Checking mass gravitational imbalance compensation method based on differential evolution algorithm

Abstract

The invention provides a differential evolution algorithm-based mass gravitational unbalance compensation detection method, and relates to the field of gravitational wave detection, and the method comprises the steps: starting from a multi-stage expansion method, and building a calculation module of a gravitational acceleration and gravitational gradient matrix; geometric parameters, spatial constraints and mass constraints of the compensation mass block are set, and weighted objective functions of gravitational acceleration and gravitational gradient matrixes are constructed; population iteration of the differential evolution algorithm is realized by dynamically adjusting variation factors and crossover probability; and finally, three-dimensional space distribution and geometric parameters of the compensation mass block are obtained according to optimization calculation. According to the method, the optimal parameters of the compensation mass block are obtained by adopting the differential evolution algorithm, each component of the gravitational acceleration and the gravitational gradient is reduced by a plurality of orders of magnitude, and the gravitational imbalance of the test mass can be effectively compensated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of gravitational wave detection, and in particular to a method for compensating for gravitational imbalance of test mass based on a differential evolution algorithm. BACKGROUND

[0002] As a key load of a space gravitational wave detection spacecraft, a spatial inertial sensor has a completely suspended cubic test mass inside, which provides an inertial reference for gravitational wave detection. Generally, the signal of gravitational wave is extremely weak, which has a very high requirement for the acceleration noise of the test mass. Due to the special structure of the spacecraft for gravitational wave detection and the complex space environment, the two test masses inside the spacecraft are affected by various disturbance forces. The spacecraft follows the motion state of the test mass through drag-free and electrostatic control technology, but due to the complexity of the environment of the spacecraft, various types of disturbance forces will inevitably introduce acceleration noise, thereby affecting the measurement of the gravitational wave signal.

[0003] In this complex system of disturbance forces, the gravitational imbalance caused by the static gravity of the spacecraft load is one of the main sources of residual acceleration noise of the test mass, and therefore it is necessary to reduce the influence of the gravitational effect on the test mass through compensation.

[0004] At present, the basic way to suppress this noise is to add a balance mass (BM), which balances the gravitational effect on the test mass through the gravitational effect generated by the balance mass, so that the additional acceleration of the test mass is smaller. Among them, the mass and position selection of the balance mass is a key factor, because they directly determine the level of the gravitational effect of the balance mass on the test mass, thereby affecting the overall compensation effect.

[0005] In the design of the balance mass for compensating for the gravitational imbalance of the test mass, the predecessors have made certain research. M. Armano et al. designed a test mass compensation scheme in LPF, the basic scheme of which is to place a balance mass on each side of the test mass along the sensitive axis, thereby compensating for the acceleration difference of the two test masses on the sensitive axis. J. P. Evans further proposed a two-step balance mass design scheme in combination with the development stage of the LPF spacecraft: one group of balance masses is placed inside the inertial sensor and does not change, and the other group of balance masses is placed outside the inertial sensor, and the balance masses in this group are designed flexibly according to the actual situation of the spacecraft design, which provides a reference for the design of balance masses for similar spacecrafts.

[0006] However, how to design and use appropriate balance masses to make the size of the residual acceleration and the gravitational gradient after compensation meet the precision requirement is still a problem to be studied. SUMMARY

[0007] The present application aims at solving the problem of low precision in the compensation method for the gravity imbalance of the proof mass in the existing spatial inertia sensor, and provides a compensation method for the gravity imbalance of the proof mass based on a differential evolution algorithm.

[0008] The above-mentioned object of the present application is achieved by the following technical solutions.

