Underground delivery pipe forward modeling method and system based on frequency domain electromagnetism

Abstract

The invention provides an underground delivery pipe three-dimensional finite element forward modeling method and system based on frequency domain electromagnetism, and the method comprises the steps: building an underground delivery pipe three-dimensional model, and carrying out the hybrid mesh generation of the underground delivery pipe three-dimensional model; introducing a time harmonic factor, constructing a frequency domain Maxwell equation set, and based on the subdivided underground delivery pipe three-dimensional model, combining the magnetic vector potential of each unit to establish a unit matrix; based on the unit matrix, assembling a linear equation set; an observation area is divided into a plurality of sub-areas, an emission source is arranged in each sub-area, an assembled linear equation set is solved for the three-dimensional models of the sub-areas with different frequencies in a parallel mode, and three-dimensional rapid forward modeling of the underground conveying pipe is achieved. According to the method, the observation area is divided into a plurality of sub-areas, and the three-dimensional model of each sub-area under different frequencies is calculated by using the parallel algorithm, so that the three-dimensional rapid forward modeling of the underground delivery pipe is realized, and the calculation efficiency of the three-dimensional forward modeling is improved.

Description

Technical Field

[0001] The present invention belongs to the field of underground transmission pipe detection and analysis, and in particular relates to a three-dimensional finite element forward modeling method and system for underground transmission pipes based on frequency domain electromagnetics. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Underground pipelines are an important part of urban infrastructure, including water supply and drainage pipelines, heat pipelines, gas pipelines, power pipelines, communication pipelines, etc. Underground pipeline detection can protect existing pipelines from construction damage, thereby saving manpower and material resources and ensuring the smooth progress of urban construction. Therefore, accurate detection of the location, direction and depth of underground pipelines is crucial for urban planning, engineering construction and maintenance.

[0004] Commonly used underground pipeline detection methods mainly include direct method, clamp method, geological radar method, etc. In the direct method, one end of the transmitter is connected to the metal pipeline to be measured, and the other end is grounded or connected to the other end of the metal pipeline. The transmitter transmits an alternating current containing a specific frequency to the pipeline, and the electromagnetic signal generated by the measured pipeline is collected by the receiver on the ground, thereby locating and determining the depth of the pipeline. This method has strong transmitter signal output, good anti-interference performance, and high positioning and depth accuracy, but it requires good grounding conditions, and the metal pipeline must have an exposed end.

[0005] The clamp method is a method used when it is impossible to directly connect the transmitter and the measured pipeline. The transmitter signal is applied to the clamp, and then the measured pipeline is clamped with the clamp to measure the induced signal generated in the pipeline, thereby locating and tracking the pipeline. This method is economical and simple, suitable for pipelines with smaller diameters, and only suitable for metal pipelines and must have exposed ends.

[0006] The geological radar method transmits high-frequency electromagnetic waves into the underground through a transmitting antenna, and uses a receiving antenna to receive the electromagnetic waves reflected back from the underground transmission pipe. The spatial position, structure, morphology and burial depth of the pipeline are inferred based on the waveform, amplitude intensity and time change characteristics of the received electromagnetic waves. This method has high accuracy and strong anti-interference ability, but is easily affected by environmental interference and has a shallow detection depth.

[0007] Traditional underground pipeline detection methods are limited by geological conditions and detection equipment, and are difficult to adapt to complex and diverse underground environments and pipeline types, resulting in unreliable detection results. Therefore, new technologies, new methods and new instruments are needed to improve the accuracy and efficiency of underground pipeline detection.

[0008] The frequency domain electromagnetic method transmits an alternating electromagnetic field containing multiple frequencies into the ground through a transmitting coil, and uses a receiving coil to record the electromagnetic response spectrum of the underground transmission pipe at each frequency to achieve the exploration of the underground transmission pipe. Different transmission frequencies can detect different depths, high frequencies are suitable for shallow layers, and low frequencies are suitable for deep layers.

