A fast calculation method for modeling forward problems of magnetic flux leakage detection

Abstract

The present invention relates to a fast calculation method for modeling forward problems of magnetic flux leakage detection, comprising: firstly, according to the finite element numerical calculation steps, the bounded area of ​​the entire magnetic flux leakage detection plane is divided by six-node triangle units, and the grid node data is processed in the form of sparse matrix; secondly, the shape function represented by the area coordinate is selected as the interpolation function; then, the equations in each unit are superimposed to establish an equation group; finally, the equation group is solved according to the orthogonal basis of the boundary condition matrix null space. Through the theoretical derivation of the finite element numerical calculation of the magnetic flux leakage field, the finite element model of the magnetic flux leakage field is established. Compared with the prior art, the present invention has the advantages of fast calculation speed and high precision.

Description

Technical Field

[0001] The invention relates to the field of magnetic flux leakage detection, and in particular to a fast calculation method for forward modeling of magnetic flux leakage detection. Background Art

[0002] Magnetic flux leakage testing is a nondestructive testing method that is very suitable for ferromagnetic materials. The basic principle of magnetic flux leakage testing is to magnetize the ferromagnetic material, and the defects on the surface or near the surface of the material cause magnetic field distortion, generate leakage magnetic field related to the geometric characteristics of the defect, and detect the defect by obtaining the leakage magnetic field signal. The forward modeling problem of magnetic flux leakage detection is essentially to use Maxwell's equations to solve the numerical problem of the electromagnetic field at a certain point in space, but considering the arbitrariness of the geometric shape of the defect in the actual problem, the solution process is difficult. At present, there are three main computational models for forward modeling problems: heuristic model, analytical model and numerical calculation model. The heuristic model generally uses a neural network model, and uses machine learning or deep learning to process the eigenvalues ​​of the magnetic flux leakage signal to establish a mapping model, but this method relies on a large amount of training data and is generally only applicable to defects of regular shapes. The analytical model is mainly a magnetic dipole model, which has the advantages of simple model and short calculation time, and its disadvantage is that the calculation result has poor accuracy. Numerical calculation models include finite difference method and finite element method. Among them, finite element method is the most widely used method in numerical calculation models. Its advantage lies in high calculation accuracy and the ability to accurately simulate complex defects under high degrees of freedom. However, its modeling process is relatively complicated, time-consuming, and has poor reproducibility. Summary of the invention

[0003] The purpose of the present invention is to provide a fast calculation method for modeling the forward problem of magnetic flux leakage detection in order to overcome the defects of the above-mentioned prior art.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A fast calculation method for modeling forward problems of magnetic flux leakage detection, the method comprising:

[0006] According to the finite element numerical calculation method, the bounded area of ​​the entire magnetic flux leakage detection plane is meshed using six-node triangular units, and the mesh node data is processed; the shape function represented by the area coordinate is selected as the interpolation function; each unit equation is superimposed to establish an equation group; and the equation group is solved;

[0007] Through the theoretical deduction of the finite element numerical calculation of the leakage magnetic field, a finite element model of the leakage magnetic field is established.

[0008] Furthermore, when dividing the mesh, six-node triangle units are used for division. The specific contents are as follows:

[0009] The entire plane bounded region Ω is divided by triangular high-order units, that is, a node is added at the midpoint of each of the three sides of the triangular unit, that is, a six-node triangular unit, and the magnetic potential inside the unit changes linearly; the magnetic potential of the six nodes is obtained based on the six-node triangular unit, and the area coordinates are used instead of the general rectangular coordinates, and then the shape function represented by the area coordinates is used as the interpolation function to obtain the magnetic potential of any point inside the triangular unit.

[0010] Furthermore, the grid node data is calculated in the form of a sparse matrix.

[0011] Furthermore, the system of equations is solved according to an orthogonal basis of the null space of the boundary condition matrix.

