A method for quantifying a weak magnetic signal

Abstract

The application discloses a kind of weak magnetic signal quantification method, based on effective field model step, magnetization intensity calculation step and magnetic permeability calculation step, angle compensation coefficient is introduced, angle-compensated magnetic permeability model is obtained, and then combined with the finite element model established, weak magnetic signal is obtained, and finite element analysis weak magnetic signal, based on angle-compensated magnetic permeability model and the gradient total characteristic parameter, angle factor and amplitude parameter calculated from weak magnetic signal, so that weak magnetic signal quantification, then through model verification step to weak magnetic signal extracts weak magnetic signal characteristic value, to verify angle-compensated magnetic permeability model.The angle-compensated magnetic permeability model obtained by the application improves the stress-magnetic permeability coupling model, introduces the angle compensation coefficient, so that the weak magnetic signal quantification of ferromagnetic material in complex environment is more accurate, avoids the error of detecting weak magnetic signal being large, effectively reduces the possibility of serious accident.

Description

Technical Field

[0001] This invention belongs to the field of quantitative research technology of weak magnetic signals, and particularly relates to a method for quantitative analysis of weak magnetic signals. Background Technology

[0002] In engineering applications, ferromagnetic materials are prone to fatigue failure and damage, which can affect their safety and service life, leading to significant economic losses. Fatigue cracks typically appear in stress concentration areas of ferromagnetic materials, and timely detection of these stress concentration areas can reduce the likelihood of serious accidents.

[0003] Therefore, the quantitative study of weak magnetic signals in stress concentration regions of ferromagnetic materials is receiving increasing attention. The environment surrounding ferromagnetic materials is complex, and the stress conditions they experience are also highly complex. When there is an angle between the magnetic field and the stress, the direction of the ambient magnetic field and the direction of the external load have a significant impact on the magnetic signal in the stress concentration region of the ferromagnetic material. However, in existing technologies, the stress-permeability coupling model does not include the influence of angle on permeability, leading to significant errors in the detection signal and failing to effectively reduce the possibility of serious accidents.

[0004] Therefore, in order to address the above shortcomings, it is necessary to study a method for quantifying weak magnetic signals. Summary of the Invention

[0005] The purpose of this invention is to provide a method for quantifying weak magnetic signals. According to this invention, an angle compensation coefficient is introduced to obtain an angle-compensated permeability model, which solves the technical problem that the stress-permeability coupling model does not include the influence of angle on permeability, causing large errors in the detection signal and failing to effectively reduce the possibility of serious accidents.

[0006] This invention provides a method for quantifying weak magnetic signals, comprising: a step based on an effective field model, a step for calculating magnetization intensity, and a step for calculating magnetic permeability; introducing an angle compensation coefficient to obtain an angle-compensated magnetic permeability model; combining this with an established finite element model to obtain a weak magnetic signal; performing finite element analysis on the weak magnetic signal; calculating the total gradient characteristic parameter, angle factor, and amplitude parameter based on the angle-compensated magnetic permeability model to quantify the weak magnetic signal; and finally, extracting the feature values ​​of the weak magnetic signal through a model verification step to verify the angle-compensated magnetic permeability model.

[0007] Optionally, in the effective field model step, based on the principle of minimum energy, the internal energy density is integrated and rearranged. Then, considering that the magnetization effect of stress on a ferromagnetic material under the action of an external magnetic field and stress is equivalent to an applied magnetic field, and combining this with the magnetostriction inside the material, the effective field model is obtained:

[0008]

[0009] Where H is the external magnetic field; α is the magnetic domain coupling coefficient; μ0 is the free permeability; and λ is the magnetostriction coefficient. The angle between the stress direction and the magnetic field.

[0010] Optionally, in the magnetization calculation step, based on the effective field model and the stress magnetization differential equation, an angle compensation coefficient is introduced to obtain an improved model of the relationship between magnetization and the effective field:

[0011]

[0012] Among them, H e The effective field is M; the magnetization is σ; the stress is μ0; and the free permeability is μ0. λ is the angle between stress and magnetic field; λ is the magnetostriction coefficient; α is the magnetic domain coupling coefficient.