[0009] The size of underground transmission pipes is very small, generally tens to hundreds of millimeters; the wall thickness of the pipes is even smaller, generally a few millimeters to tens of millimeters, which seriously affects the accuracy of forward modeling. For small-scale models, one-dimensional and two-dimensional forward interpretations are difficult to accurately obtain the spatial distribution and physical property information of underground transmission pipes, and three-dimensional forward models are more in line with actual geological conditions. In order to accurately simulate the response of underground transmission pipes in electromagnetic fields, it is necessary to use finer grids for segmentation to capture the geometric shape and physical properties of the pipelines. This will lead to an increase in the number of nodes and units, thereby increasing the number of unknowns in the linear equations to be solved in the three-dimensional forward model. Compared with one-dimensional and two-dimensional models, the computational workload and memory requirements of three-dimensional models have increased significantly, and the calculation time has increased significantly. Therefore, the selection of appropriate calculation methods is crucial to improving the efficiency of three-dimensional forward modeling of underground transmission pipes. Summary of the invention

[0010] In order to solve the above problems, the present invention proposes a forward modeling method and system for underground transmission pipes based on frequency domain electromagnetics. The present invention divides the observation area into multiple sub-areas, and uses a parallel algorithm to calculate the three-dimensional model of each sub-area at different frequencies, thereby realizing three-dimensional rapid forward modeling of underground transmission pipes and improving the computational efficiency of three-dimensional forward modeling.

[0011] According to some embodiments, the present invention adopts the following technical solutions:

[0012] The three-dimensional finite element forward modeling method of underground transmission pipe based on frequency domain electromagnetic includes the following steps:

[0013] Establishing a three-dimensional model of an underground transmission pipe, and performing hybrid meshing on the three-dimensional model of the underground transmission pipe;

[0014] The time harmonic factor is introduced to construct the frequency domain Maxwell equations. Based on the segmented three-dimensional model of the underground transmission pipe and the magnetic vector potential of each unit, the unit matrix is ​​established.

[0015] Assemble linear equations based on unit matrices;

[0016] The observation area is divided into several sub-areas, and a transmitting source is set in each sub-area. The three-dimensional models of each sub-area with different frequencies are solved in parallel to realize the three-dimensional rapid forward modeling of the underground transmission pipe.

[0017] As an optional implementation, the process of hybrid meshing the three-dimensional model of the underground transmission pipe includes: meshing the pipeline with a triangular prism mesh, meshing the remaining area with an unstructured tetrahedral mesh, and coupling the quadrilateral faces of the triangular prism mesh and the triangular faces of the tetrahedral mesh with a pyramid mesh.

[0018] As a further step, when hybrid meshing is performed on the three-dimensional model of the underground transmission pipe, the meshes in the underground transmission pipe, the measuring point area and the vicinity of the emission source are refined, while the meshes in other areas are not refined; and an unstructured tetrahedral mesh is created using a Delaunay mesh generator.

[0019] As an optional implementation, the process of introducing a time harmonic factor and constructing the frequency domain Maxwell equations includes:

[0020] Let the time harmonic variation factor be e iωt , the differential form of Maxwell's equations in the frequency domain is:

[0021]

[0022]

[0023] In the formula, H is the magnetic field intensity, E is the electric field intensity, and i is the imaginary unit. ω is the angular frequency, D is the electric flux density, J e is the external current density, t is the time, are electrical conductivity and magnetic permeability respectively. When the underground medium is isotropic, is a scalar; when the underground medium is anisotropic, is a tensor.

[0024] As an optional implementation, based on the segmented three-dimensional model of the underground transmission pipe and in combination with the magnetic vector potential of each unit, the process of establishing the unit matrix includes: performing a triple Euler rotation transformation on the anisotropic conductivity and magnetic permeability;

[0025] Expression medium constitutive relations;

[0026] The anisotropic dielectric constant is transformed by triple Euler rotation;

[0027] Then the double curl equation of the electric field is calculated, and the magnetic vector potential is introduced to obtain the control equation;

[0028] A magnetic insulation boundary condition is set at the magnetic field interface so that the tangential component of the magnetic vector potential is zero at the boundary and the current density divergence is zero;

[0029] And add the Coulomb gauge condition and introduce the gradient term of the Lagrange multiplier;

[0030] Compute the magnetic vector potential for each element, construct the element matrix and solve the linear equation system.