[0012] Furthermore, the boundary conditions are considered in solving the equations in the finite element calculation of the leakage magnetic field. For the Neumann boundary condition, no constraint conditions need to be satisfied on Ω. For the Dirichlet boundary condition, the boundary nodes are constrained, that is:

[0013]

[0014] K=N u T (K+q)N u

[0015]

[0016] Among them, M c is the global matrix containing boundary conditions, {N u}(i=1,2,...,D e ) is the standard orthogonal basis of the boundary condition matrix null space, {O r}(i=1,2,...,D e ) is a standard orthogonal basis applicable to the range of boundary condition matrices.

[0017] The magnetic flux leakage detection forward problem modeling method for rapid calculation of magnetic flux leakage defect detection provided by the present invention has at least the following beneficial effects compared with the prior art:

[0018] The present invention establishes a finite element model for analyzing leakage magnetic field. Firstly, a six-node triangular unit is used to divide a plane bounded area, and the number of grid nodes is increased, so that the interpolation of magnetic induction intensity at any point in the entire bounded area is more accurate; secondly, the grid node data is calculated in the form of a sparse matrix, which can save a lot of memory and speed up the data processing speed; finally, the magnetic potential is directly solved according to the orthogonal basis of the boundary condition matrix null space, so as to improve the calculation speed of the finite element method; by comparing with the COMSOL simulation result, the feasibility of the theoretical derivation of finite element numerical calculation is verified; by comparing with the parameters and performance of the traditional finite element model, the advantages of fast calculation speed and high precision of the finite element model established by the present invention are verified; at the same time, the influence of the width, depth and lift-off value of the defect on the axial component of the leakage magnetic field is studied, and compared with the axial component of the leakage magnetic field calculated by the COMSOL software, the effectiveness of the established model is further verified; a fast and effective forward model is provided for studying the leakage magnetic reconstruction of irregular defects, and fast and accurate leakage magnetic reconstruction can be further realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the flow of finite element numerical calculation in the method of the present invention in the embodiment;

[0020] Figure 2 Schematic diagram of a six-node triangle unit structure in the embodiment;

[0021] Figure 3 Schematic diagram of the simulation structure of the leakage magnetic field finite element model in the embodiment;

[0022] Figure 4 2 are simulation diagrams of defects of two different shapes in the embodiment, wherein sub-diagram (a) is a simulation diagram of a regular defect, and sub-diagram (b) is a simulation diagram of an irregular defect;

[0023] Figure 5 : is a magnetic potential diagram of a regular defect model in an embodiment, wherein sub-diagram (a) is a magnetic potential diagram of a model constructed by the present invention, and sub-diagram (b) is a magnetic potential diagram of a COMSOL model;

[0024] Figure 6 : is a magnetic potential diagram of the irregular defect model in the embodiment, wherein sub-diagram (a) is a magnetic potential diagram of the model constructed by the present invention, and sub-diagram (b) is a magnetic potential diagram of the COMSOL model;

[0025] Figure 7 : is the leakage magnetic field component of the regular defect in the embodiment, wherein sub-figure (a) is the axial component of the leakage magnetic field component, and sub-figure (b) is the radial component of the leakage magnetic field component;

[0026] Figure 8: is the leakage magnetic field component of the irregular defect in the embodiment, wherein sub-figure (a) is the axial component of the leakage magnetic field component, and sub-figure (b) is the radial component of the leakage magnetic field component;

[0027] Fig. 9 Schematic diagram of defect profile of leakage magnetic field in the embodiment;

[0028] Fig.10 1 is a comparison of the leakage magnetic flux components calculated by the three methods in the embodiment, wherein sub-figure (a) is the axial component of the leakage magnetic flux signal curve, and sub-figure (b) is the radial component of the leakage magnetic flux signal curve;

[0029] Fig.11 is a comparison of the axial components at different widths in the embodiments;

[0030] Fig.12 is a comparison of the axial components at different depths in the embodiment;

[0031] Fig.13 Comparison of the axial components at different lift-off values ​​in the embodiments. DETAILED DESCRIPTION

[0032] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work should belong to the scope of protection of the present invention.

