A method for measuring the total magnetic moment in the far field based on the full magnetic gradient tensor

Abstract

This invention relates to a far-field total magnetic moment measurement method based on the full magnetic gradient tensor, solving the technical problems of existing near-field measurement methods, such as inaccuracy in measuring large and complex magnetic moments, complex calculation methods, and bulky and expensive testing systems. This invention, based on the full magnetic gradient tensor, starts from the theoretical foundation of the far-field dipole equivalent method. In operation, the magnetic gradient tensor is measured instead of the magnetic field strength vector to obtain the measured magnetic moment, and the magnitude of the magnetic gradient tensor, a tensor invariant, is applied in the calculation. This method has advantages such as wide applicability, simple algorithm, ease of implementation, insensitivity to the Earth's magnetic field, and minimal influence from the attitude of the object under test and the testing platform.

Description

Technical Field

[0001] This invention belongs to the field of far-field magnetic measurement technology, and particularly relates to a method for measuring the total magnetic moment in the far field based on the full magnetic gradient tensor. Background Technology

[0002] The magnetic moment of aircraft is large and the magnetic field distribution is complex. It is difficult to accurately measure the magnetic moment and evaluate the remanent magnetic moment of the whole vehicle using the near-field analysis method for large non-magnetic dipole aircraft. Research and technical verification of accurate magnetic moment testing methods are needed.

[0003] Currently, the most commonly used method for testing the magnetic moment of spacecraft is the equatorial plotting method within near-field analysis. In this method, the spacecraft is placed on a non-magnetic turntable at the center of the Earth's magnetic field or a zero-magnetic-coil system. Several magnetic sensors with fixed intervals are placed at a certain distance from the spacecraft. The turntable is rotated to measure the magnetic field values ​​of the spacecraft at different angles. These magnetic field values ​​are functions of the rotation angle, and the magnetic moment value can be mathematically derived from the angle and the distributed magnetic field values ​​at that angle. However, for large, irregularly shaped spacecraft, the numerous and coupled internal magnetic components result in a highly complex near-field magnetic field distribution. The magnetic moment values ​​obtained by the equatorial plotting method at different altitudes vary greatly, making it impossible to determine the true magnetic moment.

[0004] The European Space Agency used the MMF (Multi-Magnetometer Modeling) method, which is effective for near-field testing of multiple dipoles. However, this method requires the construction of a high-precision, large-scale testing platform, which is expensive and complex to operate. In China, Harbin Institute of Technology and Zhejiang University proposed a magnetic multi-target identification and localization method based on sensor arrays. However, this method has a long development cycle, requires a large testing space, and the testing system is inconvenient to move and improve.

[0005] The magnetic gradient tensor has been applied in various ways both domestically and internationally. Internationally, the United States and Germany have combined the full-tensor magnetic gradient method with a high-temperature superconducting quantum interference device (SQUID). The former is used to detect unexploded ordnance at a distance, while the latter has achieved detection speeds of approximately 100 km in South Africa. 2 The full tensor measurement data is available. The Nara research group in Japan has conducted in-depth physical, algorithmic, and experimental research on magnetic gradient tensor target localization. In China, the National University of Defense Technology has studied magnetic anomaly signal detection based on the magnetic gradient tensor; Jilin University has used the full magnetic gradient tensor for geological information exploration. Overall, the theory of the magnetic gradient tensor method is relatively mature, but there are few precedents for using it for magnetic moment measurement. Summary of the Invention

[0006] In view of the above problems, a far-field total magnetic moment measurement method based on the full magnetic gradient tensor is proposed to overcome or at least partially solve the above problems.

[0007] This invention provides a method for measuring the far-field total magnetic moment based on the full magnetic gradient tensor, comprising the following steps:

[0008] ① Select a relatively open environment and use a coil or fluxgate magnetometer to measure the background magnetic field strength matrix B. 0ijk (i = X, Y, Z; j = +, -; k = x, y, z), and the gradient meter center background magnetic field strength vector B 0m (m = x, y, z). The fluxgate faces the static magnetic field, and the coil faces the alternating magnetic field. If the magnetic field in the environment is relatively uniform and the first-order gradient field can be ignored, this step can be omitted.

[0009] ② The aircraft or its components are placed into this environment from infinity. A magnetic gradient full tensor with a baseline length of d is placed at a distance r from the center of the aircraft or its components, where r ≥ 2.5 times the length of the object under test and r ≥ 10 times the diameter of the object under test. Only at this spatial scale can the object under test be equivalent to a single magnetic dipole model. In addition, 1 / 60r ≤ gradient tensor baseline length d ≤ 1 / 20r to ensure that the difference in the magnetic field can approximately replace the differential to obtain the magnetic gradient data.

