A modeling method for residual magnetic characteristics of spacecraft in a zero-magnetic chamber

Abstract

The present application discloses a method for modeling the residual magnetic characteristics of a spacecraft in a zero magnetic chamber, which belongs to the field of aerospace, and includes: placing the spacecraft to be tested on a non-magnetic turntable in the zero magnetic chamber, placing a number of magnetic sensors at preset positions according to test requirements, rotating the non-magnetic turntable, and recording the test data of the magnetic sensors at preset angles; calculating Fourier coefficients according to the test data; obtaining the spherical harmonic coefficient relationship between the spacecraft to be tested and the mirror spacecraft according to the position information of the spacecraft to be tested in the zero magnetic chamber, wherein the mirror spacecraft is a mirror image generated by each mirror interface in the zero magnetic chamber; obtaining the calculation matrix of the spherical harmonic coefficients of the spacecraft to be tested according to the spherical harmonic coefficient relationship; calculating the least squares solution of all spherical harmonic coefficients according to the Fourier coefficients and the spherical harmonic coefficient calculation matrix, thereby realizing the modeling of the magnetic characteristics of the spacecraft. The method provided in the present application takes into account the mutual coupling between the spacecraft magnetic field and the zero magnetic chamber, and can realize the mathematical modeling of the residual magnetic characteristics of various spacecraft.

Description

Technical Field

[0001] This application relates to a method for modeling the residual magnetism characteristics of a zero-magnetic indoor spacecraft, which belongs to the aerospace field. Background Technology

[0002] Since the Soviet Union launched the first artificial satellite in 1957, humankind's deep space exploration activities toward the solar system have been going on for more than 60 years. Through deep space exploration, we can learn about the surface features of the celestial bodies being explored, as well as the presence of organic matter and water. This is of great significance for humankind to understand extraterrestrial water and life information, and to understand the origin and evolution of the solar system and life.

[0003] Magnetic field measurement is a crucial task in deep space exploration. It allows for remote sensing of planetary magnetic fields, study of planetary evolutionary history, and understanding of the space environment of celestial bodies in the solar system. Obtaining scientific data through remote sensing and in-situ measurements using highly sensitive, miniaturized magnetic sensors is essential for understanding these fundamental scientific questions. In deep space magnetic exploration missions, magnetic sensors are typically mounted on various spacecraft, including orbiters, landers, and rovers. Spacecraft consist of complex mechanical, electrical, and electronic components, which themselves generate magnetic fields or contain magnetic materials, interfering with magnetic detection data. Therefore, to ensure the accuracy and reliability of magnetic detection data, the magnetic field of the spacecraft itself must be limited.

[0004] Magnetic testing facilities based on active compensation coils suffer from limitations such as large environmental magnetic disturbances and low shielding coefficients, which are major factors restricting further improvements in the accuracy of spacecraft magnetic property measurements and prevent them from meeting increasingly stringent spacecraft magnetic interference requirements. Therefore, for future high-precision deep space exploration missions, magnetic testing facilities based on passive magnetic shielding (zero magnetic chambers) are essential. However, due to the coupling between the spacecraft's own magnetic field and the shielding chamber, the use of traditional spherical harmonic function methods and multi-magnetic dipole methods can lead to deviations in the spacecraft's remanent magnetization characteristic model. Therefore, breaking through the limitations of precise mathematical measurement technology for spacecraft remanent magnetization characteristics considering the coupling effect between the spacecraft's magnetic field and the zero magnetic chamber is a critical problem that urgently needs to be solved. Summary of the Invention

[0005] The purpose of this application is to provide a method for modeling the remanent magnetization characteristics of spacecraft in a zero-magnetic-room environment. Considering the mutual coupling between the spacecraft's magnetic field and the zero-magnetic-room, various remanent magnetization characteristics of spacecraft can be simulated.

