Magnetic field coil hybrid optimization design method based on array structure

Abstract

The invention discloses a magnetic field coil hybrid optimization design method based on an array structure, and the method comprises the steps: combining a plurality of saddle-shaped coils into a coil array, and analyzing a magnetic field mathematical model of a single coil on the basis of considering the coupling effect of a high-permeability material on a coil magnetic field; and a magnetic field mathematical model of the saddle-shaped coil array is obtained according to a superposition principle. And optimizing the optimal current integer ratio between saddle-shaped coils in the array by combining the mathematical model with a particle swarm algorithm, converting the current integer ratio of the coils into a linear combination of the number of turns and the current of each coil, and optimizing the minimum number of turns and the optimal current required by each coil by using the particle swarm algorithm again. And finally, coil path planning is carried out through a depth-first search strategy, and an optimized magnetic field coil is generated. According to the invention, the uniformity of the coil is greatly improved, discretization errors are avoided, the structure is simple, and practical application is facilitated.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic field compensation, and in particular relates to a hybrid optimization design method of magnetic field coils based on an array structure. Background Art

[0002] Magnetic field compensation technology is a key technology in the field of modern technology. Its main purpose is to reduce the interference of external magnetic fields on equipment, instruments or systems. This technology has a wide range of applications in physics, biology, medicine and military fields, especially in the biomedical field, mainly used in medical equipment such as magnetic imaging. With the continuous advancement of science and technology and medicine, magnetocardiography measurement technology has gradually attracted widespread attention from researchers around the world. However, since the magnetocardiographic signal in the human body is extremely weak and the external magnetic field environment is complex and changeable, it poses a great challenge to obtain accurate magnetocardiographic signals.

[0003] In order to create an extremely weak magnetic field environment, magnetic shielding technology is usually required. Magnetic shielding technology mainly includes two methods: one is passive magnetic shielding technology with magnetic shielding structure and materials as the core, and the other is active magnetic compensation system with energized coils as the core. The active magnetic compensation system compensates for the residual magnetic field inside the magnetic shielding device by regulating the magnetic field generated by the coil, thereby improving the magnetic field shielding effect in space. The system usually consists of two parts: a high uniformity magnetic field compensation coil and a dynamic magnetic field control system.

[0004] Magnetic field compensation based on high uniformity magnetic field coils utilizes the effect of electric current generating a magnetic field in a conductor, thereby suppressing external interference magnetic fields. However, in order to generate an extremely weak magnetic field environment, it is usually necessary to combine passive magnetic shielding with active magnetic compensation technology. The compensation coil is usually placed in a high magnetic permeability material for use, but this high magnetic permeability material will change the magnetic field distribution generated by the coil and significantly reduce the uniformity of the magnetic field. Therefore, it is necessary to further suppress the ferromagnetic boundary coupling between the coil and the high magnetic permeability material and improve the performance of the coil. Summary of the invention

[0005] To solve the above technical problems, the present invention provides a hybrid optimization design method for magnetic field coils based on an array structure, which aims to compensate for the residual magnetic field inside the magnetic shielding environment and provide the required extremely weak magnetic field environment for the magnetocardiographic ultra-high resolution imaging device.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0007] A hybrid optimization design method for magnetic field coils based on an array structure, the method comprising:

[0008] Step 1, combining multiple saddle coils into a coil array, analyzing the magnetic field mathematical model of a single saddle coil based on the coupling effect of high magnetic permeability materials on the coil magnetic field, and obtaining the magnetic field mathematical model of the saddle coil array according to the superposition principle;

[0009] Step 2: Based on the magnetic field mathematical model of the saddle coil array and the particle swarm algorithm, the optimal current integer ratio between the saddle coils in the coil array is solved, and the optimal current integer ratio of the coil array is converted into a linear combination of the number of turns and the current of each saddle coil. The particle swarm algorithm is used again to optimize the minimum number of turns and the optimal current required for each coil;

[0010] Step 3: Plan the coil path using a depth-first search strategy to generate an optimized magnetic field coil structure.

