components are numbered similarly.

[0041] Figure 1 A flowchart of a ground-penetrating radar forward modeling physical equivalence method provided in an embodiment of this application is shown;

[0042] Figure 2 This illustration shows a schematic diagram of coefficient matrix generation provided in an embodiment of this application;

[0043] Figure 3 This application illustrates a physically equivalent RNN model provided in an embodiment.

[0044] Figure 4 This paper shows a two-dimensional model diagram of a ground-penetrating radar provided in an embodiment of this application;

[0045] Figure 5 This application provides B-Scan comparison images of various methods according to embodiments;

[0046] Figure 6 The present application provides various methods for comparing scattered field images according to embodiments;

[0047] Figure 7 A schematic diagram of the structure of a ground-penetrating radar forward modeling physical equivalent device provided in an embodiment of this application is shown. Detailed Implementation

[0048] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0049] It should be noted that when an element is said to be "fixed" to another element, it can be directly on the other element or there may be an intervening element. When an element is said to be "connected" to another element, it can be directly connected to the other element or there may be an intervening element. Conversely, when an element is said to be "directly" on another element, there is no intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0050] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0051] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the template description is for the purpose of describing particular embodiments only and is not intended to limit the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0053] Example 1

[0054] like Figure 1 The diagram shown is a flowchart of a ground-penetrating radar forward modeling physical equivalence method according to an embodiment of this application. The ground-penetrating radar forward modeling physical equivalence method provided in this embodiment includes the following steps:

[0055] Step S110: Perform simulation calculations on the boundary domain where the PML layer is located. By truncating the computational domain in the boundary domain, the computational formula of the PML layer is degenerated into the computational formula of the computational domain.

[0056] In this embodiment, the FDTD method (Finite-Difference Time-Domain) is used to simulate the computational domain. To truncate the computational domain, a PML layer (Perfect Matched Layer) is used as the boundary condition in the boundary domain. The degradation process mainly targets three common PML layers: BPML (Berenger Perfect Matched Layer), UPML (Uniaxial Perfect Matched Layer), and CPML (Convolutional Perfect Matched Layer). For two-dimensional TM waves, the FDTD step formula for the PML layer computational domain is as follows: (1)-(7):

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] Among them, H x H y and E z Let be the electric and magnetic field strengths for each time series, ε, σ, μ, and σ. m These represent electrical parameters, conductivity, permeability, and magnetic loss, respectively; Δx, Δy, and Δt correspond to the spatial and time steps, respectively; and (m) represents the position parameter of the current variable in two-dimensional space. For external sources.

[0065] In an alternative implementation, if BPML is used as the boundary condition, this boundary condition in TM wave mode requires adjustment of the electric field E. z The step formula for performing partial fraction decomposition is as follows:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] Where, σ ω (ω=1,2) and σ mω (ω=1,2) represents the electrical conductivity and magnetic loss in each direction of the PML layer. Let σ ω =σ,σ mω =σ m Then, by adding equations (10) and (11), the BPML calculation formula will degenerate into the FDTD calculation formulas (1), (2) and (3) in the computational domain.

[0075] In another alternative implementation, CPML is used as the boundary condition, and its step formula is:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Where, σ ω (ω=1,2) represents the conductivity in each direction within the PML layer, κ ω and a ω Let σ be an empirical parameter. ω =0, a ω =0,κ ω =1, then C ω=1, α=0. Let the coefficients CQ and CB related to Ψ in equations (10), (11) and (14) be 0. At this time, the CPML calculation formula will degenerate into the FDTD calculation formulas (1), (2) and (3) in the computational domain.

[0086] Similarly, the same degradation can be applied to the UPML formula, and by substituting different correlation coefficients, the PML formula can be used to perform numerical calculations on both the computational domain and the boundary domain simultaneously.

[0087] Step S120: Vectorize the computation formulas of the PML layer and the computation domain to obtain vector computation formulas. By controlling the variable parameter values ​​in the vector computation formulas, the degradation of the PML layer to the computation domain is achieved.

[0088] Taking the BPML boundary condition calculation formula as an example, in order to implement its calculation process using deep learning operators, it is necessary to first vectorize the calculation formula of the computational domain:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Equations (25) and (26) are the first sub-vector matrices, and equations (27) and (28) are the second sub-vector matrices. In order to realize the difference calculation, the field components of the calculation domain need to be filled with a layer of zero according to the direction of the difference, and then the two first sub-vector matrices are subtracted to obtain two second sub-vector matrices.