[0006] To achieve the above objectives, the first aspect of this application provides a method for modeling the remanent magnetization characteristics of a zero-magnetic indoor spacecraft, comprising:

[0007] The spacecraft under test is placed on a non-magnetic turntable in a zero-magnetic chamber. Several magnetic sensors are placed at preset positions according to the test requirements. The non-magnetic turntable is rotated, and the test data of the magnetic sensors are recorded at preset angles.

[0008] Calculate the Fourier coefficients based on the test data;

[0009] The spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft is obtained based on the position information of the spacecraft under test in the zero magnetic chamber. The mirror spacecraft is the mirror image generated by passing through each mirror interface in the zero magnetic chamber.

[0010] Based on the spherical harmonic coefficient relationship, a spherical harmonic coefficient calculation matrix is ​​obtained for simulating the magnetic characteristics of the spacecraft under test;

[0011] The least-squares solution of all spherical harmonic coefficients is calculated based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix to realize the magnetic characteristic model of the spacecraft.

[0012] In one embodiment, placing several magnetic sensors at preset positions according to testing requirements includes:

[0013] Based on the spacecraft modeling accuracy, magnetic field amplitude, and user requirements, several magnetic sensors are placed at preset locations.

[0014] In one implementation, calculating the Fourier coefficients based on the test data includes:

[0015] For any magnetic sensor, the corresponding Fourier coefficients are calculated using the following formula:

[0016]

[0017] In the formula, B x B y and B z These are the triaxial readings of the magnetic sensor, where m is the spherical harmonic order. It is the rotation angle of the non-magnetic turntable.

[0018] In one embodiment, obtaining the spherical harmonic coefficient relationship between the spacecraft under test and its mirror image spacecraft based on the spacecraft's position information in the zero-magnetic chamber includes:

[0019] The relationship between the spherical harmonic coefficients of the spacecraft under test and its mirror image is obtained based on the spherical harmonic function expression of the magnetic field generated by the spacecraft under test in spherical coordinates. The spherical harmonic function expression is as follows:

[0020]

[0021]

[0022]

[0023] In the formula, μ0 is the air permeability, j and m are the spherical harmonic orders, and a jm and b jmThese are the spherical harmonic coefficients, and r, θ, and φ are the three coordinates of the magnetic sensor in spherical coordinates. For the associated Legendre function normalized to the Schmitt criterion.

[0024] In one embodiment, obtaining the spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft based on the spherical harmonic function expression of the magnetic field generated by the spacecraft under test in spherical coordinates includes:

[0025] When the spherical harmonic order j = 3, the spacecraft spherical harmonic model is composed of magnetic dipoles, magnetic quadrupoles and magnetic octupoles. The spherical harmonic coefficients corresponding to the magnetic dipoles, magnetic quadrupoles and magnetic octupoles are obtained according to the spherical harmonic function expression.

[0026] Based on the spherical harmonic coefficients and the mirror image relationships of magnetic dipoles, magnetic quadrupoles, and magnetic octupoles in the zero magnetic chamber, the relationship between the spherical harmonic coefficients of the spacecraft under test and the spherical harmonic coefficients of the mirror spacecraft is obtained through a graphical method.

[0027] Based on the relationship between the spherical harmonic coefficients of the spacecraft under test and its mirror image, the relationship between the spherical harmonic coefficients of the spacecraft under test and its mirror image is derived when the spherical harmonic order j≥3.

[0028] In one embodiment, the spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft is expressed by the following expression:

[0029]

[0030] Among them, a jm and b jm It is the spherical harmonic coefficient of the spacecraft under test, a jm_镜像 and b jm_镜像 It is the spherical harmonic coefficient of the mirror spacecraft.

[0031] In one implementation, calculating the least-squares solution of all spherical harmonics based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix includes:

[0032] The matrix is ​​calculated based on the Fourier coefficients and the spherical harmonic coefficients, and the least squares solution of all spherical harmonic coefficients is calculated by inverting the generalized inverse matrix.

