Multi-target domain magnetic field interference suppression method based on matrix coil

Abstract

The invention discloses a multi-target-domain magnetic field interference suppression method based on a matrix coil, and belongs to the technical field of extremely-low-intensity magnetic field measurement and active magnetic field compensation. The method comprises the steps that a biplane rectangular coil array is arranged in a magnetic shielding barrel, an overall response matrix is constructed through a mirror image method, and initial compensation current is obtained through an L curve method; and finally, simulation verification is carried out, so that synchronous suppression of multi-target domain magnetic field interference is realized, and compensation precision and current consumption are both considered. According to the multi-target-domain magnetic field interference suppression method based on the matrix coil, the shielding boundary coupling influence can be corrected to improve the model accuracy, synchronous suppression of multi-target-domain magnetic field interference is achieved, the multi-measuring-point residual error approaches zero magnetism, meanwhile, compensation precision and current consumption are considered, and the method is suitable for large-scale popularization and application. The problem that a single algorithm is prone to falling into local optimum or high power consumption is caused is solved.

Description

Technical Field

[0001] This invention belongs to the field of extremely weak magnetic field measurement and active magnetic field compensation technology, specifically relating to a method for suppressing multi-target domain magnetic field interference based on matrix coils. Background Technology

[0002] As SERF atomic magnetometers develop towards array-based and miniaturized designs, their robustness requirements against spatially non-uniform and non-common-mode magnetic interference in motion have significantly increased, leading to an urgent need for efficient active compensation technology.

[0003] However, the existing technology has the following shortcomings: it can only achieve local compensation within a limited measurement volume. When the number of sensors increases and the target volume expands, the spatial non-uniformity of the background field makes it difficult to minimize the magnetic field residuals of multiple measurement points at the same time. Although it can adapt to the motion conditions of wearable magnetoencephalography (MEG), it fails to achieve synchronous compensation of the magnetic field of multiple spatial measurement points to zero magnetism, and does not consider the coupling effect of ferromagnetic shielding boundaries, which limits the further improvement of compensation accuracy.

[0004] Therefore, a new method is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for suppressing magnetic field interference in multiple target domains based on matrix coils. This method can correct the coupling effect of shielding boundary to improve model accuracy, achieve synchronous suppression of magnetic field interference in multiple target domains, and make the residual of multiple measurement points approach zero magnetic field. At the same time, it takes into account the compensation accuracy and current consumption, and solves the problem that a single algorithm is prone to getting trapped in local optima or causing high power consumption.

[0006] To achieve the above objectives, the present invention provides a method for suppressing multi-target domain magnetic field interference based on matrix coils, comprising the following steps: S1. Arrange a dual-plane rectangular coil array inside the magnetic shielding barrel and select multiple sampling points in the target area; based on the Biot-Savart law, calculate the unit current magnetic field response of each coil at each sampling point, and integrate all response results into the basic magnetic field response matrix. S2. Receive the basic magnetic field response matrix output by S1, approximate the side wall of the magnetic shielding barrel as an infinitely large plane, and use the mirror method to perform mirror transformation on the matrix coil to obtain an equivalent mirror coil array; calculate the magnetic field response of the mirror coil array, form the mirror response matrix, introduce the mirror intensity coefficient, and construct the overall response matrix including ferromagnetic boundary coupling. S3. Receive the overall magnetic field response matrix output by S2, define the discrete vector of the interfering magnetic field at the sampling point, and establish a compensation model; introduce regularization parameters, construct a functional and solve the closed-form solution of the compensation current; construct a set of curve points and calculate the curve curvature, select the optimal regularization parameter corresponding to the point with the maximum curvature, and obtain the initial compensation current that balances the error and the current cost. S4. Receive the optimal regularization parameter and initial compensation current output by S3. Use the initial compensation current as the initial solution to initialize the particle population, set the fitness function, iteratively optimize through the particle velocity update and position update formulas, and use an adaptive inertia weight dynamic adjustment strategy to optimize the regularization parameter to obtain the optimal compensation current. S5 receives the optimal compensation current output from S4, and combines it with the overall response matrix of S2 and the discrete vector of the interference magnetic field of S3. Using multiphysics simulation software, a finite element simulation of the magnetic field of the matrix coil is performed. The simulation results are compared with the compensation results calculated by the model at each sampling point to verify the effectiveness of the compensation model.

