A method for constructing a penetration propagation model of underground extremely low frequency signals based on finite element method

Abstract

A method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements, which relates to the technical field of non-acoustic detection and tracer positioning of underground pipeline robots. This method is based on the polarization characteristics of the target electromagnetic field, and uses the vector electromagnetic signals detected by electromagnetic sensors to identify and estimate the azimuth of the target; and optimizes the underground pipeline environment model to obtain the law of electromagnetic signals, and realizes the tracking of the target through the detected signal characteristics.

Description

Technical Field

[0001] The present invention relates to the field of underground pipeline robot tracing and positioning, and more specifically to a method for constructing an underground extremely low frequency signal penetration and propagation model based on finite elements. Background Art

[0002] Public infrastructure construction is a key indicator of a city's modernization. Urban underground utility corridors (including sewers) are crucial for ensuring the smooth functioning of urban life, often referred to as "the city's lifeline." Therefore, underground utility corridor operational inspection represents a significant transformation in urban underground space development, flood control, and public safety, both in China and globally. It will play a crucial role in supporting urban preparedness and combat operations.

[0003] At present, the operation and management of urban underground pipeline corridor systems in China are still at the manual stage, with a low degree of automation and poor adaptability. Therefore, underground pipeline corridor inspection robots can transform passive monitoring into active detection, effectively avoiding the defects caused by manual inspection and excavation. However, due to factors such as the underground environment, geographical space, and weak sensor signals, conventional navigation methods are not applicable. Therefore, a finite element-based method for constructing an underground extremely low frequency signal penetration propagation model is proposed. The characteristics of the extremely low frequency signal in different locations are analyzed. The distance of the underground robot is determined by analyzing the magnetic induction intensity and its variation pattern at the receiving end, thereby increasing the feasibility of autonomous positioning of the robot in the underground environment. Summary of the Invention

[0004] The purpose of the present invention is to establish an underground extremely low frequency signal penetration and propagation model in COMSOL, introduce the steps of establishing the simulation model in detail, obtain the signal characteristics of the receiving end under static conditions in the frequency domain, explore the magnitude and change law of the magnetic field intensity during the signal penetration process, analyze the strength of the signal under the pipeline, simulate and calculate the operating state of the receiving end, and obtain simulation data such as magnetic induction intensity and induced current, providing a direction for realizing the detection of underground environmental signals and the positioning of robots.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] The present invention provides a method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements, comprising the following steps:

[0007] (1) Determine the coil model solution domain for the extremely low frequency signal transmitter and receiver;

[0008] Simplify the coil structure of the extremely low frequency signal transmitter and receiver;

[0009] Except for the relative permeability and relative permittivity of the coil material, the conductivity, relative permeability and relative permittivity of the tube wall material, the remaining materials are regarded as models with isotropic composition and uniform material properties; among them, the physical property parameters of each material are constants; the uniformly wound coil and the magnetic core are combined into a component, and its resistance is regarded as a uniform resistance, and each point at the receiving end is selected as the solution domain; control the area of the solution model;

[0010] (2) Establish a mathematical model for the physical field analysis of the extremely low-frequency signal transmitter and receiver;

[0011] Construct a two-dimensional physical field model; construct the electromagnetic field control equation between the two coils, and construct the constitutive relations between the magnetic induction intensity and the magnetic field intensity, the current density and the electric field intensity, and the electric displacement vector and the electric field intensity, which are expressed as:

[0012] B = μ0μ r H;

[0013] In the formula, μ0 is the vacuum permeability, μ r is the material permeability, H is the magnetic field intensity, and B is the magnetic induction intensity;

[0014] J c = σE;

[0015] In the formula, σ is the material conductivity, J c is the current density, and E is the electric field intensity;

[0016] D = ε0ε r E;

[0017] In the formula, ε0 is the relative permittivity in vacuum, ε r is the relative permittivity of the material, and D is the electric displacement vector;

[0018] Display the assumed mathematical equation in the research frequency domain, set the component of the solution field as the out-of-plane vector potential, discretize the magnetic vector potential as quadratic, and set the dependent variable as the magnetic vector potential and the magnetic vector potential component;

[0019] (3) Determine the boundary model for the physical field analysis of the transmitter and receiver:

[0020] In the process of electromagnetic field calculation, the magnetic vector potential has the highest amplitude at the coil, and then decays rapidly in the external space and approaches 0. At the same time, the magnetic vector potential inside the solution domain is perpendicular to the direction of the conductor current; boundary 1 is the input boundary, and boundaries 2, 3, and 4 are output boundaries, which are set as magnetic insulation boundaries. Here, the static magnetic field finite element is used to perform relevant analysis on the object to be solved. In the static magnetic field, let:

[0021]

[0022] In the formula, A is the vector magnetic potential;

[0023] Substitute the above equation into the Maxwell differential form:

[0024]

[0025] For time-harmonic electromagnetic fields, by the vector identity and considering the electromagnetic attenuation simplifies to:

[0026]

[0027] According to the above equation, the variational equation of the electromagnetic field is derived using the method of functional, and then the electromagnetic field is approximately simulated by the finite element decomposition method;

[0028] (4) Use the frequency-domain and time-domain analysis in the COMSOL physics field simulation to divide the grid and assign properties; simulate the electromagnetic environment under extremely low-frequency conditions and perform numerical simulation calculations on electromagnetic signals;

[0029] (5) Create a parametric sweep in the study, conduct studies on multiple different positions of the receiving end at 23.5 Hz, perform polynomial fitting on the simulation data, and obtain the law of penetration and propagation of extremely low-frequency signals.

[0030] As a further improvement of the present invention, step (4) further includes: the transmitting end is excited by a 9.8 V voltage; the coil current density at the transmitting end is:

[0031]

[0032] where N is the number of turns of the uniformly wound multi-turn coil, V ind is the input voltage, e coil is the elementary charge of the coil.

[0033] As a further improvement of the present invention, step (4) further includes: the initial values of the magnetic vector potential in the r, phi, and z directions are all 0; its control equation is:

[0034]

[0035] where μ is the environmental magnetic permeability, n is the number of turns of the coil per unit length, I m is the current value of the energized coil, p is the coil length, a is the radius of the transmitting coil, and r is the distance from the coordinate origin to the receiving end.

[0036] As a further improvement of the present invention, the extremely low-frequency emission system of the extremely low-frequency signal transmitting end includes:

[0037] A battery pack;

[0038] A signal generator and a power amplifier for providing simulation signals;

[0039] The transmitting coil for emitting spatial magnetic field signals.

[0040] As a further improvement of the present invention, the extremely low frequency (ELF) signal receiving end's ELF receiving system includes:

[0041] A group of power converters;

[0042] A receiving coil for receiving spatial magnetic field signals;

[0043] A signal amplifier for the receiving end;

[0044] A band-pass filter and a 50Hz power frequency filter for filtering.

[0045] As a further improvement of the present invention, the transmitting coil adopts a parallel winding method of two sections of coils. The number of turns of the coil is selected as 5600 turns, each section is 100mm long, the inner diameter is 20mm, and the wire diameter is 0.5mm.

[0046] As a further improvement of the present invention, the amplification and filtering circuit of the band-pass filter performs frequency selection amplification on the signal with a center frequency of 23.5Hz.

[0047] As a further improvement of the present invention, for the receiving antenna of the extremely low frequency signal receiving end, a magnetic core is placed inside the solenoid sensor to reduce the magnetic resistance of the solenoid receiving antenna, and a strip-shaped ferromagnetic core is selected for the magnetic resistance.

[0048] As a further improvement of the present invention, the calculation expression for the effective magnetic permeability of the strip-shaped ferromagnetic core is:

[0049]

[0050] In the formula, m is the aspect ratio of the ferromagnetic core, and μ is the intrinsic magnetic permeability of the ferromagnetic core material.

[0051] As a further improvement of the present invention, the receiving antenna of the receiving end includes a coil skeleton, a magnet core, a solenoid coil, a protective shell, etc.; the solenoid is wound with 0.15mm enameled wire for 10000 turns, and a silicon steel rod material is selected for the magnetic core.