[0010] ③ Allow the aircraft or its components to enter their normal operating state in order to measure the magnetic moment during normal operation.

[0011] ④ The magnetic field matrix B was obtained by measuring the magnetic gradient full tensor. 1ijk and the center point magnetic field strength vector B 1m Then, the magnetic field matrix B generated by the object under test near the observation point is obtained. ijk =B 1ijk -B 0ijk The magnetic field strength B at the center point m =B 1m -B 0m .

[0012] ⑤ The magnetic gradient tensor magnitude G is calculated according to formulas (1a)-(1b) and (2). T .

[0013] ⑥ Use triaxial magnetic field strength data from the center point of the gradiometer B m The distance r is decomposed into r = (x, y, z) according to the gradient meter observation coordinate system, and the cosine of the angle between the direction of the total equivalent magnetic moment of the object under test and the observation direction is inverted using formulas (3a)-(3b).

[0014] ⑦ The total magnetic moment is calculated according to formula (4).

[0015] The raw data obtained by the magnetic gradient full tensor meter consists of magnetic flux density data in 6*3 different directions, named as follows:

[0016]

[0017] The magnetic gradient data is obtained by subtracting the data measured by sensors at different positions in the same direction from each other and then dividing by the baseline length. This results in the components of the magnetic gradient tensor matrix.

[0018] The expression for the magnetic gradient tensor matrix is ​​as follows:

[0019]

[0020] in This indicates that the gradient of the magnetic field at measurement point j along the i-th direction is calculated.

[0021] The matrix component values ​​can be calculated using the following formula, where d is the gradient baseline length.

[0022]

[0023] Then the modulus G is calculated from each matrix component. T The formula is:

[0024]

[0025] Using the magnetic field strength B at the center point of the gradiometer m According to Biot-Savart's law, the total magnetic moment vector M can be derived. In the far field, its magnitude is smaller than the true value of the magnetic moment, but it still reflects the direction of the magnetic moment. The inversion formula is:

[0026]

[0027] The formula includes the total magnetic moment vector M, the distance r, and the magnetic field strength B at the center point. m Decomposed into (M) according to the gradiometer observation coordinate system. x M y M z ) T ,(x,y,z) T and (B) x B y B z ) T “T” represents transpose, and r represents the modulus of distance r.

[0028] Perform a cosine operation on M and the distance r from the center of the gradient meter to the object being measured:

[0029]

[0030] The formula for calculating the total magnetic moment of the object under test is:

[0031]

[0032] Where μ0 is the permeability in vacuum, with a value of 4π × 10⁻⁶.-7 Wb / (m·A).

[0033] The magnetic gradient tensor in this invention is a first-order gradient tensor, which can effectively eliminate interference from the geomagnetic field and uniform magnetic fields in the environment.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] This invention discloses a far-field total magnetic moment measurement method based on the magnetic gradient full tensor. Starting from the theoretical foundation of the far-field dipole equivalence method, it uses the magnetic gradient full tensor to represent the magnetic field information at the measurement point, replacing the traditional method of measuring the magnetic field intensity vector with measuring its magnetic gradient full tensor. The full tensor magnetic gradient has the advantage of invariant modulus, i.e., G... T It does not change with the tensor meter attitude and is less affected by the attitude of the magnetic target. Compared with the equatorial mapping method and the array method, magnetic moment measurement using magnetic gradient tensor data has advantages such as simple algorithm, easy implementation, unaffected by the geomagnetic field, and less affected by the attitude of the target and test platform. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. 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.

[0037] Figure 1 This is a schematic diagram of the arrangement of an aircraft and a magnetic gradient full tensor provided in an embodiment of the present invention. In the figure, 1. Magnetic gradient full tensor, 2. Aircraft or its components;

[0038] Figure 2 A flowchart of a far-field total magnetic moment measurement method based on the full magnetic gradient tensor provided in this embodiment of the invention;

[0039] Figure 3 A physical image of the coil-type full tension meter provided in an embodiment of the present invention;

[0040] Figure 4 This is an experimental diagram of single-coil magnetic moment measurement provided in an embodiment of the present invention;

[0041] Figure 5 This is a multi-coil complex dipole model provided in an embodiment of the present invention;

[0042] Figure 6 A simulation diagram of the magnetic field of a complex static magnet provided for an embodiment of the present invention. Detailed Implementation

[0043] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0044] The terms "comprising" and "having," and any variations thereof, in the specification, embodiments, claims, and drawings of this invention are intended to cover non-exclusive inclusion, such as including a series of steps or units.