[0013] Optionally, in the permeability calculation step, based on the improved relationship model between magnetization and effective field, and combined with the relationship model between magnetization and permeability, the angle-compensated permeability model is obtained as follows:

[0014]

[0015] Among them, M s B is the saturation magnetization. s ν is the saturation magnetic induction; υ is Poisson's ratio; E is the elastic modulus; b is a constant; σ0 is the stress; α is the magnetic domain coupling coefficient; μ0 is the free permeability; a is the material planning constant; ξ is the energy per unit volume metric factor; H is the external magnetic field; γ1, γ2 are the Taylor series expansion coefficients; c is a parameter.

[0016] Optionally, a finite element model is established, and loads and constraints are applied to the finite element model. An air box is added around the finite element model, and a uniform magnetic field is applied along the X-axis of the air box to simulate the geomagnetic field. The air box mesh is divided into hexahedral elements. The permeability of each hexahedral element on the finite element model is calculated using an angle-compensated permeability model, and the calculated weak magnetic signal is subjected to finite element analysis.

[0017] Optionally, the total gradient characteristic parameters are calculated based on the obtained magnetic weakening signal. These parameters reflect the degree of anomalousness of the magnetic weakening signal based on the peak-to-peak amplitude and peak-to-valley amplitude of the gradient curve. The total gradient characteristic parameters are a general index reflecting the degree of anomalousness.

[0018]

[0019] Among them, S totalS represents the total characteristic parameter of the gradient. x S represents the peak-to-peak amplitude of the gradient curve of the weak magnetic signal. y This represents the peak-valley amplitude of the gradient curve of the weak magnetic signal.

[0020] Optionally, an angle factor is calculated based on the obtained magnetic weakening signal. The angle factor characterizes the influence of the angle between stress and the magnetic field on the magnetic weakening signal. The peak value of the magnetic weakening signal is divided by the maximum value of the peak value for normalization, resulting in a peak value that varies between 0 and 1. The angle factor is:

[0021]

[0022] Where f is the angle factor; H i The peak values ​​of the weak magnetic signal under stress in different directions; H max It is the maximum value among the peak values ​​of the weak magnetic signal under stress in different directions.

[0023] Optionally, amplitude parameters are calculated based on the obtained weak magnetic signal. These amplitude parameters are obtained by analyzing the amplitude eigenvalues ​​of the stress concentration zone in the pipeline. The amplitude parameters are as follows:

[0024]

[0025] Where, m max It is the maximum value of the amplitude of the weak magnetic signal; Average amplitude of the weak magnetic signal; Average value of amplitude change.

[0026] Optionally, in the model verification step, based on the magnetic weakening signal obtained from the finite element analysis, the characteristic values ​​of the magnetic weakening signal under different directional stresses are obtained, and based on the characteristic values ​​of the magnetic weakening signal under different directional stresses, the changing trend of the influence of different directional stresses on the characteristic values ​​of the magnetic weakening signal is analyzed to verify the angle-compensated permeability model.

[0027] Optionally, in the model verification step, the characteristic values ​​of the weak magnetic signal are the extreme values ​​of the axial component and the peak values ​​of the radial component with respect to the stress direction.

[0028] Compared to existing technologies, this invention introduces an angle compensation coefficient into the existing model relating magnetization intensity and effective field, resulting in an angle-compensated permeability model. This model then yields the total gradient characteristic parameters, angle factor, and amplitude parameters, quantifying the weak magnetic signal. The model verification process validates the correctness of the angle-compensated permeability model, making the weak magnetic signal obtained from ferromagnetic materials more accurate when there is an angle between the magnetic field and stress, effectively reducing the possibility of serious accidents. Attached Figure Description

[0029] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein:

[0030] Figure 1 This is an analysis diagram of the stress direction and magnetic permeability curves of the present invention;

[0031] Figure 2 This is a magnetic weakening signal analysis diagram under different stress directions according to the present invention;

[0032] Figure 3 This is an analysis diagram showing the relationship between the characteristic values ​​of the weak magnetic signal and the stress direction in this invention;

[0033] Figure 4 This is an analysis diagram of the variation of the total gradient characteristic parameters of the present invention with stress direction;

[0034] Figure 5 This is a diagram showing the relationship between the angle factor and the stress direction of the present invention.