[0031] As an optional implementation, based on the unit matrix, the process of assembling a linear system of equations includes numbering the global nodes and local nodes respectively. In the global node numbering, each unit matrix is ​​added to the global matrix according to the position of the local node to form a linear system of equations.

[0032] As an optional implementation, before dividing the observation area into a plurality of sub-areas, it further includes applying infinite element boundary conditions and dividing the infinite element domain with structured hexahedral grids and triangular prism grids.

[0033] As an optional implementation method, in the process of solving the assembled linear equations in parallel for the three-dimensional models of each sub-area with different frequencies, the double conjugate gradient stabilization algorithm is used to solve the linear equations, calculate the magnetic field intensity of each node, and calculate the vertical component of the magnetic field at the measuring point. Only the secondary field can reflect the information of the underground transmission pipe, and it is normalized to obtain the normalized secondary magnetic field.

[0034] As an optional implementation, the process of solving the assembled linear equations in parallel for the three-dimensional models of each sub-region at different frequencies includes:

[0035] Set the number of parallel running jobs K;

[0036] Count the number of transmission frequencies Fc and the number of transmission sources Tc;

[0037] Calculate the number of parallel groups G = Fc × Tc;

[0038] Allocate the number of parallel groups G to the child processes in sequence. If K < G, continue to assign tasks when the child process is idle.

[0039] During the operation, each subprocess refines the grids in the measurement point area and near the emission source, uses the biconjugate gradient stable iterative solver for calculation, uploads the measurement point data to the main program, and then enters the idle state, waiting for the assignment of new tasks;

[0040] When all tasks in group G are completed, the parallel operation ends;

[0041] The measuring point data of each sub-process is summarized in the main program to obtain the forward modeling results of the entire observation area at different transmission frequencies. Through data processing and drawing, the underground transmission pipeline information at different depths is reflected.

[0042] The three-dimensional finite element forward modeling system of underground transmission pipes based on frequency domain electromagnetics includes:

[0043] A modeling module is configured to establish a three-dimensional model of the underground transmission pipe and perform hybrid meshing on the three-dimensional model of the underground transmission pipe;

[0044] The unit matrix building module is configured to introduce a time harmonic variation factor, construct a frequency domain Maxwell equation group, and build a unit matrix based on the segmented three-dimensional model of the underground transmission pipe and the magnetic vector potential of each unit;

[0045] An equation assembly module, configured to assemble a linear equation system based on a cell matrix;

[0046] The equation solving module is configured to divide the observation area into several sub-areas, set a transmitting source in each sub-area, and solve the assembled linear equations in parallel for the three-dimensional models of each sub-area with different frequencies, so as to realize the three-dimensional rapid forward modeling of the underground transmission pipe.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The finite element method used in the present invention is flexible and applicable, and is good at processing the complex geometric shapes of underground transmission pipes. The node finite element divides the continuous problem domain into a finite number of units consisting of nodes, and each unit approximates the field variables through a shape function, thereby converting the partial differential equation into a linear equation system, and then solving it using a numerical method.

[0049] The present invention adopts a hybrid grid, and accurately divides different parts of the model through triangular prism grid, unstructured tetrahedron grid and structured hexahedron grid. The pipeline is divided by triangular prism grid, the rest of the area is divided by unstructured tetrahedron grid, and the infinite element domain is divided by structured hexahedron grid and triangular prism grid, so as to form a comprehensive and accurate three-dimensional model of underground transmission pipe.

[0050] The present invention uses pyramid grid coupling to connect the quadrilateral faces of triangular prism grid and the triangular faces of tetrahedron grid to improve the adaptability of the model. The grids near underground transmission pipes, measuring point areas and emission sources are refined, while the grids in other areas are kept moderately coarsened, which not only improves the calculation accuracy but also effectively saves the calculation time.