[0009] S1: determining the initial gravity acceleration and the initial gravity gradient matrix received by the proof mass in the spatial inertia sensor;

[0010] S2: establishing a spherical coordinate system with the proof mass as the center;

[0011] S3: obtaining the expression of the gravity acceleration and the gravity gradient matrix based on the multi-level expansion method and in combination with the spherical coordinate system;

[0012] S4: constructing the spatial constraint, the mass constraint and the geometric constraint of the compensation mass block;

[0013] S5: performing the normalization processing on the gravity acceleration and the gravity gradient matrix through the expression of the gravity acceleration and the gravity gradient matrix, the initial gravity acceleration and the initial gravity gradient matrix, and establishing a weighted objective function;

[0014] S6: taking the three-dimensional coordinates and the geometric parameters of the compensation mass block as the individual genes, and iteratively obtaining the optimal combination of the spatial coordinates and the geometric parameters of the compensation mass block through the differential evolution algorithm in combination with the spatial constraint, the mass constraint, the geometric constraint and the weighted objective function, so as to complete the compensation for the gravity imbalance of the proof mass.

[0015] An electronic device includes a processor, a memory, a user interface and a network interface, the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory, so that the electronic device executes a compensation method for the gravity imbalance of a proof mass based on a differential evolution algorithm.

[0016] A computer readable storage medium stores instructions, when the instructions are executed, a compensation method for the gravity imbalance of a proof mass based on a differential evolution algorithm is executed.

[0017] The technical solutions provided by the present application have the following beneficial effects:

[0018] 1.Using multi-stage expansion method to establish the calculation module of differential evolution algorithm. Taking spherical compensation mass as an example, the expressions of gravitational acceleration and each component of gravitational gradient between compensation mass and test mass are derived. Using multi-stage expansion method for calculation, reasonable selection of multipole moment order can make differential evolution algorithm have both calculation accuracy and efficiency in multiple iterations.

[0019] 2.The constraint conditions related to compensation mass are established, such as compensation mass installation position, geometric constraint and mass constraint, so that the simulation results are closer to the actual situation.

[0020] 3.The weighted objective function of gravitational acceleration and gravitational gradient matrix is established, which makes the optimization process flexible: the optimization focus can be dynamically adjusted by changing the weight to adapt to the priority changes of different tasks; at the same time, it has good robustness: normalization eliminates the difference in magnitude and avoids the dominance of a single indicator in the optimization process.

[0021] 4.The spatial layout and geometric parameters of compensation mass are taken as the individual genes of differential evolution algorithm, and the transition from global search to local search is well realized by setting the dynamically changing parameters of differential evolution algorithm, which avoids the algorithm falling into local optimum. Finally, the gravitational acceleration and gravitational gradient components on the test mass are reduced by multiple orders of magnitude, achieving good compensation effect. BRIEF DESCRIPTION OF DRAWINGS

[0022] The present application will be further described below in conjunction with the drawings and examples, in which:

[0023] Figure 1 is the flowchart of differential evolution algorithm in the embodiment of the present application;

[0024] Figure 2 is the flowchart of differential evolution algorithm in the embodiment of the present application;

[0025] Figure 3 is the flowchart of differential evolution algorithm in the embodiment of the present application;

[0026] Figure 4 is the compensation result diagram of gravitational acceleration and gravitational gradient matrix when N=3 in the embodiment of the present application;

[0027] Figure 5 is the compensation mass spatial distribution diagram when N=3 in the embodiment of the present application;

[0028] Figure 6 is the compensation result diagram of gravitational acceleration and gravitational gradient matrix when N=4 in the embodiment of the present application;

[0029] Figure 7 is the compensation mass spatial distribution diagram when N=4 in the embodiment of the present application;

[0030] Figure 8 is a compensation result diagram of the gravitational acceleration and the gravitational gradient matrix when N=5 in the embodiment of the application;

[0031] Figure 9 is a compensation mass space distribution schematic diagram when N=5 in the embodiment of the application;

[0032] Figure 10 is an electronic device structure schematic diagram in the embodiment of the application. DETAILED DESCRIPTION

[0033] In order to have a clearer understanding of the technical features, objects and effects of the application, the specific embodiments of the application will be described in detail with reference to the drawings.

[0034] The embodiment of the application provides a test mass gravitational imbalance compensation method based on a differential evolution algorithm.

