Current inversion method based on magnetic sensor array

Abstract

The invention discloses a current inversion method based on a magnetic sensor array, and the method comprises the steps: S1, setting a plurality of measurement points, uniformly dividing a conductor layout region in a to-be-measured part of a to-be-measured multi-conductor system into grids with M * N nodes, and numbering each grid node as (i, j); constructing a coordinate system and recording coordinates of all grid nodes; s2, establishing a finite element simulation calculation model, calculating a reference position coefficient matrix of all measurement points, and constructing a reference position coefficient matrix database; s3, calculating a conductor position coefficient matrix, and constructing a position coefficient matrix; s4, according to the magnetic field measurement value acquired by the magnetic sensor array, the conductor current is calculated through inversion; and S5, after resampling the magnetic field measurement value, substituting the updated measurement value and the position coefficient matrix stored in the step S4 into the linear equation set constructed in the step S4 to solve the current of each conductor. The method has the characteristics of rapid calculation and low operand while the accuracy is ensured, and the inversion calculation efficiency can be improved.

Description

Technical Field

[0001] The invention relates to a multi-conductor system current measurement technology, in particular to a current inversion method based on a magnetic sensor array. Background Art

[0002] In recent years, the technical maturity of new magnetic field sensors represented by quantum tunneling magnetoresistance effect and electron paramagnetic resonance effect has been continuously improved, and they have excellent magnetic field measurement characteristics such as high accuracy, large dynamic range, and wide bandwidth. By arranging magnetic field sensors in the space around the current-carrying conductor and forming a magnetic sensor array with a specific arrangement, and further based on the magnetic field measurement results and performing electromagnetic inversion calculations on them, non-invasive current measurement of multi-conductor systems can be achieved. By fully releasing the excellent measurement performance of magnetic field sensors, current sensor devices based on magnetic sensor arrays are expected to replace traditional electromagnetic current transformers and achieve more accurate and rapid complex dynamic load current measurement.

[0003] At present, the biggest factor restricting the improvement of the measurement accuracy of magnetic sensor arrays is the error introduced by the current inversion method. Existing current inversion methods mainly use analytical methods and numerical methods. Among them, the analytical method establishes a position coefficient matrix that characterizes the relationship between current and magnetic field through the measurement point and the conductor position, and solves the corresponding linear equations. In some cases where the position information cannot be obtained, it is also necessary to solve the nonlinear equations about the position parameters through random optimization methods. Therefore, the accurate construction of the position coefficient matrix and the solution of the equation are crucial to ensure the accuracy of current inversion. Numerical methods, especially finite element methods, mesh the calculation area and solve the discrete magnetic field distribution in each grid. Compared with analytical methods, numerical methods can more accurately construct the field source relationship of different structural feature areas, and can consider the influence of non-uniform current distribution and high magnetic permeability media in the calculation, with better accuracy and applicability. However, since the numerical method needs to re-mesh and calculate differential equations in each iteration of the random optimization of the inversion calculation, it requires more hardware computing resources to support, and it is difficult to meet the current production site The requirements of miniaturization, low power consumption, and real-time performance of current measurement devices are difficult to meet. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing current inversion method cannot ensure real-time performance while improving accuracy, and provide a current inversion method based on a magnetic sensor array, which has the characteristics of fast calculation and low computational complexity while ensuring accuracy, and can improve the inversion calculation efficiency.

[0005] The purpose of the present invention is mainly achieved through the following technical solutions:

[0006] A current inversion method based on a magnetic sensor array comprises the following steps: step S1, setting a plurality of measurement points uniformly distributed along the circumference of the outer surface of the to-be-tested part at the to-be-tested part of the to-be-tested multi-conductor system; establishing a rectangular coordinate system with the geometric center of the multi-conductor system as the origin; uniformly dividing the conductor layout area of ​​the to-be-tested part of the to-be-tested multi-conductor system into grids with M×N nodes arranged in a horizontal and vertical staggered manner, and numbering each grid node as (i, j) according to the horizontal and vertical distribution positions of the grid nodes; wherein the values ​​of M×N are all positive integers greater than or equal to 3, 1≤i≤M, 1≤j≤N; recording the coordinates of all grid nodes in the rectangular coordinate system;

[0007] Step S2, establishing a finite element simulation calculation model, calculating the magnetic induction intensity of any measurement point when the unit line current is located at all grid nodes, obtaining the reference position coefficient matrix of the measurement point, and then calculating the reference position coefficient matrix of the remaining measurement points, and constructing a reference position coefficient matrix database;