[0051] The present invention divides the observation area into several sub-areas, sets an emission source in each sub-area, and adopts parallel calculation for sub-areas of different frequencies, so as to improve the calculation efficiency of three-dimensional finite element forward modeling of frequency domain electromagnetic detection of underground transmission pipes and effectively reflect the underground transmission pipe information at different depths.

[0052] During parallel calculation, the present invention counts the number of emission frequencies and the number of emission sources, calculates the number of parallel groups according to the number of emission frequencies and the number of emission sources, sets a reasonable number of parallel operation jobs, and improves the calculation efficiency of three-dimensional finite element forward modeling.

[0053] The present invention introduces time harmonic factors and gradient terms of magnetic vector potential and Lagrange multipliers when observing decomposition and establishing unit matrices, considers anisotropic conductivity, magnetic permeability, and the constitutive relationship of the medium, sets magnetic insulation boundary conditions at the magnetic field interface, and adds Coulomb gauge conditions, so as to simulate the three-dimensional electromagnetic response of underground transmission pipes.

[0054] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0056] Figure 1 A schematic diagram of an underground transmission pipe model according to an embodiment;

[0057] Figure 2 A schematic diagram of hybrid mesh generation of a model according to an embodiment;

[0058] Figure 3 A schematic diagram of local mesh refinement of a model according to an embodiment;

[0059] Figure 4 A diagram showing the calculation result of the real part of the normalized secondary magnetic field at 16kHz in one embodiment;

[0060] Figure 5 A diagram showing the calculation result of the 16kHz normalized secondary magnetic field imaginary part in one embodiment;

[0061] Figure 6 A graph showing the calculation result of the real part of the normalized secondary magnetic field at 70kHz in one embodiment;

[0062] Figure 7 A graph showing the calculation result of the 70kHz normalized secondary magnetic field imaginary part of an embodiment;

[0063] Figure 8 The present invention is a flow chart of a three-dimensional finite element forward modeling method according to an embodiment. DETAILED DESCRIPTION

[0064] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0065] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0066] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0067] In the absence of conflict, the embodiments in this application and the features in the embodiments may be combined with each other.

[0068] Embodiment 1

[0069] Frequency domain electromagnetic underground transmission pipeline 3D finite element forward modeling based on observation decomposition, including:

[0070] 1) Establish a 3D model of the underground transmission pipe and set geometric parameters and physical parameters;

[0071] 2) Use hybrid meshing for different parts of the model. Use triangular prism meshes to mesh the pipeline, and use unstructured tetrahedral meshes to mesh the rest of the area. Use pyramid mesh coupling to connect the quadrilateral faces of the triangular prism meshes and the triangular faces of the tetrahedral meshes.

[0072] The meshes in the underground transmission pipes, measurement point areas, and near the emission sources are refined, while the meshes in other areas are not refined too much; an unstructured tetrahedral mesh is created using the Delaunay mesh generator.

[0073] 3) Establishing a unit matrix according to the three-dimensional model;

[0074] Let the time harmonic variation factor be e iωt , the differential form of Maxwell's equations in the frequency domain is:

[0075]

[0076]

[0077] In the formula, H is the magnetic field strength, unit A / m, E is the electric field strength, unit V / m, i is the imaginary unit, ω is the angular frequency, in rad / s, D is the electric flux density, in C / m 2 , J e is the external current density, in A / m 2 , t is time, unit is s, They are electrical conductivity (S / m) and magnetic permeability (H / m). When the underground medium is isotropic, is a scalar; when the underground medium is anisotropic, For a tensor:

[0078] The anisotropic conductivity and magnetic permeability can be obtained by triple Euler rotation transformation:

[0079]

[0080]

[0081] In the formula, σ ij (i, j = x, y, z) are the elements of the anisotropic conductivity tensor, μ ij (i, j = x, y, z) are the elements of the anisotropic permeability tensor, σ x , σ y , σ z is the conductivity in the x, y, and z directions, μ x , μ y , μ z is the magnetic permeability in the x, y, and z directions, α, β, and γ are the three Euler rotation angles, and R x and R z is the coordinate rotation matrix, and its expression is:

[0082]