[0035] Please refer to Figure 1 , Figure 1 is a step diagram of a test mass gravitational imbalance compensation method based on a differential evolution algorithm in the embodiment of the application, comprising:

[0036] S1: determining initial gravitational acceleration and an initial gravitational gradient matrix suffered by a test mass in a space inertial sensor;

[0037] S2: establishing a spherical coordinate system with the test mass as the center;

[0038] S3: based on a multi-level expansion method, the expression of the gravitational acceleration and the gravitational gradient matrix are obtained in combination with the spherical coordinate system;

[0039] S4: constructing space constraints, mass constraints and geometric constraints of a compensation mass block;

[0040] S5: performing normalization processing on the gravitational acceleration and the gravitational gradient matrix by using the expression of the gravitational acceleration and the gravitational gradient matrix, the initial gravitational acceleration and the initial gravitational gradient matrix, and establishing a weighted objective function;

[0041] S6: taking three-dimensional coordinates and geometric parameters of the compensation mass block as individual genes, and through the differential evolution algorithm, in combination with the space constraints, the mass constraints, the geometric constraints and the weighted objective function, the best combination of the three-dimensional coordinates and the geometric parameters of the compensation mass block is obtained through iteration, and test mass gravitational imbalance compensation is completed.

[0042] As an embodiment, the differential evolution algorithm (DE) is a heuristic search method for continuous optimization problems in real number domain, which has attracted extensive attention in the field of optimization algorithms since it was first proposed by Storn and Price in 1995. The algorithm simulates the mutation, crossover and selection processes in natural evolution, performs random exploration in continuous domain, and gradually approaches the optimal solution of the problem by combining selection and memory mechanism.

[0043] As an embodiment, the differential evolution algorithm has significant advantages compared with traditional optimization methods such as gradient descent method. First of all, it does not need to rely on the derivative information of the objective function, which makes it particularly suitable for complex optimization problems with nonlinearity and multimodality. Secondly, the algorithm performs well in solving high-dimensional optimization problems through unique mutation mechanism and efficient search ability. Specifically, the differential evolution algorithm combines the idea of population evolution with mathematical difference operation, which not only retains the global search ability of heuristic algorithms, but also realizes efficient convergence through simple parameter design.

[0044] As an embodiment, first, the initial values of the nine parameters of the gravitational acceleration components and the gravitational gradient matrix are assigned, then the differential evolution algorithm is applied to update the variables, the values are randomly updated within the constraint range according to the constraint conditions, the objective function value of each individual in the population is calculated, and the iteration loop is entered. When the termination condition is not met, the mutation, crossover and selection operations are performed in turn, then the iteration number is increased by one, the next iteration is performed, the objective function value of each individual in the population is recalculated, until the iteration number or the accuracy requirement is met, and the optimal result is obtained. The optimal result at this time is the best scheme obtained by automatic optimization, and the optimal scheme finally output corresponds to the radius of each compensation mass block and the coordinates in the spherical coordinate system.

[0045] Step S1 includes:

[0046] The initial gravitational acceleration components a x , a y , a z and the nine components F xx , F yy , F zz , F xy , F xz , F yz , F yx , F zx , F zy of the initial gravitational gradient matrix are determined.

[0047] The present application optimizes according to the following initial values:

[0048] Table 1 initial values of acceleration of gravity and each component of gravity gradient

[0049]

[0050]

[0051] Step S2 comprises:

[0052] A spherical coordinate system is established with the center of mass of the compensated test mass as the coordinate origin;

[0053] As an embodiment, a spherical coordinate system is established with the center of mass of the compensated test mass as the coordinate origin, as shown in Figure 2 .

[0054] Suppose the number of compensation masses is N, and the shape is spherical, then the position and size of the compensation masses in the spherical coordinate system are represented as:

[0055]

[0056] In the formula, X i represents the i-th spherical compensation mass; R i represents the radius of the i-th spherical compensation mass, r i represents the distance between the origin of the spherical coordinate system and the center of mass of the i-th spherical compensation mass, θ i represents the polar angle of the center of mass of the i-th spherical compensation mass, and φ represents the inclination angle of the center of mass of the i-th spherical compensation mass.