[0008] Step S3, setting the initial value of the position of each conductor in the multi-conductor system to be measured, calculating the conductor position coefficient matrix according to the four node coordinates of the grid where the geometric center coordinates of any conductor in the multi-conductor system to be measured are located in combination with the reference position coefficient matrix, and then calculating the position coefficient matrices of the remaining conductors in the multi-conductor system to be measured, and combining the position coefficient matrices of all conductors in the multi-conductor system to be measured to construct a position coefficient matrix;

[0009] Step S4, constructing a linear equation group in which the magnetic field sensor measurement value is equal to the product of the position coefficient matrix and the conductor current value, measuring the magnetic field at the measuring point by the magnetic field sensor, and solving the current of each conductor by the least square method; solving the magnetic field calculation value by the linear equation group based on the current calculation value of each conductor; calculating whether the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than a set threshold value, if so, taking the solved current of each conductor as the current measurement result and saving the current position coefficient matrix, otherwise calculating the optimized value of each conductor position by a random optimization algorithm, updating the position coefficient matrix and calculating the current value again, until the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than the set threshold value;

[0010] Step S5, after the magnetic field measurement value is resampled, the linear equations constructed in step S4 are substituted according to the updated measurement value and the position coefficient matrix saved in step S4 to solve the current of each conductor. In step S2 of the present invention, a finite element simulation calculation model is established, and the existing commercial electromagnetic finite element simulation calculation software is used to realize it. Its basic principle and process are as follows: first, a geometric model containing the measured conductor and its surrounding magnetic materials is constructed in the software, and then the geometric model is further adaptively meshed using the software, and a nonlinear equation system consisting of magnetic field differential equations in each grid can be further established, wherein the non-homogeneous terms of the grid corresponding equations where the unit line current is located are current values, and further, assuming that the magnetic field distribution in the grid is a first-order or second-order polynomial distribution, the nonlinear equation system is converted into a linear equation system by a variational method to solve the magnetic field value on each grid node. The least squares solution of solving each conductor current by the least squares method in step S4 of the present invention can be realized by applying regularization methods such as Moore-Penrose generalized inverse (SVD decomposition) and Tikhonov regularization. The random optimization algorithm used in step S4 of the present invention is implemented by existing random optimization algorithms such as gradient descent method, genetic algorithm, evolutionary algorithm, etc.

[0011] Furthermore, the magnetic induction intensity of any measuring point k at any grid node (i, j) of the conductor calculated in step S2 is expressed as B k (i, j), the reference position coefficient matrix of the measurement point k is expressed as P k , the constructed reference position coefficient matrix database is expressed as P = {P1,

[0012] P2,…,P K};in:

[0013]

[0014]

[0015] K is the number of measurement points set, k = 1, 2, …, K.

[0016] Furthermore, the number of conductors in the multi-conductor system to be measured is L, and the number of measurement points is K; the position coefficient matrix constructed in step S3 is a K×L position coefficient matrix A, and the element a in the position coefficient matrix A is kl Calculated according to the following formula:

[0017]

[0018] Among them, 1≤k≤K, 1≤l≤L, (x s (i),y s (j))、(x s (i+1),y s(j))、(x s (i),y s (j+1))、(x s (i+1),y s (j+1)) is the geometric center coordinate of the conductor (x l ,y l ) The four node coordinates of the grid, p k (i+1,j), p k (i,j+1), p k (i+1,j), p k (i+1,j+1) is an element of the reference position coefficient matrix database.

[0019] Furthermore, the linear equation system in which the magnetic field sensor measurement value constructed in step S4 is equal to the product of the position coefficient matrix and the conductor current value is expressed as:

[0020] B mea =AI cal

[0021] In the formula, B mea is the vector of actual measured values ​​of the magnetic field sensor at K measurement points, B mea =[B1,B2,…,B K ] T ;I cal is the vector of the current calculation values ​​of L conductors in the multi-conductor system to be measured, I cal =[I1,I2,…,I L ] T , A is the position coefficient matrix A.

[0022] Furthermore, the linear equations for solving the magnetic field calculation values ​​through the linear equations based on the current calculation values ​​of each conductor in step S4 are expressed as:

[0023] B cal =AI cal

[0024] B cal is a vector composed of the values ​​calculated by the magnetic field sensor at K measurement points; I cal is a vector consisting of the calculated current values ​​of L conductors in the multi-conductor system to be measured, and A is the position coefficient matrix A.