[0083]

[0084] The constitutive relation of the medium is:

[0085]

[0086]

[0087]

[0088] Where B is the magnetic flux density, unit Wb / m 2 , J is the current density, unit is A / m 2 , is the dielectric constant, in F / m. When the underground medium is isotropic, is a scalar; when the underground medium is anisotropic, is a tensor; the anisotropic dielectric constant can be obtained by triple Euler rotation transformation:

[0089]

[0090] In the formula, ε ij (i, j = x, y, z) are the elements of the anisotropic dielectric constant tensor, ε x , ε y , ε z is the dielectric constant in the x, y, and z directions;

[0091] Substituting equation (1) into equation (2), we can obtain the electric field double curl equation:

[0092]

[0093] Introduce the magnetic vector potential A:

[0094]

[0095] E=-iωA(13)

[0096] Substituting formula (7) into formula (12), we can obtain:

[0097]

[0098] Substituting equation (13) into equation (11), we get the control equation:

[0099]

[0100] Set the magnetic insulation boundary condition on the magnetic field interface so that the tangential component of the magnetic vector potential is zero at the boundary:

[0101] τ×A=0(16)

[0102] Where, τ is the tangential component;

[0103] The current density divergence is zero:

[0104]

[0105] Combining equation (8) and equation (13) and substituting them into equation (17), we can obtain:

[0106]

[0107] In order to obtain a unique magnetic vector potential, add the Coulomb gauge condition:

[0108]

[0109] In step 3), the gradient term of the Lagrange multiplier is introduced in equation (8):

[0110]

[0111] Use the Galerkin method to discretize the above formula:

[0112]

[0113] Where N is the vector shape function, are the approximate solutions of A and λ, respectively, Ω is the total domain of the computational model, Γ is the outer boundary of the grid, γ is the inner boundary of the grid, and n is the normal component;

[0114] The magnetic vector potential A of each tetrahedral unit e (x, y, z) is approximately:

[0115]

[0116] Where n e is the number of nodes of the element, is the quadratic Lagrangian shape function of the ith node in the element.

[0117] Substitute equation (22) into equation (21), construct the unit matrix and solve the linear equations to obtain A e (x, y, z).

[0118] 4) Assemble linear equations;

[0119] In the global node numbering, each unit matrix is ​​added to the global matrix according to the location of the local node to form a linear system of equations.

[0120] 5) Apply infinite element boundary conditions;

[0121] In this step, the infinite element domain is meshed using structured hexahedral meshes and triangular prism meshes.

[0122] 6) The observation area is divided into several sub-areas, and a transmitting source is set in each sub-area. The three-dimensional models of each sub-area with different frequencies are solved in parallel to solve the linear equations to achieve three-dimensional rapid forward modeling of underground transmission pipes.

[0123] In this step, the biconjugate gradient stabilization algorithm is used to solve the linear equations and the magnetic field strength of each node is calculated according to equation (14). The vertical component of the magnetic field at the measuring point H is calculated. z , and H z =H p +H s ; Among them, only the secondary field H s It can reflect the underground transmission pipe information. Since the secondary field signal is much smaller than the primary field signal H p , it needs to be normalized to obtain the normalized secondary magnetic field H abn :

[0124]

[0125] Among them, the normalized secondary magnetic field is a complex number, rewritten as:

[0126] H abn =I+iQ (24)

[0127] Where I is the in-phase component (real part) and Q is the quadrature component (imaginary part).

[0128] The specific steps for parallel computing of each sub-region at different frequencies are as follows:

[0129] Set the number of parallel running jobs K;

[0130] Count the number of emission frequencies Fc and the number of emission sources Tc;

[0131] Calculate the number of parallel groups G = Fc × Tc;

[0132] Allocate the number of parallel groups G to the sub-processes in sequence. If K < G, continue to allocate tasks when the sub-processes are idle;

[0133] During the operation of each sub-process, refine the grids near the measurement point area and the emission source, use the Bi-Conjugate Gradient Stabilized (BiCGStab) iterative solver for calculation, upload the measurement point data to the main program, and then enter the idle state to wait for the allocation of new tasks;

[0134] When all G groups of tasks are completed, end the parallel;

[0135] In the main program, summarize the measurement point data of each sub-process to obtain the forward modeling results of the entire observation area at different emission frequencies, and reflect the information of underground pipelines at different depths through data processing and plotting.