[0057] The conversion relationship between r and θ in the spherical coordinate system and the spatial rectangular coordinate system (x, y, z) is shown in the following formula:

[0058]

[0059] Since in the spherical coordinate system , the arctan function can only represent the value between , and the two do not completely correspond, the following is discussed in classification:

[0060] When x≥0 and y≥0:

[0061]

[0062] When x<0 and y≥0:

[0063]

[0064] When x<0 and y<0:

[0065]

[0066] When x≥0 and y<0:

[0067]

[0068] Step S3 includes:

[0069] If the distance from an inner object to the origin is less than the shortest distance from an outer object to the origin, the gravitational potential energy of the inner object and the outer object is expressed as follows:

[0070]

[0071] Where G is the gravitational constant, l represents the order of the multipole moment; ρ P represents the density of the inner object; r l represents the l-th power of r; represents the complex conjugate of the spherical harmonic function; represents the unit vector; d represents the differential symbol, d 3 R is a three-dimensional volume integral element, and the integral range covers the entire inner object; r represents the distance from the mass element of the test mass to the origin; ρ S (R) represents the density function of the spherical compensation mass block; ρ S (R) represents the density function of the spherical compensation mass block; Q lm represents the outer multipole moment of the outer object; q lm represents the inner multipole moment of the inner object, which is defined as:

[0072]

[0073] Where R -(l+1) represents the -(l+1)-th power of R; represents the spherical harmonic function; ρ TM (r) represents the density function of the test mass, ρ S (R) is the density function of the spherical compensation mass block; represents the complex conjugate of the spherical harmonic function, represents the unit vector;

[0074] As an embodiment, the local coordinate system is established with the center of mass of the test mass as the origin, so the test mass is the inner object, and the spherical compensation mass block is the outer object.

[0075] Y lm is a spherical harmonic function, and its expression is as follows:

[0076]

[0077] If the inner multipole moment of the geometric body is known, when the geometric body moves to the spherical coordinates When the outer multipole moments are converted from the inner multipole moments:

[0078]

[0079] where l, m represent the order and rank of the outer field spherical harmonics; l', m' represent the order and rank of the inner multipole moments of the geometric body; r l+1 represents the (l+1)th power of r; δ L-l′,l represents the Kronecker function; r is the distance of the movement of the geometric body; is the Clebsch-Gordan coefficient; q l′m′ represents the inner multipole moments before the movement of the geometric body;

[0080] Since the test mass is a cube with uniform density, the center of mass is located at the coordinate origin, and the edge length is a, then the monopole moment, i.e. l=0, is:

[0081]

[0082] where ρ TM , M TM is the density and mass of the test mass;

[0083] For a cube, due to its high symmetry, through derivation, it can be obtained that q 1m =q 2m =q 3m =0, where q 1m , q 2m , q 3m represent the values of the inner multipole moments of the cube when l=1, 2, 3;

[0084] When the cutoff order is set to l=5, it is derived that there are non-zero values when l=4, m=0, l=4, m=-4, and l=4, m=4:

[0085]

[0086] For a spherical compensation mass, assuming that its density is uniform, the coordinates are (x, y, z), according to formula (12), the outer multipole moments of the sphere are converted from its inner multipole moments;

[0087] The inner multipole moments of the sphere only have non-zero values when the monopole moment exists, and when the sphere is displaced to a position outside the origin, its outer multipole moments in the local coordinate system need to be obtained through displacement conversion;

[0088] Therefore, the outer multipole moments when l=m=0, l=4, m=0, l=4, m=4, and l=4, m=-4 need to be derived:

[0089]

[0090] where M Smass representing the spherical compensation mass;

[0091] Therefore, the inner and outer multipole moments are brought into the potential energy formula (9) to obtain the expression of the gravitational potential energy as follows:

[0092]

[0093] where V0, V 40 , V 44 , and V 4,-4 represent the gravitational potential when the order and the degree take values of l=0; l=4, m=0; l=4, m=4; and l=4, m=-4, respectively; and a represents the side length of the test mass.