[0098] Understandably, compared to using a 1×1 convolution operator in a neural network to achieve difference, the method in this application requires less computation, needing only one subtraction operation, and the introduced memory usage is negligible. By transforming the spatially related parameters and variables into matrix form, the spatially parallel computation of the PML layer can be achieved through the above formula.

[0099] Furthermore, to achieve parallel computing in the computational and boundary regions, the conductivity σ can be controlled. w ∈RH×W and magnetic loss σ mw ∈R G×W The values ​​at each position in the two matrices are used to achieve the purpose of degenerating the PML layer calculation formula, where H and W correspond to the height and width of the physical model. For example... Figure 2 As shown, make σ w and σ mw In the computational domain, the locations are equal, and the values ​​are all equal to the conductivity values ​​σ∈R in the ground-penetrating radar physical model. H×W This enables spatially parallel FDTD forward modeling simulation.

[0100] Step S130: Reconstruct the vector calculation formula into an RNN model, input the point source, initial field, and electrical parameters into the RNN model to obtain field components at a specified time sequence, wherein the field components include electric field components and magnetic field components.

[0101] Furthermore, based on the temporal structure characteristics of the RNN model, the vectorized computation is reconstructed into an RNN model, which contains multiple RNN layers, with one RNN layer corresponding to each time step. For example... Figure 3 As shown, in each RNN layer, the input is the electric field component and magnetic field component from the previous time series. and It should be noted that if there is an external source in the current time series, the amplitude of the current time series point source signal is added to the position of the point source in the electric field component matrix.

[0102] In this embodiment, the four sub-vectors are calculated using the formula CA. w ∈R H×W CB w ∈R H×W CP w ∈R H×W CQ w ∈R H×W The spatial step size Δx and time step size Δy are shared in each RNN layer and serve as the parameter matrix of the RNN module. By reusing this RNN layer multiple times, the electric and magnetic field components at a specified time sequence can be obtained by inputting a point source, initial field, and electrical parameters into each RNN layer. and Similarly, for UPML and CPML, a similar approach can be used to perform parallel computation of both the computational domain and the boundary domain using an equivalent RNN model.

[0103] Step S140: Expand the dimensions of the input parameters and field components of the RNN model to obtain the expanded three-dimensional field components and parameter tensors.

[0104] Understandably, using BPML boundary conditions as an example, in order to achieve parallel simulation of multiple ground-penetrating radar physical models, the four sub-vectors are calculated using the CA formula.w CB w CP w and CQ w From two dimensions R H×W Extended to three-dimensional R B×H×W Where H and W are the height and width of the corresponding ground-penetrating radar physical model, and B is the number of ground-penetrating radar physical models to be constructed.

[0105] The corresponding electric field components and magnetic field components and Also from two-dimensional R H×W Extended to three-dimensional R B×H×W The point source originates from a value j. n+1 / 2 Transform into point source matrix J n+1 / 2 ∈R B×H×W This allows for the addition of external sources at any location in space for any ground-penetrating radar physical model.

[0106] Step S150: By inputting the three-dimensional field components and the parameter tensor into the RNN model, multiple different ground-penetrating radar physical models are constructed. The ground-penetrating radar is simulated and calculated using each of the ground-penetrating radar physical models to obtain a simulated B-Scan image.

[0107] It should be noted that ground-penetrating radar (GPR) simulations typically require simulating multiple transmitters and receivers within the same physical model. Simulating multiple physical models simultaneously can significantly accelerate this process. By expanding the dimensions of all relevant variables and inputting them into the corresponding RNN layer, and stacking multiple RNN layers, a GPR physical model for any time series can be constructed.

[0108] Understandably, the above method still applies to three-dimensional problems. Simply introduce the number B of the ground-penetrating radar physical model before the three-dimensional electric field components, three-dimensional magnetic field components, and the original dimensions of the three-dimensional physical model, and then perform the corresponding degradation on the three-dimensional BPML to obtain the corresponding three-dimensional ground-penetrating radar physical model. Similar equivalent substitutions can be performed for boundary conditions such as UPML and CPML to achieve the goal of simultaneous forward modeling of multiple ground-penetrating radar physical models.

