A self-gravitational compensation method for space gravitational wave detection

Abstract

The application discloses a self-gravitation compensation method for space gravitational wave detection, which comprises the following steps: establishing a finite element discrete model of a spacecraft, calculating a spacecraft gravitation reference value borne by a test mass, and combining test mass parameters to obtain a reference self-gravitation linear acceleration, angular acceleration and stiffness; constructing a balance mass configuration parameter set, and screening a qualified balance mass configuration set according to an inertia sensor envelope geometric parameter and a balance mass installation condition; further constructing a self-gravitation acceleration error, a self-gravitation stiffness error and a balance mass physical mass target function, and adopting a multi-objective genetic algorithm and a multi-operator difference algorithm for two-stage optimization to output a balance mass configuration to be compensated. The application can cooperatively optimize the self-gravitation acceleration, the self-gravitation stiffness and the balance mass total mass under the condition of meeting the installation constraint, and improve the feasibility, compensation accuracy and mass utilization efficiency of the balance mass configuration design.

Description

Technical Field

[0001] This invention belongs to the field of space gravitational wave detection technology, and more specifically, relates to a self-gravity compensation method for space gravitational wave detection. Background Technology In space-based gravitational wave detection missions, a long baseline formation is constructed using several spacecraft within the spacecraft. The test mass, located within the inertial sensors of each spacecraft and in a free-floating state, serves as a purely inertial measurement benchmark. Laser interferometry between the test masses precisely captures the picometer-level baseline stretching and spatiotemporal micro-strain caused by gravitational waves, thereby detecting low- to mid-frequency gravitational wave signals. However, the assembly of components such as the spacecraft's shell, payload, and propellant results in an imperfectly uniform mass distribution. This imbalance creates an unbalanced self-gravitational field that continuously pulls on the test mass, applying additional gravitational perturbations and introducing residual acceleration noise, which can easily mask the weak gravitational wave signals.

[0002] Self-gravitational noise compensation is a technique that uses a designed balancing mass to adjust the mass distribution of the spacecraft and counteract the gravitational disturbance it causes to the test mass, thereby controlling the residual acceleration noise within the limits required by the detection mission.

[0003] In existing self-gravitational noise compensation methods, the complex configuration of spacecraft leads to significant multi-axis gravitational coupling effects. Optimizing only one axis can easily cause noise to exceed limits in other directions. Furthermore, the physical mass and layout of the balancing mass are subject to engineering constraints such as spacecraft space conflicts, making precise balancing difficult and easily leading to a decrease in the sensitivity of inertial sensors. On the other hand, using frequent adjustments to the spacecraft's attitude or increasing fuel consumption to suppress residual acceleration noise will accelerate spacecraft wear, increase the risk of failure, and shorten mission life.

[0004] Therefore, how to develop a self-gravity compensation method that can reasonably compensate for the mass of a spacecraft to suppress its residual acceleration noise has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention aims to overcome the problems of existing self-gravity noise compensation methods, which suffer from significant multi-axis gravitational coupling effects due to the complex configuration of spacecraft, the tendency for single-axis optimization to cause noise exceeding the standard in other directions, the difficulty in accurately balancing the physical mass and layout of the balancing mass due to engineering constraints such as spacecraft conflicts, and the fact that using frequent adjustments to the spacecraft's attitude or increasing fuel consumption to suppress residual acceleration noise will accelerate spacecraft wear, increase the risk of failure, and shorten mission life.

[0006] To achieve the above objectives, the present invention provides a self-gravitational compensation method for space gravitational wave detection, comprising: Establish a finite element discrete model and output the finite element node parameters. Calculate the gravitational reference value of the spacecraft's gravity on the verification mass based on the finite element node parameters and the universal gravitation formula. Obtain the mass and dimensional parameters of the inspection mass, and calculate the reference self-gravitational linear acceleration, reference self-gravitational angular acceleration and reference self-gravitational stiffness of the inspection mass based on the gravitational reference value; A set of configuration parameters for the balancing mass is selected and constructed. The set of value constraints for the configuration parameter set is generated based on the envelope geometry parameters of the pre-acquired inertial sensor. The installation conditions of the balancing mass are determined based on the separation axis theorem to screen out a qualified balancing mass configuration set. A self-gravitational acceleration error objective function is constructed based on the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration. A self-gravitational stiffness error objective function is constructed based on the reference self-gravitational stiffness. Finally, a balance mass physical mass objective function is constructed based on the qualified balance mass configuration set. A number of candidate solutions for equilibrium mass configurations are generated based on a multi-objective genetic algorithm to construct a first optimization model. The multi-objective genetic algorithm is then used to optimize the candidate solutions for equilibrium mass configurations to output a differentiated set of feasible solutions with elite feasible solutions. Each candidate solution for equilibrium mass configuration includes the configuration parameter set and spatial installation coordinates of each equilibrium mass within it. A second optimization model is constructed based on the differentiated feasible solution set, and the differentiated feasible solution set is optimized by the multi-operator difference algorithm to output the configuration of the balance mass to be compensated. Each feasible solution in the differentiated feasible solution set includes the configuration parameter set, spatial installation coordinates, and the total mass of all balance masses within it.