[0094] According to the gravitational potential energy, the force components along x, y, and z directions on the test mass are calculated as follows:

[0095]

[0096] In formula (14), r is

[0097] As an embodiment, when the multi-stage expansion method is used, the gravitational force is mainly contributed by the low-order terms. The following data are set to test the influence of the high-order terms:

[0098] Table 2 Geometric parameters of the cube and the sphere

[0099]

[0100] According to the derived equation, the single-order term gravitational force and the high-order term gravitational force between the test mass and the spherical compensation mass are calculated as follows:

[0101] Table 3 Calculation results of the single-order term and the high-order term gravitational force

[0102] Single order term High order term (l=4) F x (N)]]> -1.54129*10 -9 ]]> -7.45486*10 -13 ]]>

[0103] Therefore, the order should be retained to l=5.

[0104] The gravitational acceleration is derived when the order is retained to l=5, as follows:

[0105]

[0106] The expression of the gravitational gradient matrix is as follows:

[0107]

[0108] According to the symmetry of the gravitational gradient matrix, i.e., F xy =F yx , F xz =F zx , and F yz =Fzy The nine components are reduced to six as follows:

[0109]

[0110] By formula (16) derivation, F yy , F zz , F yz .

[0111] As an embodiment, the calculation of the gravitational acceleration and the gravitational gradient components between the compensation mass and the test mass of other shapes still uses the multi-level expansion method. The higher the order of the multipole moment is retained, the higher the calculation accuracy is.

[0112] Step S4 includes:

[0113] As an embodiment, to design a compensation mass meeting the requirements, firstly, the material and the actual shape thereof need to be considered. The material selection of the compensation mass needs to consider three main factors: (1) high density, so as to achieve a higher compensation efficiency with a smaller volume of the compensation mass; (2) high processability, so as to be easily processed into an arbitrary shape; and (3) low magnetism, so as to avoid the magnetic field interference on the test mass. The tungsten alloy can better meet the above three conditions, and therefore, the compensation mass is generally made of the material. In the present application, the density of the tungsten alloy is set to 19250 kg / m 3 .

[0114] As an embodiment, there are two common installation positions of the compensation mass, one is installed in the external spherical shell region of the test mass, and the other is installed on the cylindrical cover surface of the inertial sensor. In the present application, the installation in the external spherical shell region is taken as an example. The internal cavity radius of the spherical shell is 0.064 m. This distance is the minimum envelope spherical radius of the electrode cage, which ensures that the installation of the spherical compensation mass does not have geometric intersection with the electrode cage, and the outer diameter of the compensation region is 0.5 m.

[0115] The compensation mass is made of tungsten alloy, and the density is set to 19250 kg / m 3 ;

[0116] The spatial constraint of the compensation mass is shown in the following formula:

[0117] r IS <r i <r max (18)

[0118] Wherein, r IS represents the envelope spherical radius of the electrode cage of the inertial sensor, r max represents the maximum outer diameter of the installation of the compensation mass; and r i represents the outer diameter of the installation of the i

[0119] As an embodiment, in order to use the compensation mass to achieve the maximum compensation effect, the total mass M of the compensation mass needs to be constrained, and there cannot be geometric intersection between each compensation mass.

[0120] The constraint of the total mass of the compensation mass is represented as follows:

[0121]

[0122] Wherein m i represents the mass of the i-th compensation mass; M max represents the maximum total mass of the compensation mass;

[0123] Let (x i , y i , z i , R i be the centroid coordinate position and the radius of the sphere installed by the i-th compensation mass, and (x j , y j , z j , R j be the centroid coordinate position and the radius of the sphere installed by the j-th compensation mass, then the geometric constraint is represented as follows:

[0124]

[0125] Step S5 includes:

[0126] As an embodiment, in the actual compensation task, the weighted objective function is used to well perform the weight distribution, which focuses on the optimization of the residual gravitational acceleration, the optimization of the gravitational gradient matrix, and the balanced optimization of both.