[0109] Furthermore, ground-penetrating radar physical equivalent simulation models constructed for three boundary conditions (BPML, UPML, and CPML) were used to perform simulation calculations on the ground-penetrating radar and quickly obtain simulated B-Scan images.

[0110] The calculation results of the ground-penetrating radar physical model in this invention are compared with those of the traditional FDTD simulation method. The similarity between the B-Scan image and the scattered field image in the prediction results of different methods is observed; the higher the similarity, the more reliable the method.

[0111] Establish such as Figure 4 The physical model shown includes four media types, with a computational domain size of 2m × 2m and a PML layer thickness of 0.1m. The relative electrical parameters and conductivity of the media are shown in Table 1. The transmitter and receiver are spaced 0.03m apart, with a scan step size of 0.04m, totaling 46 groups. A Ricker wave with a center frequency of 1.5e9Hz is used as the transmitter's wave source. The spatial and temporal sampling steps are Δx = Δy = 0.01m and Δt = 1.18 × 10⁻⁶, respectively. -11 s, a total of 1000 time steps were sampled.

[0112]

[0113] Table 1 Electrical parameters of the medium in the physical model

[0114] Figure 5 The images are ground-penetrating radar B-Scan images obtained by the traditional FDTD method and the ground-penetrating radar physical model proposed in this application under different boundary conditions. Figure 6 This is the scattering field image at time 1000 when the transmitter is located at (0.20, 1.50). It can be seen that the ground-penetrating radar physical model maintains high consistency with FDTD when using different PML layers, verifying the accuracy of this invention.

[0115]

[0116] Table 2 Comparison of CPU Simulation Time

[0117] Table 2 shows the CPU performance of each method. Figure 4 The simulation time required for the model shows that the ground-penetrating radar forward modeling physical equivalent method of this application has a faster simulation time and can obtain results that are highly consistent with the FDTD method in a shorter time.

[0118] The ground-penetrating radar forward modeling physical equivalence method provided in this application embodiment simulates the computational domain of the PML layer. By truncating the computational domain at the boundary of the PML layer, the computational formula of the PML layer is degenerated into the computational formula of the computational domain. The computational formula of the computational domain is vectorized to obtain a vector computational formula. Forward modeling of the ground-penetrating radar is performed by controlling the variable parameter values ​​in the vector computational formula. The vector computational formula is reconstructed into an RNN model. Point source, initial field, and electrical parameters are input into the RNN model to obtain field components at a specified time sequence, including electric and magnetic field components. The dimensions of the input parameters and field components of the RNN model are expanded to obtain expanded three-dimensional field components and parameter tensors. By inputting the three-dimensional field components and parameter tensors into the RNN model, multiple different ground-penetrating radar physical models are constructed. Simulation calculations of the ground-penetrating radar are performed using each of these physical models to obtain simulated B-Scan images. The ground-penetrating radar forward modeling physical equivalent method proposed in this application integrates a perfectly matched layer and a computational domain. Compared with traditional simulation methods, it significantly improves simulation efficiency while ensuring the accuracy of simulation results. It can also perform forward modeling of multiple different physical models simultaneously, thereby improving the utilization rate of computing equipment.

[0119] Example 2

[0120] like Figure 7 The diagram shown is a structural schematic of a ground-penetrating radar forward modeling physical equivalent device 700 according to an embodiment of this application. The device includes:

[0121] The degradation module 710 is used to perform simulation calculations on the boundary domain where the PML layer is located. By truncating the calculation domain in the boundary domain, the calculation formula of the PML layer is degenerated into the calculation formula of the calculation domain.

[0122] The simulation module 720 is used to vectorize the calculation formulas of the PML layer and the computational domain to obtain vector calculation formulas. By controlling the variable parameter values ​​in the vector calculation formulas, the degradation of the PML layer to the computational domain is realized.

[0123] The reconstruction module 730 is used to reconstruct the vector calculation formula into an RNN model, inputting the point source, initial field, and electrical parameters into the RNN model to obtain field components with a specified time sequence, wherein the field components include electric field components and magnetic field components.

[0124] The extension module 740 is used to extend the dimensions of the input parameters and field components of the RNN model to obtain extended three-dimensional field components and parameter tensors.