[0033] Example

[0034] The present invention relates to a method for modeling a forward problem of magnetic flux leakage detection with fast calculation, which establishes a finite element model of magnetic flux leakage. By improving the grid division and the solution method of magnetic flux leakage, and processing the grid node data in the form of sparse matrix, the calculation accuracy of the finite element method can be improved, the calculation time can be shortened, and the method has great flexibility. The specific steps of the method of the present invention include:

[0035] Step 1: Divide the bounded area of ​​the entire magnetic flux leakage detection plane using six-node triangular units, and process the grid node data in the form of a sparse matrix.

[0036] Step 2: Select the shape function represented by area coordinates as the interpolation function.

[0037] Step 3: Superimpose the equations in each unit to establish a system of equations.

[0038] Step 4: Solve the system of equations based on the orthogonal basis of the null space of the boundary condition matrix.

[0039] Step 5: Based on the theoretical derivation of steps 1 to 4, a finite element model of the leakage magnetic field is established.

[0040] The main principles and specific processes involved in the above steps include:

[0041] 1. Description of the forward problem

[0042] The forward modeling problem of magnetic flux leakage detection is to solve the leakage magnetic field from known defects. In essence, it uses Maxwell's equations to solve the electromagnetic field at a certain point in space. Since the magnetic flux leakage detection process is in a static or low-speed state, it is generally believed that solving the leakage magnetic field in a static magnetic field is accurate enough.

[0043] 1.1 Physical model of leakage magnetic field:

[0044] In a static magnetic field, the Maxwell equations and corresponding boundary conditions can determine the relationship between the stable magnetic field formed by the current density in a homogeneous medium and the magnetic induction intensity:

[0045]

[0046]

[0047] B=μH (3)

[0048] Among them, B is the magnetic induction intensity, also called magnetic flux density, H is the magnetic field intensity, μ is the material magnetic permeability, and J is the current density. Due to the passivity of the magnetic field, according to vector analysis, that is, the passive field It must be expressed as the curl of another vector, usually introducing the vector magnetic potential A, and we have:

[0049]

[0050] From (2), (3), and (4), we can get:

[0051]

[0052] From the vector analysis formula we know The non-time-varying field takes A to meet the specification conditions The differential equation of the magnetic vector potential A is:

[0053]

[0054] For a plane static magnetic field, the current density and magnetic potential only have z-direction components, and a two-dimensional field solution can be used. The magnetic field has only two components, x and y, so the above equation (6) can be simplified to:

[0055]

[0056] For the partial differential equations of magnetostatic problems, there are two choices of boundary conditions for each edge or face:

[0057] Dirichlet condition: On the boundary Γ1, hu = r (8)

[0058] Neumann condition: on the boundary Γ2

[0059] Among them, h and r are functions of space, u is the solution, is the outward unit normal, q and g are functions defined on a plane bounded domain. Γ1 represents the boundary of the solution domain, and Γ2 represents the boundary of the medium inside the solution domain.

[0060] 2. Finite element numerical realization and finite element numerical calculation of leakage magnetic field:

[0061] For many partial differential equations raised in theoretical research and practical application problems, it is very difficult or even impossible to find analytical solutions due to the complexity of their boundaries and boundary conditions. Therefore, it is necessary to use computers to study the numerical solutions of partial differential equations, among which the most widely used is the finite element method.