[0127] The weighted objective function is represented as follows:

[0128] f(x)=ω acc ·f acc +ω grad ·f grad (21)

[0129]

[0130] In the formula, the parameter subscript 0 represents the initial value of the initial gravitational acceleration and the initial gravitational gradient matrix; the subscript c represents the gravitational acceleration and the gravitational gradient effect caused by the compensation mass on the test mass; the subscript t represents the optimization threshold value for normalization; ω acc , ω grad respectively represent the weighting coefficients of the gravitational acceleration and the gravitational gradient matrix; f acc , f gradThe normalized results of the gravitational acceleration and the gravitational gradient matrix;

[0131] As an embodiment, in the objective function design, due to the huge difference in the dimension and magnitude of the acceleration and the gradient, direct weighting will lead to a certain item dominating the optimization process. By normalization, the two can be mapped to the same order of magnitude, ensuring that the weight reflects the true optimization priority, so in f acc , f grad , normalization processing is performed;

[0132] As an embodiment, for different initial values and different optimization indicators, different weighting functions and different optimization thresholds need to be selected. In this optimization, the following parameters are selected: ω acc is 0.45, ω grad is 0.55, and the optimization threshold is 1*10 -12 .

[0133] The gravitational acceleration and the gravitational gradient matrix after compensation of the compensation mass are represented as follows, where the subscript b represents the compensated value:

[0134]

[0135] In an embodiment of the present application, according to the initial value (initial gravitational acceleration and initial gravitational gradient matrix) given in step S1, the spatial layout and geometric parameters of the compensation mass are found through the differential evolution algorithm, which can effectively compensate the gravitational acceleration and the gravitational gradient components. The following are the data and effects of several different numbers of compensation masses.

[0136] When the number of compensation masses N=3, the parameters of the compensation mass are shown in Table 5, the compensation effect is shown in Table 6 and Figure 4 , and the spatial diagram of the compensation mass is shown in Figure 5 .

[0137] Table 5 Compensation mass parameter table when N=3

[0138]

[0139] Table 6 Gravitational acceleration and gravitational gradient matrix compensation results when N=3

[0140]

[0141]

[0142] Table 7 Compensation mass parameter table when N=4

[0143]

[0144] Table 8 Compensation mass parameter table when N=4

[0145]

[0146]

[0147] Table 9: Compensation mass parameters for N=5

[0148]

[0149] Table 10: Gravitational acceleration, gravitational gradient matrix compensation results for N=5

[0150]

[0151] For N=4, the parameters of the compensation mass are shown in Table 7, the compensation effect is shown in Table 8 and Table 9, and the spatial distribution of the compensation mass is shown in Table 10. Figure 6 Figure 7 For N=5, the parameters of the compensation mass are shown in Table 9, the compensation effect is shown in Table 10 and Table 11, and the spatial distribution of the compensation mass is shown in Table 12.

[0152] For N=5, the parameters of the compensation mass are shown in Table 9, the compensation effect is shown in Table 10 and Table 11, and the spatial distribution of the compensation mass is shown in Table 12. Figure 8 Figure 9 For N=5, the parameters of the compensation mass are shown in Table 9, the compensation effect is shown in Table 10 and Table 11, and the spatial distribution of the compensation mass is shown in Table 12.

[0153] The application also discloses an electronic device. Referring to Figure 10 , Figure 10 is a structural schematic diagram of an electronic device disclosed by the embodiment of the application. The electronic device 500 comprises at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.

[0154] The communication bus 502 is configured to realize the connection and communication between the components.

[0155] The user interface 503 comprises a display screen, and optionally, the user interface 503 further comprises a standard wired interface and a wireless interface.

[0156] The network interface 504 optionally comprises a standard wired interface and a wireless interface (such as a WI-FI interface).

[0157] The application also discloses a computer readable storage medium, which stores a plurality of instructions, and the instructions are suitable for being loaded by a processor to execute the above-mentioned inspection quality gravitational imbalance compensation method based on a differential evolution algorithm.

[0158] The above are only exemplary embodiments of the disclosure, and cannot limit the range of the disclosure. Any equivalent changes and modifications made according to the teachings of the disclosure are still within the scope of the disclosure.

[0159] ​​This application is intended to cover any variations, uses, or adaptations of the disclosure, including what is presently described and understood, and including modifications and other uses of the technology covered by the disclosure and the general principles underlying the disclosure. The specification and drawings are, accordingly, to be regarded as illustrative and not restrictive.