[0033] The second aspect of this application provides a zero-magnetic indoor spacecraft remanent magnetization characteristic modeling device, comprising:

[0034] The test module is used to place the spacecraft under test on a non-magnetic turntable in a zero-magnetic chamber, place several magnetic sensors at preset positions according to test requirements, rotate the non-magnetic turntable, and record the test data of the magnetic sensors at preset angles.

[0035] The calculation module is used to calculate the Fourier coefficients based on the test data;

[0036] The calculation module is also used to obtain the spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft based on the position information of the spacecraft under test in the zero magnetic chamber, wherein the mirror spacecraft is a mirror image generated by passing through each mirror interface in the zero magnetic chamber.

[0037] The calculation module is also used to obtain a spherical harmonic coefficient calculation matrix for simulating the magnetic characteristics of the spacecraft under test based on the spherical harmonic coefficient relationship.

[0038] The modeling module is used to calculate the least squares solution of all spherical harmonic coefficients based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix, thereby realizing the magnetic characteristic modeling of the spacecraft.

[0039] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the first aspect or any embodiment of the first aspect.

[0040] The fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the first aspect or any embodiment of the first aspect.

[0041] As can be seen from the above, this application provides a method for modeling the remanent magnetization characteristics of spacecraft in a zero-magnetic chamber. It considers the coupling effect between the zero-magnetic chamber and the spacecraft's magnetic field to model the spacecraft's magnetic characteristics, accurately predicting the magnetic field distribution generated by the spacecraft. Furthermore, since the magnetic interference in the zero-magnetic chamber is significantly lower than in a typical laboratory environment, the computational accuracy is also significantly improved. Simultaneously, the method provided in this application is applicable to application scenarios with different spherical harmonic orders and different mirror interfaces of the zero-magnetic chamber. Different types and numbers of magnetic sensors can be set according to the testing needs of different application scenarios to achieve the measurement of various remanent magnetization characteristics of spacecraft. This overcomes the limitation of background environmental magnetic interference on the accuracy of spacecraft remanent magnetization modeling, significantly improving the accuracy of spacecraft magnetic characteristic modeling. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A schematic diagram of a zero-magnetic indoor test for the remanent magnetization characteristics of a spacecraft under test, provided as an embodiment of this application;

[0044] Figure 2 A schematic diagram of a zero-magnetic indoor spacecraft under test provided in this application embodiment;

[0045] Figure 3 A mirror image of a magnetic dipole provided in an embodiment of this application;

[0046] Figure 4 A mirror image of a magnetic quadrupole provided in an embodiment of this application;

[0047] Figure 5 A schematic diagram of the independent components of a magnetic octapole provided in an embodiment of this application;

[0048] Figure 6 This is a comparative schematic diagram of magnetic field distribution calculation provided for an embodiment of this application. Detailed Implementation

[0049] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0050] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0051] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0052] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0053] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0054] Example 1

[0055] This application provides a method for modeling the residual magnetism characteristics of a zero-magnetic indoor spacecraft, such as... Figure 1 As shown, the method includes:

[0056] The S100 places the spacecraft under test on a non-magnetic turntable in the zero-magnetic chamber, places several magnetic sensors at preset positions according to the test requirements, rotates the non-magnetic turntable, and records the test data of the magnetic sensors at preset angles.

[0057] Optionally, the number and type of magnetic sensors can be adjusted according to the spacecraft modeling accuracy, magnetic field amplitude, and user needs.

[0058] In one implementation, the magnetic sensors are fluxgate sensors, and there are two of them. Figure 1 For example, sensor 1 and sensor 2 are located at distances r1 and r2 from the center of the spacecraft under test, respectively.

[0059] In one implementation, the readings of the magnetic sensor are recorded every 10 degrees when the non-magnetic turntable is rotated to obtain test data.