[0035] Figure 6 This is a diagram showing the relationship between the amplitude parameters and stress direction of the present invention;

[0036] Figure 7 This is a comparison diagram of the characteristic values ​​of the weak magnetic signal in the model verification step of this invention;

[0037] Figure 8 This is a diagram showing the relationship between the angle factor and the stress direction in the model verification step of this invention.

[0038] Figure 9 This is a diagram showing the relationship between stress direction and total gradient characteristic parameters in the model verification step of this invention.

[0039] Figure 10 This is a diagram showing the relationship between stress direction and amplitude parameters in the model verification step of this invention. Detailed Implementation

[0040] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Unless otherwise specified, the techniques used in the embodiments are conventional means well known to those skilled in the art.

[0041] It should be noted that, unless otherwise stated, the technical or scientific terms used in this invention should be understood in their ordinary sense by those skilled in the art. The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0042] This embodiment provides a method for quantifying weak magnetic signals, including: based on an effective field model step, a magnetization calculation step, and a permeability calculation step, an angle compensation coefficient is introduced to obtain an angle-compensated permeability model. Then, combined with the established finite element model, a weak magnetic signal is obtained, and the weak magnetic signal is analyzed by finite element analysis. Based on the angle-compensated permeability model, the total gradient characteristic parameter, angle factor, and amplitude parameter are calculated to quantify the weak magnetic signal. Finally, the weak magnetic signal feature values ​​are extracted through a model verification step to verify the angle-compensated permeability model.

[0043] This embodiment provides a method for quantifying weak magnetic signals, wherein the finite element model is a long-distance oil and gas pipeline.

[0044] In the effective field model step, this embodiment utilizes the principle of minimum energy as follows:

[0045]

[0046] In formula (1), E is the internal energy density, J / m 3 α1, α2, and α3 are the unit cosines of the magnetization vector; B1 and B2 are constants; e xx e yy e zz e xy e yz and e zx C represents the components of the deformation tensor. 11 C 12 and C 44 σ is the elastic modulus, MPa; σ is the stress, MPa; α is the magnetic domain coupling coefficient; μ0 is the free permeability, 4π × 10⁻⁶. -7 NA -2 M is the magnetization, Am -1 ;Φ mag Thermodynamic internal energy density caused by interdomain coupling, J / m 3 ;Φ hys It is a function of the derivative of the magnetization intensity obtained from the ideal magnetization curve.

[0047] Relative to e xx e yy e zz Integral result:

[0048]

[0049] In formula (2), b is a constant.

[0050] Magnetostriction was obtained by sorting. The expression:

[0051]

[0052] In formula (3), b is a constant; Y is Young's modulus, Pa; M s Am is the saturation magnetization. -1 .

[0053] When a ferromagnetic material is subjected to an external magnetic field and stress, the effect of stress on the magnetization of the material is equivalent to an applied external magnetic field, and the initial effective field H e The model is:

[0054]

[0055] In formula (4), The angle between stress and magnetic field is in degrees.

[0056] Combining formulas (3) and (4), we obtain the effective field H. e The model is:

[0057]

[0058] In formula (5), α is the magnetic domain coupling coefficient; μ0 is the vacuum permeability of 4π×10⁻⁶. -7 NA -2 λ is the magnetostriction coefficient, in ppm.

[0059] In the magnetization calculation step, the definition is... Let be the angle compensation coefficient, then the angle compensation coefficient is expressed as:

[0060]

[0061] Angle compensation coefficient By introducing a model relating magnetization to the effective field, an improved model relating magnetization to the effective field is obtained:

[0062]

[0063] Magnetization M and permeability μ rThe relationship model is as follows:

[0064] M=(μ r -1)H (8)

[0065] In the permeability calculation step, the improved relationship model between magnetization and effective field (7) and the relationship between magnetization M and permeability μ are combined. r The relationship model (8) leads to the angle-compensated permeability model:

[0066]