Claims

1. A method for compensating for gravitational imbalance of test mass based on differential evolution algorithm, characterized in that: The method comprises the following steps: S1: Determine the initial gravitational acceleration and initial gravitational gradient matrix of the test mass in the space inertial sensor; S2: Establish a spherical coordinate system with the inspection mass as the center; S3: Based on the multi-level expansion method and combined with the spherical coordinate system, the expressions of gravitational acceleration and gravitational gradient matrix are obtained; S4: Constructing the spatial constraints, mass constraints and geometric constraints of the compensation mass block; S5: normalize the gravitational acceleration and gravitational gradient matrix through the expressions of gravitational acceleration and gravitational gradient matrix, and establish a weighted objective function; S6: Taking the three-dimensional coordinates and geometric parameters of the compensation mass block as individual genes, through the differential evolution algorithm, combined with spatial constraints, mass constraints, geometric constraints and weighted objective function, the optimal combination of spatial coordinates and geometric parameters of the compensation mass block is iteratively obtained to complete the compensation of the gravitational imbalance of the inspection mass.

2. The method for compensating for gravitational imbalance of a test mass based on a differential evolution algorithm according to claim 1, wherein: Step S1 includes: Determine the components a of the initial gravitational acceleration along the three coordinate axes to which the test mass is subjected x 、a y 、a z and the nine components of the initial gravitational gradient matrix F xx 、F yy 、F zz 、F xy 、F xz 、F yz 、F yx 、F zx 、F zy .

3. The method for compensating for gravitational imbalance of a test mass based on a differential evolution algorithm according to claim 2, wherein: Step S2 includes: Establish a spherical coordinate system with the center of mass of the compensated test mass as the coordinate origin; Assuming the number of compensation mass blocks is N and the shape is spherical, the position and size of the compensation mass blocks in the spherical coordinate system are expressed as: Where, X i represents the i-th spherical compensation mass block; R i represents the radius of the i-th spherical compensation mass block, r i represents the distance between the origin of the spherical coordinate system and the center of mass of the i-th spherical compensation mass block, θ i represents the polar angle of the center of mass of the ith spherical compensation mass block, represents the tilt angle of the center of mass of the i-th spherical compensation mass block; The conversion relationship between r and θ in the spherical coordinate system and the spatial rectangular coordinate system (x, y, z) is shown in the following formula: Since the spherical coordinate system The arctan function can only express between The two values ​​are not completely corresponding. The following is a classification discussion: When x ≥ 0 and y ≥ 0: When x<0 and y≥0: When x<0 and y<0: When x≥0 and y<0:

4. The method for compensating for gravitational imbalance of a test mass based on a differential evolution algorithm according to claim 3, wherein: Step S3 includes: For any two objects in a spatial coordinate system, if the distance from one inner object to the origin is less than the shortest distance from the other outer object to the origin, then the gravitational potential energy between the inner object and the outer object can be expressed as follows: Where G is the universal gravitational constant, l represents the order of the multipole moment; ρ P Indicates the density of the object; r l represents the power of r; represents the complex conjugate of the spherical harmonics; represents the unit vector; d represents the differential symbol, d 3 R is the three-dimensional volume integral element, and the integral range covers the entire internal object; r represents the distance from the mass element of the test mass to the origin; ρ S (R) represents the density function of the spherical compensating mass block; ρ S (R) represents the density function of the spherical compensating mass block; Q lm represents the external multipole moment of the external object; q lm represents the internal multipole moment of the internal object, which are defined as follows: Among them: R -(l+1) represents R to the power of -(l+1); represents spherical harmonics; ρ TM (r) represents the density function of the inspection mass, ρ S (R) is the density function of the spherical compensation mass block; represents the complex conjugate of the spherical harmonics, represents a unit vector; Y lm is a spherical harmonic function, and its expression is as follows: If the interior multipole moment of a geometric body is known, when the geometric body is moved to spherical coordinates When , the outer multipole moment is converted from the inner multipole moment: Where l and m represent the order and series of the external field spherical harmonics; l' and m' represent the order and series of the multipole moments in the geometry; r l+1 represents r to the (l+1)th power; δ L-l′,l represents the Kronecker function; r is the distance the geometric body moves; is the Klebsch-Gordon coefficient; q l′m′ represents the internal multipole moment of the geometric body before it moves; Since the test mass is a cube with uniform density, its center of mass is at the origin, and its side length is a, its monopole moment, i.e., l = 0, is: where ρ TM 、M TM To test the density and quality of the mass; For the cube, due to its high symmetry, q can be deduced as 1m =q 2m =q 3m =0, where q 1m ,q 2m ,q 3m represents the value of the multipole moment in the cube when l = 1, 2, 3; When the cutoff order is set to l = 5, it is deduced that there are non-zero values ​​when l = 4, m = 0, l = 4, m = -4, and l = 4, m = 4: For a spherical compensating mass block, assuming its density is uniform and its coordinates are (x, y, z), according to formula (12), the external multipole moment of the sphere is converted from its internal multipole moment; The internal multipole moment of a sphere has a non-zero value only when it is a monopole moment. When the sphere is displaced to a position outside the origin, its external multipole moment in the local coordinate system needs to be obtained through displacement transformation; Therefore, it is necessary to derive the exterior multipole moments when l = m = 0, l = 4, m = 0, l = 4, m = 4, and l = 4, m = -4: Among them, M S The mass representing the spherical compensation mass; Therefore, up to l = 5, the inner multipole moment and the outer multipole moment are substituted into the potential energy formula (9), and the expression of gravitational potential energy is obtained as follows: Among them, V0, V 40 、V 44 、V 4,-4 represents the gravitational potential when the order and series are l = 0; l = 4, m = 0; l = 4, m = 4; l = 4, m = -4 respectively; a represents the side length of the test mass; Based on the gravitational potential energy, calculate the components of the force acting on the test mass along x, y, and z: In formula (14), r is Keeping the order to l = 5, the gravitational acceleration is derived as follows: The gravitational gradient matrix expression is: According to the symmetry of the gravitational gradient matrix, F xy =F yx 、F xz =F zx 、F yz =F zy , simplifying the nine components to six, as follows: By deducing from formula (16), we can get F yy 、F zz 、F yz .

5. The method for compensating for gravitational imbalance of a test mass based on a differential evolution algorithm according to claim 1, wherein: Step S4 includes: The compensation mass block is made of tungsten alloy with a density of 19250 kg / m 3 ; The spatial constraint of the compensation mass block is expressed as follows: r IS ＜r i ＜r max (18) where r IS Indicates the radius of the inertial sensor electrode cage envelope, r max Indicates the maximum outer diameter of the compensation mass block installation; r i represents the outer diameter of the installation of the i-th compensation mass block; The total mass of the compensation mass block is constrained as follows: where m i represents the mass of the i-th compensation mass block; M max Indicates the maximum total mass of the compensation mass block; Assume (x i ,y i ,z i ), R i is the coordinate position of the center of mass and the radius of the sphere where the i-th compensation mass block is installed, (x j ,y j ,z j ), R j is the coordinate position of the center of mass of the jth compensation mass block and the radius of the sphere, the geometric constraints are expressed as follows:

6. The method for compensating for gravitational imbalance of a test mass based on a differential evolution algorithm according to claim 1, wherein: Step S5 includes: The weighted objective function is as follows: f(x)=ω acc ·f acc +oh grad ·f grad (21) Where, the parameter subscript 0 represents the initial value of the initial gravitational acceleration and initial gravitational gradient matrix; the subscript c represents the gravitational acceleration and gravitational gradient effect caused by the compensation mass block on the test mass; the subscript t represents the optimization threshold, which is used for normalization; ω acc 、ω grad Respectively represent the weighting coefficients of gravitational acceleration and gravitational gradient matrix; f acc 、f grad Represents the normalized results of gravitational acceleration and gravitational gradient matrix; The gravitational acceleration and gravitational gradient matrices after compensation by the compensation mass block are expressed as follows, where the subscript b represents the compensated value:

7. An electronic device, characterized in that: It includes a processor, a memory, a user interface and a network interface, the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device executes the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, and when the instructions are executed by a computer, the method according to any one of claims 1 to 6 is executed.

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