[0045] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0046] A schematic diagram of measuring the magnetic moment of an object using the magnetic gradient tensor described in this invention is shown below. Figure 1 As shown, the specific measurement procedure is as follows: Figure 2 The details are as follows:

[0047] Step 100: Select a relatively open environment and use a coil or fluxgate magnetometer to measure the background magnetic field strength matrix B. 0ijk (i = X, Y, Z; j = +, -; k = x, y, z), if the magnetic field in the environment is relatively uniform and the first-order gradient field can be ignored, then step 100 is omitted;

[0048] Step 101: Measure the magnetic field strength vector B at the center of the gradient meter. 0m (m = x, y, z);

[0049] Step 200: Dispose of the aircraft or its components from infinity into the environment;

[0050] Step 201: Place a magnetic gradient full tensor with a baseline length of d at a distance r from the center of the aircraft or its components, where r ≥ 2.5 times the length of the object to be measured and r ≥ 10 times the diameter of the object to be measured, and 1 / 60r ≤ gradient meter baseline length d ≤ 1 / 20r;

[0051] Step 300: Allow the aircraft or its components to enter normal operating condition in order to measure its magnetic moment during normal operation;

[0052] Step 400: Measure the magnetic field matrix B using a magnetic gradient full tensor meter. 1ijk and the center point magnetic field strength vector B 1m ;

[0053] Step 401: Calculate the magnetic field matrix B generated by the object under test near the observation point. ijk =B 1ijk -B 0ijk The magnetic field strength B at the center pointm =B 1m -B 0m ;

[0054] Step 500: According to the formula

[0055]

[0056]

[0057]

[0058] The magnetic gradient tensor magnitude G was calculated. T ;

[0059] Step 600: Decompose the distance r into r = (x, y, z) according to the gradient meter observation coordinate system, and use the formula

[0060]

[0061]

[0062] To invert the cosine of the angle between the direction of the total equivalent magnetic moment of the object under test and the observation direction, cosφ;

[0063] Step 700: According to the formula

[0064]

[0065] The total magnetic moment was calculated.

[0066] Following this process, two instances were tested. First, the following were performed: Figure 4 The single-coil dipole magnetic moment measurement shown uses a self-made coil tensor meter for the magnetic gradient total tensor. Figure 3 As shown.

[0067] The working principle of a coil tensor is as follows:

[0068] According to Faraday's law of electromagnetic induction, the formula for the induced voltage of a coil sensor is as follows:

[0069]

[0070] Where n is the number of turns of the coil, and A is the area of ​​the magnetic field directly opposite the coil.

[0071] For the magnetic field at the center point of the gradiometer

[0072]

[0073] Where f is the frequency of the alternating magnetic field, i.e., the electrical signal input to the coil under test, and t represents time.

[0074] From (5) and (6), we can obtain the relationship between the measured voltage and the magnetic field at the center point as follows:

[0075] Therefore, the magnetic field strength at the center point is

[0076]

[0077] According to (1a)-(1b) and (8), the magnetic gradient tensor matrix can be obtained.

[0078]

[0079] Where d is the baseline length of the magnetic gradiometer.

[0080] The radius of the coil dipole measured in the experiment was 3 cm, with a total of 227 turns, and it was made of copper wire with a diameter of 1 mm. When a 16Vpp@6000Hz sinusoidal signal was input, its equivalent impedance was 110.48Ω. Using the formula for calculating magnetic moment, its magnetic moment can be easily calculated to be 0.0321 Am. 2 Multiple measurements of the coil dipole were performed using this method, and the errors were all within ±6%.

[0081] Then, using the aforementioned instruments and methods, complex magnets composed of two or three small coil dipoles (such as...) Figure 5 Measurements were performed (as shown). Theoretically, the magnetic field of any complex magnetic object can be equivalently replaced by multiple dipoles. Furthermore, when the measurement distance is greater than three times the distance between the two farthest dipoles in a group of dipoles, regardless of the number of dipoles in the object under test, or their orientation and magnitude, the magnetic field generated can be equivalent to that of a single dipole. Therefore, a complex magnet can always be equivalent to a single dipole in the far field, a fact verified in submarine detection technology. We measured the total far-field magnetic moment of a complex magnet using the method described in this invention, and the experimental results agree well with the vector sum of the magnetic moments of each dipole used. For multi-dipole combinations with different attitudes, this method can measure their equivalent total far-field magnetic moment with an error within 10%.