[0067] In formula (9), the angle-compensated permeability model (9) takes X70 steel as an example, and the saturation magnetization M s = 1.585 × 10⁶ A / m, saturation magnetic induction intensity B s =1.99 A / m, Poisson's ratio υ = 0.3, elastic modulus E = 207 GPa, constant b = 1.672, stress σ0 = 104 MPa, magnetic domain coupling coefficient α = 0.001, free permeability μ0 = 4π × 10 -7 NA -2 Parameter c = 0.1, material planning constant a = 1000 A / m, energy per unit volume metric ξ = 24.5 × 10⁻⁶ 3 Pa, external magnetic field H = 40 A / m, Taylor series expansion coefficients γ1, γ2

[0068] Establishing a finite element model: In this embodiment, X70 steel in actual engineering applications is used as the analysis object. The finite element model is a three-dimensional model of the X70 pipe. A pipe model with a length of 2000mm, a diameter of 1016mm, and a wall thickness of 14.5mm is established. An axial crack with a length of 30mm, a width of 1mm, and a depth of 3mm is established on the inner wall of the pipe. The stress concentration area at the crack tip is used as the analysis area.

[0069] The element type in the preprocessing is solid96, and the mesh is divided into hexahedral elements.

[0070] Loads and constraints are applied to the X70 pipe. The constraints are applied radially and axially at both ends of the pipe wall. The loads are applied to the inner wall of the X70 pipe to simulate the working internal pressure of the X70 pipe. The change of stress direction in the stress concentration zone is simulated by changing the crack direction.

[0071] Add an air box around the X70 pipe model, and apply a 40Am pressure along the X-axis of the air box. -1A uniform magnetic field was used to simulate the Earth's magnetic field. The air box was meshed into hexahedral elements, and the corresponding weak magnetic signal was obtained through finite element analysis. Assuming the permeability of the air box is 1, the permeability of each hexahedral element on the X70 pipe was calculated using an angle-compensated permeability model, and the weak magnetic signal was obtained through finite element analysis.

[0072] This embodiment analyzes the magnetic weakening signal under stress in different directions. Based on the characteristics of the magnetic weakening signal under stress in different directions, the changes in its radial and axial components with the stress direction are analyzed, thus quantifying the magnetic weakening signal. Since the stress concentration area of ​​the X70 pipeline experiences complex stress directions, a single directional stress cannot replace the influence of stresses in different directions. Angle compensation is applied to the stress to make the obtained magnetic weakening signal more realistic. Therefore, the stress is decomposed in the X, Y, and Z directions to obtain three permeabilities in these three directions. These three permeabilities are then substituted into an angle-compensated permeability model for calculation and analysis.

[0073] like Figure 1 As shown, the permeability increases non-linearly with increasing stress. Due to the differences in the angle between stress and the magnetic field in different directions, the stress-permeability curves also differ for each direction. When the stress magnitude is the same, the angle between stress and the magnetic field affects the permeability, which increases with increasing angle. Furthermore, the larger the stress value in different directions, the greater the impact on permeability, and the more pronounced the increasing trend of permeability. This trend provides a theoretical basis for the quantification of the weak magnetic signal in this embodiment.

[0074] like Figure 2 As shown in (a), the radial component of the magnetic weakening signal exhibits sinusoidal fluctuations, and the magnetic weakening signal has two positive and negative peaks. From Figure 2 (b) It can be seen that the axial component has two maximum points and two minimum points, and the two maximum points are symmetrical about the perpendicular bisector of the line connecting the maximum points. The two maximum points are symmetrical, and the two minimum points are also symmetrical.

[0075] according to Figure 2 As can be seen from the enlarged portion of the image, as the angle between stress and magnetic field increases from 15° to 51°, the overall amplitude of the weak magnetic signal decreases. This allows us to derive the trend of the weak magnetic signal, which facilitates the calculation of the total gradient characteristic parameter, angle factor, and amplitude parameter, and helps to quantify the weak magnetic signal.

[0076] Furthermore, in this embodiment, the influence of stress direction on the magnetic weakening signal is extracted. Figure 2 The extreme values ​​of the ordinate and the peak values ​​of the ordinate of the radial component in the axial component curve.