[0007] Optionally, the step of establishing a finite element discrete model and outputting finite element node parameters, and calculating the gravitational reference value of the spacecraft's gravity on the verification mass based on the finite element node parameters and the universal gravitation formula, specifically includes: Construct a three-dimensional geometric model of the space gravitational wave detector and obtain the original parameter set. Based on the FEM and the original parameter set, establish a finite element discrete model and output the finite element node parameters. Based on the finite element node parameters and the universal gravitation formula, the gravitational reference value of the spacecraft's gravity on the test mass is calculated.

[0008] Optionally, the acquisition of the mass and dimensional parameters of the inspection mass, and the calculation of the reference self-gravitational linear acceleration, reference self-gravitational angular acceleration, and reference self-gravitational stiffness of the inspection mass based on the gravitational reference value, specifically includes: Let the reference self-gravitational acceleration be... Obtain the quality value of the inspection and set it as... According to the gravitational reference value ,get: Let the reference self-gravitational angular acceleration be Obtain the dimensional values ​​of the inspection quality on the X, Y, and Z axes and set them as... , and Based on the Euler equations, the following calculations were performed: In the formula: , and These represent the angular accelerations on the X, Y, and Z axes of the i-th grid node corresponding to the inspection quality, respectively. Let the component of the gravitational reference value in the e direction be... Let K be the reference self-gravitational stiffness in the j-direction, then: In the formula: e and All are represented as the X-axis, Y-axis, or Z-axis; This represents the initial centroid coordinates for quality inspection. It represents the displacement of the inspection mass along the X-axis, Y-axis, or Z-axis.

[0009] Optionally, the selection and construction of the configuration parameter set for the balancing mass involves generating a set of value constraints for the configuration parameter set based on the pre-acquired envelope geometry parameters of the inertial sensor, and determining the installation conditions of the balancing mass based on the separating axis theorem to filter out a qualified balancing mass configuration set. Specifically, this includes: Several balancing masses with circular arc patch configurations are selected, and the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, radial thickness, and the number of balancing masses matching each test mass are extracted for each balancing mass, and a configuration parameter set is constructed. Based on the pre-acquired inner diameter of the inner cylinder, axial mounting height range, and circumferential angle range of the inertial sensor, a set of constraint values ​​for the configuration parameter set is generated, wherein the envelope geometric parameters include the inner diameter of the inner cylinder, the axial mounting height range, and the circumferential angle range. Based on the separation axis theorem, the three-dimensional image of each balancing mass is projected onto the two-dimensional projection range of the cylindrical mounting reference plane of the inertial sensor, so that the installation conditions are qualified when there is no overlap between any two balancing masses.

[0010] Optionally, several balancing masses, all with a circular arc patch configuration, are selected. The circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, radial thickness, and the number of balancing masses matching each test mass are extracted for each balancing mass. A configuration parameter set is then constructed, specifically including: A cylindrical coordinate system is established with the central axis of the cylindrical region of the inertial sensor's inner cavity as the Z-axis. Any balancing mass with an arc patch configuration is pre-installed in the cylindrical region to determine the circumferential start angle and circumferential end angle. The axial top height and axial bottom height are determined based on the axial boundary of the cylindrical region along the Z-axis. Obtain the radial thickness of the balance mass and the number of balance masses matching each inspection mass to form a configuration parameter set. : In the formula: Represented as the first A balanced mass; Represented as the circumferential starting angle; Represented as the circumferential termination angle; This is expressed as the axial top height; This is expressed as the axial bottom height; Expressed as radial thickness; This is represented as the number of balanced masses that match each inspection quality.