[0011] The beneficial effects of the present invention are:

[0012] In order to solve the problem of environmental magnetic field interference during magnetocardiography measurement, the present invention provides a coil that can generate a maximum magnetic field deviation of less than 1% in a large rectangular area. This performance is significantly better than the existing saddle coils and nested saddle coils. After closed-loop compensation using this coil, the 1-40 Hz magnetic field fluctuation in the device is reduced to 3.09 pT. Compared with the forward-designed coil, this coil has higher uniformity and greatly improves the ability to compensate for the magnetic field. Compared with the reverse-designed target field method coil, this coil has no discretization error and a simple structure, which is convenient for practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is the array coil model;

[0014] Figure 2 Optimize the flow chart for PSO;

[0015] Figure 3 Optimize the flow chart for DFS;

[0016] Figure 4 This is the schematic diagram of the array coil magnetic field compensation system;

[0017] Figure 5 Implementing example diagrams for array coil applications;

[0018] Figure 6 The saddle-shaped array coil and its expansion diagram according to an embodiment of the present invention;

[0019] Figure 7a is a current path diagram of the first group of saddle-shaped array coils according to an embodiment of the present invention;

[0020] Figure 7b is a current path diagram of the second group of saddle-shaped array coils according to an embodiment of the present invention;

[0021] Figure 7c FIG. 4 is a current path diagram of the third group of saddle-shaped array coils according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] The present invention provides a hybrid optimization design method for magnetic field coils based on an array structure. By combining multiple saddle coils into a coil array, and considering the coupling effect of high magnetic permeability materials on the coil magnetic field, the magnetic field mathematical model of a single coil after coupling is analyzed, and the magnetic field mathematical model of the saddle coil array is obtained according to the superposition principle. The mathematical model is combined with a particle swarm algorithm (PSO) to solve the optimal current integer ratio of the coils in the array. In order to simplify the coil winding and reduce the coil constant, the current integer ratio of the coil is equivalent to a linear combination of the number of turns of the coil and the current, and the particle swarm algorithm (PSO) is combined again to optimize the minimum number of turns and the optimal current required for each coil. Finally, the coil path is planned by the depth first search principle (DFS) to generate an optimized magnetic field coil. Compared with the coil designed by the forward method, the magnetic field coil based on the array structure has a larger magnetic field uniformity area, higher uniformity and a simpler calculation model. Compared with the coil designed by the target field method, the magnetic field coil based on the array structure does not have a discretization error, and has a simpler and regular coil structure, which is more convenient for practical application.

[0024] Specifically, a hybrid optimization design method for magnetic field coils based on an array structure is designed for the active magnetic field compensation coil in the internal space of a magnetic shield constructed of high magnetic permeability materials. The coil array is mainly composed of a plurality of saddle-shaped coils arranged and combined. A target area of ​​uniform magnetic field is set in the middle of the array coil. A suitable current is passed through a single coil to generate the required magnetic field. The array coil model is shown in the figure below. Figure 1 shown.

[0025] The saddle-shaped array coil in the high magnetic permeability material is modeled. In the cylindrical coordinate system, the relationship between the coil current density and the magnetic field on the cylindrical surface is established by Biot-Savart Law. The magnetic field components in all directions can be obtained by Fourier-Bessel series expansion. :

[0026] ,

[0027] Where: Represents the coordinates of any point in the cylindrical coordinate system. is the vacuum permeability, represents the radial distance between the target field point and the current source point in the cylindrical coordinate system, is an imaginary unit, and are the modified Bessel functions of the first and second kinds, and is the corresponding first-order derivative, and is the introduced integral parameter, is the current density component The Fourier transform of .

[0028] For a single-ended open cylindrical high permeability shielding layer, the analytical method and the mirror method are needed to establish the magnetic field coefficient of a single saddle coil in a high permeability material. , the model is:

[0029] ,

[0030] in,

[0031] ,

[0032] The expressions of the intermediate parameters involved in the formula are:

[0033] ,

[0034] Where: and are the inner radius and outer radius of the shield barrel respectively, is the relative permeability of the high permeability material, is the current density coefficient and can be calculated by the following steps.