[0062] The finite element method is a method for obtaining approximate solutions based on the variational principle and discretization. Starting from the boundary value problem of the partial differential equation, an integral of the energy functional is found, and it is allowed to take the extreme value under the premise of satisfying the first-class boundary conditions, that is, a conditional variation problem is formed. This conditional variation problem is equivalent to the boundary value problem of the partial differential equation. Then the conditional variation problem is used as the object to solve the partial differential equation problem. In the solution process, the solution area of ​​the field is divided into a finite number of units, so an interpolation function is constructed in the unit, and the interpolation function is substituted into the integral of the energy functional, and then the functional is discretized into a multivariate function. An algebraic equation system is obtained by the method of finding the extreme value of the multivariate function extreme value. Finally, the numerical solution is obtained by solving this equation system. The finite element method occupies a dominant position due to its flexible unit definition, easy handling of boundary conditions, and positive definite symmetric coefficient matrix.

[0063] For ferromagnetic materials with known defects, solving the leakage magnetic field by applying an external magnetic field is to solve the partial differential equation of the static magnetic field. For the partial differential equation in the leakage magnetic field, it is very difficult or even impossible to find an analytical solution due to its complex boundaries and boundary conditions, so it is necessary to use computers to study the numerical solution of the partial differential equation, among which the finite element method is the most widely used.

[0064] The finite element method is a method for obtaining approximate solutions based on the variational principle and discretization. By combining the partial differential equation satisfied by the magnetic field with the boundary conditions, the magnetic field distribution can be uniquely determined. According to the variational principle, the partial differential equation can be equivalent to a conditional variation problem, that is, the extreme value problem of the energy functional. The conditional variation problem corresponding to formula (6) is:

[0065]

[0066] Γ1:hu=r (11)

[0068] Where Ω is a planar bounded region, W(A Z ) is called energy functional. The problem of solving the partial differential equation of the leakage magnetic field is transformed into the problem of finding the extreme value of the energy functional, and the approximate solution is obtained by the finite element method, and finally the magnetic induction intensity distribution of the leakage magnetic field can be obtained. The specific steps of using finite element numerical calculation are as follows: Figure 1 As shown. Figure 1 It can be seen that the finite element numerical calculation is divided into 4 steps, among which the discretization of the region, the selection of the interpolation function and the solution of the system of equations affect the calculation accuracy and speed of the finite element method. The finite element model established using the mesh2D software package in MATLAB (referred to as the traditional finite element model in this patent) has a slow calculation speed and is difficult to provide a fast and effective forward model for magnetic flux leakage reconstruction. Therefore, the present invention proposes a finite element numerical calculation method that can be solved quickly, while further improving the calculation accuracy. The specific steps and theoretical derivation of the finite element numerical calculation in the present invention are given below.

[0069] 2.1 Discreteness of regions:

[0070] In any finite element analysis, domain discretization is an important step because the way the domain is discretized will affect the accuracy of the numerical results. In this step, the planar bounded region is divided into many small regions, i.e. meshing, and these small regions are called elements.

[0071] The entire plane bounded region Ω is divided by triangular units. The traditional finite element method uses three-node triangular units for meshing, that is, the three vertices of the triangle are used to interpolate any point inside the triangle, but the magnetic potential inside the unit is a constant, so it cannot reflect the actual change of magnetic potential well. In order to make up for this shortcoming, triangular high-order units can be used, that is, a node is added at the midpoint of each of the three sides of the triangular unit, such as Figure 2 As shown in the figure, it is called a six-node triangle unit. The magnetic potential inside this unit is no longer a constant, but changes linearly, which can better reflect the actual magnetic potential state, so the required magnetic potential is more accurate.

[0072] When using six-node triangular elements, area coordinates are used instead of general rectangular coordinates, which not only simplifies the coefficient matrix calculations, but also does not change with the shape and orientation of the triangular element.