[0077] like Figure 3As shown, the extreme values ​​of the axial component and the peak values ​​of the radial component both decrease with the increase of the angle between the stress and the magnetic field, and the sensitivity of the characteristic value changes gradually decreases, thus revealing the changing trends of the extreme values ​​of the axial component and the peak values ​​of the radial component of the weak magnetic signal.

[0078] The gradient curve of the magnetic weakening signal exhibits more typical characteristics in the stress concentration region than the magnetic weakening signal itself. The total characteristic parameter of the gradient, Sttotal, is defined as...

[0079]

[0080] In formula (11), S x For (dH) x ) / d x Peak-to-peak amplitude of the curve; S y For (dH) y ) / d x The peak-to-trough amplitude of the curve. Due to S x and S y It reflects the degree of abnormality of the weak magnetic signal; therefore, Statotal is used as the overall indicator reflecting the degree of abnormality.

[0081] like Figure 4 As shown, the angle between stress and magnetic field has a significant impact on the total gradient characteristic parameter Stotal. As the angle between stress and magnetic field increases from 15° to 51°, the total gradient characteristic parameter Stotal decreases approximately exponentially, indicating that the rate of change of the weak magnetic signal decreases with the increase of the angle between stress and magnetic field.

[0082] In this embodiment, an angle factor f is used to characterize the effect of the angle between stress and the magnetic field on the magnetic weakening signal. The peak value of the magnetic weakening signal under different stress directions is divided by the maximum value among the peak values ​​of the magnetic weakening signals under different stress directions for normalization, so that the peak value of the magnetic weakening signal varies between 0 and 1.

[0083] The expression for the angle factor f is:

[0084]

[0085] In formula (12), f is the angle factor; H i The peak values ​​of the weak magnetic signal under stress in different directions; H max It is the maximum value among the peak values ​​of the weak magnetic signal under stress in different directions.

[0086] like Figure 5 As shown, the angle factor decreases nonlinearly with the increase of the angle between stress and magnetic field. The rate of decrease of the radial angle factor is 50% lower than that of the axial angle factor. Thus, the angle between stress and magnetic field in different directions has a significant impact on the angle factor of the axial magnetic weakening signal, thereby enabling the quantification of the magnetic weakening signal.

[0087] The amplitude eigenvalue method is used to analyze the characteristics of the weak magnetic signal in the stress concentration zone of the pipeline. The amplitude parameter R of the weak magnetic signal is defined as follows:

[0088]

[0089] In formula (13), the average amplitude of the weak magnetic signal is... Average value of amplitude change for:

[0090]

[0091] In formula (14), N is the number of samples of the weak magnetic signal; m i The amplitude of the weak magnetic signal at the sampling point is expressed in A / m.

[0092] like Figure 6 As shown, it can be seen that as the angle increases from 15° to 51°, the amplitude parameter of the radial component of the magnetic weakening signal continuously decreases, exhibiting an exponential decreasing relationship. Meanwhile, the amplitude parameter of the axial component of the magnetic weakening signal increases approximately linearly, and its amplitude is 33% higher than that of the radial component. This indicates that the axial component of the magnetic weakening signal in ferromagnetic materials is more sensitive to changes in stress direction and is more easily affected by stress direction.

[0093] This embodiment also includes a model verification step to verify the correctness of the angle-compensated permeability model. The specific steps are as follows:

[0094] The experiment used the TSC-2M-8 weak magnetic field detection equipment from the Russian Power Diagnostics Company to collect weak magnetic signals with an accuracy of 0.001 A / m.

[0095] The experimental material was an X70 pipe with artificial cracks, which was 6 mm long, 1016 mm in diameter, and 4.5 mm thick.

[0096] In the model verification process of this embodiment, a pipeline pressure test with cracks of different sizes under the geomagnetic field environment was designed, and the pipeline was pressure tested by a water pump.

[0097] A crack measuring 30 mm in length, 1 mm in width, and 3 mm in depth was found in the pipe, and strain gauges in different orientations were attached to the crack tip. During the pressure test, weak magnetic signals at different locations in the stress concentration area were detected, and repeatability experiments were performed to ensure the accuracy of the verification results in the model validation step.