[0035] According to the structure of a single saddle coil, the current density under the magnetic field coefficient model can be analyzed as:

[0036] ,

[0037] Where: is the Heaviside function, is the Dirac function, and are the starting and ending azimuths of the saddle coil, and are the starting and ending heights, is the current magnitude, Indicates that the radius in the cylindrical coordinate system is The coordinates of any point at the time.

[0038] According to the Fourier transform formula of current density, the Fourier transform of current density of a single saddle coil structure is obtained as follows:

[0039] ,

[0040] Therefore, after decoupling by the mirror method, the current density coefficient of a single saddle coil structure is:

[0041] ,

[0042] Where: Takes 0, 1 or 0, -1.

[0043] After the coil model is analyzed, the magnetic field component coefficients in the cylindrical coordinate system are transformed into the magnetic field component coefficients in the Cartesian coordinate system, and the magnetic field component coefficients in the Cartesian coordinate system of a single saddle coil for any point in space can be obtained.

[0044] ,

[0045] At this point, the mathematical model of the saddle coil array has been established. is the magnetic field component coefficient in the Cartesian coordinate system.

[0046] like Figure 2 As shown, select the appropriate discrete method to get the target area in an orderly manner. The target point coordinates are set, and the magnetic field at the center of the target area is set to According to the mathematical model of saddle coil, the corresponding relationship between saddle array coil and target point is established. The coil array consists of The magnetic field relationship is:

[0047] ,

[0048] Based on the above relationship, in order to find a constrained solution, the matrix inversion solution is directly transformed into an optimization problem constrained by the solution conditions. The maximum relative deviation of the magnetic field at the discrete points in the target area is used as the objective function, and the PSO algorithm is optimized.

[0049] During the optimization process, the number of independent variables is (this From above saddle coil relationship), population Depend on particles, of which The position and velocity of a particle are and The particle position represents a possible solution to the problem, and its corresponding objective function value can be used as the fitness of the particle. In each iteration, the particle passes through the individual extreme value and group extreme value Update its own velocity and position:

[0050] ,

[0051] in, is the current iteration number; are the individual and group learning factors that determine the impact of particles on the optimization trajectory; is a random number between 0 and 1. is the inertia weight, which determines the particle's ability to retain its original velocity, If the value is larger, the global convergence ability is stronger and the local convergence ability is weaker. If the value is smaller, the local convergence ability is stronger and the global convergence ability is weaker. The representative is Particles, Representative Particle element, Refers to The optimal position found among the particles is Refers to the best position searched so far, so you can Dynamic adjustment is performed, using a linear decreasing weight strategy, the expression of which is as follows:

[0052] ,

[0053] represents the maximum evolutionary generation; represents the minimum inertia weight; represents the maximum inertia weight; Indicates the current iteration number;

[0054] The constraints of the coil parameter optimization model are:

[0055] ,

[0056] Where: is the relative deviation of the magnetic field, is the magnetic field strength at any point, It is The current ratio of the coils.

[0057] Through a PSO optimization, the coil current is obtained The optimal ratio of the current between each coil in the array is to simplify the coil structure and reduce the coil constant of the coil. Decomposed into three groups of linear combinations of the number of turns and coil currents:

[0058] ,

[0059] Where: It is The current ratio of the coils, are the three sets of current ratios to be optimized, is the number of turns at that current.

[0060] Taking the minimum number of turns required for each array as the objective function, a quadratic PSO algorithm is used to optimize the number of turns of the three arrays. Ratio of coil current , the constraints of the nonlinear optimization model are:

[0061] ,

[0062] Where: is the set of non-negative integers, It refers to The number of turns of the coil.

[0063] After the secondary PSO optimization, three groups of different currents and the number of turns of each array under different currents are obtained.

[0064] like Figure 3 As shown in the figure, the coil parameters obtained after the quadratic PSO optimization are used for coil path planning through the depth-first search algorithm (DFS). Depth-first search is an algorithm for traversing graphs. In coil optimization, using DFS will make the coil path go deeper along each path until there are no more nodes to visit. If there are multiple paths to a node, one of the paths is selected to move forward and mark the node. If the path is blocked, the algorithm will backtrack to the previous node and select another path to continue exploring until all vertices are traversed.

