Helmholtz Coil Device Magnetic Field Uniformity Optimization Method Based on Differential Evolution Algorithm

Abstract

The present invention provides a method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm, comprising the following steps: Step S1: Construct an improved Helmholtz coil device model; Step S2: Derive and construct a partial differential equation of the magnetic field of the improved Helmholtz coil device according to Maxwell's equations; Step S3: Use the differential evolution algorithm to optimize the improved Helmholtz coil device to determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved device under different application scenarios, so as to achieve the optimal magnetic field uniformity of the improved Helmholtz coil device. Applying this technical solution can determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved Helmholtz coil device, and achieve the optimal magnetic field uniformity of the improved device.

Description

Technical Field

[0001] The present invention relates to the technical field of modeling of the magnetic field of Helmholtz coils, and in particular to a method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm. Background Art

[0002] Currently, devices for generating a uniform magnetic field are mainly divided into coil-type devices and magnetic core-type devices. Among them, coil-type devices avoid the large-scale use of magnetic core materials compared with magnetic core-type devices, have a simple overall structure, and are convenient for production and manufacturing. Coil-type devices can be further divided into Helmholtz coil devices and energized solenoid devices. Among them, an energized solenoid requires a relatively large length to have relatively excellent magnetic field uniformity, and the uniformity is slightly lower than that of Helmholtz coils and the material consumption is large. Therefore, Helmholtz coils are more widely produced and used.

[0003] However, the magnetic field of a traditional Helmholtz coil device usually also difficult to meet the actual applications with high requirements for magnetic field uniformity. For this reason, many scholars have studied to improve the magnetic field uniformity of Helmholtz coil devices. Among them, an improvement method of expanding the coil spacing on the basis of the unchanged radius of the traditional Helmholtz coil and adding a single coil parallel to the axis and having the same shape as the coil of the traditional device at the center of the axis is relatively easy to implement, and the magnetic field uniformity of the improved Helmholtz coil device is significantly improved and the overall structure is simple and convenient for production and manufacturing. However, the optimal setting of the coil spacing and the radius of the newly added central coil of the improved device in different application scenarios is difficult and complex, which will result in the magnetic field uniformity of the improved device not reaching the best in actual applications and still needing further optimization. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm, which can determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved Helmholtz coil device in different application scenarios, so as to achieve the optimal magnetic field uniformity.

[0005] To achieve the above object, the present invention adopts the following technical scheme: A method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm, comprising the following steps:

[0006] Step S1: Construct a model of an improved Helmholtz coil device;

[0007] Step S2: Derive and construct a partial differential equation of the magnetic field of the improved Helmholtz coil device according to Maxwell's equations;

[0008] Step S3: Use the differential evolution algorithm to optimize the improved Helmholtz coil device to determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved device under different application scenarios, so as to optimize the magnetic field uniformity of the improved Helmholtz coil device.

[0009] In a preferred embodiment, the specific steps of step S1 are as follows:

[0010] Step S11: Construct a geometric model of the improved Helmholtz coil device;

[0011] Step S12: Set the material parameters of the improved Helmholtz coil device model;

[0012] Step S13: Perform finite element mesh division on the geometric model of the improved Helmholtz coil device.

[0013] In a preferred embodiment, the partial differential equation in step S2 is specifically:

[0014]

[0015] Where, is the Hamiltonian operator, ε0 is the vacuum permittivity, σ is the conductivity, μ0 is the vacuum permeability, J e is the current density caused by the external current, B is the magnetic induction intensity, A is the magnetic vector potential, and H is the magnetic field intensity.

