Design method of cylindrical surface coil with adjustable coil constants

Abstract

The invention relates to a coil constant adjustable cylindrical surface coil design method, which comprises the following steps: setting a target area in the center of a cylinder, and determining that any point on a cylindrical surface generates a magnetic field in the target area; taking the non-uniformity of the magnetic field and a difference value between a coil constant and a set coil constant in the optimization process as optimization targets, calculating the optimization targets according to a coil parameter combination obtained by a multi-target optimization algorithm, determining coil parameters to be optimized, and obtaining an actual coil winding according to the coil parameters; the method is matched with magnetometer correction and comprises the steps that a base is arranged, a three-axis coil is installed in a base groove, a positioning column is arranged on the plane of the base, and a three-axis magnetometer tool is combined for positioning the magnetometer in the space. According to the invention, extremely-high-uniformity reference fields with different intensities can be generated, the correction requirements of different magnetometers in various application scenes are met, and accurate correction independent of an extremely-high-precision current source is realized in combination with a scalar correction method.

Description

Technical Field

[0001] This invention relates to the field of magnetic field measurement technology, and in particular to a design method for a cylindrical coil with an adjustable coil constant. Background Technology

[0002] Triaxial magnetometers, as important instruments for magnetic field measurement, are widely used in geological exploration, aerospace magnetic detection, biomedical imaging, and basic scientific research. However, due to factors such as manufacturing, installation, and environmental interference, triaxial magnetometers inevitably exhibit errors such as non-orthogonality error, proportional coefficient error, zero-point offset, and soft / hard iron offset. These errors result in significant deviations between the measured magnetic field values ​​and the true values, further impacting practical applications. Therefore, it is necessary to calibrate the triaxial magnetometer according to the actual application scenario before use. Scalar calibration, a widely used magnetometer calibration method, uses the total magnetic field as a reference and does not require the magnetometer's attitude information. Therefore, whether using a stable geomagnetic field in the suburbs or generating a uniform magnetic field using a coil as a magnetic source, the key is to have a stable magnetic field as a standard magnetic field. Different types of magnetometers operate in different magnetic field environments, leading to varying calibration accuracy requirements. For example, SQUID magnetometers typically have a measurement range on the order of mT, while ultra-sensitive atomic magnetometers used for extremely weak magnetic field measurements require near-zero magnetic environments, achieving sensitivity on the order of fT. Meanwhile, some magnetometers with wide dynamic ranges, such as fluxgate magnetometers, can measure magnetic fields up to μT, but their error parameters vary with changes in the magnetic field environment. Therefore, to meet the calibration requirements of different types of triaxial magnetometers for various applications, it is necessary to design high-precision coil arrays as standard magnetic sources to simulate magnetic field environments of corresponding strengths. Summary of the Invention

[0003] To meet the calibration requirements of triaxial magnetometers with varying measurement accuracies under different operating conditions, this invention provides a cylindrical coil design method with adjustable coil constants. This method involves designing a set of cylindrical coils with adjustable coil constants (i.e., current-to-magnetic field conversion coefficients) based on a stable, weak magnetic environment in a magnetically shielded chamber. These coils generate extremely high-uniformity reference fields of varying intensities by superimposing or canceling the magnetic fields excited by coaxial coils. This satisfies the calibration requirements of different magnetometers in various application scenarios. Combined with scalar calibration methods, this achieves accurate calibration without relying on extremely high-precision current sources.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for designing a cylindrical coil with adjustable coil constant, comprising:

[0006] Set a base, install the triaxial coil in the base groove, and set a positioning post on the base plane to position the magnetometer in space in conjunction with the triaxial magnetometer tooling.

[0007] Setting the triaxial coil includes: setting a target region at the center of the cylinder, and determining the magnetic field generated at any point on the cylinder surface in the target region;

[0008] Using the non-uniformity of the magnetic field and the difference between the coil constant during the optimization process and the set coil constant as optimization objectives, the optimization objectives are calculated based on the coil parameter combination obtained by the multi-objective optimization algorithm to determine the optimal coil parameters.

