A method and apparatus for calculating the AC magnetic field of a product at a distance

Abstract

This application provides a method and apparatus for calculating the AC magnetic field of a product at a distance. The method includes: constructing an imaginary sphere with the product center as the center; arranging k triaxial magnetometer probes on the sphere surface and sequentially recording the position coordinates of the triaxial magnetometer probes; collecting magnetic flux density data measured by the triaxial magnetometer probes; substituting the position data and magnetic flux density data of the triaxial magnetometer probes into the magnetic field equation to establish a well-determined or overdetermined equation and solving the coefficients of the magnetic field equation to obtain the magnetic field distribution function of the magnetic flux density at different positions r at time t1; obtaining the function of the magnetic field equation coefficients changing with time; substituting the function of the magnetic field equation coefficients changing with time into the magnetic field distribution function to obtain the distribution function of the AC magnetic field in space; and substituting the coordinates of any position in the far field into the distribution function to obtain the waveform of the magnetic flux density generated by the product at the measured position changing with time.

Description

Technical Field

[0001] This application relates to the field of magnetic field measurement technology, and more specifically, to a method and apparatus for calculating the AC magnetic field of a product at a distance. Background Technology

[0002] When designing spacecraft, the impact of the spacecraft's own magnetic field on the spacecraft's performance needs to be considered. Therefore, it is necessary to accurately measure the magnetic field data around the spacecraft so as to avoid magnetic field risks at the beginning of the spacecraft manufacturing process.

[0003] Currently, spacecraft and single-unit testing mainly focuses on DC magnetic field information. However, with the increasing demand for space magnetic field detection, the target magnetic field information has been expanded from DC magnetic field information to AC magnetic field in the range of 0-20kHz. At present, the magnetic field measurement methods cannot be applied to AC magnetic field. Summary of the Invention

[0004] The purpose of this application is to provide a method and apparatus for calculating the AC magnetic field of a product at a distance, which can solve at least one of the technical problems mentioned above. The specific solution is as follows:

[0005] According to a specific embodiment of this application, this application provides a method for calculating the distant alternating magnetic field of a product, including:

[0006] Step S1: Construct an imaginary sphere with the product center as the center, arrange k triaxial magnetometer probes on the surface of the sphere, and record the position coordinates r1(x1,y1,z1) of the triaxial magnetometer probes to r1(x1,y1,z1) in sequence. k (x k ,y k ,z k );

[0007] Step S2: At time t1, collect the magnetic induction intensity data B(r1) to B(r) measured by the triaxial magnetometer probe. k ), where the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data;

[0008] Step S3: Substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field equation to establish a well-determined or overdetermined equation and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1.

[0009]

[0010] Step S4: Select different times t2, t3, ... t within a period. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t);

[0011] Step S5: Calculate the intrinsic function α, which varies with time, of the coefficients of the magnetic field equation. lm (t) and external function β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field.

[0012]

[0013] Step S6: Substitute the coordinates of any position in the far field into the distribution function B(r,t) in step S5 to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time.

[0014] In some embodiments, in step S3, the position data and magnetic induction intensity data of the triaxial magnetometer probe are substituted into the magnetic field equation to establish a well-determined or overdetermined equation and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm ,include:

[0015] Step S31: Let the center coordinates of the magnetic source of the product be (x0, y0, z0), and then correlate them sequentially with the position coordinates r1(x1, y1, z1) of the triaxial magnetometer probe to r k (x k ,y k ,z k Subtracting the two values, the polar angle θ corresponding to the magnetic source center for each of the triaxial magnetometer probe positions is calculated using the following formula. n With azimuth

[0016]

[0017] Where n represents any value from 1 to k;

[0018] Step S32: Adjust the polar angle θ as described above. n With azimuth Substituting the spherical harmonics into the corresponding spherical harmonics yields their respective spherical harmonic functions v. lm (θ, φ) and ω lm (θ, φ);

[0019] Step S33: Select different expansion orders l and m, expand the magnetic field distribution function B(r), establish well-determined or overdetermined equations, and solve for the intrinsic coefficient α of the magnetic field equations.lm and exogenous coefficient β lm .