[0073] 2.2 Selection of interpolation function:

[0074] exist Figure 2 In the triangular unit shown in FIG. , the position of any point P can be determined by three area ratios, as shown in formula (12):

[0075]

[0076] Where S1 is the area of ​​triangle IJM, S2, S3, S4 are the areas of triangle PJM, triangle PMI, and triangle PIJ respectively. These three ratios are called the area coordinates of point P. Since S2+S3+S4=S1, according to formula (12), we can get the relationship:

[0077] L I +L J +L M =1 (13)

[0078] The area S1 of triangle IJM is:

[0079]

[0080] Among them, (x I ,y I ),(x J ,y J ),(x M ,y M ) are the coordinates of the three nodes I, J, and M, so the areas of triangles PJM, PMI, and PIJ are:

[0081]

[0082] As with the simple triangular element, let:

[0083]

[0084] Substituting formulas (14) to (16) into (12), we obtain:

[0085]

[0086] Then, inside the triangular unit, the magnetic potential A at any point P is P It can be obtained by the following linear interpolation:

[0087]

[0088] Among them, A I ,A J ,A M ,A D ,A E ,A F The magnetic potentials of nodes I, J, M, D, E, and F are defined as:

[0089]

[0090] Among them, N I ,N J ,N M ,N D ,N E ,N F are all shape functions expressed in area coordinates, also called interpolation functions, then:

[0091] A P =N I A I +N J A J +N M A M +N D A D +N E A E +N F A F (20)

[0092] Formula (20) can also be expressed as:

[0093] A P =[N][δ] (21)

[0094] Where, [N] = [N I ,N J ,N M ,N D ,N E ,N F ], [δ] = [A I ,A J ,A M ,A D ,A E ,A F ].

[0095] If the magnetic potentials of the six nodes on the triangular unit are known, the magnetic potential of any point inside the triangular unit can be calculated through the interpolation function.

[0096] 2.3 Establishment of the equation system

[0097] set up D for A eThe basis function of the dimensional subspace can be rewritten into formula (10) according to the divided units:

[0098]

[0099] Among them, e n is any unit area, r n is the boundary of the unit, D e and U m are the number of nodes and the number of elements respectively.

[0100] Therefore, the integral over each cell is calculated as:

[0101]

[0102]

[0103]

[0104]

[0105] Among them, {δ} e is the nodal solution on the element, {F} e is the unit excitation or boundary value, {K} e is the unit coefficient matrix.

[0106] Substituting formulas (23) to (26) into (22), for the sake of superposition, first calculate {δ} e ,{F} e ,{F} e Expand to D e dimensional vector and D e ×D e The data on the grid are then superimposed. Therefore, the linear equation system can be obtained:

[0107] KA=F (27)

[0108] Where K is D e ×D e Finite element coefficient matrix, F is D e ×1 excitation or boundary value, A is D e ×1 magnetic potential.

[0109] 2.4 Solution of Equations

[0110] To solve formula (27), we need to consider the boundary conditions. For Neumann boundary conditions, since they are natural boundary conditions, no constraints need to be satisfied on Ω. For Dirichlet boundary conditions, the boundary nodes need to be constrained. Therefore, we have:

[0111]

[0112]

[0113]

[0114] Among them, M c is the global matrix containing boundary conditions, {N u}(i=1,2,...,D e ) is the standard orthogonal basis of the null space of the boundary condition matrix, {O r}(i=1,2,...,D e ) is a standard orthogonal basis applicable to the boundary condition matrix range, and in the entire solution process, A, F, K, and H are all in the form of sparse matrices. Using sparse matrices to store data containing many zero-value elements can save a lot of memory and speed up data processing.

[0115] The magnetic potential at each node in the model can be obtained by formulas (28) to (30), and the magnetic potential at any position in the model can be calculated according to the interpolation function of formula (21). Since the solution of the leakage magnetic field is to obtain the magnetic induction intensity in the leakage magnetic field, then:

[0116]

[0117] The magnetic induction intensity of the constructed model can be calculated by formula (31). In practice, solving the leakage magnetic field means solving the magnetic induction intensity within a certain range above the defect. Therefore, the present invention solves the entire plane bounded area through finite element numerical calculation, and then extracts the magnetic induction intensity 1 mm above the defect, which is consistent with the sensor installation position in the actual detection.