[0009] The optimal coil parameters are input into the flow function model to obtain the coil flow function, and the actual coil winding is obtained based on the coil flow function.

[0010] Optionally, determining the magnetic field generated at any point on the cylindrical surface in the target region includes:

[0011] A flow function is introduced onto the cylindrical surface to determine the current density of the coil on the cylindrical surface;

[0012] A target region is set at the center of the cylinder. Based on the current density and the coordinates of a point in the target region, the magnetic field generated by the coil in the cylindrical coordinate system is obtained using Biot-Savart's law:

[0013]

[0014] in, The magnetic field generated by the coil The permeability of free space, Let be the integral range of the flow function of the cylindrical surface. Let G be the coordinates of a point on the cylindrical surface where the coil lies. The coordinates of the target area point, The current density on the cylindrical surface, This is the distance between a point on the cylindrical surface and the target point. z and z are the angular and axial coordinates of the cylindrical coordinate system, respectively;

[0015] Using the magnetic field generated by the coil, determine the magnetic field generated at any point on the cylindrical surface in the target region:

[0016]

[0017] in, The magnetic field generated at any point on the cylindrical surface in the target region. , Let be the maximum of the orders of the two Fourier series. For undetermined coefficients, This is the system matrix.

[0018] Optionally, the current density flow function of the coil on the cylindrical surface includes: a current density flow function for generating a magnetic field coil in the Y direction, a current density flow function for generating a magnetic field coil in the X direction, and a current density flow function for generating a magnetic field coil in the Z direction.

[0019] The current density flow function that generates the Y-direction magnetic field coil includes:

[0020]

[0021] in, , They are respectively direction and angle Two current density flow function components in the direction, For undetermined coefficients, , These are the orders of the two Fourier series, with the maximum value being... and , The half-height of the cylindrical surface. R is the radius of the cylindrical surface.

[0022] Optionally, the system matrix include:

[0023]

[0024] in, , For the target area , coordinate, and It forms the trigonometric function basis of Fourier series.

[0025] Optionally, calculating the optimization objective based on the coil parameter combination obtained from the multi-objective optimization algorithm includes:

[0026] Step 1: Take the magnetic field non-uniformity and the difference between the coil constant during the optimization process and the set coil constant as the optimization target, and take the radius of the cylinder where the coil is located, the half height of the radius of the cylinder where the coil is located, and the number of discrete contour lines as the parameters to be optimized, and initialize the parameters and minimum tolerance of the NSGA-II algorithm.

[0027] Step 2: Stratify the initial population solutions according to Pareto dominance and calculate the crowding degree of solutions in the same layer. Iterate according to non-dominated sorting and crowding degree to retain the optimal solution. Select the solutions with low level and high crowding degree as the parent generation. Then form the offspring population through crossover and mutation, and merge the offspring and parent generations.

[0028] Step 3: Repeat step 2 until the maximum number of iterations or the minimum tolerance is met, and obtain the Pareto solution set.

[0029] Optionally, the dominance conditions for hierarchical Pareto dominance include:

[0030]

[0031] in, , To solve for the values ​​of x and y on the i-th objective.

[0032] Optionally, calculating the crowding degree of the solutions at the same level includes:

[0033]

[0034] in, The crowding degree of the solutions at the same level. Let m be the objective function value of the next solution immediately following the current solution i after sorting. Let m be the objective function value of the solution immediately preceding the current solution i after sorting. Let m be the maximum value of the entire population on the target m. Let M be the minimum value of the entire population on objective m, and M be the total number of objective functions.

[0035] Optionally, obtaining the actual coil winding includes:

[0036] In the Pareto solution set, the combination of coil parameters A and B that meets the requirements of coil constant and non-uniformity is selected as the optimal coil parameters. The optimal coil parameters are then input into the flow function model to obtain the coil flow function.

[0037] Discretize the coil current function to obtain the actual coil winding.