[0020] In some embodiments, in step S32, the spherical harmonic function v lm (θ,φ) and ω lm (θ,φ) satisfy the following relationship:

[0021]

[0022] In some embodiments, step S33 involves selecting different expansion orders l and m to expand the magnetic field distribution function B(r), including:

[0023] According to the endogenous coefficient α lm The highest is the quadrupole field, with an external coefficient β. lm To expand for a uniform magnetic field, i.e., the coefficient α lm Take l in =2, coefficient β lm Take l out =1, where l starts from l=1, and m is expanded as follows: m=-l, ...,+l.

[0024] In some embodiments, in step S3, establishing the overdetermined equation includes: the number of magnetic induction intensity data 3k is greater than the number of unknowns q, where q = (l in +2)l in +(l out +2)l out +3.

[0025] In some embodiments, in step S4, different times t2, t3, ... t within a period are selected. p By repeating steps S2-S3, the function α representing the change of the coefficients of the magnetic field equation with time can be obtained. lm (t) and β lm (t), including:

[0026] Select different times t2, t3, ... t within a period p Repeating steps S2-S3 yields the expansion coefficients α', α”...... and β', β”...... at different times; the intrinsic coefficients α of each expansion order are obtained through fitting. lm and exogenous coefficient β lm Time-varying intrinsic function α lm (t) and external function β lm (t).

[0027] In some embodiments, in step S1, k is greater than or equal to 3.

[0028] In some embodiments, the magnetic field equations are also pre-constructed.

[0029] In some embodiments, the pre-constructed magnetic field equation includes:

[0030] If the test specimen is placed inside an imaginary sphere, and the magnetic field source is located outside the imaginary sphere, then the magnetic field B at any point inside the imaginary sphere can be expressed as:

[0031]

[0032] Where μ0 is the free permeability, and V satisfies the Laplace equation:

[0033]

[0034] The magnetic field at any point r inside the imaginary sphere can be expressed as:

[0035]

[0036] This application also proposes a device for calculating the AC magnetic field of a product at a distance, comprising:

[0037] The configuration unit is used to construct an imaginary sphere with the product center as the center, and to uniformly arrange k triaxial magnetometer probes on the circumferential surface of the tangent plane passing through the center of the sphere, and to sequentially record the position coordinates r1(x1,y1,z1) to r k (x k ,y k ,z k );

[0038] The acquisition unit is used to acquire magnetic flux density data B(r1) to B(r) measured by the triaxial magnetometer probe at time t1. k ), where the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data;

[0039] The calculation unit is used to substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field equation, establish a well-determined or overdetermined equation, and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1.

[0040]

[0041] The fitting unit is used to select different times t2, t3, ... t within a period. pRepeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t);

[0042] The building block is used to construct the intrinsic function α, which varies with time in the coefficients of the magnetic field equation. lm (t) and external function β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field.

[0043]

[0044] The calculation unit is used to substitute the coordinates of any position in the far field into the distribution function B(r,t) in step S5 to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time.

[0045] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects:

[0046] The purpose of this invention is to provide a high-precision measurement method for alternating magnetic fields that can be scaled by distance. This method focuses magnetic source information onto an imaginary sphere, arranges magnetometers around the sphere for measurement, separates the magnetic field information inside and outside the sphere (i.e., separates the magnetic source information from interfering magnetic field information), and then reconstructs the magnetic source information through a multi-stage unfolding of the sphere, thereby calculating the alternating magnetic induction intensity at the extrapolated position.

[0047] This invention utilizes magnetic field distance scaling to measure near-field magnetic field inversion of magnetic source information, and then forward modeling to obtain the target distance magnetic induction intensity. This effectively measures long-distance AC magnetic induction intensity, avoiding the problem of insufficient magnetic induction intensity generated by the product at a distance, which is lower than the ambient magnetic field, thus preventing the acquisition of the true generated magnetic induction intensity. Furthermore, this invention employs spatial signal separation technology to separate internal and external AC magnetic field information, reducing environmental magnetic field interference. Attached Figure Description

[0048] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0049] Figure 1 A flowchart illustrating the method for calculating the AC magnetic field of a product at a distance in this embodiment is shown.