[0125] The construction module 750 is used to construct multiple different ground-penetrating radar physical models by inputting the three-dimensional field components and the parameter tensor into the RNN model, and to perform simulation calculations on the ground-penetrating radar through each of the ground-penetrating radar physical models to obtain simulated B-Scan images.

[0126] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0127] The calculation module is used to perform simulation calculations on the boundary domain using the FDTD method, and to construct the step formula of the PML layer using the PML layer as the boundary condition in the boundary domain.

[0128] An adjustment module is used to degenerate the calculation formula of the PML layer into the calculation formula of the calculation domain by adjusting the correlation coefficient in the step formula.

[0129] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0130] The vectorization module is used to vectorize the computation formulas of the PML layer and the computation domain to obtain two first sub-vector matrices;

[0131] The zero-filling module is used to perform a layer of zero-filling on the field components of the computational domain according to the difference direction, and to perform difference calculation on the two first sub-vector matrices to obtain two second sub-vector matrices.

[0132] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0133] A first setting module is used to set the position of the conductivity in the calculation domain and the position of the magnetic loss in the calculation domain to the same position;

[0134] The second setting module is used to set the conductivity and magnetic loss in the computational domain to be equal to the conductivity value in the ground penetrating radar physical model, thereby realizing the degradation of the PML layer to the computational domain.

[0135] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0136] The first input module is used to reconstruct the vector calculation formula into the RNN model, which contains multiple RNN layers. In each RNN layer, the electric field component and magnetic field component of the previous time sequence are input.

[0137] The second input module is used to use the sub-vector calculation formula as the parameter matrix of the RNN model, and input the point source, initial field, and electrical parameters into each of the RNN layers to obtain the electric field components and magnetic field components of the specified time sequence.

[0138] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0139] The first extended submodule is used to extend the dimensions of the electric field component and the magnetic field component to obtain a three-dimensional sub-vector calculation formula and a three-dimensional field component.

[0140] The second extended submodule is used to extend the point source into a point source matrix. The dimensions of the three-dimensional subvector calculation formula, the three-dimensional field components, the parameter tensor, and the point source matrix include the height, width, and number of ground-penetrating radar physical models to be constructed.

[0141] Optionally, the aforementioned ground-penetrating radar forward modeling physical equivalent device 700 further includes:

[0142] The stacking module is used to input the three-dimensional field components, the parameter tensor and the point source matrix into the corresponding RNN layer, and stack each RNN layer a preset number of times to construct multiple ground-penetrating radar physical models.

[0143] The ground-penetrating radar forward modeling physical equivalent device provided in this application, by integrating a perfectly matched layer and a computational domain, significantly improves simulation efficiency while ensuring the accuracy of simulation results compared to traditional simulation methods. It can also perform forward modeling of multiple different physical models simultaneously, thereby improving the utilization rate of computing equipment.

[0144] This disclosure also provides a computer device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the ground-penetrating radar forward modeling physical equivalence method described in Embodiment 1.

[0145] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the ground-penetrating radar forward modeling physical equivalence method described in Embodiment 1.

[0146] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that, as an alternative implementation, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0147] In addition, the functional modules or units in the various embodiments of the present invention can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0148] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a smartphone, personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0149] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A ground-penetrating radar forward modeling physical equivalence method, characterized in that, The method includes: Simulation calculations are performed on the boundary domain where the PML layer is located. By truncating the computational domain in the boundary domain, the computational formula of the PML layer is degenerated into the computational formula of the computational domain. The computation formula of the computation domain is vectorized to obtain a vector computation formula. By controlling the variable parameter values ​​in the vector computation formula, the degradation of the PML layer to the computation domain is realized. The vector calculation formula is reconstructed into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components at a specified time. The field components include electric field components and magnetic field components. The dimensions of the input parameters and field components of the RNN model are expanded to obtain the expanded three-dimensional field components and parameter tensors. By inputting the three-dimensional field components and the parameter tensor into the RNN model, multiple different ground-penetrating radar physical models are constructed. The ground-penetrating radar is then simulated and calculated using each of the ground-penetrating radar physical models to obtain simulated B-Scan images.