[0038] Optionally, discretizing the coil current function includes:

[0039]

[0040] in, These are the contour lines discretized on the cylindrical surface. The minimum value of the flow function on the surface. The maximum value of the flow function on the surface. This represents the number of discrete contour lines.

[0041] Optionally, the method further includes:

[0042] The actual coil winding is calculated using Biot-Savart's law to obtain the coil constant of a single coil group. Coils on the same axis are connected in parallel in the same circuit, and the resistance in the series circuit of the coils is adjusted to change the ratio of the currents flowing through the two coils, thus obtaining the final coil constant and determining its range.

[0043]

[0044] in, , coaxial , The coil constant, It is the ratio of the current flowing through the two coils.

[0045] The beneficial effects of this invention are as follows:

[0046] For different magnetic field measurement ranges of different types of triaxial magnetometers, the adjustable coil constant of this invention can generate highly uniform magnetic fields of different intensities that meet calibration requirements under the same current conditions. These magnetic fields can be used as reference magnetic fields for triaxial magnetometer calibration, and the same coil can meet the calibration requirements of different types of magnetometers. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart illustrating a method for designing a cylindrical coil with adjustable coil constant according to an embodiment of the present invention.

[0049] Figure 2 This is a schematic diagram of stream function discretization according to an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the x-axis coil according to an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of the y-axis coil according to an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of the z-axis coil according to an embodiment of the present invention;

[0053] Figure 6 This is an assembly diagram of an embodiment of the present invention; wherein, 1-base, 2-x-axis A coil, 3-x-axis B coil, 4-y-axis A coil, 5-y-axis B coil, 6-z-axis A coil, 7-z-axis B coil;

[0054] Figure 7 This is a schematic diagram of the base according to an embodiment of the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] like Figure 1 As shown, this embodiment discloses a design method for a cylindrical coil with adjustable coil constant, including: setting a triaxial coil: setting a target region at the center of the cylinder, and determining that any point on the cylindrical surface generates a magnetic field in the target region; using the magnetic field non-uniformity and the difference between the coil constant during the optimization process and the set coil constant as optimization targets, calculating the optimization targets based on the coil parameter combination obtained by the multi-objective optimization algorithm, determining the coil parameters to be optimized, and obtaining the actual coil winding based on the coil parameters; setting a base, installing the triaxial coil in the base groove, and setting a positioning post on the base plane, and using a triaxial magnetometer fixture to position the magnetometer in space.

[0058] Furthermore, determining the magnetic field generated at any point on the cylindrical surface in the target region includes: introducing a stream function on the cylindrical surface to determine the current density of the coil on the cylindrical surface; setting the target region at the center of the cylinder, and obtaining the magnetic field calculation matrix of the coil based on the current density and the coordinates of the point in the target region; and using the magnetic field calculation matrix to determine the magnetic field generated at any point on the cylindrical surface in the target region.

[0059] Due to the relatively limited space in the magnetic shielding room, to save space, reduce geometric errors caused by assembly, and for application in some cylindrical magnetic shielding devices, the coil configuration is designed as a single-turn coil on a cylindrical surface. The adjustable coil constant is achieved through the superposition and cancellation of the magnetic fields generated by the coil group. The coil group uses a pair of sub-coils, referred to as coil A and coil B, both of which can generate a highly uniform magnetic field within the same target area. Since their coil constants are similar, when using the same type of current source, applying opposite currents to the two coils causes their opposing magnetic fields to cancel each other out, achieving a very weak uniform magnetic field. Conversely, to simulate the geomagnetic environment or higher-intensity magnetic fields, currents in the same direction are applied, and the magnetic fields generated by the two coils are superimposed to meet calibration requirements under higher magnetic field strength conditions. By designing three sets of six coils in orthogonal directions on the same axis, a magnetic field in any direction can be obtained.

[0060] like Figure 2 As shown, the design methods for the three axial coils are similar. This invention takes the design process of a coil generating the Y-direction magnetic field (By) as an example. The current density on the cylindrical surface satisfies the two-dimensional current continuity equation. A stream function is introduced on the cylindrical surface. In cylindrical coordinates, the following conditions are met:

[0061]

[0062] in, For angle Current density current function components in the direction, Let z be the current density flow function component in the z-direction. This is the coil current function.