[0060] S200 calculates the Fourier coefficients based on the test data;

[0061] Optionally, when there are two magnetic sensors, the corresponding Fourier coefficients are calculated using the following formula:

[0062]

[0063] In the formula, B x B y and B z This is the triaxial reading of sensor 1, B x1 B y1 and B z1 These are the triaxial readings of sensor 2, where m is the spherical harmonic order. This represents the rotation angle of the non-magnetic turntable. When using a larger number of magnetic sensors, the above formula can be further extended to obtain the Fourier coefficients corresponding to each magnetic sensor.

[0064] S300 obtains the spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft based on the position information of the spacecraft under test in the zero magnetic chamber, wherein the mirror spacecraft is the mirror image generated by passing through each mirror interface in the zero magnetic chamber;

[0065] In one implementation, to obtain the spherical harmonic coefficient calculation matrix, it is necessary to consider the calculation matrix under the interaction of the spacecraft's magnetic properties and the zero magnetic chamber (also known as the shielded chamber). This embodiment takes the case of the spacecraft being coupled to the bottom surface (-z plane) of the zero magnetic chamber as an example. In this case, the mirrored spacecraft is a mirror image generated by passing through the bottom mirror interface of the zero magnetic chamber. Figure 2 As shown, the mirror image method reveals that, due to the presence of the zero magnetic chamber, the magnetic field data measured by sensors 1 and 2 within the zero magnetic chamber are actually generated jointly by the original image spacecraft and the mirror image spacecraft. To obtain the spherical harmonic coefficient calculation matrix considering the magnetic field generated by the mirror image spacecraft, the relationship between the spherical harmonic coefficients of the original image spacecraft and the mirror image spacecraft is also needed. The following analysis uses a spherical harmonic model of order j=3 as an example to analyze the relationship between the two. The spherical harmonic function expression of the magnetic field generated by the spacecraft in spherical coordinates is shown below:

[0066]

[0067]

[0068]

[0069] In the formula, μ0 is the air permeability, j and m are the spherical harmonic orders, and a jm and b jm These are the spherical harmonic coefficients, and r, θ, and φ are the three coordinates of the magnetic sensor in spherical coordinates. The expression for the associated Legendre function, which is Schmitt quasi-normalized, is as follows:

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] In the formula, θ is the pitch angle of the magnetic sensor in spherical coordinates. Let be a function of the spherical harmonic order j and m.

[0076] Optionally, when the spherical harmonic order j = 3, the spacecraft spherical harmonic model consists of a magnetic dipole, a magnetic quadrupole, and a magnetic octupole. The spherical harmonic coefficients corresponding to the magnetic dipole, magnetic quadrupole, and magnetic octupole are obtained according to the spherical harmonic function expression. Based on the spherical harmonic coefficients and the mirror image relationship of the magnetic dipole, magnetic quadrupole, and magnetic octupole in the shielded room, the relationship between the spherical harmonic coefficients of the spacecraft under test and the mirror image spacecraft is obtained through a graphical method. The relationship between the spherical harmonic coefficients of the spacecraft under test and the mirror image spacecraft can be extended to higher orders to obtain the relationship between the spherical harmonic coefficients of the spacecraft under test and the mirror image spacecraft when the spherical harmonic order j ≥ 3.

[0077] In one implementation, the spherical harmonic coefficient corresponding to the magnetic dipole is a. 10 a 11 and b 11 And the following relationship exists:

[0078] a 10 =M z ,b 11 =M y ,a 11 =M x

[0079] Therefore, the mirror image of the magnetic dipole along the z-axis is very simple, as follows: Figure 3 As shown, the magnetic dipole-related spherical harmonic function of the mirror spacecraft can be obtained as follows:

[0080] a 10_镜像 =a 10 ,b 11_镜像 =-b 11 ,a 11_镜像 =-a 11

[0081] Similarly, the mirror image of the magnetic quadrupole along the z-axis can also be obtained graphically, such as... Figure 4 As shown. A magnetic quadrupole consists of two magnetic dipoles that are close together and in opposite directions, and it has only five independent components. Figure 4 It can be seen that the magnetic quadrupole-related spherical harmonic function of the mirror spacecraft is as follows:

