An optimization method for a low-power three-axis Helmholtz coil model

Abstract

The present invention relates to the technical field of modeling of Helmholtz coils, and specifically discloses an optimization method for a low-power three-axis Helmholtz coil model, comprising: step S1: defining a target cubic magnetic field area; defining parameters: the side length of the homogeneous area, the minimum magnetic field in the homogeneous area, and the magnetic field inhomogeneity; step S2: based on a particle swarm algorithm, taking the minimum magnetic field inhomogeneity as the first optimization goal, obtaining the first m groups of coil parameters with the minimum magnetic field inhomogeneity; step S3: defining a power loss function f, taking the minimum total power loss as the second optimization goal among the m groups of coil parameters obtained, obtaining the group with the minimum total power loss and the minimum magnetic field inhomogeneity in all parameter groups as the optimal coil parameter; step S4: establishing a low-power three-axis Helmholtz coil model according to the optimal coil parameters. The three-axis Helmholtz coil designed by the present technical solution can generate a magnetic field area with a certain volume and good uniformity by consuming only relatively low power.

Description

Technical Field

[0001] The invention relates to the technical field of modeling of Helmholtz coils, and in particular to an optimization method for a low-power three-axis Helmholtz coil model. Background Art

[0002] Uniform magnetic fields are widely used in various fields such as industry, materials, basic science, and medicine. Among them, the Helmholtz coil is the most commonly used device to create a uniform magnetic field in a small area. Common Helmholtz coil structures are circular and square. Compared with circular coils, square Helmholtz coils are mostly used in large applications because they are easier to install and have better center accessibility. In addition, some multi-coil structures including three-coil, four-coil, and five-coil structures have been proposed and studied. These multi-coil structures significantly improve the uniformity of the magnetic field. However, in most Helmholtz coil structure designs, either only the field uniformity of the center point or only the field uniformity on the axis is considered, which will limit most applications because a certain volume of uniform field is required in these applications.

[0003] In the medical field, a uniform magnetic field needs to be generated inside the patient's body for imaging during magnetic resonance imaging; for bioelectromagnetic research, a large amount of uniform magnetic field exposure is required, and the bioelectromagnetic effect depends on the direction of the magnetic field. In the magnetic field immunity test, a uniform magnetic field needs to be generated in a cubic area to immerse the device under test for testing. In addition, some electromagnetic compatibility tests may also need to generate a uniform magnetic field in a specific area to simulate the electromagnetic field in the actual working environment; it can be seen that the above applications all require a uniform magnetic field area with a certain volume. Summary of the invention

[0004] The purpose of the present invention is to provide an optimization method for a low-power three-axis Helmholtz coil model to solve the following technical problems:

[0005] How to solve the problem that the traditional coil design method only considers the field uniformity at the center point or axis and cannot meet many practical application requirements while also optimizing the power loss of the coil.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A method for optimizing a low-power three-axis Helmholtz coil model, the method comprising:

[0008] Step S1: defining a target cubic magnetic field region; the target cubic magnetic field region defines three parameters, which are: the side length of the homogeneous region, the minimum magnetic field of the homogeneous region, and the magnetic field inhomogeneity;

[0009] Step S2: Based on the particle swarm algorithm, taking the minimum magnetic field inhomogeneity as the first optimization goal, the parameters of the first m groups of coils with the minimum magnetic field inhomogeneity are obtained;

[0010] Step S3: define the power loss function f, and among the m groups of coil parameters obtained, take the minimum total power loss as the second optimization goal, and obtain the group with the minimum total power loss and the smallest magnetic field inhomogeneity among all parameter groups as the optimal coil parameters.

[0011] Step S4: Establishing a low-power three-axis Helmholtz coil model according to the optimal coil parameters.

[0012] Furthermore, the magnetic field inhomogeneity η is defined as the maximum magnetic field B in the homogeneous region. max The minimum magnetic field B in the homogeneous region min The ratio is calculated as:

[0013] Among them, B max Indicates the maximum magnetic field in the homogeneous region; B min Indicates the minimum magnetic field in the homogeneous region.