[0063] Using a two-dimensional Fourier series to represent the current density, and taking advantage of the symmetry of the coil, the current density of the coil on the cylindrical surface can be expressed as:

[0064]

[0065] in , These are the z-direction and angle, respectively. Two current density flow function components in the direction, Let be the coefficients to be determined, m and n be the orders of the two Fourier series, with maximum values ​​of M and N, H be the half-height of the cylinder, and R be the radius of the cylinder.

[0066] A target region was set at the center of the cylinder, and the coordinates of a point within the target region were... The coordinates of the point on the cylindrical surface where the coil is located are... Therefore, according to Biot-Savart's law, the magnetic field generated by the coil can be obtained as follows:

[0067]

[0068] in Let be the free permeability, and S be the integral range of the flow function of the cylindrical surface. Based on the expression for the magnetic field generated by a current element in space, the magnetic field generated at any point on the cylindrical surface in the target region can be derived:

[0069]

[0070] in:

[0071]

[0072]

[0073] Further, the optimization objectives are calculated as follows: Step 1, using the magnetic field non-uniformity and the difference between the optimized coil constant and the set coil constant as two optimization objectives, and using the cylinder half-height H, radius R, and number of discrete isosurfaces K as the parameters to be optimized, and initializing the parameters and minimum tolerance of the NSGA-II algorithm; Step 2, stratifying the initialized population solutions according to the Pareto dominance relationship, calculating the crowding degree of solutions in the same layer, iterating according to the non-dominated sorting and crowding degree to retain the optimal solution, selecting the low-level and high-crowding solutions as the parent generation, and then forming the offspring population through crossover and mutation, merging the offspring and parent generations; Step 3, repeating Step 2 until the maximum number of iterations or the minimum tolerance is met to obtain the Pareto solution set.

[0074] Specifically, this is a multi-objective optimization problem. Since the triaxial coil group has six coils, there are physical constraints on the parameters of each coil due to application and manufacturing considerations. Therefore, the optimization object needs to select coil parameters that conform to reality from a Pareto solution set. We use the NSGA-II algorithm, with the magnetic field non-uniformity E... m and the optimized coil constant With setting the coil constant The difference between them serves as two optimization objectives. NSGA-II calculates the convergence and diversity of multi-objective optimization by balancing non-dominated sorting and crowding. First, the population solutions are hierarchically divided according to Pareto dominance, where solution x dominates solution y under the following condition:

[0075] For all optimization objectives, the solution x is no weaker than y, and for at least one objective, x is strictly better than y:

[0076]

[0077] in, To find the value of x at the i-th objective, the crowding degree of solutions at the same level is then calculated using the following formula:

[0078]

[0079] Where M represents the number of optimization objectives, after calculation, solutions with low levels and high crowding are preferentially selected as parents. Then, through crossover and mutation, a offspring population is formed. Parent and offspring are merged, and the process iterates again according to non-dominated sorting and crowding retention to obtain the Pareto solution set. We can obtain a set of solutions that perform well on both objectives. From this set, we can select Pareto coil parameter combinations that meet application requirements and satisfy practical physical constraints, achieving extremely high uniformity while satisfying coil constant requirements. The coil design methods for the other two axes are basically the same as described above.

[0080] Furthermore, the optimal coil parameters are selected from the Pareto solution set, which meet the requirements of coil constant and non-uniformity. The optimal coil parameters are then input into the flow function model to obtain the coil flow function. The coil flow function is then discretized to obtain the actual coil winding.

[0081] Specifically, at the initial design stage, the order M, N, and the coordinates of the target area are pre-set, allowing for direct... The calculations were then performed, and the coil was set to generate a magnetic field. They are all equal to the same constant value. The problem is transformed into an overdetermined equation, and the solution obtained is the coefficients to be determined. To avoid the singular matrix problem, Tikhonov regularization is used, and a penalty function is introduced. The error function is expressed as:

[0082]

[0083] in, These are the weighting coefficients. Let be the Tikhonov matrix, which is chosen here as the identity matrix. The optimal value can be obtained by minimizing the error function. .