[0098] By changing the stress direction from 15° to 51° and comparing the axial extrema and radial peak of the weak magnetic signal in the model verification step, the obtained data parameters show that the gradient total characteristic parameter Stotal, angle factor and amplitude parameter obtained by the angle-compensated permeability model in this embodiment are close to the data parameters in the verification experiment step, thus verifying the accuracy of the gradient total characteristic parameter, angle factor and amplitude parameter obtained by the angle-compensated permeability model.

[0099] In this embodiment, as Figure 7 As shown in (a), the axial extremum decreases nonlinearly with increasing angle between stress and magnetic field, and the axial signal error of the angle-compensated permeability model is reduced by 41%. From Figure 7 (b) It can be seen that the radial peak value decreases non-linearly with the increase of the angle between stress and magnetic field, and the radial signal error is reduced by 54%, indicating that the calculation result of the angle-compensated permeability model has a smaller error. It is evident that the eigenvalue changes obtained by the angle-compensated permeability model after introducing the angle compensation coefficient are consistent with the data parameters in the model verification experiment, indicating that the angle-compensated permeability model accurately reflects the changing trend of the weak magnetic signal under different stress directions. For the weak magnetic signal of the X70 pipeline, the angle-compensated permeability model in this embodiment is significantly better than the calculation results of the model in the prior art.

[0100] Figure 8 As shown, in this embodiment, both the axial angle factor and the radial angle factor decrease nonlinearly with the increase of the angle between stress and magnetic field, and the rate of decrease of the axial angle factor is 46% higher than that of the radial angle factor. The angle between stress and magnetic field has a significant impact on the angle factor of the axial weak magnetic signal. After the finite element model is combined with the angle-compensated permeability model, the obtained angle factor is close to the angle factor in the model verification step, which verifies the accuracy of the angle-compensated permeability model in this embodiment.

[0101] Figure 9 As shown, in this embodiment, the total gradient characteristic parameter decreases exponentially with the increase of the angle between the stress and the magnetic field. When the angle between the stress and the magnetic field changes by 50°, the total gradient characteristic parameter decreases by 83%. After the finite element model is combined with the angle-compensated permeability model, the obtained total gradient characteristic parameter is close to the total gradient characteristic parameter in the model verification step, which verifies the accuracy of the angle-compensated permeability model in this embodiment.

[0102] Figure 10 As shown in this embodiment, as the angle increases from 15° to 51°, the amplitude parameter R of the radial component of the magnetic weakening signal... y It continuously decreases, exhibiting an exponential decreasing relationship. Meanwhile, the amplitude parameter R of the axial component of the weak magnetic signal... x The change in axial amplitude parameter R increases approximately linearly. x Higher than the radial amplitude parameter Ry The change indicates that the axial weak magnetic signal is more susceptible to the influence of the angle between stress and magnetic field. After the finite element model is combined with the angle-compensated permeability model, the amplitude parameters obtained are close to the amplitude parameters in the model verification step, which verifies the accuracy of the angle-compensated permeability model in this embodiment.