[0082] a 20_镜像 =-a 20 ,

[0083] b 21_镜像 =b 21 ,a 21_镜像 =a 21

[0084] b 22_镜像 =-b 22 ,a 22_镜像 =-a 22

[0085] As for the magnetic octupole, it is composed of two magnetic quadrupoles that are close together and in opposite directions, resulting in a total of 24 combinations. The magnetic octupole has only 7 independent components, such as... Figure 5 As shown, with U xyz For example, U xyz This represents a magnetic octet configuration, with the subscripts indicating the following: First, a magnetic dipole is placed along the x-axis. Then, it is translated a certain distance along the y-axis, and a magnetic dipole in the -x-axis direction is copied. These two magnetic dipoles constitute a magnetic quadrupole U. xy Finally, the magnetic quadrupole is translated a certain distance along the z-axis, and a copy of the magnetic quadrupole-U with the opposite orientation is made. xy These two magnetic quadrupoles together form a magnetic octupole U. xyz The magnetic octet-related spherical harmonic function of the mirror spacecraft is as follows:

[0086] a 30_镜像 =a 30 ,

[0087] b 31_镜像 =-b 31 ,a 31_镜像 =-a 31

[0088] b 32_镜像 =b 32 ,a 32_镜像 =a 32

[0089] b 33_镜像 =-b 33 ,a 33_镜像 =-a 33

[0090] Based on the spherical harmonic functions related to the magnetic dipole, magnetic quadrupole, and magnetic octupole, the relationship between the spherical harmonic coefficients of the spacecraft under test and its mirror image is as follows:

[0091]

[0092] Among them, a jm and b jm It is the spherical harmonic coefficient of the spacecraft under test, a jm_镜像 and b jm_镜像 These are the spherical harmonic coefficients of the mirror spacecraft. Based on the above derivation, the correspondence of spherical harmonic coefficients can be further extended to higher orders; the specific formulas are not elaborated here.

[0093] S400 obtains the spherical harmonic coefficient calculation matrix for simulating the magnetic characteristics of the spacecraft under test based on the spherical harmonic coefficient relationship;

[0094] In one implementation, when the magnetic sensor is configured as follows: Figure 1 and 2 As shown, based on the above relationships of spherical harmonic coefficients, the corresponding spherical harmonic coefficient calculation matrix can be obtained as follows:

[0095] j = 1, 2, 3

[0096]

[0097] j = 2, 3

[0098]

[0099] j=3

[0100]

[0101] j = 1, 2, 3

[0102]

[0103] j = 1, 2, 3

[0104]

[0105] j = 2, 3

[0106]

[0107] j=3

[0108]

[0109]

[0110] Where, r a and r b θ represents the distances between the mirror spacecraft and sensor 1 and sensor 2, respectively. a Let θ be the angle between the line connecting the mirror spacecraft and the spacecraft under test and the line connecting the mirror spacecraft and sensor 1. b The angle between the line connecting the mirror spacecraft and the spacecraft under test and the line connecting the mirror spacecraft and sensor 2.

[0111] S500 calculates the least squares solution of all spherical harmonic coefficients based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix, thereby realizing the magnetic characteristic modeling of the spacecraft.

[0112] In one implementation, a matrix is ​​calculated based on the Fourier coefficients and the spherical harmonic coefficients. The spherical harmonic coefficients are then solved using the method of generalized inverse matrix inversion to obtain the least-squares solution for all spherical harmonic coefficients as follows:

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] Based on the least squares solution of all the spherical harmonic coefficients mentioned above, the magnetic field distribution generated by the spacecraft can be obtained, and its remanent magnetization characteristics can be analyzed.