[0011] Optionally, based on the pre-acquired inner diameter of the inertial sensor's inner cylinder, the axial mounting height range, and the circumferential angle range, a set of configuration parameter values ​​and constraints is generated, specifically including: The inner diameter of the inertial sensor's inner cylinder, axial installation height range, and circumferential angle range are obtained based on the actual configuration data of the space gravitational wave detector. Based on the inner diameter of the inner cylinder, the axial installation height range, and the circumferential angle range, a set of constraint values ​​for the configuration parameter set is generated: In the formula: and These represent the lower and upper limits of the configuration parameter set, respectively. , , , as well as respectively represent the upper limit values of the circumferential start angle, circumferential end angle, axial top height, axial bottom height, and radial thickness; , , , and respectively represent the lower limit values of the circumferential start angle, circumferential end angle, axial top height, axial bottom height, and radial thickness.

[0012] As an optional implementation, the step of projecting the three-dimensional image of each balance mass onto the two-dimensional projection interval of the cylindrical mounting reference surface of the inertial sensor based on the separating axis theorem, determining that the mounting condition is qualified when there is no overlap between the projections of any two balance masses, so as to screen out a qualified balance mass configuration set, specifically comprises: mapping each balance mass into a three-dimensional reference coordinate system based on the geometric parameters of the balance mass to obtain a three-dimensional image; projecting the three-dimensional image of each balance mass onto the two-dimensional projection interval of the cylindrical mounting reference surface of the inertial sensor, and performing overlap detection on the projection intervals of the projections of any two balance masses according to the separating axis theorem to obtain a first overlap identifier Overlap1 and a second overlap identifier Overlap2; when Overlap1=false and Overlap2=false, determining that any two balance masses do not overlap, so that the mounting condition is qualified, to screen out the qualified balance mass configuration set.

[0013] As an optional implementation, the step of constructing a self-gravitational acceleration error objective function according to the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration, constructing a self-gravitational stiffness error objective function based on the reference self-gravitational stiffness, and constructing a balance mass physical mass objective function based on the qualified balance mass configuration set, specifically comprises: constructing the self-gravitational acceleration error objective function based on the exterior point penalty function according to the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration : wherein: represents the distribution characteristic of the total mass of the spacecraft pre-installed with the balance mass; represents the self-gravitational acceleration to which the test mass obtained by calculation after the balance mass is pre-installed is subjected; represents the preset target value of the self-gravitational acceleration to which the i-th test mass is subjected; represents the number of the preset target values of the self-gravitational acceleration of all the test masses; The linear weighting coefficient representing the self-gravitational acceleration deviation of each inspection quality; This represents the penalty weighting coefficient for the additional deviation after the self-gravitational acceleration deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Based on the baseline self-gravitational stiffness, and using the exterior point penalty function, an objective function for the self-gravitational stiffness error is constructed. : In the formula: This represents the self-gravitational stiffness of the test mass calculated after the balance mass is pre-installed; It represents the preset target value of the self-gravitational stiffness experienced by the i-th test mass; The number of preset target values ​​for the self-gravitational stiffness of all inspected quality; Linear weighting coefficient for the self-gravitational stiffness deviation of each inspection quality; It is represented as the penalty weighting coefficient for the additional deviation after the self-gravitation stiffness deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Based on a qualified balanced mass configuration set and according to the homogeneous firmware quality calculation formula, a balanced mass physical mass objective function is constructed. : In the formula: Material density expressed as equilibrium mass; Represented as the starting angle from the circumference To the circumferential termination angle Direction angle; R represents the radius of the inertial sensor.

[0014] Optionally, the step of generating several candidate solutions for balanced quality configurations based on a multi-objective genetic algorithm, constructing and optimizing these candidate solutions using a first optimization model to output a differentiated feasible solution set with elite feasible solutions, specifically includes: Based on the elite feasible non-dominated sorting genetic algorithm, several candidate solutions for balanced quality configurations are generated. Based on the objective functions of self-gravitational acceleration error, self-gravitational stiffness error, value constraint set, and qualified equilibrium mass configuration set function, the first optimization model is constructed as follows: An elite feasible non-dominated sorting genetic algorithm with g-domination improved sorting logic is adopted to iteratively optimize several balanced quality configuration candidate solutions to select elite candidate solutions. Elite candidate solutions and non-elite candidate solutions are stored hierarchically to output a differentiated feasible solution set.