[0136] Embodiment 2

[0137] The three-dimensional finite element forward modeling method for underground pipelines based on frequency-domain electromagnetics, as Figure 8 shown, includes the following steps:

[0138] (1) Use COMSOL Multiphysics software to construct a three-dimensional model of the underground pipeline. The model size is 30×30×40m, the air conductivity is 10 -8 S / m, the background conductivity is 0.01S / m, and the relative permittivity is 1. Lay two underground pipelines with different burial depths. The outer diameter of the shallow underground plastic pipe is 50mm, the wall thickness is 3mm, the burial depth is 0.7m, the pipeline conductivity is 10 -8 S / m, and the pipeline is filled with copper wire, and the conductivity of the copper wire is 5.95×10 7 S / m; the outer diameter of the deep underground steel pipe is 508mm, the wall thickness is 10mm, the burial depth is 3m, the pipeline conductivity is 9.93×10 6 S / m, and the pipeline is filled with water, and the conductivity of the water is 0.1S / m. Arrange a vertical coplanar transmitting and receiving device. The diameters of the transmitting coil and the receiving coil are 0.1m, the distance between the transmitting and receiving coils is 2m, the height from the ground is 0.2m, the transmitting current is 1A, and the transmitting frequencies are 16kHz and 70kHz. The schematic diagram of the model is as Figure 1 shown.

[0139] (2) The pipeline is meshed with a triangular prism grid, and the number of grid cells distributed along the sweep direction is 100. The remaining area is meshed with an unstructured tetrahedral grid, and the grid near the transceiver coil is refined. Figure 2 As shown, the local mesh refinement is as follows Figure 3 As shown. The mesh edge length of the transceiver coil is 0.008m, and the unit growth rate is 1. Pyramid mesh coupling is used to connect the quadrilateral faces of the triangular prism mesh and the triangular faces of the tetrahedral mesh. The number of nodes in the model is 32362, and the number of elements is 138679. Among them, the number of tetrahedral elements is 109679, the number of triangular prism elements is 24200, and the number of pyramid elements is 4800.

[0140] (3) Calculate the shape functions of different units, calculate the magnetic vector potential of the unit according to equation (21), and then substitute it into equation (21) to solve the unit matrix.

[0141] (4) Number the global nodes and local nodes respectively. In the global node numbering, each unit matrix is ​​added to the global matrix according to the position of the local node to form a system of linear equations.

[0142] (5) Infinite element boundary conditions are applied. The thickness of the infinite element boundary layer is 3 m and the number of layers is 6. It is divided using structured hexahedral grids and triangular prism grids.

[0143] (6) The observation area is divided into 1369 sub-areas, and a transmitting source is set in each sub-area. The measuring point is 2m away from the transmitting source. The transmitting sources are distributed in the x- and y-axis directions from 6m to 24m, with a spacing of 0.5m. The study adopts batch scanning, setting the transmitting frequencies to 16kHz and 70kHz, the number of transmitting frequencies to 2, and the number of transmitting sources to 1369.

[0144] (7) Set the number of parallel running jobs to K and the number of parallel groups G to 2×1369=2738. Allocate 2738 tasks to K child processes. The computational efficiency of different numbers of parallel jobs is shown in Table 1.

[0145] Table 1

[0146] Number of parallel groups G Number of parallel jobs K Calculation time (h) 2738 1 186 2738 24 8 2738 48 4

[0147] During the operation of each subprocess, the grids near the transmitting coil and the receiving coil are refined, and the linear equations are solved using the double conjugate gradient stable iterative solver. Then, the magnetic field strength of the node is calculated according to equation (14), and then the vertical component of the magnetic field H at the measuring point is calculated. z , and upload the measured point data to the main program, then enter the idle state, waiting for the assignment of new tasks. When all 2738 groups of tasks are completed, the parallel operation ends.