[0065] After DFS, three groups of array coil structures and windings can be obtained. At this point, the hybrid optimization of the array coil is completed.

[0066] like Figure 4 As shown, the array coil is used as an actuator to compensate the magnetic field. The compensation system first collects magnetic field data through an optically pumped magnetometer, then reads the magnetic field data through a PC and transmits the signal to a control circuit. After being processed by the control circuit, the signal is sent to a current source, which supplies power to the array coil.

[0067] In order to facilitate practical application, the current signal output of the single channel on the current source board is maintained, and the three sets of coils are divided by resistors to form a coil system. The coil system uses resistors Proportioning method to accurately proportion coils Current ,like Figure 5 shown.

[0068] Example

[0069] like Figure 6As shown in the figure, the measuring area of ​​the single-ended open-type magnetocardiographic measuring device is designed to be 300×300×200mm. The magnetocardiographic measuring device is a single-ended open cylindrical barrel with a radius of 425mm, a material thickness of 1.5mm, and a relative magnetic permeability of 20000. Based on the above conditions, the designed coil is a saddle array coil. The radius of a single saddle coil is 400mm. There are 40 saddle coils of equal size forming a saddle array coil with a total length of 800mm.

[0070] After the above-mentioned mathematical modeling of the saddle coil and model hybrid optimization, three sets of coil structures and coil paths are obtained, such as Figure 7a-7c As shown, the numbers in the figure represent the path order, the arrows represent the direction, and the current ratio of the three groups of coils is 6:16:29 from top to bottom according to the figure.

[0071] After finite element software simulation, the theoretical maximum deviation of the array coil in the measurement area of ​​the magnetocardiographic measurement device is less than 1%. After using the coil to perform closed-loop compensation on the magnetocardiographic measurement device, the average power spectrum density of the 1-40Hz magnetic field noise in the device was reduced by 63.82%, and the peak-to-peak value of the 1-40Hz magnetic field fluctuation was reduced from 12.40pT to 3.09pT. This greatly reduces the interference of the external magnetic field of the magnetocardiographic measurement device and effectively improves the imaging quality and accuracy of the magnetocardiographic image.

[0072] In summary, the coil design method of the present invention combines the model analysis in the forward design method and the matrix solution in the inverse design method, which not only avoids the errors caused by discretization in the inverse design, reduces the complexity of the coil, and facilitates practical application, but also solves the problem that the coil is limited to a fixed shape in the forward design, improves the design flexibility, and the optimization design method has a certain degree of versatility.

[0073] In addition, the coil design of the present invention uses a two-stage particle swarm algorithm (PSO) and a depth-first search (DFS) for hybrid optimization and coil path planning. The first PSO optimizes the optimal current integer ratio of the coil array, and the second PSO optimizes the minimum number of turns required for each coil in the linear combination. DFS optimization is used to plan the coil path and generate an optimized array coil. It is also proposed to use a resistor ratio method to accurately match different currents, solving the problem of the coil requiring multi-channel current input.

[0074] Therefore, the advantage of the present invention is that it can generate a highly uniform magnetic field in a large area, and can generate a magnetic field with a maximum deviation of less than 1% in a rectangular area. The performance is better than the existing coils. Compared with the target field method coil, the coil of the present invention is simpler and convenient for practical application.

[0075] The specific embodiments 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 embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A hybrid optimization design method for magnetic field coils based on an array structure, characterized in that: The method comprises: Step 1, combining multiple saddle coils into a coil array, analyzing the magnetic field mathematical model of a single saddle coil based on the coupling effect of high magnetic permeability materials on the coil magnetic field, and obtaining the magnetic field mathematical model of the saddle coil array according to the superposition principle; Step 2: Based on the magnetic field mathematical model of the saddle coil array and the particle swarm algorithm, the optimal current integer ratio between the saddle coils in the coil array is solved, and the optimal current integer ratio of the coil array is converted into a linear combination of the number of turns and the current of each saddle coil. The particle swarm algorithm is used again to optimize the minimum number of turns and the optimal current required for each coil; Step 3: Plan the coil path using a depth-first search strategy to generate an optimized magnetic field coil structure.