[0007] Preferably, the specific process for calculating the magnetic field response per unit current in S1 based on the Biot-Savart law is as follows: The formula for the magnetic field generated by a unit coil current element is: ; In the formula, For conductor segment The magnetic induction intensity vector generated at the target field point in space; The vacuum permeability; For passing through the conductor segment The current intensity; For conductor segment Current element vector on; For the current element The position vector pointing to the target field point; is the position vector. The modulus length; The coordinates of the four vertices of a single rectangular coil are: ; ; ; ; In the formula, , , , This refers to the vertex of the rectangular coil; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; For rectangular coils in Width in the axial direction; For rectangular coils in Length in the axial direction; The magnetic field of each line segment is calculated by integration and then superimposed to obtain the field point of a single coil. The total magnetic field generated is expressed as: ; In the formula, , , , The four sides that make up the rectangular coil The basic magnetic field response matrix is ​​then obtained by integrating these components, and is expressed as follows: ; ; In the formula, It is a current vector; This represents the total number of sampling points selected within the target area; This represents the total number of rectangular coils deployed. The basic magnetic field response matrix; For the first The coil in the first The unit current response generated at each sampling point along the selected axis.

[0008] Preferably, the formula for constructing the overall response matrix G in S2 is: ; In the formula, This is the mirror response matrix; The response matrix includes the boundary coupling effect of the magnetically shielded barrel; This is the mirror intensity coefficient.

[0009] Preferably, the specific implementation process of S3 is as follows: The compensation model is as follows: ; In the formula, The discrete vector of the interfering magnetic field; The residual magnetic field vector after compensation; The regularization functional is: ; In the formula, For standard regularization matrix; For the target functional; For regularization parameters; For residual magnetic field Norm square; For the cost of electric current Norm square; when hour, ,in It is the identity matrix; right Taking the derivative and setting it to zero, we obtain the normal equation, which is expressed as: ; Compensation current closed solution ; right Singular value decomposition, represented as: ; In the formula, , It is an orthogonal matrix; It is a non-negative singular value matrix; The spectral domain form solution is: ; In the formula, for The Left singular vectors, for The Right-hand singular vectors; The regularization parameter is The compensation current vector at that time; for The One singular value; for rank; L-curve point set, represented as: ; In the formula, Logarithmic grid; The formula for calculating curvature is: ; In the formula, For L-curve in parameters Curvature at that point; For L-curve parameters; Let x be the x-coordinate of the L-curve; The ordinate of the L-curve; For parameters The first derivative; For parameters The first derivative; For parameters The second derivative; For parameters The second derivative of .

[0010] Preferably, the specific implementation process of S4 is as follows: The fitness function is expressed as: ; In the formula, The fitness function value; Each particle in the swarm corresponds to a 10-dimensional compensation current vector, and the initial state of the swarm is... As the baseline distribution; The particle velocity update formula is expressed as: ; In the formula, For the first Particle iteration The position at this time; For the corresponding speed; Inertial weights; For an individual, the best historical position; The optimal position for the entire population; , For learning factors; , for Random numbers that are independently and uniformly distributed on the same surface; The adaptive inertia weight adjustment strategy is expressed as: ; In the formula, For the first The particle in the first The fitness value of the dimension; For the current population Minimum fitness; For the current population Average fitness of dimensions; , These are the preset upper and lower limits of inertia weight.