[0050] Figure 2This embodiment shows a schematic diagram of the structure for calculating the AC magnetic field of the product at a distance.

[0051] Figure 3 A schematic diagram of the signal spatial separation method of the AC magnetic field model in this embodiment is shown.

[0052] Figure 4 A schematic diagram of the process for calculating the remote AC magnetic field device of the product in this embodiment is shown.

[0053] Figure 5 This embodiment shows a schematic diagram of the placement of the AC magnetic field magnetometer for calculating the AC magnetic field of the product at a distance. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0055] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the application. The singular forms “a,” “said,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms, and “multiple” generally includes at least two unless the context clearly indicates otherwise.

[0056] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0057] It should be understood that although the terms "second," "third," etc., may be used to describe structures in the embodiments of this application, these structures should not be limited to these terms. These terms are only used to distinguish different structures. For example, without departing from the scope of the embodiments of this application, a second component may also be referred to as a second component, and similarly, a second component may also be referred to as a second component.

[0058] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device that includes said element.

[0059] Currently, the testing of spacecraft and individual units in my country mainly focuses on DC magnetic field information. Because the magnetic induction intensity generated at the remote location of the product is relatively small, its magnitude is close to that of the environmental interference magnetic field. Therefore, measurements are subject to strong interference, resulting in significant errors. It is necessary to measure the magnetic induction intensity closer to the product, which is on a higher order than the environmental interference magnetic field, to reduce the influence of the environmental magnetic field. This allows for the calculation of the product's magnetic moment information and the calculation of the remote magnetic induction intensity.

[0060] For DC magnetic fields, the magnetic moment of the magnetic source can be deduced by measuring the magnetic flux density at a sufficient number of locations in the near field of the magnetic source; this is known as magnetic field inversion. Then, using the magnetic moment information, the magnetic flux density at the desired location in space can be calculated; this is known as magnetic field forward modeling. However, alternating current magnetic fields change over time, and the magnetic moment is a fixed quantity that cannot describe the change of the magnetic field over time. Therefore, the method of measuring the magnetic field to deduce the magnetic moment is not suitable for measuring alternating current magnetic fields.

[0061] For DC magnetic fields, a magnetic field mapping method can be used. In this method, the spacecraft is placed in the Earth's magnetic field or rotated on a non-magnetic turntable at the center of a zero-magnetic-coil system. Several magnetometer sensors are placed at a certain distance from the spacecraft to measure the magnetic field in the space surrounding the spacecraft. The distributed magnetic field, which is a function of the rotation angle, is mathematically inverted to obtain its magnetic moment. However, this rotational measurement method is only suitable for measuring relatively stable DC magnetic fields. For AC magnetic fields, the magnetic induction intensity changes over time, and the magnetic field changes during rotation, making it impossible to obtain accurate results for AC magnetic fields.

[0062] Based on this, this application provides a high-precision measurement method for alternating magnetic fields that can be scaled by distance. This method focuses magnetic source information onto an imaginary sphere, arranges magnetometers around the sphere to measure the magnetic field, separates the magnetic source information from the interfering magnetic field information inside and outside the sphere, and then reconstructs the magnetic source information through a multi-stage unfolding of the sphere, thereby calculating the magnetic induction intensity at the extrapolated position.

[0063] The optional embodiments of this application are described in detail below with reference to the accompanying drawings.

[0064] According to the specific implementation of this application, such as Figure 1As shown, this application provides a method for calculating the AC magnetic field of a product at a distance, comprising:

[0065] Step S1: Construct an imaginary sphere with the product center as the center, arrange k triaxial magnetometer probes on the surface of the sphere, and record the position coordinates r1(x1,y1,z1) of the triaxial magnetometer probes to r1(x1,y1,z1) in sequence. k (x k ,y k ,z k );

[0066] Step S2: At time t1, collect the magnetic induction intensity data B(r1) to B(r) measured by the triaxial magnetometer probe. k ), where the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data;

[0067] Step S3: Substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field equation to establish a well-determined or overdetermined equation and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1.

