A hybrid optimization design method for magnetic field coils based on array structure

Abstract

The application discloses a kind of based on array structure's magnetic field coil hybrid optimization design method, the multiple saddle coils are combined into coil array by the method, and on the basis of considering the coupling effect of high magnetic permeability material to coil magnetic field, the mathematical model of the magnetic field of single coil is solved, and the mathematical model of the magnetic field of saddle coil array is obtained according to superposition principle.The mathematical model is used to combine particle swarm optimization algorithm to optimize the best current integer ratio between the saddle coils in array, the current integer ratio of coil is converted into the linear combination of the number of turns and current of each coil, and particle swarm optimization algorithm is used again to optimize the minimum number of turns and optimal current required by each coil.Finally, the optimized magnetic field coil is generated by the coil path planning of depth-first search strategy.The application greatly improves the uniformity of coil, has no discretization error and simple structure, and is convenient for practical application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of magnetic field compensation, and particularly relates to a hybrid optimization design method of a magnetic field coil based on an array structure. BACKGROUND

[0002] Magnetic field compensation technology is a key technology in the field of modern technology, and 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 the fields of physics, biology, medicine and military, especially in the field of biomedicine, mainly for medical equipment such as magnetic imaging. With the continuous progress of science and technology and medicine, magnetocardiography technology has gradually attracted widespread attention from researchers around the world. However, due to the extremely weak magnetic signals in the human body and the complex and variable external magnetic field environment, it has brought great challenges to obtain accurate magnetocardiography signals.

[0003] In order to create an extremely weak magnetic field environment, it is usually necessary to use magnetic shielding technology. Magnetic shielding technology mainly includes two ways: one is the passive magnetic shielding technology with magnetic shielding structure and material as the core, and the other is the active magnetic compensation system with energized coil 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 the space. The system is usually composed 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 current generating magnetic field in conductors, thereby achieving suppression of external interference magnetic field. However, in order to create an extremely weak magnetic field environment, passive magnetic shielding and active magnetic compensation technology are usually combined. The compensation coil is usually placed inside high magnetic permeability material, but such high magnetic permeability material will change the magnetic field distribution generated by the coil, significantly reducing 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

[0005] To solve the above technical problems, the application provides a hybrid optimization design method of a magnetic field coil 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 a magnetocardiography ultra-high resolution imaging device.

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

[0007] A hybrid optimization design method of a magnetic field coil based on an array structure, the method comprising:

[0008] Step 1: Combine multiple saddle coils into a coil array. Considering the coupling effect of high magnetic permeability materials on the coil magnetic field, the magnetic field mathematical model of a single saddle coil is analyzed, and the magnetic field mathematical model of the saddle coil array is obtained according to the superposition principle.

[0009] Step 2: Based on the mathematical model of the magnetic field 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. 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 again used 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] To address the issue of ambient magnetic field interference during magnetocardiography measurements, this invention provides a coil capable of generating a maximum magnetic field deviation of less than 1% within a large rectangular area. This performance significantly outperforms existing saddle coils and nested saddle coils. Using this coil for closed-loop compensation, the 1-40 Hz magnetic field fluctuation within the device is reduced to 3.09 pT. Compared to coils designed using forward methods, this coil exhibits greater uniformity, significantly improving its ability to compensate for magnetic fields. Compared to inversely designed target field method coils, this coil has no discretization error and a simpler structure, making it suitable for practical applications. 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 principle diagram of the array coil magnetic field compensation system;

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

[0018] Figure 6 This is a saddle-shaped array coil and its expanded diagram according to an embodiment of the present invention;

[0019] Figure 7a This 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 This 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 Current path diagram of the third group of saddle array coils in the embodiment of the present application. DETAILED DESCRIPTION

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

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

[0024] Specifically, a hybrid optimization design method of magnetic field coils based on array structure is provided for the design of magnetic field active compensation coils in the internal space of a magnetic shield constructed by high permeability material. The coil array is mainly composed of multiple saddle coils arranged and combined, and a target area of uniform magnetic field is arranged in the middle of the array coil. The required magnetic field is generated by passing appropriate current through a single coil, and the array coil model diagram is as shown in Figure 1 .