[0148] (8) According to the magnetic field formula of the vertical coplanar transceiver in free space Calculate the primary field value H of the two frequencies respectively p Where m is the magnetic moment, unit: Am 2 , r is the sending and receiving distance, unit is m.

[0149] (9) In the main program, the measurement point data of each subprocess are summarized, and the real and imaginary parts of the normalized secondary magnetic field are calculated by formula (23). When the transmission frequency is 16kHz, the real and imaginary parts of the normalized secondary magnetic field are calculated as follows: Figure 4 , Figure 5 As shown; the real and imaginary parts of the normalized secondary magnetic field calculated when the transmission frequency is 70kHz are as follows Figure 6 , Figure 7 As shown in the figure, different transmission frequencies can detect different depths. High frequencies reflect shallow underground plastic pipe information, while low frequencies reflect deep underground steel pipe information. This method can clearly reflect the direction and range of underground transmission pipes, and improve the accuracy and efficiency of underground transmission pipe detection.

[0150] Embodiment 3

[0151] The three-dimensional finite element forward modeling system of underground transmission pipes based on frequency domain electromagnetics includes:

[0152] A modeling module is configured to establish a three-dimensional model of the underground transmission pipe and perform hybrid meshing on the three-dimensional model of the underground transmission pipe;

[0153] The unit matrix building module is configured to introduce a time harmonic variation factor, construct a frequency domain Maxwell equation group, and build a unit matrix based on the segmented three-dimensional model of the underground transmission pipe and the magnetic vector potential of each unit;

[0154] An equation assembly module, configured to assemble a linear system of equations based on a cell matrix;

[0155] The equation solving module is configured to divide the observation area into several sub-areas, set a transmitting source in each sub-area, and solve the assembled linear equations in parallel for the three-dimensional models of each sub-area with different frequencies, so as to realize the three-dimensional rapid forward modeling of the underground transmission pipe.

[0156] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art within the spirit and principle of the present invention without creative labor shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional finite element forward modeling method for underground transmission pipes based on frequency domain electromagnetics is characterized by: The following steps are involved: Establishing a three-dimensional model of an underground transmission pipe, and performing hybrid meshing on the three-dimensional model of the underground transmission pipe; The time harmonic factor is introduced to construct the frequency domain Maxwell equations. Based on the segmented three-dimensional model of the underground transmission pipe and the magnetic vector potential of each unit, the unit matrix is ​​established. Assemble linear equations based on unit matrices; The observation area is divided into several sub-areas, and a transmitting source is set in each sub-area. The three-dimensional models of each sub-area with different frequencies are solved in parallel to realize the three-dimensional rapid forward modeling of the underground transmission pipe.

2. The frequency domain electromagnetic three-dimensional finite element forward modeling method for underground transmission pipes according to claim 1 is characterized in that: The process of hybrid meshing the underground transmission pipe three-dimensional model includes: meshing the pipeline with triangular prism mesh, meshing the remaining area with unstructured tetrahedral mesh, and coupling and connecting the quadrilateral faces of the triangular prism mesh and the triangular faces of the tetrahedral mesh with pyramid mesh.

3. The frequency domain electromagnetic-based three-dimensional finite element forward modeling method for underground transmission pipes according to claim 2 is characterized in that: When performing hybrid meshing on the three-dimensional model of the underground transmission pipe, the meshes in the underground transmission pipe, the measuring point area and the vicinity of the emission source are refined, and the meshes in other areas are not refined; Use the Delaunay mesh generator to create an unstructured tetrahedral mesh.

4. The three-dimensional finite element forward modeling method for underground transmission pipes based on frequency domain electromagnetics according to claim 1 is characterized in that Time harmonic variation factor, the process of constructing Maxwell equations in frequency domain includes: Let the time harmonic variation factor be e iωt , the differential form of Maxwell's equations in the frequency domain is: In the formula, H is the magnetic field intensity, E is the electric field intensity, and i is the imaginary unit. ω is the angular frequency, D is the electric flux density, J e is the external current density, t is the time, They are electrical conductivity and magnetic permeability respectively. When the underground medium is isotropic, is a scalar; when the underground medium is anisotropic, is a tensor.