[0118] It is worth mentioning that in the process of finite element numerical calculation, the differences from the traditional finite element model are mainly reflected in: first, the six-node triangular unit is used to divide the grid, which has the advantage of high calculation accuracy compared with the three-node triangular unit in the traditional finite element; second, when solving the system of equations, the data is processed in the form of sparse matrix, which speeds up the calculation of the matrix compared with the full matrix form in the traditional finite element; finally, the magnetic potential A is solved by using the orthogonal basis of the zero space of the boundary condition matrix.

[0119] In the traditional finite element model, the magnetic potential is solved by the inverse of the finite element coefficient matrix. Since a certain error will be generated, the error is usually reduced by iteration until the result converges, that is:

[0120] A0=K -1 F (31)

[0121]

[0122]

[0123] A [n+1] =A [n] +J n [n] g n [n] (34)

[0124] Among them, A0 and g n They represent the initial solution and error after inverting K, J n is the Jacobian matrix, ⊙ represents the inner product of a vector or matrix, when When it is less than a certain threshold, the iteration is stopped and the magnetic potential A can be obtained. When it is greater than the threshold, g needs to be recalculated n and J n , continue to iterate until convergence. If the preset number of iterations is reached and convergence has not yet occurred, the model needs to be re-meshed and then iterated to solve, which dramatically increases the computational cost.

[0125] In summary, the present invention has fast calculation speed and high calculation accuracy in theory.

[0126] 3. Model verification and analysis

[0127] 3.1 Feasibility verification of the model

[0128] In order to verify the feasibility of the fast finite element modeling and solution method for magnetic flux leakage defect detection proposed in the present invention, this embodiment uses the PDE toolbox to establish a finite element model of the magnetic field leakage, such as Figure 3 shown.

[0129] Figure 3 It includes ferromagnetic specimens with known defects, magnetic yokes, excitation coils, and air solution domains. Considering the geometric size and magnetization effect of the magnetization device, local magnetization is generally selected for the material to be tested. By detecting the magnetic field signal in the magnetization area, it is determined whether there are defects in the area and the geometric shape of the defects. Therefore, this model uses the magnetic yoke method to locally magnetize the ferromagnetic specimen, and the magnetization current is selected as direct current, which can generate a stable magnetic field. The size of the ferromagnetic specimen in the model is 100mm×10mm, and the current density in the excitation coil is 1000A / m 2 , the relative magnetic permeability of the ferromagnetic specimen and the yoke is 500, the relative magnetic permeability of the air domain is 1, and the magnetic potential on the boundary is 0. Regular defects and irregular defects are modeled separately, and the defect contours are as follows Figure 4As shown in the figure, the width of the regular defect is 5mm, the depth is 3mm, the width of the irregular defect is 10mm, the depth is 0mm~4mm, the detection range is 30mm~70mm, the detection lift-off value is 1mm, and the vector D=(d1,d2,d3,...,d 81 ) indicates that the number of defect sampling points is 81.

[0130] Through the established model and COMSOL software modeling and calculation, the magnetic potential of the model is obtained, such as Figure 5 and Figure 6 As shown, Figure 7 and Figure 8 are the radial and axial components of the leakage magnetic field, respectively.

[0131] Figure 5 and Figure 6 In the figure, the magnetic potential on each curve is equal, and the magnetic potential obtained by the constructed model and COMSOL calculation is between 0 and 30 mWb / m. Figure 7 and Figure 8 In the figure, the solid line represents the leakage magnetic field component of the COMSOL software, and the dotted line represents the leakage magnetic field component of the built model. The variation pattern of the leakage magnetic field components calculated by the built model and COMSOL at the sampling point is the same, that is, the maximum value of the axial component of the leakage magnetic field of the regular defect is at the center of the defect, and the radial component is in opposite directions on both sides of the defect, with maximum and minimum values ​​near the edge of the defect. The axial and radial components of the leakage magnetic field of the irregular defect have fluctuated, but overall they are in line with the law that the amplitude of the axial and radial components is positively correlated with the defect depth. Figures 5 to 8 It can be seen that under the same conditions, the magnetic potential obtained by the established model and COMSOL calculation is very close, and the extracted axial and radial components are also very close, indicating that the established leakage magnetic field finite element model is correct, and it also shows that the theoretical derivation of the finite element calculation method is feasible.