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

[0026] ,

[0027] In the formula: 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 the imaginary unit, and are the first and second kinds of modified Bessel functions, and are the corresponding first derivatives, and is an introduced integral parameter, is the Fourier transform of the current density component .

[0028] For single-ended open cylindrical high permeability shield layer, it is necessary to use analytical method and mirror method to establish the magnetic field coefficient of single saddle coil under high permeability material , the model is:

[0029] ,

[0030] where,

[0031] ,

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

[0033] ,

[0034] In the formula: and are the inner and outer radii of the shield barrel, is the relative permeability of high permeability material, is the current density coefficient, which can be obtained by the following steps.

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

[0036] ,

[0037] In the formula: is the Heaviside function, is the Dirac function, and are the starting and ending azimuth angles of the saddle coil, and are the starting and ending heights, is the current size, represents the coordinates of any point in the cylindrical coordinate system when the radius is .

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

[0039] ,

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

[0041] ,

[0042] In the formula: Take 0, 1 or 0, -1.

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

[0044] ,

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

[0046] As Figure 2 shown, a suitable discrete method is selected to obtain the coordinates of the target points in the target area in order, and the magnetic field at the center point of the target area is set to According to the mathematical model of the saddle coil, the corresponding relationship between the saddle array coil and the target point is established, the coil array is composed of saddle coils arranged in an array, and the magnetic field relationship is:

[0047] ,

[0048] Based on the above relationship, in order to obtain the constrained solution, the direct solution of matrix inversion is converted into an optimization problem with the solution conditions as constraints, and the PSO algorithm optimization is performed with the maximum magnetic field relative deviation of the discrete points in the target area as the objective function.

[0049] In the optimization process, the number of independent variables is (this is obtained from the relationship of the saddle coils), the population is composed of particles, wherein the position and speed of the th particle are and respectively. The particle position represents a possible solution to the problem, and the corresponding objective function value can be used as the fitness of the particle. In each iteration process, the particle updates its speed and position through the individual extreme value and the group extreme value :

[0050] ,

[0051] wherein, 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 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 Among the particles element, Refers to The optimal position found among the particles, Refers to the best position searched so far, so it can be used during the search process Dynamic adjustment is performed using a linear decreasing weight strategy, which is expressed 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 the current ratio between the coils. In order to simplify the coil structure and reduce the coil constant, the coil current Decomposed into three groups of linear combinations of the number of turns of the array and the coil current:

[0058] ,

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

[0060] The quadratic PSO algorithm optimization is performed with the minimum number of turns required for each array as the objective function, and the number of turns of the three groups of arrays is optimized and the coil current ratio The constraint of the nonlinear optimization model is:

[0061] ,

[0062] In the formula: refers to the set of non-negative integers, refers to the number of turns of the coil. After the quadratic PSO optimization, the number of turns of each array at different currents is obtained.

[0063] As shown in

[0064] , 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 a graph. In coil optimization, using DFS will make the coil path advance along each path deeply until there is no node to visit. If a node has multiple paths, one of them is selected to advance and the node is marked. If the path is not available, the algorithm will backtrack to the previous node and select another path to continue exploring until all vertices are traversed. Figure 3 Through DFS, the coil structure and winding of the three groups of arrays can be obtained, and thus the hybrid optimization of the array coil is completed.