[0025] Furthermore, the calculation formula for calculating whether the ratio of the second norm of the magnetic field calculated value minus the magnetic field measured value to the second norm of the magnetic field measured value in step S4 is less than the set threshold is expressed as:

[0026]

[0027] In the formula, B calis the vector of values ​​calculated by the magnetic field sensor at K measurement points, B mea is the vector of the actual measured values ​​of the magnetic field sensor at K measurement points, (x,y) = ((x1,y1), (x2,y2), …, (x l ,y l ),…,(x L ,y L )) is the optimization variable, representing the coordinates of the geometric center position of the conductor, L is the number of conductors in the multi-conductor system to be tested, l=1,2,…,L.

[0028] In summary, compared with the prior art, the present invention has the following beneficial effects: the present invention has the characteristics of high accuracy and high adaptability of numerical methods, and avoids repeated finite element calculations through analytical solutions, greatly reducing the demand for computing resources. The present invention proposes a method for constructing a position coefficient matrix through a reference coefficient matrix database and the interpolation method in step S3, which can reduce the hardware requirements and computing delays of the magnetic sensor array current measurement device, and is of great significance to the miniaturization of the device, low cost, and the real-time improvement of the measurement data. In this way, the present invention has the characteristics of fast calculation and low amount of calculation while ensuring accuracy, which can improve the efficiency of inversion calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0030] Figure 1 A flowchart of a specific embodiment of the present invention;

[0031] Figure 2 It is a schematic diagram of the structure of the multi-core power cable under test and the arrangement of magnetic field measurement points;

[0032] Figure 3 It is a schematic diagram of the area where the conductors may exist in the multi-conductor system to be tested;

[0033] Figure 4 Schematic diagram of the relationship between conductor position and grid position. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0035] Example:

[0036] like Figure 1As shown, a current inversion method based on a magnetic sensor array comprises the following steps: step S1, setting a plurality of measurement points uniformly distributed along the circumference of the outer surface of the to-be-tested part at the to-be-tested part of the to-be-tested multi-conductor system; establishing a rectangular coordinate system with the geometric center of the multi-conductor system as the origin; uniformly dividing the conductor layout area of ​​the to-be-tested part of the to-be-tested multi-conductor system into a grid with M×N nodes arranged in a horizontal and vertical staggered manner, and numbering each grid node as (i, j) according to the horizontal and vertical distribution positions of the grid nodes; wherein the values ​​of M×N are all positive integers greater than or equal to 3, 1 ≤i≤M,1≤j≤N; record the coordinates of all grid nodes in the rectangular coordinate system; step S2, establish a finite element simulation calculation model, calculate the magnetic induction intensity of any measuring point when the unit line current is located at all grid nodes, obtain the reference position coefficient matrix of the measuring point, and then calculate the reference position coefficient matrix of the remaining measuring points to build a reference position coefficient matrix database; step S3, set the initial value of the position of each conductor in the multi-conductor system to be measured, and calculate the reference position coefficient matrix database according to the four node coordinates of the grid where the geometric center coordinates of any conductor in the multi-conductor system to be measured are located in combination with the reference position The conductor position coefficient matrix is ​​calculated by setting the position coefficient matrix to obtain the conductor position coefficient matrix, and then the position coefficient matrices of the remaining conductors in the multi-conductor system to be measured are calculated, and the position coefficient matrix is ​​constructed by combining the position coefficient matrices of all conductors in the multi-conductor system to be measured; step S4, constructing a linear equation group in which the magnetic field sensor measurement value is equal to the product of the position coefficient matrix and the conductor current value, the magnetic field sensor measures the magnetic field at the measuring point, and the current of each conductor is solved by the least square method; the magnetic field calculation value is solved by the linear equation group based on the current calculation value of each conductor; calculate whether the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than a set threshold value, if it is less than, the solved current of each conductor is used as the current measurement result and the current position coefficient matrix is ​​saved, otherwise, the optimized value of each conductor position is calculated by a random optimization algorithm, and the current value is calculated again after the position coefficient matrix is ​​updated, until the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than the set threshold value; step S5, after the magnetic field measurement value is resampled, the updated measurement value and the position coefficient matrix saved in step S4 are substituted into the linear equation group constructed in step S4 to solve the current of each conductor.

[0037] This embodiment is applied to a current inversion method for a YJLV22-3×300 steel-belt armored three-core cable, comprising the following steps:

[0038] Step S1, set 24 measuring points evenly distributed along the circumference of the outer surface of the tested part of the steel strip armored three-core cable to be tested. In this embodiment, a magnetic field sensor is arranged at each measuring point, and the 24 magnetic field sensors constitute a magnetic sensor array. A rectangular coordinate system is established with the geometric center of the multi-conductor system as the origin. The conductor layout area (the area where the conductor may exist) in the tested part of the steel strip armored three-core cable to be tested is evenly divided into a grid of 20×20 nodes, and the grid nodes are numbered as (i, j) (1≤i≤20, 1≤j≤20) according to the lateral and longitudinal distribution positions of the grid nodes, and the coordinates of all grid nodes (x s (i),y s (j)). The measurement points are arranged as follows: Figure 2 As shown, Figure 2 The names corresponding to the reference numerals are: 1. cable conductor, 2. insulation filling, 3. steel tape armor, 4. outer insulation sheath, 5. measurement point. In this embodiment, the areas where the conductors in the multi-conductor system to be measured may exist are as follows: Figure 3 shown.