[0014] Furthermore, the side length s of the homogeneous region represents the spatial volume of the uniform magnetic field, and the minimum magnetic field B of the homogeneous region min Characterizes the magnetic field strength;

[0015] Through the homogeneous area side length s, the minimum magnetic field B in the homogeneous area min The field uniformity optimization within a cubic region with a side length of s is achieved by limiting the field deviation with the magnetic field inhomogeneity η.

[0016] Furthermore, the homogeneous region side length s, the homogeneous region minimum magnetic field B min For a uniform magnetic field defined by the magnetic field inhomogeneity η, there are m groups of coil parameters that meet the conditions.

[0017] Furthermore, the step S2 is specifically as follows:

[0018] Step S21, converting the optimization problem of the field inhomogeneity of the three-axis Helmholtz coil, the side length of each axis coil, and the current through each coil into a particle swarm problem, and randomly initializing the particle speed and position;

[0019] Step S22, initializing the individual particle swarms and the global optimal position and optimal value;

[0020] Step S23, updating the position and velocity of particles in the particle swarm according to the particle position formula and the particle velocity formula;

[0021] Step S24: Calculate the magnetic field inhomogeneity η corresponding to the i-group coil parameters i, and update the individual historical optimal position and historical optimal value and the global historical optimal position and historical optimal value;

[0022] Step S25: Set the iteration termination condition to determine the magnetic field inhomogeneity η i Is it less than 0.0005 and whether the maximum number of iterations is reached: otherwise, jump to step S23, and if so, store the first m groups of data with the smallest magnetic field inhomogeneity.

[0023] Furthermore, it also includes: designing the total power consumption P of the coil system and the conductor mass V:

[0024] P = 4ρJaNI;

[0025] V = 4aNI / J;

[0026] Among them, ρ represents the resistivity of the conductor material; J represents the current density passing through; a represents the side length of the square coil; NI represents the total ampere-turns.

[0027] Furthermore, the total power consumption P of the coil system and the conductor mass V are both proportional to a×NI at the same current density, and the calculation formula of the power loss function f is:

[0028] f = a × NI.

[0029] Furthermore, the step S3 specifically includes:

[0030] The power loss functions f of the m groups of coils are obtained by calculation, and a group of coil parameters with the smallest total power loss function f is selected as the optimal parameters of the low-power three-axis Helmholtz coil.

[0031] Furthermore, the step S4 specifically includes:

[0032] Ansys software was used to establish a low-power three-axis Helmholtz coil model according to the optimal coil parameters.

[0033] The beneficial effects of the present invention are as follows: the present invention defines a cubic uniform magnetic field area, uses a particle swarm algorithm to obtain m groups of coil data with good magnetic field uniformity, and makes the calculation process more efficient; a simple function reflecting the coil power consumption is derived according to the relationship between the coil power consumption and various parameters, and a group of data with the lowest power is selected as the optimal design parameters of the coil; it is ensured that under the premise of generating magnetic fields of the same size, the three-axis Helmholtz coil designed with the optimal coil parameters only needs to consume lower power to provide a magnetic field area with a certain volume and good uniformity.

[0034] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0036] Figure 1 A model diagram of a square triaxial Helmholtz coil frame containing a newly defined cubic homogeneous region according to the present invention;

[0037] Figure 2 This is a flow chart of a method for determining optimal parameters of a tri-axis Helmholtz coil in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] See also Figure 1 As shown, the present invention is an optimization method for a low-power three-axis Helmholtz coil model, which specifically includes:

[0040] Step S1: Based on the requirements of some current applications for the area of ​​a field uniform region, a more comprehensive and reasonable cubic uniform magnetic field region is defined, wherein the parameters involved include the side length of the homogeneous region, the minimum magnetic field of the homogeneous region, and the magnetic field inhomogeneity;

[0041] In defining a more comprehensive and reasonable cubic uniform magnetic field, three parameters are used, namely the side length of the cubic homogeneous region (expressed as s), the minimum magnetic field in the uniform region (expressed as B min ) and magnetic field inhomogeneity (denoted as η).

[0042] The magnetic field inhomogeneity is defined as the ratio of the maximum magnetic field to the minimum magnetic field in the uniform area, and the calculation formula is:

[0043]

[0044] In the formula,

[0045] B max represents the maximum magnetic field in the homogeneous region;

[0046] B min Indicates the minimum magnetic field in the homogeneous region.