[0052] The present invention uses COMSOL to simulate the penetration and propagation model of underground extremely low frequency signals, which is of great significance for the precise positioning of underground pipeline robots. Its specific beneficial effects include:

[0053] The present invention develops a method for constructing a penetration and propagation model of underground extremely low frequency signals based on finite elements. Considering multiple factors such as operating voltage and ambient magnetic field intensity, the induced current, magnetic induction intensity, and energy distribution within the solution domain of the receiving end coil are solved, which conforms to the actual operating conditions and better meets the complex physical states in actual engineering. The model construction method is simple and practical, and has positioning feasibility, accuracy, and applicability.

[0054] The energy transfer between ordinary induction coils is very limited. Since the frequency is relatively high, detection or positioning can only be achieved at close range, and it is greatly affected by the material thickness and lift-off. It is difficult to achieve the penetration and propagation of signals through underground pipelines. Therefore, a model for the penetration and propagation of underground extremely low-frequency signals is established through simulation. Under the condition of extremely low frequency, a better penetration effect can be produced, which helps to capture signals and provides support for the positioning of underground pipeline robots.

[0055] The traditional signal positioning method is not applicable due to factors such as the underground environment, geographical space, and weak sensing signals, and it is difficult to accurately position signals. Through simulation numerical calculations, the relationship between distance and signal characteristics can be deduced, the relationship between voltage intensity and the relative position of coils is studied, and the penetration and propagation ability of signals in the presence of pipelines is analyzed, which has guiding significance for the extremely low-frequency positioning of underground robots. Brief Description of the Drawings

[0056] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0057] Figure 1 is a simplified structural diagram of the model of the present application (the transmitting end and the receiving end are in a vertical state);

[0058] Figure 2 is a two-dimensional schematic diagram of the penetration model of the present application;

[0059] Figure 3 is the mesh and quality constructed by the present application using the finite element principle;

[0060] Figure 4 is a graph of the change law of the z-direction coordinate and the magnetic field when the receiving end and the transmitting end of the present application are perpendicular;

[0061] Figure 5 is a graph of the change law of the z-direction coordinate and the magnetic field when the receiving end and the transmitting end of the present application are horizontal;

[0062] Figure 6 is a logarithmic amplitude graph of the r component of the magnetic intensity in the time domain of the present application;

[0063] Figure 7 is the voltage change at different horizontal distances of the receiving end of the present application in the time domain. Detailed Embodiment

[0064] The present invention will be further described below in conjunction with the accompanying drawings of the specification:

[0065] The present invention provides a method for constructing an underground extremely low-frequency signal penetration and propagation model based on finite elements, which is characterized in that it includes:

[0066] S1: Select two-dimensional space dimension and establish the magnetic field interface in AC / DC: It is used to calculate the electric and magnetic fields in static and low-frequency systems. The "Magnetic Field" interface is used to calculate the magnetic field distribution and induced current distribution inside and around coils, conductors, and magnets, and supports steady-state, frequency-domain, small-signal analysis, and time-domain modeling in two and three dimensions.

[0067] S2: Establish the coordinates of the underground extremely low-frequency transmitter and receiver. The coordinate information of the transmitter and receiver includes the r-plane direction and the z-plane direction. The simple structure diagram of the model is as Figure 1 shown, and its two-dimensional schematic diagram is as Figure 2 shown.

[0068] S3: According to the position information of the transmitter coil and the receiver coil and the pipeline information: Add a finite element domain with a side length of 10 m in "Components" to establish the transceiver model of the extremely low-frequency system. Since the transceiver coils are simple geometric bodies, they can be reduced to two-dimensional rectangles to simulate the coils. Add the rectangular models of each coil, magnetic core, and pipeline in turn. Select "Copper", "Air", "High-strength Steel", and "Silicon Steel" in the "Material Library" and add them to the solution domain.

[0069] S4: Mesh generation: During the mesh generation process, the mesh should be made denser in the areas where the physical field changes. At the same time, the magnetic field changes more at the junction of different domains, so the mesh at the boundary is denser. The mesh generation and its quality are as Figure 3 shown

[0070] S5: In the research, parametric scanning is performed on the receiver at different positions in the z direction. Without adding a pipeline, numerical simulation is performed on the signals of the receiver at different positions, and the horizontal / vertical direction of the receiver relative to the transmitter is changed, and the operation is repeated.