[0039] Step S2, establish a finite element simulation calculation model corresponding to the measurement scenario, and calculate the magnetic induction intensity B at the measurement point k (k = 1, 2, ..., 24) when the unit line current is located at the grid node (i, j) k (i, j), and obtain the reference position coefficient matrix P of the measurement point k k , further calculate the reference position coefficient matrix of all measurement points, and construct the reference position coefficient matrix database P = {P1, P2, ..., P 24}, a total of 24×20×20=9600 data.

[0040] in,

[0041]

[0042]

[0043] In the formula (1), the denominator 1 represents the unit current.

[0044] Step S3, set the initial value of each conductor position (x1 (0) ,y1 (0) )、(x2 (0) ,y2 (0) )、(x3 (0) ,y3 (0) ), the reference position coefficient matrix database P is saved in the calculation unit of the measuring device, and the conductor position coefficient matrix of the three conductors to be measured with the conductor positions located at (x1, y1), (x2, y2), and (x3, y3) is solved during calculation. A position coefficient matrix A of size 24×3 can be constructed, in which the element a kl(1≤k≤24,1≤l≤3) is constructed according to formula (3).

[0045]

[0046] Among them, (x s (i),y s (j))、(x s (i+1),y s (j))、(x s (i),y s (j+1))、(x s (i+1),y s (j+1)) is the geometric center coordinate of the conductor (x l ,y l )The four node coordinates of the grid, such as Figure 4 In this embodiment, the reference position coefficient matrix database P is stored in the computing unit of the measuring device, and the measurement results of the magnetic sensor array are collected, stored and processed by the measuring device.

[0047] Step S4, inversely calculate the conductor current based on the magnetic field measurement value collected by the magnetic sensor array. Step S4 includes the following steps:

[0048] Step S41, establish the linear equation group shown in equation (4), and solve the current of each conductor by the least square method.

[0049] B mea =AI cal (4)

[0050] in,

[0051] B mea is the vector of actual measured values ​​of the magnetic induction sensor at K measurement points, B mea =[B1,B2,B3] T

[0052] I cal is the vector of the current calculation values ​​of the three conductors, I cal =[I1,I2,I3] T

[0053] Step S42, based on the current calculation value I of the conductor cal Solve the calculated value of the magnetic field, as shown in equation (5).

[0054] B cal =AI cal (5)

[0055] Step S43, calculate the objective function value of formula (6), and determine whether it is less than a set threshold ε, which is set to 1% in this embodiment. If it is established, Ical It is the current measurement result and saves the current position coefficient matrix A * ; If not, the conductor position optimization value (x1 (h+1) ,y1 (h+1) )、(x2 (h+1) ,y2 (h+1) )、(x3 (h+1) ,y3 (h+1) ), substitute into equation (3) to update the position coefficient matrix and calculate the current value again.

[0056]

[0057] in,

[0058] (x,y)=((x1,y1), (x2,y2), (x3,y3)) is the optimization variable, representing the coordinates of the geometric center position of the conductor.

[0059] ||v|| represents the bi-norm of vector v, which is defined as the square root of the sum of all elements, that is,

[0060]

[0061] Among them, v refers to any matrix, and n is the number of elements in the vector v.

[0062] Step S5: After the magnetic field measurement value is resampled, the updated measurement value is compared with A * Substitute into equation (4) to solve for the current I of each conductor cal .