[0015] Optionally, the second optimization model is constructed based on the differentiated feasible solution set, and the differentiated feasible solution set is optimized using a multi-operator difference algorithm to output the configuration of the equilibrium mass to be compensated. Each feasible solution in the differentiated feasible solution set includes a configuration parameter set, spatial installation coordinates, and the total mass of all equilibrium masses within it, specifically including: Construct a second optimization model based on the differentiated feasible solution set: The differentiated feasible solution set is adaptively iteratively optimized using a multi-operator difference algorithm. The feasible solution with the minimum total mass of all equilibrium masses within it, whose objective functions of self-gravitational acceleration error and gravitational stiffness error are both ≤0, is defined as the equilibrium mass configuration to be compensated.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes a self-gravitational compensation method for space gravitational wave detection. By establishing a finite element discrete model and calculating the gravitational reference value of the spacecraft's gravity on the test mass, it achieves accurate modeling of the multi-axis gravitational field under complex spacecraft configurations, providing fundamental data for subsequent multi-physical quantity coupling analysis. Furthermore, by calculating the reference self-gravitational acceleration, angular acceleration, and stiffness of the test mass based on the gravitational reference value, it achieves a quantitative characterization of the multi-axis gravitational coupling effect, avoiding noise exceeding limits in other directions caused by single-axis optimization. Finally, by selecting a set of equilibrium mass configuration parameters and screening for suitable configurations based on the separated axis theorem, it achieves engineering constraints on the physical mass and layout of the equilibrium mass. The invention employs explicit modeling of the bundle to ensure that candidate solutions meet space installation feasibility requirements. Furthermore, it establishes a multi-objective optimization framework by constructing objective functions for self-gravitational acceleration error, self-gravitational stiffness error, and equilibrium mass physical mass, simultaneously balancing noise suppression effects with engineering implementation costs. Further, it generates differentiated feasible solution sets based on a multi-objective genetic algorithm, combining global search capabilities with local refinement capabilities to avoid getting trapped in local optima. Finally, it utilizes a multi-operator difference algorithm to perform secondary optimization on the differentiated feasible solution sets, achieving accurate output of the equilibrium mass configuration to be compensated, minimizing residual acceleration noise while ensuring total mass constraints. This invention eliminates the need for frequent spacecraft attitude adjustments or increased fuel consumption, thereby reducing mechanical wear and failure risks and extending mission life.

[0017] As can be seen from the above, the technical solution of the present invention can effectively solve the problems of existing self-gravitational noise compensation methods, which are prone to significant multi-axis gravitational coupling effects due to the complex configuration of spacecraft, easy to cause noise exceeding the standard in other directions due to optimization of only one axis, difficulty in accurately balancing the physical mass and layout of the balance mass due to engineering constraints such as spacecraft conflicts, and the fact that using frequent adjustments to the spacecraft attitude or increasing fuel consumption to suppress residual acceleration noise will accelerate the wear of the spacecraft, increase the risk of failure, and shorten the mission life.

[0018] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a self-gravitational compensation method for space gravitational wave detection, as described in an embodiment of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to more fully understand the technical solutions of the present invention, exemplary embodiments of the present invention will be described more comprehensively and in detail below with reference to the accompanying drawings. Obviously, the one or more embodiments of the present invention described below are merely one or more specific ways to implement the technical solutions of the present invention, and are not exhaustive. It should be understood that other ways belonging to a general inventive concept can be used to implement the technical solutions of the present invention, and should not be limited to the embodiments described exemplary. Based on one or more embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] Reference Figure 1 The present invention provides a self-gravitational compensation method for space gravitational wave detection, comprising: Step S1: Establish a finite element discrete model and output the finite element node parameters. Calculate the gravitational reference value of the spacecraft's gravity on the test mass based on the finite element node parameters and the universal gravitation formula. Step S2: Obtain the mass and dimensional parameters of the inspection mass, and calculate the reference self-gravitational linear acceleration, reference self-gravitational angular acceleration and reference self-gravitational stiffness of the inspection mass based on the gravitational reference value; Step S3: Select and construct the configuration parameter set of the balancing mass, generate the value constraint set of the configuration parameter set according to the envelope geometry parameters of the pre-acquired inertial sensor, and determine the installation conditions of the balancing mass based on the separation axis theorem to screen out a qualified balancing mass configuration set. Step S4: Construct a self-gravitational acceleration error objective function based on the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration; construct a self-gravitational stiffness error objective function based on the reference self-gravitational stiffness; and construct a balance mass physical mass objective function based on the qualified balance mass configuration set. Step S5: Generate several candidate solutions for equilibrium mass configurations based on a multi-objective genetic algorithm to construct the first optimization model, and optimize the several candidate solutions for equilibrium mass configurations using the multi-objective genetic algorithm to output a differentiated feasible solution set with elite feasible solutions. Each candidate solution for equilibrium mass configuration includes the configuration parameter set and spatial installation coordinates of each equilibrium mass within it. Step S6: Construct a second optimization model based on the differentiated feasible solution set, and optimize the differentiated feasible solution set through a multi-operator difference algorithm to output the configuration of the balance mass to be compensated. Each feasible solution in the differentiated feasible solution set includes a set of configuration parameters, spatial installation coordinates, and the total mass of all balance masses within it.