[0068]

[0069] Where l and m are the order of the function expansion, v lm (θ,φ) and ω lm (θ, φ) are spherical harmonic functions, and μ0 is the free permeability;

[0070] Step S4: Select different times t2, t3, ... t within a period. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t);

[0071] Step S5: Calculate the intrinsic function α, which varies with time, of the coefficients of the magnetic field equation. lm (t) and external function β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field.

[0072]

[0073] Step S6: Substitute the coordinates of any position in the far field into the distribution function B(r,t) in step S5 to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time.

[0074] This application utilizes magnetic field distance scaling to measure near-field magnetic field inversion of magnetic source information, and then forward modeling to obtain the target distance magnetic induction intensity. This effectively measures long-distance magnetic induction intensity, avoiding the problem of insufficient magnetic induction intensity generated by the product at long distances, which is lower than the ambient magnetic field, thus preventing the acquisition of the true generated magnetic induction intensity. Furthermore, this application employs spatial signal separation technology to separate internal and external magnetic field information, reducing environmental magnetic field interference.

[0075] like Figure 2 As shown, in step S1, the product to be tested is placed on the stage, and the center of the stage plane is recorded as the origin. An imaginary sphere is constructed with the product as the center. k triaxial magnetometer probes are arranged on the surface of the sphere (the number is changed according to the actual measurement needs), and the probe position coordinates r1(x1,y1,z1) to r are recorded sequentially. k (x k ,y k ,z k Optionally, to improve measurement accuracy, the k triaxial magnetometer probes are evenly distributed on the sphere; alternatively, to improve measurement accuracy, the k triaxial magnetometer probes are evenly distributed on the same circumference along the sphere.

[0076] In some embodiments, in step S3, the position data and magnetic induction intensity data of the triaxial magnetometer probe are substituted into the magnetic field equation to establish a well-determined or overdetermined equation and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm ,include:

[0077] Step S31: Let the center coordinates of the magnetic source of the product be (x0, y0, z0), and then correlate them sequentially with the position coordinates r1(x1, y1, z1) of the triaxial magnetometer probe to r k (x k ,y k ,z k Subtracting the two values, the position r of each triaxial magnetometer probe is calculated according to formulas (4), (5), and (6). n The polar angle θ corresponding to the center of the magnetic source n With azimuth

[0078]

[0079] Where n represents any value from 1 to k;

[0080] Step S32: Adjust the polar angle θ as described above. nWith azimuth Substituting the spherical harmonics into the corresponding spherical harmonics yields their respective spherical harmonic functions v. lm (θ, φ) and ω lm (θ, φ);

[0081] Step S33: Select different expansion orders l and m, expand the magnetic field distribution function B(r), establish well-determined or overdetermined equations, and solve for the intrinsic coefficient α of the magnetic field equations. lm and exogenous coefficient β lm .

[0082] In some embodiments, in step S32, the spherical harmonic function v lm (θ, φ) and ω lm (θ, φ) satisfy the following relationship:

[0083]

[0084] Among them, Y lm Let i be a normalized spherical harmonic function, where i is the imaginary unit.

[0085] In some embodiments, step S33 involves selecting different expansion orders l and m to expand the magnetic field distribution function B(r), including:

[0086] According to the endogenous coefficient α lm The highest is the quadrupole field, with an external coefficient β. lm To expand for a uniform magnetic field, i.e., the intrinsic coefficient α lm Take l in =2, external coefficient β lm Take l out =1, where l starts from l=1, and m is expanded as follows: m=-l, ...,+l.

[0087] Based on the test product, environmental conditions, measurement conditions, and required accuracy, determine the expansion order. That is, the expansion order *l* in the formula does not need to be expanded to an infinite order; it only needs to be expanded to the required finite order. Here, the intrinsic expansion coefficient is taken as *l*. in =2, external expansion coefficient is l out Taking 1 as an example, the highest internal field is a quadrupole field, and the surrounding field is a uniform magnetic field.