[0047] In addition, the side length of the homogeneous region (s) characterizes the spatial volume of the uniform magnetic field, and the minimum magnetic field (B min ) characterizes the magnetic field strength; the length of the cube homogeneous region (s), the minimum magnetic field in the homogeneous region (B min ) and magnetic field inhomogeneity (η) limit the field deviation and ensure that the field in the cubic region with a side length of s has good uniformity.

[0048] In a specific implementation, a specific uniform magnetic field defined by the side length of the homogeneous region, the minimum magnetic field in the homogeneous region and the magnetic field inhomogeneity is as follows: Figure 1 The three-axis Helmholtz coil model diagram drawn by Ansys software is shown in the figure, where:

[0049] The middle cubic area is a cubic homogeneous area with a side length of s. There is a pair of Helmholtz coils symmetrical about its center of mass O in different directions around this area. The innermost coil L1 has a side length of g1 and a current In1. The outer coil L2 has a side length of g3 and a current In2. The outermost coil L3 has a side length of g5 and a current In3. The distance between L1 and the coil L1' symmetrical about the center of mass O is g2, the distance between L2 and the coil L2' symmetrical about the center of mass O is g4, and the distance between L1 and the coil L3' symmetrical about the center of mass O is g6. There will be m groups of coil parameters that can meet the conditions.

[0050] Step S2: Based on the particle swarm algorithm, taking the minimum magnetic field inhomogeneity as the first optimization goal, the parameters of the first m groups of coils with the minimum magnetic field inhomogeneity are obtained, which specifically includes the following steps:

[0051] Step S21, transform the optimization problem of the field inhomogeneity of the three-axis Helmholtz coil, the side length of each axis coil, and the current through each coil into a particle swarm problem, set the number of particles to 1000, the side length s of the homogeneous zone to 0.2 m, and the minimum magnetic field B min Set to 0.001T and randomly initialize the particle velocity V i 、Position X i ;

[0052] Step S22, initializing individual and global optimal positions and optimal values;

[0053] Step S23, updating the position and velocity of particles in the particle swarm according to the particle position and velocity formula;

[0054] Step S24, calculating the magnetic field inhomogeneity η corresponding to a set of coil parameters, and updating the individual historical optimal position and historical optimal value and the global historical optimal position and historical optimal value;

[0055] Step S25, set the iteration termination condition to determine whether the magnetic field inhomogeneity η is less than 0.0005, and the real number judgment condition is set to improve the algorithm execution speed without affecting the magnetic field uniformity; and whether the maximum number of iterations is reached, otherwise jump to step S23; if yes, jump out of the loop and store the first m groups of data with the smallest magnetic field inhomogeneity.

[0056] Step S3: define a function f reflecting power consumption, and among the m groups of coil parameters obtained, take the minimum total power consumption as the second optimization goal, and obtain a group of optimal coil parameters with the minimum power consumption and relatively good magnetic field uniformity among all parameter groups.

[0057] When designing a coil, the primary considerations are the total system power consumption (represented by P) and the conductor quality (reflected by the conductor volume, represented by V), which reflects the system's power capacity, coil heating, and construction costs; these two parameters can be approximately expressed as:

[0058] P=4ρJaNI

[0059] V=4aNI / J

[0060] In the formula,

[0061] ρ represents the resistivity of the conductor material;

[0062] J represents the current density passing through;

[0063] a represents the side length of the square coil;

[0064] NI stands for total ampere-turns, since coils usually have multiple turns.

[0065] As an embodiment of the present invention, the total power consumption of the coil system and the conductor mass are both proportional to a×NI at the same current density, so the calculation formula of the function f reflecting the power consumption is:

[0066] f = a × NI;

[0067] Next, the power f of each of the m groups of coils is calculated, and a group of coil parameters with the smallest total power consumption f is selected as the optimal parameters of the low-power three-axis Helmholtz coil.

[0068] The above steps to determine the optimal parameters of the low-power three-axis Helmholtz coil are as follows: Figure 2As shown, and after calculation, if you want to generate a uniform minimum magnetic field of 0.001T for a cube with a side length of 0.2m, you can set the parameters as follows: g1=0.5932m, g2=0.2020m, g3=0.6932m, g4=0.2002m, g5=0.7932m, g6=0.2128m, I n1=448.4659A, I n2=447.4802A, I n3=485.0262A.