[0121] In one embodiment, based on the above steps S100-S500, a mathematical model of the remanent magnetization characteristics of the spacecraft can be established by means of the mirror method and the inherent relationship between the spherical harmonic coefficients in the magnetic characteristic models of the original image spacecraft and the mirror image spacecraft, and the remanent magnetization characteristics of the spacecraft can be directly analyzed by means of the mathematical model of the remanent magnetization characteristics of the spacecraft.

[0122] In one application scenario, to verify the zero-magnetic indoor spacecraft remanent magnetization characteristic modeling method proposed in this application embodiment, the magnetic field distributions with an elevation angle of π / 2 and radii of 0.55m and 0.8m, respectively, were calculated using the finite element method, the zero-magnetic outdoor remanent magnetization measurement method, and the zero-magnetic indoor remanent magnetization measurement method. Figure 6 As shown in the figure. The random magnetic interference amplitudes outside and inside the zero-magnetic-field chamber were set to 200 nT and 10 nT, respectively. The magnetic object under test was tested using a triaxially magnetized 10cm × 10cm × 10cm permanent magnet with a triaxial magnetic moment of 0.1 Am. 2 The coordinates of the placement are (0.1m, 0, 0). It can be seen that the zero-magnetic-room spacecraft remanent magnetization modeling method proposed in this application accurately predicts the magnetic field distribution generated by the spacecraft by considering the mutual coupling between the zero-magnetic-room and the spacecraft's magnetic field. Furthermore, since the magnetic interference in the zero-magnetic-room is significantly lower than in a typical laboratory environment, the calculation accuracy is also significantly improved, verifying the effectiveness and accuracy of the method in this application.

[0123] As can be seen from the above, the embodiments of this application provide a method for modeling the remanent magnetization characteristics of spacecraft within a zero-magnetic chamber, revealing the mutual coupling mechanism between the zero-magnetic chamber and the spacecraft's magnetic field. This method overcomes the limitation of background magnetic interference on the modeling accuracy of spacecraft remanent magnetization and significantly improves the modeling accuracy. Furthermore, taking a spherical harmonic order j=3 and a mirror image of the bottom surface of the zero-magnetic chamber as examples, a calculation matrix for the spherical harmonic coefficients considering the mutual coupling between the zero-magnetic chamber and the spacecraft's magnetic field is given. This matrix can be easily extended to higher spherical harmonic orders and mirror images of various surfaces of the zero-magnetic chamber. In addition, the arrangement, quantity, and type of magnetic sensors can be adjusted with a high degree of freedom according to testing needs.

[0124] Example 2

[0125] This application provides a zero-magnetic indoor spacecraft remanent magnetization characteristic modeling device, which includes a testing module, a calculation module, and a modeling module;

[0126] The testing module is used to place the spacecraft under test on a non-magnetic turntable in a zero-magnetic chamber, place several magnetic sensors at preset positions according to the testing requirements, rotate the non-magnetic turntable, and record the test data of the magnetic sensors at preset angles.

[0127] The calculation module is used to calculate the Fourier coefficients based on the test data;

[0128] The calculation module is also used to obtain the spherical harmonic coefficient relationship between the spacecraft under test and the mirror spacecraft based on the position information of the spacecraft under test in the zero magnetic chamber, wherein the mirror spacecraft is a mirror image generated by passing through each mirror interface in the zero magnetic chamber.

[0129] The calculation module is also used to obtain a spherical harmonic coefficient calculation matrix for simulating the magnetic characteristics of the spacecraft under test based on the spherical harmonic coefficient relationship.

[0130] The modeling module is used to calculate the least squares solution of all spherical harmonic coefficients based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix, thereby realizing the magnetic characteristic modeling of the spacecraft.

[0131] This application also provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The memory stores software programs and modules, and the processor executes various functional applications and data processing by running the software programs and modules stored in the memory. The memory and processor are connected via a bus. Specifically, the processor implements any of the steps in Embodiment 1 by running the computer program stored in the memory.