[0088] Substituting the above data into the formula and expanding, we obtain the following expansion:

[0089]

[0090]

[0091] In the above, for different expansion orders l, m has a corresponding α. lm ,βlm and the corresponding spherical harmonic functions and In intrinsic order l in =2, exogenous order l out Under the condition that α = 1, there are a total of 8 α values. lm With 3 β lm Unknown, along with polar angle and azimuth angle θ. The coordinates (x, y, z) of the magnetic source center are determined, where x, y, and z are unknowns. In this case, the equation has a total of 8 + 3 + 3 = 14 unknowns (if the order changes, the number of unknowns becomes q = (l...). in +2)l in +(l out +2)l out Collect a total of k×3=3k magnetic induction intensity data, establish a well-determined or overdetermined equation (the number of measurement points 3k needs to be greater than or equal to the number of unknowns q, the more measurement points, the higher the accuracy of the result) and solve it, and finally obtain the distribution function B(r) of magnetic induction intensity at different locations r at time t1.

[0092] In some embodiments, in step S4, different times t2, t3, ... t within a period are selected. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t), including:

[0093] Select different times t2, t3, ... t within a period p Repeating steps S2-S3 yields the expansion coefficients α', α”...... and β', β”...... at different times; the expansion coefficients α for each order are obtained through fitting. lm and β lm Time-varying intrinsic function α lm (t) and external function β lm (t).

[0094] In some embodiments, in step S1, k is greater than or equal to 3.

[0095] In some embodiments, the magnetic field equations are also pre-constructed. For example... Figure 3 As shown, the pre-constructed magnetic field equation includes: placing the test piece inside an imaginary sphere, with the magnetic field source located outside the imaginary sphere, then the magnetic field B at any point inside the imaginary sphere can be expressed as:

[0096]

[0097] Where μ0 is the free permeability, and V satisfies the Laplace equation:

[0098]

[0099] For multi-point measurement systems, the solution to the Laplace equation can be extended to a spherical harmonic function. In this case, the magnetic field at any point r inside the imaginary sphere can be expressed as:

[0100]

[0101] α lm and β lm These are the expansion coefficients describing the "internal" and "external" sources of the sphere, denoted as the internal source coefficient α. lm and exogenous coefficient β lm ,θ, These are the polar angle and azimuth angle of the test point, respectively. The polar angle represents the angle between the line connecting the origin to the point and the Z-axis, while the azimuth angle represents the angle between the projection of the line connecting the origin to the point onto the XY plane and the positive X-axis. and These are all standardized spherical harmonic functions. Their expressions are as follows:

[0102]

[0103] Since magnetic monopoles do not exist, in this embodiment, the expansion order for both internal and external sources starts from l = 1. For each l-th order, the expansion degree starts from m = -l, ..., +l, at which point the total number of coefficients for the l-th order is 2l + 1 (internal and external).

[0104] In the formula, the polar angle and azimuth angle θ of the test point, It depends on the coordinates of the magnetic source point and the magnetometer. The magnetometer coordinates should be set accurately before measurement, while the magnetic source point coordinates should be set as unknowns and obtained by solving the above equations in order to accurately establish the magnetic field model.

[0105] In the formula, due to the endogenous coefficient α lm l in The field generated by the term = 1 represents the dipole field, and decreases to 1 / r with distance. 3 The quadrupole field (l=2) decreases to 1 / r 4 External coefficient β lm Chinese out =1 represents a uniform external magnetic field, and increasing l represents a higher-order field gradient, and so on. As can be seen from the formula, this expression naturally incorporates distance scaling. Once the coefficients are determined to a sufficiently high order, the magnetic field induced by the magnetic source inside the sphere can be predicted anywhere in space.