[0103] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for quantifying weak magnetic signals, characterized in that: Based on the effective field model step, magnetization calculation step, and permeability calculation step, an angle compensation coefficient is introduced to obtain an angle-compensated permeability model. Then, combined with the established finite element model, a weak magnetic signal is obtained. Based on the finite element analysis of the weak magnetic signal, the gradient total characteristic parameter, angle factor, and amplitude parameter are calculated based on the angle-compensated permeability model and the obtained weak magnetic signal to quantify the weak magnetic signal. Finally, the weak magnetic signal characteristic value is extracted through the model verification step to verify the angle-compensated permeability model. In the effective field model step, based on the principle of minimum energy, the internal energy density is integrated and rearranged. Then, considering the effect of stress on the magnetization of ferromagnetic materials under external magnetic fields and stress, which is equivalent to the applied magnetic field, and combining the magnetostriction inside the material, the effective field model is obtained: （1） Where H is the external magnetic field; α is the magnetic domain coupling coefficient; μ0 is the free permeability; and λ is the magnetostriction coefficient. The angle between the stress direction and the magnetic field; In the magnetization calculation step, the definition is... Let be the angle compensation coefficient, then the angle compensation coefficient is expressed as: (6) In the magnetization calculation step, based on the effective field model and the stress magnetization differential equation, an angle compensation coefficient is introduced to obtain an improved relationship model between magnetization and the effective field: （2） Among them, H e The effective field is M; the magnetization is σ; the stress is μ0; and the free permeability is μ0. λ is the angle between stress and magnetic field; λ is the magnetostriction coefficient; α is the magnetic domain coupling coefficient; Magnetization M and permeability μ r The relationship model is as follows: (8) In the permeability calculation step, based on the improved relationship model between magnetization and effective field, and combined with the relationship model between magnetization and permeability, the angle-compensated permeability model is obtained as follows: (3) Among them, M s B is the saturation magnetization. s ν is the saturation magnetic induction; υ is Poisson's ratio; E is the elastic modulus; b is a constant; σ0 is the stress; α is the magnetic domain coupling coefficient; μ0 is the free permeability; a is the material planning constant; ξ is the energy per unit volume metric factor; H is the external magnetic field; γ1, γ2 are the Taylor series expansion coefficients; c is a parameter.

2. The method for quantifying weak magnetic signals according to claim 1, characterized in that, A finite element model was established, and loads and constraints were applied to the finite element model. An air box was added around the finite element model, and a uniform magnetic field was applied along the X-axis of the air box to simulate the geomagnetic field. The air box mesh was divided into hexahedral elements. The permeability of each hexahedral element on the finite element model was calculated using an angle-compensated permeability model, and the calculated weak magnetic signal was subjected to finite element analysis.

3. The method for quantifying weak magnetic signals according to claim 2, characterized in that: The total gradient characteristic parameters are calculated based on the obtained weak magnetic signal. These parameters reflect the degree of anomalousness of the weak magnetic signal based on the peak-to-peak and peak-to-valley amplitudes of the gradient curve. The total gradient characteristic parameters are a general index reflecting the degree of anomalousness. (4) Among them, S total S represents the total characteristic parameter of the gradient. x S represents the peak-to-peak amplitude of the gradient curve of the weak magnetic signal. y This represents the peak-valley amplitude of the gradient curve of the weak magnetic signal.

4. The method for quantifying weak magnetic signals according to claim 2, characterized in that: The angle factor is calculated based on the obtained magnetic weakening signal. The angle factor characterizes the influence of the angle between stress and the magnetic field on the magnetic weakening signal. The peak value of the magnetic weakening signal is divided by the maximum value of the peak value for normalization, resulting in a peak value that varies between 0 and 1. The angle factor is: (5) Where f is the angle factor; H i The peak values ​​of the weak magnetic signal under stress in different directions; H max It is the maximum value among the peak values ​​of the weak magnetic signal under stress in different directions.

5. The method for quantifying weak magnetic signals according to claim 2, characterized in that: The amplitude parameters are calculated based on the obtained weak magnetic signal. These amplitude parameters are derived from the amplitude eigenvalue method used to analyze the amplitude parameters in the pipe stress concentration zone. The amplitude parameters are: (6) Where, m max It is the maximum value of the amplitude of the weak magnetic signal; Average amplitude of the weak magnetic signal; Average value of amplitude change.

6. The method for quantifying weak magnetic signals according to claim 2, characterized in that, In the model verification step, based on the magnetic weakening signal obtained from finite element analysis, the characteristic values ​​of the magnetic weakening signal under stress in different directions are obtained. Based on the characteristic values ​​of the magnetic weakening signal under stress in different directions, the changing trend of the influence of stress in different directions on the characteristic values ​​of the magnetic weakening signal is analyzed to verify the magnetic permeability model with angle compensation.

7. The method for quantifying weak magnetic signals according to claim 6, characterized in that, In the model verification step, the characteristic values ​​of the weak magnetic signal are the extreme values ​​of the axial component and the peak value of the radial component with respect to the stress direction.

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