[0084] Finally, after completing this series of calculations, the actual coil winding is obtained by discretizing the stream function using K isosurfaces:

[0085]

[0086] In this design, the two most important performance indicators of the coil are the maximum magnetic field non-uniformity E. m And the coil constant k, which serves as the magnetic field resolution of the coil-power supply system. c (nT / A), its calculation formula is as follows:

[0087]

[0088] in, I is the magnetic field generated by the coil at the center point of the target region, and I is the current flowing through the coil. The key parameters that significantly affect these two performance characteristics in coil design are the half-height H of the cylinder, the radius R, and the number of discrete isosurfaces K.

[0089] Furthermore, determining the range of coil constants includes: calculating the actual coil windings using Biot-Savart's law, obtaining the coil constant of a single coil, connecting coils of the same axis in parallel in the same circuit, and adjusting the resistance in the coil branch to change the ratio of the current flowing through the two coils to obtain the final coil constant, and determining the range of coil constants.

[0090] Specifically, the coil constant (nT / A), serving as the magnetic field control accuracy of the coil-power supply system and as the reference magnetic source for calibration, should match the measurement accuracy of the triaxial vector magnetometer. In this design, the variability of the coil constant is achieved by adjusting the overall coil constant of the combination of coils A and B. The coil constant of the combined coil is defined as the ratio of the magnetic field jointly generated by coils A and B to the current in coil A, where the coil with the smaller coil constant is considered coil A. Coils A and B, operating in the same axis, are connected in parallel in a circuit, powered by a single current source. The resistance value connected in series in the A and B coil branches is adjusted to change the ratio of the currents flowing through the two coils. The final expression for the coil constant is:

[0091]

[0092] in, , The coil constants, k, of the coaxial coils A and B are respectively. I This represents the ratio of the currents flowing through the two coils. Therefore, the theoretical range for the coil constant is... .

[0093] like Figure 3-7 A mounting base was designed for the three-axis six-coil system, which can install the three-axis coils in the slot. A positioning post was designed on the plane of the base. With the help of the three-axis magnetometer tooling, the magnetometer can be positioned in space. The positioning device includes: base 1, x-axis A coil 2, x-axis B coil 3, y-axis A coil 4, y-axis B coil 5, z-axis A coil 6, and z-axis B coil 7.

[0094] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for designing a cylindrical coil with adjustable coil constant, characterized in that, include: Set a base, install the triaxial coil in the base groove, and set a positioning post on the base plane to position the magnetometer in space in conjunction with the triaxial magnetometer tooling. Setting the triaxial coil includes: setting a target region at the center of the cylinder, and determining the magnetic field generated at any point on the cylinder surface in the target region; Using the non-uniformity of the magnetic field and the difference between the coil constant during the optimization process and the set coil constant as optimization objectives, the optimization objectives are calculated based on the coil parameter combination obtained by the multi-objective optimization algorithm to determine the optimal coil parameters. The optimal coil parameters are input into the flow function model to obtain the coil flow function, and the actual coil winding is obtained based on the coil flow function.

2. The method for designing a cylindrical coil with adjustable coil constant according to claim 1, characterized in that, Determining the magnetic field generated at any point on the cylindrical surface in the target region includes: A flow function is introduced onto the cylindrical surface to determine the current density of the coil on the cylindrical surface; A target region is set at the center of the cylinder. Based on the current density and the coordinates of a point in the target region, the magnetic field generated by the coil in the cylindrical coordinate system is obtained using Biot-Savart's law. in, The magnetic field generated by the coil The permeability of free space, Let be the integral range of the flow function of the cylindrical surface. Let G be the coordinates of a point on the cylindrical surface where the coil lies. The coordinates of the target area point, The current density on the cylindrical surface, This is the distance between a point on the cylindrical surface and the target point. z and z are the angular and axial coordinates of the cylindrical coordinate system, respectively; Using the magnetic field generated by the coil, determine the magnetic field generated at any point on the cylindrical surface in the target region: in, The magnetic field generated at any point on the cylindrical surface in the target region. , Let be the maximum of the orders of the two Fourier series. For undetermined coefficients, This is the system matrix.