[0011] Therefore, the present invention employs the above-mentioned method for suppressing multi-target domain magnetic field interference based on matrix coils. Compared with the prior art, the technical solution of the present invention has the following beneficial effects: (1) By adopting the technical means of dual-plane rectangular coil array and multi-sampling point joint modeling, the problem of "multi-measurement point synchronous compensation" that traditional small-channel coils cannot synchronously minimize the residuals of multiple measurement points is overcome, thereby realizing the synchronous suppression of magnetic field interference in multiple target domains, and the residuals of multiple measurement points can approach zero magnetic field; (2) By adopting the mirror method and constructing an overall response matrix with ferromagnetic boundary coupling, the shortcomings of existing technologies that ignore the coupling effect of ferromagnetic shielding boundary are overcome, thereby correcting the coupling effect of shielding boundary on magnetic field and improving the accuracy of compensation model; (3) The L-curve method and the adaptive inertial weighted particle swarm optimization (PSO) two-stage algorithm are adopted to overcome the contradiction that a single algorithm is prone to getting trapped in local optima or causing high power consumption, as well as the problem that it is difficult to balance accuracy and engineering practicality. In this way, the magnetic field residual and coil current amplitude are constrained at the same time, and the compensation accuracy and current consumption are balanced.

[0012] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating an embodiment of a multi-target domain magnetic field interference suppression method based on matrix coils according to the present invention; Figure 2 This is a schematic diagram of the spatial layout of an embodiment of a multi-target domain magnetic field interference suppression method based on matrix coils according to the present invention; Figure 3 This is a bar chart comparing the magnetic field compensation effects of an embodiment of a multi-target domain magnetic field interference suppression method based on matrix coils according to the present invention. Figure 4 This is a bar chart comparing the errors before and after optimization of the PSO (Adaptive Particle Swarm Optimization) algorithm in an embodiment of the multi-target domain magnetic field interference suppression method based on matrix coils according to the present invention. Figure 5 This is a bar chart comparing the magnetic field compensation model and simulation results of an embodiment of the multi-target domain magnetic field interference suppression method based on matrix coils according to the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0015] Example 1 like Figures 1-2 As shown, this embodiment provides a method for suppressing multi-target domain magnetic field interference based on matrix coils. It should be understood that the specific parameters, models and protocols mentioned in this embodiment are merely examples to help those skilled in the art understand the present invention, and are not intended to limit the present invention.