[0071] S6: Repeat the operation of S5 under the shielding state of the added pipeline and the shielding state of the soil, compare the strength of the signals, and analyze the law of the receiver signals.

[0072] S7: Perform numerical simulation on the voltage signals at different positions under time-domain conditions.

[0073] In the traditional geometric modeling method, the air domain, fluid domain, and metal domain need to be manually defined in the software. Among them, the metal domain includes a multi-turn coil wound uniformly, a magnetic core, and a pipeline wall. Among them, the multi-turn coil and the magnetic core are made of different materials and have different physical properties such as material density, conductivity, relative permeability, and relative permittivity.

[0074] For the initialization modeling of magnetic vector potential provided by this application, the receiving end only needs to establish an overall domain, that is, a rectangular model, to form a union of the receiving coil and the magnetic core, and ensure the correctness of the material properties of the air domain, coil domain, and magnetic core domain. As can be seen from the number of meshes in this application, the number of meshes is dense at the field change points and the quality is good, such as Figure 4 shown.

[0075] In an example of the present invention, the coil is connected to a sinusoidal alternating current with an amplitude of 9.8V, 5600 turns, and a frequency of 23.5Hz. Of course, those skilled in the art can also select other frequencies and alternating current amplitudes, which should be included in the protection scope of the present invention.

[0076] Such as Figure 1 shown: is a simple structure diagram of the present invention. Among them, the transmitting end includes a silicon iron magnetic core and a copper coil evenly wound with 5600 turns, the receiving end includes a silicon iron magnetic core and a coil evenly wound with 10000 turns, the relative permittivity of the geotechnical material is 5, the relative permeability is 1, and the conductivity is 0.01S / m; the pipeline material is made of high-strength alloy steel, the relative permittivity is 1, the relative permeability is 100, and the conductivity is 4.032e6S / m;

[0077] Such as Figure 4 shown: is the variation law of the magnetic induction intensity in the z direction when the vertical distance from the transmitting end of this application in the frequency domain is 0.4m; it can be seen that in this penetration model, when the receiving end and the transmitting end are perpendicular, the magnetic intensity forms an anti-phase double-peak curve in the z direction, and the corresponding electrical signal will also change according to this law; Figure 5 When the receiving end and the transmitting end are parallel, a higher signal peak can be generated, but the energy and duration of the signal are smaller, so the preferred embodiment when they are perpendicular is discussed and described.

[0078] Such as Figure 6 shown: is the logarithmic amplitude curve diagram of the r component of the magnetic intensity in the time domain of this application; when the receiving end coordinates are 0m or 1m, their logarithmic amplitudes are almost equal, while when they are 2m or 3m, the logarithmic amplitudes decrease significantly, which is similar to the law shown in Figure 4 and Figure 7 ; at the same time, there is an obvious linear relationship in the logarithmic amplitude at the end of the period (frequency 23.5Hz, period about 0.04255s).

[0079] The preferred embodiment of the present invention is shown in the drawings. Although the present invention has been described in detail with reference to the preferred embodiment, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified and equivalently replaced without departing from the purpose and scope of the technical solutions of the present invention, and should also be included in the protection scope of the present invention.