[0132] It should be understood that, in the embodiments of this application, the processor may be a Central Processing Unit (CPU), but it may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0133] Memory may include read-only memory, flash memory, and random access memory, and provides instructions and data to the processor. Some or all of the memory may also include non-volatile random access memory.

[0134] It should be understood that if the integrated modules / units described above are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0135] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0136] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the above device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0137] It should be noted that the methods and detailed examples provided in the above embodiments can be incorporated into the apparatus and devices provided in the embodiments, and can be referred to each other, without further elaboration.

[0138] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0139] In the embodiments provided in this application, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / device embodiments described above are merely illustrative. For instance, the division of the modules or units described above is merely a logical functional division, and in actual implementation, it can be divided in other ways. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0140] 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, and should all be included within the protection scope of this application.

Claims

1. A method for modeling the residual magnetic characteristics of a spacecraft in a zero-magnetic chamber, characterized in that: include: Place the spacecraft to be tested on a non-magnetic turntable in the zero-magnetic chamber, place several magnetic sensors at preset positions according to test requirements, rotate the non-magnetic turntable, and record the test data of the magnetic sensors at every preset angle; Calculate Fourier coefficients according to the test data; According to the position information of the spacecraft to be tested in the zero magnetic chamber, the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is obtained, wherein the mirror spacecraft is a mirror image generated by each mirror interface in the zero magnetic chamber; According to the spherical harmonic coefficient relationship, a spherical harmonic coefficient calculation matrix for simulating the magnetic characteristics of the spacecraft to be tested is obtained; Calculating the least square solution of all spherical harmonic coefficients according to the Fourier coefficients and the spherical harmonic coefficient calculation matrix to achieve magnetic characteristic modeling of the spacecraft; Calculating Fourier coefficients according to the test data comprises: For any magnetic sensor, the corresponding Fourier coefficient is calculated by the following formula: In the formula, B x , B y and B z is the triaxial reading of the magnetic sensor, m is the spherical harmonic number, is the rotation angle of the non-magnetic turntable; The method of obtaining the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft according to the position information of the spacecraft to be tested in the zero magnetic chamber comprises: The relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is obtained according to the spherical harmonic function expression of the magnetic field generated by the spacecraft to be tested in spherical coordinates. The spherical harmonic function expression is: Where μ0 is the air permeability, j is the order of the spherical harmonics, m is the degree of the spherical harmonics, and a jm and b jm are the spherical harmonic coefficients, r, θ and φ are the three coordinates of the magnetic sensor in spherical coordinates, is the Schmidt quasi-normalized associated Legendre function; The spherical harmonic coefficient relationship between the spacecraft to be tested and the mirror spacecraft is obtained according to the spherical harmonic function expression of the magnetic field generated by the spacecraft to be tested in spherical coordinates, including: When the spherical harmonic order j=3, the spacecraft spherical harmonic model is composed of a magnetic dipole, a magnetic quadrupole and a magnetic octupole, and the spherical harmonic coefficients corresponding to the magnetic dipole, the magnetic quadrupole and the magnetic octupole are obtained according to the spherical harmonic function expression; According to the spherical harmonic coefficients and the mirror image relationship between the magnetic dipole, the magnetic quadrupole and the magnetic octupole in the zero magnetic chamber, the relationship between the spherical harmonic coefficients of the spacecraft to be measured and the spherical harmonic coefficients of the mirror image spacecraft is obtained by a graphical method; According to the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the spherical harmonic coefficients of the mirror spacecraft, the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is derived when the spherical harmonic order j≥3; The relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is expressed by the following expression: Among them, a jm and b jm is the spherical harmonic coefficient of the spacecraft to be measured, a jm_镜像 and b jm_镜像 are the spherical harmonic coefficients of the mirror spacecraft.