[0063] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A current inversion method based on a magnetic sensor array, characterized in that: The following steps are involved: Step S1, setting a plurality of measuring points evenly distributed along the circumference of the outer surface of the to-be-tested part at the to-be-tested part of the to-be-tested multi-conductor system; A rectangular coordinate system is established with the geometric center of the multi-conductor system as the origin; the conductor layout area of ​​the tested part of the multi-conductor system is evenly divided into grids with M×N nodes arranged in a horizontal and vertical staggered manner, and each grid node is numbered as (i, j) according to the horizontal and vertical distribution positions of the grid nodes; wherein the values ​​of M×N are all positive integers greater than or equal to 3, 1≤i≤M, 1≤j≤N; the coordinates of all grid nodes in the rectangular coordinate system are recorded; Step S2, establishing a finite element simulation calculation model, calculating the magnetic induction intensity of any measurement point when the unit line current is located at all grid nodes, obtaining the reference position coefficient matrix of the measurement point, and then calculating the reference position coefficient matrix of the remaining measurement points, and constructing a reference position coefficient matrix database; Step S3, setting the initial value of the position of each conductor in the multi-conductor system to be measured, calculating the conductor position coefficient matrix according to the four node coordinates of the grid where the geometric center coordinates of any conductor in the multi-conductor system to be measured are located in combination with the reference position coefficient matrix, and then calculating the position coefficient matrices of the remaining conductors in the multi-conductor system to be measured, and combining the position coefficient matrices of all conductors in the multi-conductor system to be measured to construct a position coefficient matrix; Step S4, constructing a linear equation group in which the magnetic field sensor measurement value is equal to the product of the position coefficient matrix and the conductor current value, measuring the magnetic field at the measuring point by the magnetic field sensor, and solving the current of each conductor by the least square method; solving the magnetic field calculation value by the linear equation group based on the current calculation value of each conductor; calculating whether the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than a set threshold value, if so, taking the solved current of each conductor as the current measurement result and saving the current position coefficient matrix, otherwise calculating the optimized value of each conductor position by a random optimization algorithm, updating the position coefficient matrix and calculating the current value again, until the ratio of the second norm of the magnetic field calculation value minus the magnetic field measurement value to the second norm of the magnetic field measurement value is less than the set threshold value; Step S5: After the magnetic field measurement values ​​are resampled, the updated measurement values ​​and the position coefficient matrix saved in step S4 are substituted into the linear equations constructed in step S4 to solve the currents of each conductor.

2. A current inversion method based on a magnetic sensor array according to claim 1, characterized in that: The magnetic induction intensity of any measuring point k at any grid node (i, j) of the conductor calculated in step S2 is expressed as B k (i, j), the reference position coefficient matrix of the measurement point k is expressed as P k , the constructed reference position coefficient matrix database is expressed as P = {P1, P2, ..., P K };in: K is the number of measurement points set, k = 1, 2, …, K.

3. The current inversion method based on a magnetic sensor array according to claim 1, characterized in that: The number of conductors in the multi-conductor system to be measured is L, and the number of measurement points is K; the position coefficient matrix constructed in step S3 is a K×L position coefficient matrix A, and the element a in the position coefficient matrix A is kl Calculated according to the following formula: Among them, 1≤k≤K, 1≤l≤L, (x s (i),y s (j))、(x s (i+1),y s (j))、(x s (i),y s (j+1))、(x s (i+1),y s (j+1)) is the geometric center coordinate of the conductor (x l ,y l ) The four node coordinates of the grid, p k (i+1,j), p k (i,j+1), p k (i+1,j), p k (i+1,j+1) is an element of the reference position coefficient matrix database.

4. The current inversion method based on a magnetic sensor array according to claim 1, characterized in that: The linear equation system in which the magnetic field sensor measurement value constructed in step S4 is equal to the product of the position coefficient matrix and the conductor current value is expressed as: B mea =AI cal In the formula, B mea is the vector of actual measured values ​​of the magnetic field sensor at K measurement points, B mea =[B1,B2,…,B K ] T ; I cal is the vector of the current calculation values ​​of L conductors in the multi-conductor system to be tested, I cal =[I1,I2,…,I L ] T , A is the position coefficient matrix A.

5. The current inversion method based on a magnetic sensor array according to claim 1, characterized in that: In step S4, the linear equation system for solving the magnetic field calculation value through the linear equation system based on the current calculation value of each conductor is expressed as: B cal =AI cal B cal is a vector composed of the values ​​calculated by the magnetic field sensor at K measurement points; I cal is a vector consisting of the calculated current values ​​of L conductors in the multi-conductor system to be measured, and A is the position coefficient matrix A.

6. The current inversion method based on a magnetic sensor array according to claim 1, characterized in that: The calculation formula for calculating whether the ratio of the magnetic field calculation value minus the magnetic field measurement value to the magnetic field measurement value is less than the set threshold in step S4 is expressed as: In the formula, B cal is the vector of values ​​calculated by the magnetic field sensor at K measurement points, B mea is the vector of the actual measured values ​​of the magnetic field sensor at K measurement points, (x,y) = ((x1,y1), (x2,y2), …, (x l ,y l ),…,(x L ,y L )) is the optimization variable, representing the coordinates of the geometric center position of the conductor, L is the number of conductors in the multi-conductor system to be tested, l=1,2,…,L.

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