[0082] Furthermore, we used this measurement method to conduct simulation tests on large and complex permanent magnets. The magnetic field lines and magnetic field strength around the target are as follows: Figure 6 As shown, it consists of three magnetic moments, each with a moment of 301.6 Am in the Z direction. 2 150.0 Am in the X direction 2 and -Z direction 169.6Am 2 It consists of permanent magnet blocks, with a total length of about 1.5m and a maximum width of about 0.8m.

[0083] A magnetic gradient tensor was constructed using six identical fluxgate magnetometers. Measurements were taken at a distance of 11.4 m from the object under test, with a tensor baseline of 1 m. The calculated equivalent total magnetic moment was 207.4 Am. 2 The total magnetic moment calculated theoretically is 199.8 Am. 2 In comparison, the error is only 3.8%.

[0084] The following is a comparison of this method with other magnetic moment measurement methods.

[0085]

[0086] Beneficial effects: For 10 -2 Am 2 Small magnetic moments on the order of magnitude and 10 2 Am 2 The large magnetic moment on the order of magnitude, tested on both AC coils and permanent magnets, demonstrates the broad applicability of this detection method. Furthermore, by keeping the target stationary and rotating the full tensormeter, the results show that the magnetic gradient tensor magnitude G remains constant regardless of the tensormeter's orientation. T They remain almost unchanged. This demonstrates the advantage of the invariance of the magnetic gradient tensor modulus: changes in the attitude of the test platform do not affect the measured magnitude of the magnetic moment.

[0087] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring the far-field total magnetic moment based on the full magnetic gradient tensor, characterized in that, The method includes: ① Select a relatively open environment and use a coil or fluxgate magnetometer to measure the background magnetic field strength matrix B. 0ijk i = X, Y, Z; j = +, -; k = x, y, z, where i and j represent the position of the triaxial magnetometer, k represents the direction of the magnetic field components measured by the triaxial magnetometer, and the gradient meter center background magnetic field strength vector B. 0m m = x, y, z, the fluxgate faces the static magnetic field, and the coil faces the alternating magnetic field. If the magnetic field in the environment is relatively uniform and the first-order gradient field can be ignored, this step can be omitted. ② The aircraft or its components are placed into the environment from infinity. A magnetic gradient full tensor with a baseline length of d is placed at a distance r from the center of the aircraft or its components, where r ≥ 2.5 times the length of the object under test and r ≥ 10 times the diameter of the object under test. Only at this spatial scale can the object under test be equivalent to a single magnetic dipole model. In addition, 1 / 60r ≤ gradient tensor baseline length d ≤ 1 / 20r to ensure that the difference of the magnetic field can be approximately replaced by the differential to obtain magnetic gradient data. ③ Allow the aircraft or its components to enter normal operating condition in order to measure its magnetic moment during normal operation; ④ The magnetic field matrix B was obtained by measuring the magnetic gradient full tensor. 1ijk and the center point magnetic field strength vector B 1m Then let B ijk =B 1ijk -B 0ijk B m =B 1m -B 0m The magnetic field generated by the object under test near the observation point is obtained; ⑤ According to the formula The magnetic gradient tensor magnitude G at each angle was calculated. T In equation (1b), d is the length of the gradient meter baseline; ⑥ Use triaxial magnetic field strength data from the center point of the gradiometer B m The distance r from the center of the gradiometer to the object to be measured is decomposed into r = (x, y, z) according to the gradiometer observation coordinate system, and then the formula is used. To invert the cosine of the angle between the direction of the total equivalent magnetic moment of the object under test and the observation direction, cosφ; ⑦ According to the formula The total magnetic moment was calculated, where μ0 is the permeability in vacuum, with a value of 4π × 10⁻⁶. -7 Wb / (m·A); The magnetic gradient total tensor includes two types: coil type and fluxgate type. The working principle of the coil type includes: According to Faraday's law of electromagnetic induction, the formula for the induced voltage of a coil sensor is as follows: Where n is the number of turns of the coil, and A is the area of ​​the magnetic field directly opposite the coil; for the magnetic field at the center point of the gradient meter, Where f is the frequency of the alternating magnetic field, i.e., the electrical signal input to the coil under test, and t represents time; from (5) and (6), the relationship between the measured voltage and the magnetic field at the center point can be obtained as follows: Therefore, the magnetic field strength at the center point is: According to (1a)-(1b) and (8), the magnetic gradient tensor matrix is: Where d is the baseline length of the magnetic gradiometer.

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