[0132] 3.2 Verification of model validity

[0133] The validity of the model refers to the fast calculation speed and high accuracy of the model. In order to verify the validity of the model, a leakage magnetic field finite element model is established and compared with the traditional finite element model and the calculation results of COMSOL. Fig. 9 It is the defect profile of the leakage magnetic field. The number of sampling points is 81, the detection range is 30mm~70mm, and the detection lift-off value is 1mm. Fig.10 This is a comparison of the magnetic flux leakage signals calculated by these three methods.

[0134] Fig. 9 The width of the medium defect is 10mm and the depth is 0-3mm. It is an irregular defect. Fig.10In the figure, the solid line represents the leakage magnetic field component of the COMSOL software, the dashed line represents the leakage magnetic field component of the established model, and the dot-dash line represents the leakage magnetic field component of the traditional finite element model. Fig. 9 and Fig.10 It can be seen that the axial and radial components of the finite element forward model established by the present invention are very close to those of the COMSOL software; while the traditional finite element model has some deviations compared with the COMSOL software, and the deviations are related to the meshing of the model. Table 1 shows the parameters and experimental performance indicators of the three models.

[0135] Table 1 Model parameters and performance comparison

[0136]

[0137] In Table 1, RMSE represents the root mean square error of the calculation results of the COMSOL finite element model. Since the traditional finite element model consumes a lot of computing time or even cannot be solved when the mesh size is less than 0.6 mm, the mesh size of this model is set to 0.6 mm. The number of mesh nodes is 8662, and the RMSE is 1.28×10 -2 The calculation time is 79s. The mesh size of the finite element model constructed in the present invention is 0.5mm-0.1mm, the number of mesh nodes is 165765, and the orthogonal basis of the boundary condition matrix null space is used to directly solve the model, and the RMSE is 4.81×10 -4 , the calculation time is 4.1s. The number of grid nodes in the traditional finite element model is only 5.2% of the finite element model built by the present invention, its RMSE is 26 times that of the model built by the present invention, and its calculation time is 19 times that of the model built by the present invention. When the mesh size and the number of nodes of the model built by the present invention are similar to those of the COMSLO model, the calculation time is only 37% of the latter. As can be seen from Figure 10 and Table 1, the traditional finite element model uses three-node triangles for meshing, and the small number of grid nodes is the main reason for the deviation. At the same time, it uses the full matrix form to process data and uses the iterative method to solve the model, which greatly increases the calculation time. The finite element model built by the present invention uses six-node triangles for meshing, which can obtain more grid node data, and uses the form of sparse matrix to calculate the data on the grid. At the same time, the model is directly solved according to the orthogonal basis of the boundary condition matrix null space, thereby shortening the calculation time and making the calculation result more accurate.

[0138] In order to verify the influence of the established model on the leakage magnetic field when the defect width, depth and lift-off value change, the axial component calculated by COMSOL software was compared in the experiment. Fig.11The axial component of the leakage magnetic field is given when the lift-off value is 1mm, the defect depth is 3mm, and the defect width is 3mm, 5mm, and 7mm respectively. Fig.12 The axial component of the leakage magnetic field is given when the lift-off value is 1mm, the defect width is 5mm, and the defect depth is 2mm, 4mm, and 6mm respectively. Fig.13 The axial component of the leakage magnetic field is given when the defect depth is 3mm, the width is 5mm, and the lift-off values ​​are 1mm, 3mm, and 5mm respectively.