[0022] This invention proposes a self-gravitational compensation method for space gravitational wave detection. By establishing a finite element discrete model and calculating the gravitational reference value of the spacecraft's gravity on the test mass, it achieves accurate modeling of the multi-axis gravitational field under complex spacecraft configurations, providing fundamental data for subsequent multi-physical quantity coupling analysis. Furthermore, by calculating the reference self-gravitational acceleration, angular acceleration, and stiffness of the test mass based on the gravitational reference value, it achieves a quantitative characterization of the multi-axis gravitational coupling effect, avoiding noise exceeding limits in other directions caused by single-axis optimization. Finally, by selecting a set of equilibrium mass configuration parameters and screening for suitable configurations based on the separated axis theorem, it achieves engineering constraints on the physical mass and layout of the equilibrium mass. The invention employs explicit modeling of the bundle to ensure that candidate solutions meet space installation feasibility requirements. Furthermore, it establishes a multi-objective optimization framework by constructing objective functions for self-gravitational acceleration error, self-gravitational stiffness error, and equilibrium mass physical mass, simultaneously balancing noise suppression effects with engineering implementation costs. Further, it generates differentiated feasible solution sets based on a multi-objective genetic algorithm, combining global search capabilities with local refinement capabilities to avoid getting trapped in local optima. Finally, it utilizes a multi-operator difference algorithm to perform secondary optimization on the differentiated feasible solution sets, achieving accurate output of the equilibrium mass configuration to be compensated, minimizing residual acceleration noise while ensuring total mass constraints. This invention eliminates the need for frequent spacecraft attitude adjustments or increased fuel consumption, thereby reducing mechanical wear and failure risks and extending mission life.

[0023] In one embodiment, in step S1, a finite element discrete model is established and finite element node parameters are output. Based on the finite element node parameters and the universal gravitation formula, the gravitational reference value of the spacecraft's gravity acting on the test mass is calculated, specifically including: Step S11: Construct a three-dimensional geometric model of the space gravitational wave detector and obtain the original parameter set. Based on the Finite Element Method (FEM) and the original parameter set, establish a finite element discrete model and output the finite element node parameters. Step S12: Based on the finite element node parameters and the universal gravitation formula, calculate the gravitational reference value of the spacecraft's gravity on the test mass.

[0024] In one specific embodiment, in step S11, a three-dimensional geometric model of the space gravitational wave detector is constructed and the original parameter set is obtained. Based on the FEM and the original parameter set, a finite element discrete model is established and the finite element node parameters are output, specifically including: Step S111: Input the actual configuration data of the space gravitational wave detector into the 3D modeling tool to construct a 3D geometric model; Step S112: Based on the three-dimensional reference coordinate system in the three-dimensional geometric model, obtain the spatial coordinates and material density of each spacecraft and its corresponding inertial sensor and test mass. The original parameter set includes spatial coordinates and material density. Step S113: Based on spatial coordinates and material density, the three-dimensional geometric model is divided into a network according to FEM to discretize the three-dimensional geometric model into several finite element elements and establish a finite element discrete model, wherein each finite element element includes several mesh nodes. Step S114: Extract the node mass and node coordinates of each mesh node in each finite element based on the finite element discrete model, wherein the finite element node parameters include node mass and node coordinates.

[0025] Specifically, the actual configuration data of the space gravitational wave detector is obtained based on the actual construction requirements of the space gravitational wave detection mission. That is, the external geometric information and assembly position information of each spacecraft are pre-set at the beginning of the formation of the space gravitational wave detector, so as to construct a three-dimensional geometric model based on a three-dimensional modeling tool. The three-dimensional modeling tool in the embodiments of the present invention can be CAD or SolidWorks, but the present invention is not limited to this, and any three-dimensional modeling tool that can achieve the same technical effect as the present invention is acceptable.

[0026] By discretizing the three-dimensional geometric model into several finite element elements and establishing a finite element discrete model, the continuous spatial structure of each spacecraft in the three-dimensional geometric model is decomposed into several finite element elements, which simplifies the calculation difficulty, improves the calculation accuracy, and facilitates subsequent node mass calculation.