[0016] In a preferred embodiment, the specific steps of step S3 are as follows:

[0017] Step S31: Set the multiple of the coil spacing of the enlarged improved device compared to the coil spacing of the traditional device as the variable parameter of the differential evolution algorithm, and set the range of its value;

[0018] Step S32: Set the multiple of the radius of the newly added central coil compared to the radius of the coil of the traditional device as the variable parameter of the differential evolution algorithm, and set the range of its value;

[0019] Step S33: Set the population size of the differential evolution algorithm and randomly generate variable parameter values;

[0020] Step S34: According to the variable parameter values, use the finite element method to calculate the partial differential equation in S2 to obtain the magnetic field distribution of the improved Helmholtz coil device;

[0021] Step S35: Calculate the magnetic field uniformity objective function expression according to the magnetic field distribution, and obtain the optimal objective function value and the optimal values of the coil spacing of the improved device and the radius of the newly added central coil at this time;

[0022] Step S36: When the upper limit of the number of iterations is not reached, perform "mutation, crossover, and selection" on various swarm individuals to update the variable parameter values of various swarm individuals and repeat Step S34 and Step S35 until the optimal magnetic field uniformity of the improved Helmholtz coil device is obtained and the result is output, and the optimal device model and its magnetic field intensity distribution are obtained.

[0023] In a preferred embodiment, the geometric model is: on the basis of the unchanged radius of the traditional Helmholtz coil, the coil spacing is enlarged, and a single coil parallel to and having the same shape as the coils of the traditional device is added at the center of the axis.

[0024] In a preferred embodiment, the material parameters include relative permittivity, relative permeability, and conductivity.

[0025] In a preferred embodiment, in Step S35, the specific expression of the magnetic field uniformity objective function is:

[0026]

[0027] The smaller the value of the magnetic field uniformity objective function, the better. Among them, f1, f2, and s are magnetic field uniformity evaluation indicators, and w1, w2, and w s are the corresponding weights of the magnetic field uniformity indicators f1, f2, and s, which are set differently according to the actual application requirements; V is the volume of the magnetic field region inside the improved Helmholtz coil device, and V eff is the volume of the magnetic field region within 0.3% of the magnetic field intensity error at the center of the coils of the improved device, that is, the magnetic field inside the device satisfies H center ·0.997 ≤ H ≤ H center ·1.003, where H center is the magnetic field intensity at the center of the coils of the improved device; H max is the maximum value of the magnetic field intensity in the magnetic field region inside the improved Helmholtz coil device, and H min is the minimum value, and H mean is the average value; is the instantaneous value during the iteration of the variable parameters of the differential evolution algorithm, and p is a set of 100 variable data points obtained by taking 5 values before and after at appropriate intervals at the instantaneous values of two variables. This evaluation indicator s is used to evaluate the influence of the error caused by manufacturing the coils on the magnetic field uniformity.

[0028] Compared with the prior art, the present invention has the following beneficial effects: By using the differential evolution algorithm to optimize the improved Helmholtz coil device, the present invention solves the problem that it is difficult and complex to optimally set the coil spacing and the radius of the newly added central coil in different application scenarios, which leads to the magnetic field uniformity not reaching the best. It can determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved Helmholtz coil device, so as to achieve the optimal magnetic field uniformity. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flowchart of the method according to the preferred embodiment of the present invention;

[0030] Figure 2 It is an initial model diagram of the improved Helmholtz coil device according to the preferred embodiment of the present invention;

[0031] Figure 3 It is a schematic diagram of the magnetic field uniformity evaluation area of the initial improved device according to the preferred embodiment of the present invention;

[0032] Figure 4 It is a process diagram of variable parameter optimization according to the preferred embodiment of the present invention;

[0033] Figure 5 It is a model diagram of the optimized improved Helmholtz coil device according to the preferred embodiment of the present invention;

[0034] Figure 6 It is a magnetic field intensity distribution diagram of the optimized improved device according to the preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0037] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] As Figures 1-6 shown, the embodiment of the present invention provides a method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm, which specifically includes the following steps:

[0039] Step S1: Construct a model of the improved Helmholtz coil device. As shown in Figure 2 its initial model diagram, the specific steps are as follows:

[0040] Step S11: Construct the geometric model of the improved Helmholtz coil device. On the basis of the unchanged radius of 100 mm of the traditional Helmholtz coil, expand its coil spacing. Set the multiple of the expanded coil spacing of the initial improved device compared to the coil spacing of 100 mm of the traditional device to be 2, that is, double the coil spacing of the traditional device to 200 mm. And add a single coil parallel to the axis of the traditional device coil and with the same shape at the center of the coil axis. Set the multiple of the radius of the newly added central coil compared to the radius of the traditional device coil to be 1, that is, the same as the radius of the traditional device coil, which is 100 mm. Set the number of turns of the newly added central coil to be 2 times the number of turns of the traditional device coil, which is 300 turns, that is, 600 turns;

[0041] Step S12: Set the material parameters of the improved Helmholtz coil device model, including relative permittivity, relative permeability, and conductivity;

[0042] Step S13: Conduct finite element mesh division on the geometric model of the improved Helmholtz coil device.

[0043] Step S2: Derive and construct the partial differential equation of the magnetic field of the improved Helmholtz coil device according to Maxwell's equations. The specific partial differential equation obtained is:

[0044]

[0045] Where, is the Hamiltonian operator, ε0 is the vacuum permittivity, σ is the conductivity, μ0 is the vacuum permeability, J e is the current density caused by the external current, B is the magnetic induction intensity, A is the magnetic vector potential, and H is the magnetic field intensity.

[0046] Step S3: Use the differential evolution algorithm to optimize the improved Helmholtz coil device to determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved device in different application scenarios, so as to make the magnetic field uniformity of the improved Helmholtz coil device reach the optimal. The specific steps are as follows:

[0047] Step S31: Set the multiple of the expanded coil spacing of the improved device compared to the coil spacing of the traditional device as the variable parameter of the differential evolution algorithm. In this embodiment, set the range of its value to be 1-10;

[0048] Step S32: Set the multiple of the radius of the newly added central coil compared to the radius of the traditional device as the variable parameter of the differential evolution algorithm. In this embodiment, set the range of its value to be 1-5;

[0049] Step S33: Set the population size of the differential evolution algorithm and randomly generate variable parameter values. In this embodiment, the population size is set to 30;

[0050] Step S34: According to the variable parameter values, use the finite element method to calculate the partial differential equation in S2 to obtain the magnetic field distribution of the improved Helmholtz coil device;

[0051] Step S35: Calculate the magnetic field uniformity objective function expression based on the magnetic field distribution, and obtain the optimal objective function value and the optimal values of the coil spacing and the radius of the newly added central coil of the corresponding improved device at this time. The magnetic field uniformity objective function expression is specifically:

[0052]

[0053] The smaller this value is, the better. Among them, f1, f2, and s are magnetic field uniformity evaluation indicators, and w1, w2, and w s are the corresponding weights of the magnetic field uniformity indicators f1, f2, and s, and are set differently according to the requirements of actual applications; V is the volume of the magnetic field region inside the improved Helmholtz coil device, which is the volume of the evaluation region shown in Figure 3 in the initial improved device, and V eff is the volume of the magnetic field region within 0.3% of the magnetic field intensity error at the center of the coils of the improved device, which is the volume of the evaluation region shown in Figure 3 in the initial improved device where the magnetic field satisfies H center ·0.997 ≤ H ≤ H center ·1.003, where H center is the magnetic field intensity at the center of the coils of the improved device; H max is the maximum magnetic field intensity of the magnetic field region inside the improved Helmholtz coil device, which is the maximum magnetic field intensity of the evaluation region shown in Figure 3 in the initial improved device, H min is the minimum value, and H mean is the average value; is the instantaneous value during the iteration process of the variable parameters of the differential evolution algorithm, and p is a set of 100 variable data points obtained by taking 5 values before and after at appropriate intervals at the instantaneous values of two variables. This evaluation indicator s is used to evaluate the impact of the error caused by manufacturing the coils on the magnetic field uniformity.

[0054] Step S36: When the iteration count upper limit is not reached, perform "mutation, crossover, selection" on each population individual to update the variable parameter values of each population individual and repeat Step S34 and Step S35 until the optimal magnetic field uniformity of the improved Helmholtz coil device is obtained and the result is output. The iteration process is as shown in Figure 4As shown, the optimal device model and its magnetic field intensity distribution are obtained. The optimized improved Helmholtz coil device model is as follows Figure 5 shown, and the magnetic field intensity distribution of the optimized improved device is as follows Figure 6 shown.