[0016] The present invention provides a method for suppressing multi-target domain magnetic field interference based on matrix coils, comprising the following steps: S1. Deploy a dual-plane rectangular coil array inside the magnetically shielded container, and select multiple sampling points within the target area; based on the Biot-Savart law, calculate the magnetic field response of each coil at each sampling point with unit current, and integrate all response results into the basic magnetic field response matrix. ( dimension, The number of sampling points. (Number of coils) In this step, based on the Biot-Savart law, the magnetic field response per unit current at each sampling point of each coil is calculated, as shown in the formula: ; In the formula, For conductor segment The magnetic induction intensity vector generated at the target field point in space; The vacuum permeability; For passing through the conductor segment The current intensity; For conductor segment Current element vector on; For the current element The position vector pointing to the target field point; is the position vector. The modulus length; For a single rectangular coil, the coordinates of the vertices of its four line segments are as follows: ; ; ; ; In the formula, , , , This refers to the vertex of the rectangular coil; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; For rectangular coils in Width in the axial direction; For rectangular coils in Length in the axial direction; line segment The coordinates of any point on can be represented as , The range of values ​​is ; According to the Biot-Savart law, line segment The generated total magnetic field To The integral is expressed as: ; In the formula, The magnetic field strength vector generated by segment at the target field point; The vacuum permeability; The current intensity passing through the rectangular coil; For integration variables; , , The coordinates of the target field point in the three-dimensional coordinate system; for Unit vector along the axial direction; for Unit vector along the axial direction; The distance from the current element to the field point is the cube of the distance. Similarly, the magnetic fields generated by the other three line segments can be derived. , , According to the principle of magnetic field superposition, a single rectangular coil at the field point The total magnetic field generated is expressed as: ; In the formula, , , , These are the four sides that make up the rectangular coil; Then, the magnetic fields of each coil are vector-summed to obtain the field point. The total magnetic field; Assume that the volume contains Each sampling point The coil, the first The coil in the first The unit current response of each sampling point to the selected axis is denoted as... All response results are integrated into the basic magnetic field response matrix, which is expressed as: ; ; In the formula, It is a current vector; This represents the total number of sampling points selected within the target area; This represents the total number of rectangular coils deployed. The basic magnetic field response matrix; For the first The coil in the first The unit current response generated at each sampling point for the selected axial direction; S2, Receives the fundamental magnetic field response matrix output by S1 The sidewall of the magnetically shielded barrel is approximated as an infinitely large plane. The matrix coils are then transformed using the image method to obtain an equivalent image coil array. The magnetic field response of the image coil array is calculated, forming the image response matrix, and an image intensity coefficient is introduced. (Under ideal high permeability) Construct the response matrix that includes the magnetic shielding barrel boundary coupling effect, as follows: ; In the formula, This is the mirror response matrix; The response matrix includes the boundary coupling effect of the magnetically shielded barrel; Image intensity coefficient; S3, Receives the overall magnetic field response matrix output from S2 Define the interfering magnetic field in Discrete vector of sampling points (Unit: nT), establish a compensation model, expressed as: ; In the formula, The discrete vector of the interfering magnetic field; The residual magnetic field vector after compensation; To strike a balance between fitting error and current "cost," a regularization parameter is introduced, and a functional is constructed as follows: ; In the formula, For standard regularization matrix; For the target functional; For regularization parameters; For residual magnetic field Norm square; For the cost of electric current Norm square; when ( When the matrix is ​​an identity matrix, it is normalized. , Through the Taking the derivative and setting it to zero, the normal equation is expressed as: ; Therefore, the closed-form solution for the compensation current , represented as: ; To facilitate the analysis of the properties and selection of Tikhonov solutions with respect to λ ,right Perform singular value decomposition (SVD), expressed as: ; In the formula, , It is an orthogonal matrix; It is a non-negative singular value matrix; Substituting SVD into the solution of the normal equation, we obtain the spectral domain form, which is expressed as: ; In the formula, for The Left singular vectors, for The Right-hand singular vectors; The regularization parameter is The compensation current vector at that time; for The One singular value; for rank; ; In spectral representation, the residual norm and the solution norm are respectively: ; ; In the formula, The regularization parameter is The residual magnetic field norm at that time; The regularization parameter is The current norm at that time; To select the optimal Construct the L-curve point set, represented as: ; In the formula, Logarithmic grid; And calculate the curvature of the curve, expressed as: ; In the formula, For L-curve in parameters Curvature at that point; For L-curve parameters; Let x be the x-coordinate of the L-curve; The ordinate of the L-curve; For parameters The first derivative; For parameters The first derivative; For parameters The second derivative; For parameters The second derivative; Select the optimal regularization parameter corresponding to the point of maximum curvature Its corresponding The initial compensation current vector This is the optimal compromise between error and current penalty; S4 receives the output of S3. and ,by As the initial solution, the Adaptive Inertia Weighted Particle Swarm Optimization (PSO) algorithm is initiated to further optimize the regularization parameters. Improve compensation performance; A fitness function is defined to balance the magnetic field residual and the current cost, guiding the particle's optimization direction. It is expressed as: ; In the formula, The fitness function value; Initialize the particle swarm, with each particle corresponding to a specific 10-dimensional compensation current vector. The initial state of the swarm is obtained using S3. Using the baseline distribution, the search space is reduced, and optimization efficiency is improved; Entering the iterative optimization phase, each particle updates its velocity and position based on its individual historical best position and the global best position of the population. The particle velocity update formula is expressed as: ; In the formula, For the first Particle iteration The position at this time; For the corresponding speed; Inertial weights; For an individual, the best historical position; The optimal position for the entire population; , For learning factors; , for Random numbers that are independently and uniformly distributed on the same surface; The position update formula is expressed as: ; In the formula, For the first Particle iteration The position at this time; Considering that the standard PSO is prone to premature convergence in multi-peak noise-sensitive scenarios such as multi-point magnetic compensation, a dynamic adjustment strategy based on adaptive inertia weight is introduced: ; In the formula, For the first The particle in the first The fitness value of the dimension; For the current population Minimum fitness; For the current population Average fitness of dimensions; , These are the preset upper and lower limits of the inertia weight; Dynamically adjust using an adaptive inertia weighting strategy Balance global exploration with local search and optimize regularization parameters. To obtain the optimal compensation current ; S5, Receive the optimal compensation current output from S4 Combined with the overall response matrix of S2 Discrete vector of the interference magnetic field of S3 The magnetic field of the matrix coil was simulated using COMSOL Multiphysics 6.3 software. The simulation results were compared with the compensation results calculated by the model at each sampling point to verify the effectiveness of the compensation model.