[0106] The above process establishes a spatial model of the magnetic field. The following section will add a time dimension to the AC magnetic field spatial model. For the AC magnetic field being measured, its frequency range is 0-20kHz. Even at a frequency as high as 20kHz, the wavelength of the magnetic field is λ=c / f≈1.5×10⁻⁶. 4 m is several orders of magnitude larger than the distance we need to scale (usually less than 10 m). Therefore, the finite propagation effect can be ignored, and any change in the time field can be instantaneously covered over the entire scaling distance. This allows us to sequentially separate the time and space dependencies of the alternating magnetic field, and to introduce the time-dependent magnetic field into the expansion coefficients of the magnetic field formula. At this point, the alternating magnetic field at any point r in space can be expressed as:

[0107]

[0108] That is, under alternating magnetic fields, the multipole coefficient itself α lm and β lm It becomes a function that changes over time.

[0109] As can be seen from the formula for alternating magnetic fields, if measurements are taken at every point on the surface of a sphere and an infinite number of coefficients are considered, the above theoretical method can be integrated over the entire sphere. The basis functions of the internal and external expansions are mutually orthogonal, and all coefficients can be uniquely determined. This means that the accuracy of the magnetic field model can gradually improve with the increase of the expansion order. In practical engineering applications, the number of measurement points can be appropriately adjusted and reduced according to specific needs and cost requirements, but it is necessary to ensure that the number of independently measured magnetic field B is equal to or greater than the number of independent parameters to be determined in order to obtain the final result.

[0110] After measuring the magnetic induction intensity at a sufficient number of locations, a well-determined or overdetermined equation of the form B(r)=xG(y) can be established and solved to obtain a spatial distribution model of the magnetic field at a certain moment, where x represents the expansion coefficient matrix and G(y) represents the spherical harmonic function related to the coordinates of the magnetic source point.

[0111] This application also proposes a device for calculating the AC magnetic field of a product at a distance, such as... Figure 4 As shown, it includes:

[0112] Configuration unit 401 is used to construct an imaginary sphere with the product center as the center, arrange k triaxial magnetometer probes on the surface of the sphere, and sequentially record the position coordinates r1(x1,y1,z1) to r k (x k ,y k ,z k );

[0113] Acquisition unit 402 is used to acquire magnetic flux density data B(r1) to B(r) measured by the triaxial magnetometer probe at time t1. k ), where the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data;

[0114] The calculation unit 403 is used to substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field equation, establish a well-determined or overdetermined equation, and solve for the intrinsic coefficient α of the magnetic field equation. lm and exogenous coefficient β lm This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1.

[0115]

[0116] Fitting unit 404 is used to select different times t2, t3, ... t within a period. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t);

[0117] Building unit 405 is used to construct the intrinsic function α, which varies with time in the coefficients of the magnetic field equation. lm (t) and external function β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field.

[0118]

[0119] The calculation unit 406 is used to substitute the coordinates of any position in the far field into the distribution function B(r,t) in step S5 to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time.

[0120] The envelope size of the product under test is 500 mm. The AC magnetic field information generated by the product at a distance of 1000 mm is measured.

[0121] Example:

[0122] The test product with an envelope radius of 500 mm is placed in a zero-magnetic environment. An imaginary sphere with a diameter of 650 mm is constructed around it. Eight triaxial magnetometer detectors are fixed on a support and evenly placed around the horizontal plane of the sphere. Figure 5As shown, 8 × 3 = 24 magnetic field data points were collected, resulting in 24 equations. Assuming the internal expansion coefficient of the product reaches order l = 2 (i.e., a quadrupole) and the external expansion coefficient is order l = 1 (i.e., a uniform environmental magnetic field), there are 8 + 3 = 11 undetermined coefficients and three unknowns: the coordinates of the magnetic source center (x, y, z). There are a total of 11 + 3 = 14 unknowns and 24 equations. By establishing and solving the overdetermined equation B(r) = xG(y), the magnetic source information can be obtained by measuring the magnetic field data near the product. Furthermore, the magnetic field information at the product's location 1000 mm from the measured position can be calculated.