2. The hybrid optimization design method of magnetic field coils based on array structure according to claim 1 is characterized in that: The step 1 comprises: Modeling the saddle array coil in a high permeability material, and obtaining the magnetic field components in all directions through Fourier-Bessel series expansion : ， Where: Represents the coordinates of any point in the cylindrical coordinate system. represents the vacuum permeability, represents the radial distance between the target field point and the current source point in the cylindrical coordinate system, is an imaginary unit, and denotes the modified Bessel functions of the first and second kinds, and is the corresponding first-order derivative, and is the introduced integral parameter, is the current density component Fourier transform of The magnetic field coefficient of a single saddle coil in high permeability materials is established using analytical and mirror methods. : ， Among them, the intermediate parameters , The expressions of the intermediate parameters involved in the formula are: ， Where: and are the inner radius and outer radius of the shield barrel respectively, is the relative permeability of the high permeability material, is the current density coefficient; Transform the magnetic field component coefficients in the cylindrical coordinate system into the magnetic field component coefficients in the Cartesian coordinate system, and obtain the magnetic field component coefficients in the Cartesian coordinate system of a single saddle coil for any point in space: ， In the formula, is the magnetic field component coefficient in the Cartesian coordinate system.

3. The hybrid optimization design method of magnetic field coils based on array structure according to claim 2 is characterized in that: In step 2, solving the optimal current integer ratio between the saddle coils in the coil array based on the magnetic field mathematical model of a single saddle coil in combination with a particle swarm algorithm includes: Get the target area in order The target point coordinates are set, and the magnetic field at the center of the target area is set to , based on the mathematical model of a single saddle coil, The corresponding relationship between the saddle coil array composed of saddle coils and the target point: ， The maximum relative deviation of the magnetic field at the discrete points in the target area is used as the objective function to optimize the PSO algorithm. In the optimization process, the number of independent variables is set to , population Depend on particles, of which The position and velocity of a particle are and , the particle position represents a possible solution to the problem, and its corresponding objective function value is used as the fitness of the particle. In each iteration, the particle passes through the individual extreme value and group extreme value Update its own velocity and position: ， in, is the current iteration number; It is the individual and group learning factor; is a random number between 0 and 1. is the inertia weight, subscript The representative is Particles, Representative Particle element, Refers to The optimal position found among the particles is Refers to the best position searched so far. Dynamic adjustment is performed, using a linear decreasing weight strategy, the expression of which is as follows: ， represents the maximum evolutionary generation; represents the minimum inertia weight; represents the maximum inertia weight; Indicates the current iteration number; The constraints of the coil parameter optimization model are: ， Where: is the relative deviation of the magnetic field, is the magnetic field strength at any point, It is The current ratio of the coils.

4. The hybrid optimization design method of magnetic field coils based on array structure according to claim 2 is characterized in that: In step 2, converting the optimal current integer ratio of the coil array into a linear combination of the number of turns and the current of each saddle coil includes converting the coil current ratio Decomposed into three groups of linear combinations of the number of turns and coil currents: ， Where: It is The current ratio of the coils, are the three sets of current ratios to be optimized, Corresponding to the current ratio Number of turns under current.

5. The hybrid optimization design method of magnetic field coils based on array structure according to claim 1, characterized in that: In step 2, the particle swarm algorithm is used again to optimize the minimum number of turns and the optimal current required for each coil, including taking the minimum number of turns required for each array as the objective function and optimizing the number of turns of the three arrays. Ratio of coil current , the constraints of the nonlinear optimization model are: ， Where: is the set of non-negative integers, It refers to The number of turns of the coil.

6. The hybrid optimization design method of magnetic field coils based on array structure according to claim 1, characterized in that: In step 3, the coil path planning is performed by a depth-first search strategy to generate an optimized magnetic field coil structure, including the coil moving along each path until no node can be accessed anymore. If a node has multiple paths, one of the paths is selected to move forward and the node with multiple paths is marked. If one path is blocked, backtrack to the node with multiple paths and select another path to continue exploring until all nodes are traversed.

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