[0055] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations fall within the scope defined by the appended claims.

Claims

1. A method for optimizing the magnetic field uniformity of a Helmholtz coil device based on a differential evolution algorithm, characterized in that, It includes the following steps: Step S1: Construct an improved Helmholtz coil device model; Step S2: Derive and construct a partial differential equation for the magnetic field of the improved Helmholtz coil device according to Maxwell's equations; Step S3: Optimize the improved Helmholtz coil device by using the differential evolution algorithm to determine the optimal values of the coil spacing and the radius of the newly added central coil of the improved device under different application scenarios, so as to make the magnetic field uniformity of the improved Helmholtz coil device reach the optimal; The specific content of step S1 is as follows: Step S11: Construct a geometric model of the improved Helmholtz coil device; Step S12: Set the material parameters of the improved Helmholtz coil device model; Step S13: Perform finite element mesh division on the geometric model of the improved Helmholtz coil device; The specific partial differential equation in step S2 is as follows: Among them, is the Hamiltonian operator, ε0 is the vacuum permittivity, σ is the conductivity, μ0 is the vacuum permeability, J e is the current density caused by the external current, B is the magnetic induction intensity, A is the magnetic vector potential, and H is the magnetic field strength; The specific content of step S3 is as follows: Step S31: Set the multiple of the coil spacing of the expanded improved device compared with the coil spacing of the traditional device as the variable parameter of the differential evolution algorithm, and set the range of its value; Step S32: Set the multiple of the radius of the newly added central coil compared with the radius of the coil of the traditional device as the variable parameter of the differential evolution algorithm, and set the range of its value; Step S33: Set the population size of the differential evolution algorithm and randomly generate variable parameter values; Step S34: According to the variable parameter values, use the finite element method to calculate the partial differential equation in S2 to obtain the magnetic field distribution of the improved Helmholtz coil device; Step S35: Calculate the magnetic field uniformity objective function expression according to the magnetic field distribution, and obtain the optimal objective function value and the optimal values of the coil spacing of the corresponding improved device and the radius of the newly added central coil at this time; Step S36: When the upper limit of the iteration times is not reached, perform "mutation, crossover, selection" on each population individual to update the variable parameter values of each population individual and repeat steps S34 and S35 until the optimal magnetic field uniformity of the improved Helmholtz coil device is obtained and the result is output, and the optimal device model and its magnetic field strength distribution are obtained; The geometric model is: on the basis of the unchanged radius of the traditional Helmholtz coil, expand its coil spacing and add a single coil parallel to the axis and having the same shape as the coil of the traditional device at the axis center; In step S35, the specific magnetic field uniformity objective function expression is as follows: The smaller the value of the magnetic field uniformity objective function, the better. Among them, f1, f2, and s are magnetic field uniformity evaluation indicators, and w1, w2, and w s are the corresponding weights of the magnetic field uniformity indicators f1, f2, and s, and are set differently according to the requirements of actual applications; V is the volume of the magnetic field region inside the improved Helmholtz coil device, and V eff is the volume of the magnetic field region within 0.3% of the magnetic field intensity error at the center of the coil of the improved device, that is, the magnetic field inside the device satisfies H center ·0.997 ≤ H ≤ H center ·1.003, where H center is the magnetic field intensity at the center of the coil of the improved device; H max is the maximum value of the magnetic field intensity in the magnetic field region inside the improved Helmholtz coil device, and H min is the minimum value, and H mean is the average value; is the instantaneous value during the iteration of the variable parameters of the differential evolution algorithm, and p is a set of 100 variable data points obtained by taking 5 values before and after at set intervals at the values of two variables. This evaluation indicator s is used to evaluate the influence of the error caused by the production and manufacturing of the coil on the magnetic field uniformity.

2. The method for optimizing the magnetic field uniformity of the Helmholtz coil device based on the differential evolution algorithm according to claim 1, characterized in that The material parameters include relative permittivity, relative permeability and conductivity.

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