[0017] like Figures 3-5 As shown, this embodiment highlights the effectiveness of magnetic field interference suppression by comparing the magnetic field strength before and after compensation; it demonstrates the optimization value of the algorithm by optimizing the reduction of errors before and after using the PSO algorithm; and it verifies the reliability of the compensation model by verifying the consistency between the model calculation and the simulated magnetic field data.

[0018] Therefore, the present invention adopts the above-mentioned method for suppressing magnetic field interference in a multi-target domain based on a matrix coil. This method can correct the coupling effect of the shielding boundary to improve the accuracy of the model, realize the synchronous suppression of magnetic field interference in a multi-target domain, and make the residual of multiple measurement points approach zero magnetic field. At the same time, it takes into account the compensation accuracy and current consumption, and solves the problem that a single algorithm is prone to getting trapped in local optima or causing high power consumption.

[0019] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0020] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for suppressing multi-target domain magnetic field interference based on matrix coils, characterized in that, Includes the following steps: S1. A dual-plane rectangular coil array is set up inside the magnetic shielding barrel, and multiple sampling points are selected within the target area; Based on the Biot-Savart law, the magnetic field response of each coil at each sampling point is calculated, and all response results are integrated into the basic magnetic field response matrix. S2. Receive the basic magnetic field response matrix output by S1, approximate the side wall of the magnetic shielding barrel as an infinitely large plane, and use the mirror method to perform mirror transformation on the matrix coil to obtain an equivalent mirror coil array. Calculate the magnetic field response of the mirror coil array, form the mirror response matrix, introduce the mirror intensity coefficient, and construct the overall response matrix including ferromagnetic boundary coupling; S3. Receive the overall magnetic field response matrix output by S2, define the discrete vector of the interfering magnetic field at the sampling point, and establish a compensation model; introduce regularization parameters, construct a functional, and solve the closed-form solution of the compensation current. Construct a set of curve points and calculate the curve curvature. Select the optimal regularization parameter corresponding to the point with the maximum curvature to obtain the initial compensation current that balances the error and the current cost. S4. Receive the optimal regularization parameter and initial compensation current output by S3. Use the initial compensation current as the initial solution to initialize the particle population, set the fitness function, iteratively optimize through the particle velocity update and position update formulas, and use an adaptive inertia weight dynamic adjustment strategy to optimize the regularization parameter to obtain the optimal compensation current. S5 receives the optimal compensation current output from S4, and combines it with the overall response matrix of S2 and the discrete vector of the interference magnetic field of S3. Using multiphysics simulation software, a finite element simulation of the magnetic field of the matrix coil is performed. The simulation results are compared with the compensation results calculated by the model at each sampling point to verify the effectiveness of the compensation model.