2. The method for modeling the residual magnetic characteristics of a spacecraft in a zero magnetic chamber according to claim 1, characterized in that: Placing a plurality of magnetic sensors at preset positions according to test requirements includes: Several magnetic sensors are placed at preset positions according to the spacecraft modeling accuracy, magnetic field amplitude, and user needs.

3. The method for modeling the residual magnetic characteristics of a spacecraft in a zero magnetic chamber according to claim 1 or 2, characterized in that: The least square solution of calculating all spherical harmonic coefficients according to the Fourier coefficients and the spherical harmonic coefficient calculation matrix comprises: A matrix is ​​calculated based on the Fourier coefficients and the spherical harmonic coefficients, and the least squares solution of all spherical harmonic coefficients is calculated by a generalized inverse matrix inversion method.

4. A device for modeling the residual magnetic characteristics of a spacecraft in a zero-magnetic chamber, characterized in that: include: The test module is used to place the spacecraft to be tested on a non-magnetic turntable in the zero-magnetic chamber, place a number of magnetic sensors at preset positions according to the test requirements, rotate the non-magnetic turntable, and record the test data of the magnetic sensors at every preset angle; A calculation module, used for calculating Fourier coefficients according to the test data; The corresponding Fourier coefficients are calculated by the following formula: In the formula, B x , B y and B z is the triaxial reading of the magnetic sensor, m is the spherical harmonic number, is the rotation angle of the non-magnetic turntable; The calculation module is also used to obtain the spherical harmonic coefficient relationship between the spacecraft to be tested and the mirror spacecraft according to the position information of the spacecraft to be tested in the zero magnetic chamber, wherein the mirror spacecraft is a mirror image generated by each mirror interface in the zero magnetic chamber; The method of obtaining the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft according to the position information of the spacecraft to be tested in the zero magnetic chamber comprises: The relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is obtained according to the spherical harmonic function expression of the magnetic field generated by the spacecraft to be tested in spherical coordinates. The spherical harmonic function expression is: Where μ0 is the air permeability, j is the order of the spherical harmonic function, m is the spherical harmonic number, and a jm and b jm are the spherical harmonic coefficients, r, θ and φ are the three coordinates of the magnetic sensor in spherical coordinates, is the Schmidt quasi-normalized associated Legendre function; The spherical harmonic coefficient relationship between the spacecraft to be tested and the mirror spacecraft is obtained according to the spherical harmonic function expression of the magnetic field generated by the spacecraft to be tested in spherical coordinates, including: When the spherical harmonic order j=3, the spacecraft spherical harmonic model is composed of a magnetic dipole, a magnetic quadrupole and a magnetic octupole, and the spherical harmonic coefficients corresponding to the magnetic dipole, the magnetic quadrupole and the magnetic octupole are obtained according to the spherical harmonic function expression; According to the spherical harmonic coefficients and the mirror image relationship between the magnetic dipole, the magnetic quadrupole and the magnetic octupole in the zero magnetic chamber, the relationship between the spherical harmonic coefficients of the spacecraft to be measured and the spherical harmonic coefficients of the mirror image spacecraft is obtained by a graphical method; According to the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the spherical harmonic coefficients of the mirror spacecraft, the relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is derived when the spherical harmonic order j≥3; The relationship between the spherical harmonic coefficients of the spacecraft to be tested and the mirror spacecraft is expressed by the following expression: Among them, a jm and b jm is the spherical harmonic coefficient of the spacecraft to be measured, a jm_镜像 and b jm_镜像 are the spherical harmonic coefficients of the mirror spacecraft; The calculation module is also used to obtain a spherical harmonic coefficient calculation matrix for simulating the magnetic characteristics of the spacecraft to be tested according to the spherical harmonic coefficient relationship; The modeling module is used to calculate the least square solution of all spherical harmonic coefficients based on the Fourier coefficients and the spherical harmonic coefficient calculation matrix to achieve magnetic characteristic modeling of the spacecraft.

5. An electronic device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method according to any one of claims 1 to 3 when executing the computer program.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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