Claims

1. A method for constructing an underground extremely low frequency signal penetration and propagation model based on finite element, characterized in that, It includes the following steps: (1) Determine the coil model solution domains of the extremely low frequency (ELF) signal transmitter and receiver; Simplify the coil structures of the ELF signal transmitter and receiver; Except for the relative magnetic permeability and relative permittivity of the coil material, the conductivity of the tube wall material, relative magnetic permeability and relative permittivity, the remaining materials are regarded as models with isotropic composition and uniform material properties; where the physical property parameters of each material are constants; Combine the uniformly wound coil and the magnetic core into one component, and regard its resistance as a uniform resistance, and select each point of the receiver as the solution domain; Control the area of the solution model; (2) Establish a mathematical model for the physical field analysis of the ELF signal transmitter and receiver; Construct a two-dimensional physical field model; Construct the electromagnetic field control equations between the two coils, and construct the constitutive relations between the magnetic induction intensity and the magnetic field intensity, the current density and the electric field intensity, and the electric displacement vector and the electric field intensity, which are expressed as: ； In the formula, is the vacuum permeability, is the relative permeability of the material, is the magnetic field strength, is the magnetic induction intensity; ； wherein, is the material conductivity, is the current density, is the electric field strength; ； In the formula, is the relative permittivity in vacuum, is the relative permittivity of the material, is the electric displacement vector; Display the assumed mathematical equations in the research frequency domain, set the components of the solution field as the out-of-plane vector potential, discretize the magnetic vector potential as quadratic, and set the dependent variables as the magnetic vector potential and the magnetic vector potential components; (3) Determine the boundary models for the physical field analysis of the transmitter and receiver: During the process of electromagnetic field calculation, the magnetic vector potential has the highest amplitude at the coil, and then decays rapidly in the external space and tends to 0. At the same time, the magnetic vector potential inside the solution domain is perpendicular to the direction of the conductor current; Boundary 1 is the input boundary, and boundaries 2, 3, and 4 are output boundaries, which are set as magnetic insulation boundaries. Here, relevant analysis is carried out on the object to be solved by the finite element of the static magnetic field. In the static magnetic field, let: ； In the formula, is the vector magnetic potential; Substitute into the Maxwell differential form: ； wherein, is the environmental magnetic permeability. For a time-harmonic electromagnetic field, by the vector identity and considering , the electromagnetic attenuation is simplified to: ； According to , the variational equation of the electromagnetic field is derived by using the method of functional, and then the electromagnetic field is approximately simulated by the finite element decomposition method; (4) Use the frequency domain and time domain analysis in the COMSOL physical field simulation to divide the mesh and assign characteristics; Simulate the electromagnetic environment under ELF conditions and perform numerical simulation calculations on the electromagnetic signals; (5) Create a parametric sweep in the research, study the receiver at multiple different positions at 23.5 Hz, perform polynomial fitting on the simulation data, and obtain the law of the penetration and propagation of the ELF signal.

2. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite element, characterized in that: Step (4) also includes: The transmitter is excited by a 9.8 V voltage; The coil current density of the transmitter is: ； In the formula, is the number of turns of the uniform multi-turn coil, is the input voltage, is the elementary charge of the coil.

3. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements according to claim 1, characterized in that: Step (4) further includes: the initial values of the magnetic vector potential in , , directions are all 0; and its control equation is: ； In the formula, is the environmental magnetic permeability, is the number of turns of the coil per unit length, is the current value of the energized coil, is the coil length, is the radius of the transmitting coil, is the distance from the coordinate origin to the receiving end.

4. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements according to claim 1, characterized in that: The ELF emission system of the ELF signal transmitter includes: A battery pack; A signal generator and a power amplifier for providing simulation signals; A transmitting coil for transmitting spatial magnetic field signals.

5. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite element, as claimed in claim 4, wherein: The ELF receiving system of the ELF signal receiver includes: A group of power converters; A receiving coil for receiving spatial magnetic field signals; A signal amplifier for the receiver; A band-pass filter and a 50 Hz power frequency filter for filtering.

6. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite element, characterized in that: The transmitting coil adopts a parallel winding method of two coils, selects 5600 turns of coil, each section is 100 mm long, the inner diameter is 20 mm, and the wire diameter is 0.5 mm.

7. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements according to claim 6, characterized in that: The amplification and filtering circuit of the band-pass filter performs frequency selection and amplification on the signal with a center frequency of 23.5 Hz.

8. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite element according to claim 6, characterized in that: For the receiving antenna of the ELF signal receiver, a magnetic core is placed inside the solenoid sensor to reduce the magnetic resistance of the solenoid receiving antenna, and a strip-shaped ferromagnetic core is selected as the magnetic resistance.

9. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite element, characterized in that: The calculation expression for the effective magnetic permeability of the strip-shaped ferromagnetic core is: ； In the formula, is the aspect ratio of the ferromagnetic core.

10. A method for constructing an underground extremely low frequency signal penetration propagation model based on finite elements according to claim 6, characterized in that: The receiving antenna of the receiving end includes a coil skeleton, a magnetic core, a solenoid coil, and a protective housing; the solenoid is formed by winding 10,000 turns of enameled wire with a diameter of 0.15 mm, and the magnetic core is made of silicon steel rod material.

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