2. The method for suppressing multi-target domain magnetic field interference based on matrix coils according to claim 1, characterized in that, The specific process for calculating the magnetic field response per unit current in S1 based on the Biot-Savart law is as follows: The formula for the magnetic field generated by a unit coil current element is: ； In the formula, For conductor segment The magnetic induction intensity vector generated at the target field point in space; The vacuum permeability; For passing through the conductor segment The current intensity; For conductor segment Current element vector on; For the current element The position vector pointing to the target field point; is the position vector. The modulus length; The coordinates of the four vertices of a single rectangular coil are: ； ； ； ； In the formula, , , , This refers to the vertex of the rectangular coil; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; The center of the rectangular coil is at Coordinates along the axis; For rectangular coils in Width in the axial direction; For rectangular coils in Length in the axial direction; The magnetic field of each line segment is calculated by integration and then superimposed to obtain the field point of a single coil. The total magnetic field generated is expressed as: ； In the formula, , , , The four sides that make up the rectangular coil The basic magnetic field response matrix is ​​then obtained by integrating these components, and is expressed as follows: ； ； In the formula, It is a current vector; This represents the total number of sampling points selected within the target area; This represents the total number of rectangular coils deployed. The basic magnetic field response matrix; For the first The coil in the first... The unit current response generated at each sampling point along the selected axis.

3. The method for suppressing multi-target domain magnetic field interference based on matrix coils according to claim 2, characterized in that, The formula for constructing the overall response matrix G in S2 is: ； In the formula, This is the mirror response matrix; The response matrix includes the boundary coupling effect of the magnetically shielded barrel; This is the mirror intensity coefficient.

4. The method for suppressing multi-target domain magnetic field interference based on matrix coils according to claim 3, characterized in that, The specific implementation process of S3 is as follows: The compensation model is as follows: ； In the formula, The discrete vector of the interfering magnetic field; The residual magnetic field vector after compensation; The regularization functional is: ； In the formula, For standard regularization matrix; For the target functional; For regularization parameters; For residual magnetic field Norm square; For the cost of electric current Norm square; when hour, ,in It is the identity matrix; right Taking the derivative and setting it to zero, we obtain the normal equation, which is expressed as: ； Compensation current closed solution ； right Singular value decomposition, represented as: ； In the formula, , It is an orthogonal matrix; It is a non-negative singular value matrix; The spectral domain form solution is: ； In the formula, for The Left singular vectors, for The Right-hand singular vectors; The regularization parameter is The compensation current vector at that time; for The One singular value; for rank; L-curve point set, represented as: ； In the formula, Logarithmic grid; The formula for calculating curvature is: ； In the formula, For L-curve in parameters Curvature at that point; For L-curve parameters; Let x be the x-coordinate of the L-curve; The ordinate of the L-curve; For parameters The first derivative; For parameters The first derivative; For parameters The second derivative; For parameters The second derivative of .

5. The method for suppressing multi-target domain magnetic field interference based on matrix coils according to claim 1, characterized in that, The specific implementation process of S4 is as follows: The fitness function is expressed as: ； In the formula, The fitness function value; Each particle in the swarm corresponds to a 10-dimensional compensation current vector, and the initial state of the swarm is... As the baseline distribution; The particle velocity update formula is expressed as: ； In the formula, For the first Particle iteration The position at this time; For the corresponding speed; Inertial weight; For an individual, the best historical position; The optimal position for the entire population; , For learning factors; , for Random numbers that are independently and uniformly distributed on the same surface; The adaptive inertia weight adjustment strategy is expressed as: ； In the formula, For the first The particle in the first The fitness value of the dimension; For the current population Minimum fitness; For the current population Average fitness of dimensions; , These are the preset upper and lower limits of inertia weight.

6. A computer device, characterized in that, include: A processor configured to be coupled to memory, read and execute instructions and / or program code in the memory to perform the method as described in any one of claims 1-5.

7. A computer-readable medium, characterized in that, The computer-readable medium stores computer program code that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1-5.

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