[0065] As shown in

[0066] , the array coil is used as an actuator to compensate for the magnetic field. The compensation system first collects magnetic field data through an optical pumping magnetometer, then reads the magnetic field data through a PC, and transmits the signal to a control circuit. After the signal is processed by the control circuit, it is sent to a current source, which supplies power to the array coil. Figure 4 In order to facilitate practical application, the current signal output of a single channel on the current source board is maintained, and the three groups of coils are connected in parallel through resistors to form a coil system. The coil system uses resistors

[0067] to accurately match the current of the coil , as shown in . Figure 5

[0068] Embodiment

[0069] As shown in Figure 6 ​​As shown, the measurement region of the single-end opening type magnetocardiography measuring device is designed as 300*300*200mm, the magnetocardiography measuring device is a single-end opening cylindrical barrel with a radius of 425mm and a material thickness of 1.5mm, the relative magnetic permeability of the material is 20000, based on the above conditions, the coil is designed as a saddle array coil, the single saddle coil has a radius of 400mm, and the 40 saddle coils with equal size are combined to form a saddle array coil with a total length of 800mm.

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

[0071] Through finite element software simulation, the theoretical maximum deviation of the array coil in the measurement region of the magnetocardiography measuring device is less than 1%, and after using the coil to perform closed-loop compensation on the magnetocardiography measuring device, the average power spectral density of the 1-40Hz magnetic field noise in the device is reduced by 63.82%, and the peak-to-peak value of the 1-40Hz magnetic field fluctuation is reduced from 12.40pT to 3.09pT. Greatly reduces the interference of the external magnetic field of the magnetocardiography measuring device, effectively improves the imaging quality and accuracy of the magnetocardiogram.

[0072] In summary, the coil design method of the present application combines model analysis in the forward design method and matrix solution in the reverse design method, which not only avoids the errors caused by discretization in reverse design, reduces the complexity of the coil and facilitates practical application, but also solves the problem of coil limitation in fixed shape in forward design, improves the flexibility of design, and the optimization design method has certain universality.

[0073] In addition, the coil design of the present application uses two-stage particle swarm optimization (PSO) and depth-first search (DFS) for hybrid optimization and coil path planning, the first PSO optimizes the best 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 for coil path planning to generate the optimized array coil. And the method of using resistance matching is proposed to accurately match different currents, solving the problem of multiple channel current input required by the coil.

[0074] Therefore, the advantage of the present application is that it can generate a high uniformity magnetic field in a large area, and can generate a magnetic field with a maximum deviation of less than 1% in a rectangular area, which is superior to the existing coil, and compared with the target field method coil, the coil of the present application is simpler and more convenient for practical application.

[0075] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application, and it should be understood that the above-described is only a specific embodiment of the present application and is not intended to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A hybrid optimization design method for magnetic field coils based on an array structure, characterized in that: The method comprises: Step 1: Combine multiple saddle coils into a coil array, analyze 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 obtain the magnetic field mathematical model of the saddle coil array based on the superposition principle; including: 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 the 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 methods : ， Among them, the intermediate parameters , The expressions of the intermediate parameters involved in the formula are: ， Where: and are the inner and outer radii of the shield barrel, 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: ， Where, is the magnetic field component coefficient in the Cartesian coordinate system; Step 2: Based on the mathematical model of the magnetic field 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. 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 again used to optimize the minimum number of turns and the optimal current required for each coil. The method of solving the optimal current integer ratio between the saddle coils in the coil array based on the mathematical model of the magnetic field of a single saddle coil and the particle swarm algorithm includes: 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 , based on the mathematical model of a single saddle coil, establish 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 extremes 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 Among the particles element, Refers to The optimal position found among the particles, Refers to the best position searched so far. Dynamic adjustment is performed using a linear decreasing weight strategy, which is expressed 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; 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, 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 current of each saddle coil includes converting the coil current ratio Decomposed into three groups of linear combinations of the number of turns of the array and the coil current: ， 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.

3. 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 optimizing the number of turns of the three groups of arrays with the minimum number of turns required for each array as the objective function. Ratio of coil current , the constraints of the nonlinear optimization model are: ， Where: is the set of non-negative integers, It refers to the The number of turns of the coil.

4. The hybrid optimization design method of magnetic field coils based on array structure according to claim 1, characterized in that: In step 3, coil path planning is performed using a depth-first search strategy to generate an optimized magnetic field coil structure, including: the coil moves along each path until no node can be accessed. 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, backtracking to the node with multiple paths and selecting another path to continue exploring until all nodes are traversed.

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