2. The ground-penetrating radar forward modeling physical equivalence method according to claim 1, characterized in that, Simulation calculations are performed on the boundary domain containing the PML layer. By truncating the computational domain within the boundary domain, the computational formula of the PML layer is degenerated into the computational formula of the computational domain, including: The boundary domain is simulated using the FDTD method, and the PML layer is used as the boundary condition in the boundary domain to construct the step formula of the PML layer. By adjusting the correlation coefficient in the step formula, the calculation formula of the PML layer is degenerated into the calculation formula in the calculation domain.

3. The ground-penetrating radar forward modeling physical equivalence method according to claim 1, characterized in that, The vector computation formula includes a first sub-vector matrix and a second sub-vector matrix. The computation formula of the computation domain is vectorized to obtain the vector computation formula, which includes: The computational formula of the computational domain is vectorized to obtain two first sub-vector matrices; Based on the difference direction, the field components of the computational domain are zero-filled with one layer, and the difference calculation is performed on the two first sub-vector matrices to obtain two second sub-vector matrices.

4. The ground-penetrating radar forward modeling physical equivalence method according to claim 1, characterized in that, The variable parameter values ​​include electrical conductivity and magnetic loss. By controlling the variable parameter values ​​in the vector calculation formula, the degradation of the PML layer to the computational domain is achieved, including: In the computational domain, the position of the conductivity in the computational domain is set to the same position as the position of the magnetic loss in the computational domain; In the computational domain, both the conductivity and the magnetic loss are set to be equal to the conductivity value in the ground-penetrating radar physical model, so as to unify the formulas of the PML layer and the computational domain.

5. The ground-penetrating radar forward modeling physical equivalence method according to claim 3, characterized in that, The vector calculation formula also includes four sub-vector calculation formulas. These formulas are reconstructed into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components at a specified time sequence. These field components include electric field components and magnetic field components, including: The vector calculation formula is reconstructed into the RNN model, which contains multiple RNN layers. In each RNN layer, the electric field component and magnetic field component of the previous time series are input. The sub-vector calculation formula is used as the parameter matrix of the RNN model, and the point source, initial field, and electrical parameters are input into each RNN layer to obtain the electric field component and magnetic field component of the specified time sequence.

6. The ground-penetrating radar forward modeling physical equivalence method according to claim 5, characterized in that, The dimensions of the input parameters and field components of the RNN model are expanded to obtain expanded three-dimensional field components and parameter tensors, including: By expanding the dimensions of each of the sub-vector calculation formulas, the electric field components, and the magnetic field components, we obtain three-dimensional sub-vector calculation formulas and three-dimensional field components. The point source is expanded into a point source matrix. The dimensions of the three-dimensional sub-vector calculation formula, the three-dimensional field components, the parameter tensor, and the point source matrix include the height, width, and number of ground-penetrating radar physical models to be constructed.

7. The ground-penetrating radar forward modeling physical equivalence method according to claim 6, characterized in that, By inputting the three-dimensional field components and the parameter tensor into the RNN model, multiple different ground-penetrating radar physical models are constructed, including: The three-dimensional field components, the parameter tensor, and the point source matrix are input into the corresponding RNN layers, and the RNN layers are stacked a preset number of times to construct multiple ground-penetrating radar physical models.

8. A ground-penetrating radar forward modeling physical equivalent device, characterized in that, The device includes: The degradation module is used to perform simulation calculations on the boundary domain where the PML layer is located. By truncating the computational domain in the boundary domain, the calculation formula of the PML layer is degenerated into the calculation formula of the computational domain. The simulation module is used to vectorize the computation formula of the computation domain to obtain a vector computation formula. By controlling the variable parameter values ​​in the vector computation formula, the degradation of the PML layer to the computation domain is realized. The reconstruction module is used to reconstruct the vector calculation formula into an RNN model. The point source, initial field, and electrical parameters are input into the RNN model to obtain field components with a specified time sequence. The field components include electric field components and magnetic field components. An extension module is used to extend the dimensions of the input parameters and field components of the RNN model to obtain extended three-dimensional field components and parameter tensors. The module is used to construct multiple different ground-penetrating radar physical models by inputting the three-dimensional field components and the parameter tensor into the RNN model, and to perform simulation calculations on the ground-penetrating radar through each of the ground-penetrating radar physical models to obtain simulated B-Scan images.

9. A computer device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the ground-penetrating radar forward modeling physical equivalent method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the ground-penetrating radar forward modeling physical equivalent method according to any one of claims 1-7.

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