[0139] Figure 11 to Figure 13 In the figure, the axial components of the leakage magnetic field obtained by the constructed model and COMSOL software are completely overlapped. Fig.11 In the figure, the larger the defect width is, the smaller the peak value of the axial component of the leakage magnetic field is, and the wider the convex part of the axial component is. Fig.12 In the figure, the deeper the defect depth, the larger the peak value of the axial component of the leakage magnetic field, while the shape of the axial component does not change much. Fig.13 In the figure, as the lift-off value increases, the peak value of the axial component of the leakage magnetic field decreases, and the change trend of the axial component at the defect edge slows down. Figure 11 to Figure 13 It can be seen that the variation of the axial component of the leakage magnetic field in the constructed model with different defect width, depth and detection lift-off value is completely consistent with the finite element model in the COMSOL software, which further verifies the effectiveness of the model constructed in the present invention.

[0140] The present invention establishes a finite element model of leakage magnetic field by theoretical derivation of finite element numerical calculation of partial differential equations in leakage magnetic field. First, a six-node triangular unit is used to divide the plane bounded area, and the number of grid nodes is increased, so that the interpolation of magnetic induction intensity at any point in the entire area is more accurate; secondly, the grid node data is calculated in the form of sparse matrix, which can save a lot of memory and speed up the data processing speed; finally, the magnetic potential is directly solved according to the orthogonal basis of the boundary condition matrix null space, which improves the calculation speed of the finite element method. By comparing with the COMSOL simulation results, the feasibility of the theoretical derivation of finite element numerical calculation is verified; by comparing with the parameters and performance of the traditional finite element model, the advantages of fast calculation speed and high precision of the finite element model constructed by the present invention are verified; at the same time, the influence of the width, depth and lift-off value of the defect on the axial component of the leakage magnetic field is studied, and compared with the axial component of the leakage magnetic field calculated by COMSOL software, the effectiveness of the constructed model is further verified. A fast and effective forward model is provided for studying the leakage magnetic reconstruction of irregular defects, and it provides the possibility for fast and accurate leakage magnetic reconstruction.

[0141] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A fast calculation method for modeling forward problems of magnetic flux leakage detection, characterized in that: include: According to the finite element numerical calculation method, the bounded area of ​​the entire magnetic flux leakage detection plane is meshed using six-node triangle elements, and the mesh node data is processed; Select the shape function represented by the area coordinates as the interpolation function; superimpose each unit equation to establish an equation system; solve the equation system; Through theoretical deduction of finite element numerical calculation of leakage magnetic field, a finite element model of leakage magnetic field is established; The grid node data is calculated in the form of sparse matrix; Solve the system of equations based on an orthogonal basis in the null space of the boundary condition matrix; The specific contents of the division using six-node triangular elements are as follows: The entire plane bounded region Ω is divided by using triangular high-order units, that is, adding a node at each midpoint of the three sides of the triangular unit, that is, a six-node triangular unit, and the magnetic potential inside the unit changes linearly; based on the six-node triangular unit, the magnetic potential of the six nodes is obtained, and the general rectangular coordinates are replaced by area coordinates, and then the shape function represented by the area coordinates is used as an interpolation function to obtain the magnetic potential of any point inside the triangular unit; The boundary conditions are considered in solving the equations in the finite element calculation of the leakage magnetic field. For the Neumann boundary condition, no constraint conditions need to be satisfied on Ω. For the Dirichlet boundary condition, the boundary nodes are constrained, that is: Among them, M c is the global matrix containing boundary conditions, {N u }(i=1,2,...,D e ) is the standard orthogonal basis of the boundary condition matrix null space, {O r }(i=1,2,...,D e ) is a standard orthogonal basis applicable to the boundary condition matrix range, F is D e ×1 excitation or boundary value, q and g are functions defined on a plane bounded domain, r is a function of space, and K is D e ×D e Finite element coefficient matrix, A is D e ×1 magnetic potential, De is the number of nodes.

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