[0123] The purpose of this invention is to provide a high-precision measurement method for alternating magnetic fields that can be scaled by distance. This method focuses magnetic source information onto an imaginary sphere, arranges magnetometers around the sphere for measurement, separates the magnetic field information inside and outside the sphere (i.e., separates the magnetic source information from interfering magnetic field information), and then reconstructs the magnetic source information through a multi-stage unfolding of the sphere, thereby calculating the magnetic induction intensity at the extrapolated position.

[0124] This invention utilizes magnetic field distance scaling to measure near-field magnetic field inversion information of the magnetic source and then forward model the magnetic induction intensity at the target distance. This allows for effective measurement of magnetic induction intensity at long distances, avoiding the problem of failing to collect the actual magnetic induction intensity due to the low magnetic induction intensity generated by the product at long distances, which is lower than the ambient magnetic field.

[0125] This invention uses spatial signal separation technology to separate internal and external magnetic field information, thereby reducing environmental magnetic field interference.

[0126] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0127] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for calculating the AC magnetic field of a product at a distance, characterized in that, include: Step S1: Construct an imaginary sphere with the product center as the center, arrange k triaxial magnetometer probes on the surface of the sphere, and record the position coordinates r1 (x1, y1, z1) of the triaxial magnetometer probes to r1 (x1, y1, z1) in sequence. k (x k ,y k ,z k ); Step S2: At time t1, collect the magnetic induction intensity B(r1) to B(r) measured by the triaxial magnetometer probe. k ), Wherein, the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data; Step S3: Substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field equation to establish... Establish well-determined or overdetermined equations and solve for the intrinsic coefficients of the magnetic field equations. and external coefficients This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1. Where l and m are the order of the function expansion, and It is a spherical harmonic function. The vacuum permeability; Step S4: Select different times t2, t3, ... t within a period. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t); Step S5: Calculate the function α of the coefficients of the magnetic field equation as a function of time. lm (t) and β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field. ； Step S6: Substitute the coordinates of any position in the far field into the spatial distribution function B(r,t) of the alternating magnetic field in step S5 to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time. In step S3, the position data and magnetic induction intensity data of the triaxial magnetometer probe are substituted into the magnetic field equation to establish a well-determined or overdetermined equation and solve for the intrinsic coefficients of the magnetic field equation. and external coefficients ,include: Step S31: Let the center coordinates of the magnetic source of the product be (x0, y0, z0), and then correlate them sequentially with the position coordinates r1(x1, y1, z1) of the triaxial magnetometer probe to r k (x k ,y k ,z k Subtracting the two values, the position r of each triaxial magnetometer probe is calculated according to the following formula. n The polar angle θ corresponding to the center of the magnetic source n With azimuth φ n Where n represents any value from 1 to k; Step S32: Adjust the polar angle θ as described above. n With azimuth φ n Substituting the spherical harmonics into the equations yields their respective spherical harmonic functions. and ; Step S33: Select different expansion orders l and m, expand the magnetic field distribution function B(r), establish well-determined or overdetermined equations, and solve for the intrinsic coefficients of the magnetic field equations. and external coefficients ; In step S33: different expansion orders l and m are selected to expand the magnetic field distribution function B(r), including: According to the endogenous coefficient The highest is the quadrupole field, with an external coefficient. To expand for a uniform magnetic field, i.e., the intrinsic coefficient Take l in =2, external coefficient Take l out =1, where, l from l Starting with 1, m expands as follows: m = − l , ..., + l .

2. The method according to claim 1, characterized in that, In step S32, the spherical harmonic function and The following relationship must be satisfied: ； Among them, Y lm Let be a normalized spherical harmonic function, i be the imaginary unit, l and m be the order of the function expansion, θ be the polar angle, and φ be the azimuth angle.

3. The method according to claim 1, characterized in that, In step S3, the establishment of overdetermined equations This includes: the number of magnetic field strength data points 3k is greater than the number of unknowns q, where q =(l in +2)l in +(l out +2)l out + 3。 4. The method according to claim 1, characterized in that, In step S4, different times t2, t3, ... t within a period are selected. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t), including: Select different times t2, t3, ... t within a period p Repeating steps S2-S3 will yield the results at different times. The expansion coefficients α', α''...... and β', β''...... are obtained by fitting the intrinsic coefficients α for each order of expansion. lm and exogenous coefficient β lm Time-varying intrinsic function α lm (t) and external function β lm (t).