[0069] Next, the low-power three-axis Helmholtz coil model was established using Ansys software according to the optimal coil parameters. Figure 1 shown.

[0070] The three-axis Helmholtz coil designed according to this parameter can provide a magnetic field area that meets the specified volume and uniformity requirements with the lowest power consumption.

[0071] The above contents are merely examples and explanations of the concept of the present invention. The technicians in this technical field may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the concept of the invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A method for optimizing a low-power three-axis Helmholtz coil model, characterized in that: The method comprises: Step S1: defining a target cubic magnetic field region; the target cubic magnetic field region defines three parameters, which are: the side length of the homogeneous region, the minimum magnetic field of the homogeneous region, and the magnetic field inhomogeneity; Step S2: Based on the particle swarm algorithm, taking the minimum magnetic field inhomogeneity as the first optimization goal, the parameters of the first m groups of coils with the minimum magnetic field inhomogeneity are obtained; Step S3: defining a power loss function f, taking the minimum total power loss as the second optimization goal among the m groups of coil parameters obtained, and obtaining the group with the minimum total power loss and the minimum magnetic field inhomogeneity among all parameter groups as the optimal coil parameters; Step S4: establishing a low-power three-axis Helmholtz coil model according to the optimal coil parameters; The magnetic field inhomogeneity η is defined as the maximum magnetic field B in the homogeneous region. max The minimum magnetic field B in the homogeneous region min The ratio is calculated as: Among them, B max Indicates the maximum magnetic field in the homogeneous region; B min represents the minimum magnetic field in the homogeneous region; The side length s of the homogeneous region represents the spatial volume of the uniform magnetic field. The minimum magnetic field B in the homogeneous region min Characterizes the magnetic field strength; Through the homogeneous area side length s, the minimum magnetic field B in the homogeneous area min and the magnetic field inhomogeneity η to limit the field deviation and achieve the uniformity optimization of the magnetic field in a cubic region with a side length of s; The step S2 is specifically as follows: Step S21, converting the optimization problem of the field inhomogeneity of the three-axis Helmholtz coil, the side length of each axis coil, and the current through each coil into a particle swarm problem, and randomly initializing the particle speed and position; Step S22, initializing the individual particle swarms and the global optimal position and optimal value; Step S23, updating the position and velocity of particles in the particle swarm according to the particle position formula and the particle velocity formula; Step S24: Calculate the magnetic field inhomogeneity η corresponding to the i-group coil parameters i , and update the individual historical optimal position and historical optimal value and the global historical optimal position and historical optimal value; Step S25: Set the iteration termination condition to determine the magnetic field inhomogeneity η i Is it less than 0.0005 and whether the maximum number of iterations has been reached: otherwise, jump to step S23, and if yes, store the first m groups of data with the smallest magnetic field inhomogeneity; The step S3 specifically includes: The power loss functions f of the m groups of coils are obtained by calculation, and a group of coil parameters with the smallest total power loss function f is selected as the optimal parameters of the low-power three-axis Helmholtz coil.

2. The optimization method of a low-power three-axis Helmholtz coil model according to claim 1, characterized in that: The homogeneous region side length s, the homogeneous region minimum magnetic field B min And the magnetic field defined by the magnetic field inhomogeneity η, there are m sets of coil parameters that meet the conditions.

3. The optimization method of a low-power three-axis Helmholtz coil model according to claim 1, characterized in that: Also includes: Design the total power consumption P and conductor mass V of the coil system: P = 4ρJaNI; V = 4aNI / J; Among them, ρ represents the resistivity of the conductor material; J represents the current density passing through; a represents the side length of the square coil; NI represents the total ampere-turns.

4. The optimization method of a low-power three-axis Helmholtz coil model according to claim 3, characterized in that: The total power consumption P of the coil system and the conductor mass V are both proportional to a×NI at the same current density, so the calculation formula of the power loss function f is: f = a × NI.

5. The optimization method of a low-power three-axis Helmholtz coil model according to claim 1, characterized in that: The step S4 specifically includes: Ansys software was used to establish a low-power three-axis Helmholtz coil model according to the optimal coil parameters.

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