5. The three-dimensional finite element forward modeling method for underground transmission pipes based on frequency domain electromagnetics according to claim 1 or 4, characterized in that: Based on the segmented three-dimensional model of the underground transmission pipe and combined with the magnetic vector potential of each unit, the process of establishing the unit matrix includes: performing triple Euler rotation transformation on the anisotropic conductivity and magnetic permeability; Expression medium constitutive relations; The anisotropic dielectric constant is transformed by triple Euler rotation; Then the double curl equation of the electric field is calculated, and the magnetic vector potential is introduced to obtain the control equation; A magnetic insulation boundary condition is set at the magnetic field interface so that the tangential component of the magnetic vector potential is zero at the boundary and the current density divergence is zero; And add the Coulomb gauge condition and introduce the gradient term of the Lagrange multiplier; Compute the magnetic vector potential for each element, construct the element matrix and solve the linear equation system.

6. The frequency domain electromagnetic three-dimensional finite element forward modeling method for underground transmission pipes according to claim 1 is characterized in that: Based on the unit matrix, the process of assembling the linear equation system includes numbering the global nodes and local nodes respectively. In the global node numbering, each unit matrix is ​​added to the global matrix according to the position of the local node to form the linear equation system.

7. The frequency domain electromagnetic three-dimensional finite element forward modeling method for underground transmission pipes according to claim 1 is characterized in that: Before dividing the observation area into several sub-areas, it also includes applying infinite element boundary conditions and dividing the infinite element domain with structured hexahedral grids and triangular prism grids.

8. The frequency domain electromagnetic based three-dimensional finite element forward modeling method for underground transmission pipes according to claim 1 is characterized in that: In the process of solving the assembled linear equations in parallel for the three-dimensional models of each sub-area with different frequencies, the double conjugate gradient stable algorithm is used to solve the linear equations, calculate the magnetic field intensity of each node, and calculate the vertical component of the magnetic field at the measuring point. Only the secondary field can reflect the information of the underground transmission pipe, which is normalized to obtain the normalized secondary magnetic field.

9. The frequency domain electromagnetic three-dimensional finite element forward modeling method for underground transmission pipes according to claim 1 or 8, characterized in that: The process of solving the assembled linear equations in parallel for the three-dimensional models of each sub-region at different frequencies includes: Set the number of parallel running jobs K; Count the number of transmission frequencies Fc and the number of transmission sources Tc; Calculate the number of parallel groups G = Fc × Tc; Allocate the number of parallel groups G to the child processes in sequence. If K < G, continue to assign tasks when the child process is idle. During the operation, each subprocess refines the grids in the measurement point area and near the emission source, uses the biconjugate gradient stable iterative solver for calculation, uploads the measurement point data to the main program, and then enters the idle state, waiting for the assignment of new tasks; When all tasks in group G are completed, the parallel operation ends; The measuring point data of each sub-process is summarized in the main program to obtain the forward modeling results of the entire observation area at different transmission frequencies. Through data processing and drawing, the underground transmission pipeline information at different depths is reflected.

10. A three-dimensional finite element forward modeling system for underground transmission pipes based on frequency domain electromagnetics is characterized by: include: A modeling module is configured to establish a three-dimensional model of the underground transmission pipe and perform hybrid meshing on the three-dimensional model of the underground transmission pipe; The unit matrix building module is configured to introduce a time harmonic variation factor, construct a frequency domain Maxwell equation group, and build a unit matrix based on the segmented three-dimensional model of the underground transmission pipe and the magnetic vector potential of each unit; An equation assembly module, configured to assemble a linear equation system based on a cell matrix; The equation solving module is configured to divide the observation area into several sub-areas, set a transmitting source in each sub-area, and solve the assembled linear equations in parallel for the three-dimensional models of each sub-area with different frequencies, so as to realize the three-dimensional rapid forward modeling of the underground transmission pipe.

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