3. The method for designing a cylindrical coil with adjustable coil constant according to claim 2, characterized in that, The current density flow function of the coil on the cylindrical surface includes: the current density flow function of the coil that generates the magnetic field in the Y direction, the current density of the coil that generates the magnetic field in the X direction, and the current density flow function of the coil that generates the magnetic field in the Z direction. The current density flow function that generates the Y-direction magnetic field coil includes: in, , They are respectively direction and angle Two current density flow function components in the direction, For undetermined coefficients, , These are the orders of the two Fourier series, with the maximum value being... and , The half-height of the cylindrical surface. R is the radius of the cylindrical surface.

4. The method for designing a cylindrical coil with adjustable coil constant according to claim 3, characterized in that, The system matrix include: in, , For the target area , coordinate, and It forms the trigonometric function basis of Fourier series.

5. The method for designing a cylindrical coil with adjustable coil constant according to claim 1, characterized in that, The optimization objective is calculated based on the coil parameter combination obtained from the multi-objective optimization algorithm, including: Step 1: Take the magnetic field non-uniformity and the difference between the coil constant during the optimization process and the set coil constant as the optimization target, and take the radius of the cylinder where the coil is located, the half height of the radius of the cylinder where the coil is located, and the number of discrete contour lines as the parameters to be optimized, and initialize the parameters and minimum tolerance of the NSGA-II algorithm. Step 2: Stratify the initial population solutions according to Pareto dominance and calculate the crowding degree of solutions in the same layer. Iterate according to non-dominated sorting and crowding degree to retain the optimal solution. Select the solutions with low level and high crowding degree as the parent generation. Then form the offspring population through crossover and mutation, and merge the offspring and parent generations. Step 3: Repeat step 2 until the maximum number of iterations or the minimum tolerance is met, and obtain the Pareto solution set.

6. The method for designing a cylindrical coil with adjustable coil constant according to claim 5, characterized in that, The dominance conditions for hierarchical Pareto dominance include: in, , To solve for the values ​​of x and y on the i-th objective.

7. The method for designing a cylindrical coil with adjustable coil constant according to claim 5, characterized in that, Calculating the crowding degree of the solutions at the same level includes: in, The crowding degree of the solutions at the same level. Let m be the objective function value of the next solution immediately following the current solution i after sorting. Let m be the objective function value of the solution immediately preceding the current solution i after sorting. Let m be the maximum value of the entire population on the target m. Let M be the minimum value of the entire population on objective m, and M be the total number of objective functions.

8. The method for designing a cylindrical coil with adjustable coil constant according to claim 5, characterized in that, Obtaining the actual coil winding includes: In the Pareto solution set, the combination of coil parameters A and B that meets the requirements of coil constant and non-uniformity is selected as the optimal coil parameters. The optimal coil parameters are then input into the flow function model to obtain the coil flow function. Discretize the coil current function to obtain the actual coil winding.

9. The method for designing a cylindrical coil with adjustable coil constant according to claim 8, characterized in that, Discretizing the coil current function includes: in, These are the contour lines discretized on the cylindrical surface. The minimum value of the flow function on the surface. The maximum value of the flow function on the surface. This represents the number of discrete contour lines.

10. The method for designing a cylindrical coil with adjustable coil constant according to claim 8, characterized in that, The method also includes: The actual coil winding is calculated using Biot-Savart's law to obtain the coil constant of a single coil group. Coils on the same axis are connected in parallel in the same circuit, and the resistance in the series circuit of the coils is adjusted to change the ratio of the currents flowing through the two coils, thus obtaining the final coil constant and determining its range. in, , coaxial , The coil constant, It is the ratio of the current flowing through the two coils.

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