5. The method according to claim 1, characterized in that, In step S1, k is greater than or equal to 3.

6. The method according to claim 1, characterized in that, It also includes pre-constructing magnetic field equations.

7. The method according to claim 6, characterized in that, The pre-constructed magnetic field equations include: If the test specimen is placed inside an imaginary sphere, and the magnetic field source is located outside the imaginary sphere, then the magnetic field B at any point inside the imaginary sphere can be expressed as: in, For the free permeability, V satisfies the Laplace equation: The magnetic field at any point r inside the imaginary sphere is represented as: 。 8. A device for calculating the alternating magnetic field of a product at a distance, characterized in that, include: The configuration unit is used to construct an imaginary sphere with the product center as the center, arrange k triaxial magnetometer probes on the surface of the sphere, and sequentially record the position coordinates r1 (x1, y1, z1) of the triaxial magnetometer probes to r k (x k ,y k ,z k ); The acquisition unit is used to acquire the magnetic induction intensity data B(r1) measured by the triaxial magnetometer probe at time t1. To B(r) k ), where the magnetic flux density B(r) is a vector, containing components in the x, y, and z directions. x B y B z data; The calculation unit is used to substitute the position data and magnetic induction intensity data of the triaxial magnetometer probe into the magnetic field square. The process involves establishing well-determined or overdetermined equations and solving for the intrinsic coefficients of the magnetic field equations. and external coefficients This allows us to obtain the magnetic field distribution function B(r) of the magnetic induction intensity at different locations r at time t1. Where l and m are the order of the function expansion, and It is a spherical harmonic function. The vacuum permeability; Substituting the position data and magnetic flux density data of the triaxial magnetometer probe into the magnetic field equation, a well-determined or overdetermined equation is established, and the intrinsic coefficients of the magnetic field equation are solved. and external coefficients ,include: Step S31: Let the center coordinates of the magnetic source of the product be (x0, y0, z0), and then correlate them sequentially with the position coordinates r1(x1, y1, z1) of the triaxial magnetometer probe to r k (x k ,y k ,z k Subtracting the two values, the position r of each triaxial magnetometer probe is calculated according to the following formula. n The polar angle θ corresponding to the center of the magnetic source n With azimuth φ n Where n represents any value from 1 to k; Step S32: Adjust the polar angle θ as described above. n With azimuth φ n Substituting the spherical harmonics into the equations yields their respective spherical harmonic functions. and ; Step S33: Select different expansion orders l and m, expand the magnetic field distribution function B(r), establish well-determined or overdetermined equations, and solve for the intrinsic coefficients of the magnetic field equations. and external coefficients ; In step S33: different expansion orders l and m are selected to expand the magnetic field distribution function B(r), including: According to the endogenous coefficient The highest is the quadrupole field, with external coefficients. To expand for a uniform magnetic field, i.e., the intrinsic coefficient Take l in =2, external coefficient Take l out =1, where, l from l Starting with 1, m expands as follows: m = − l , ..., + l ; The fitting unit is used to select different times t2, t3, ... t within a period. p Repeating steps S2-S3 will yield the intrinsic function α, which represents the coefficients of the magnetic field equation as a function of time. lm (t) and external function β lm (t); The building block is used to construct the intrinsic function α, which varies with time in the coefficients of the magnetic field equation. lm (t) and external function β lm Substituting (t) into the magnetic field distribution function B(r) from step S3, we obtain the spatial distribution function B(r,t) of the alternating magnetic field. ； The calculation unit is used to substitute the coordinates of any position in the far field into the spatial distribution function B(r,t) of the alternating magnetic field in step S5, so as to obtain the waveform B(t) of the magnetic induction intensity generated by the product at the position to be measured as a function of time.

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