[0027] It is worth noting that in the FEM processing flow, the spacecraft, inertial sensor and inspection mass are independent geometric entities. Each geometric entity is pre-assigned a unique material density. The mesh is divided along the interface of different geometric entities. Thus, each finite element element generated includes only a single geometric entity and matches only one material density.

[0028] In one specific embodiment, the node mass is obtained by calculating the element volume by reading the geometric dimensions of each finite element in the finite element discrete model, calculating the total element mass based on the element volume and the matching material density, and distributing the total element mass to each corresponding mesh node according to the element shape function.

[0029] Specifically, when the same mesh node is shared by multiple finite element elements, the node mass of each mesh node is the sum of the masses allocated to it.

[0030] The total mass of the element is obtained by multiplying the element volume by the density of the matching material, and the node coordinates of each mesh node are extracted synchronously through the finite element discretization model.

[0031] Furthermore, the element volume is calculated by integrating the Jacobian integral derived from the corresponding element shape function using the corresponding spatial coordinates as input. The element shape function is uniquely determined by pre-selected solid element types in the FEM, such as tetrahedral and hexahedral elements, and is a standard mathematical function built into the corresponding element theory, requiring no additional manual derivation. Moreover, the mass allocation operation is part of the consistent mass matrix construction step in the complete standard FEM workflow. This operation is performed after the geometric mesh is discretized, the material density of each finite element is calculated, and the total mass of the element is determined. The FEM automatically calls the shape function weighting coefficients of the corresponding finite element and distributes the overall mass of each finite element to all its connected nodes according to the weights. This operating principle of the FEM is existing technology; therefore, it will not be elaborated further here.

[0032] In one specific embodiment, in step S12, based on the finite element node parameters and the universal gravitation formula, the gravitational reference value of the spacecraft acting on the test mass is calculated, specifically including: Let the gravitational reference value be... Based on node mass, node coordinates, and the law of universal gravitation, we obtain: In the formula: G is represented as the gravitational constant; The density of the material is expressed as the material density for quality inspection. Represented as the first corresponding spacecraft and inertial sensor The node quality of each grid node, among which... ; , and Represented as the first corresponding spacecraft and inertial sensor The coordinates of each grid node; x, y, and z represent any infinitesimal volume element within the test mass. , where .

[0033] Specifically, the calculation of the gravitational reference value can reveal the original gravitational perturbation reference value of the spacecraft to the test mass, providing a physical reference for the subsequent addition of the balancing mass and the evaluation of the compensation effect.

[0034] In one embodiment, in step S2, the mass and dimensional parameters of the inspection mass are obtained, and the reference self-gravitational linear acceleration, reference self-gravitational angular acceleration, and reference self-gravitational stiffness experienced by the inspection mass are calculated based on the gravitational reference value. Specifically, this includes: Step S21: Let the reference self-gravitational acceleration be... Obtain the quality value of the inspection and set it as... According to the gravitational reference value ,get: Step S22: Let the reference self-gravitational angular acceleration be... Obtain the dimensional values ​​of the inspection quality on the X, Y, and Z axes and set them as... , and Based on the Euler equations, the following calculations were performed: In the formula: , and These represent the angular accelerations on the X, Y, and Z axes of the i-th grid node corresponding to the inspection quality, respectively. Step S23: Let the component of the gravitational reference value in the e direction be... Let K be the reference self-gravitational stiffness in the j-direction, then: In the formula: e and All are represented as the X-axis, Y-axis, or Z-axis; This represents the initial centroid coordinates for quality inspection. It represents the displacement of the inspection mass along the X-axis, Y-axis, or Z-axis.

[0035] Specifically, the calculation of the baseline self-gravitational acceleration provides the acceleration field generated by the spacecraft's own gravity, which can be used to reflect the additional interference caused by the spacecraft's own gravity on the operation of the test mass. The mass and dimensional parameters of the test mass are obtained from the actual configuration data of the space gravitational wave detector.

[0036] The calculation of the baseline self-gravitational angular acceleration can reflect the rotational disturbances caused by the spacecraft's own gravity, and can be used to assess and verify errors in mass attitude or orbital coupling.

[0037] The calculation of the baseline self-gravitational stiffness can characterize the rate of change of the spacecraft's own gravity with the displacement of the test mass, providing data support for subsequent calculations. Furthermore, the initial centroid coordinates of the test mass are extracted based on a three-dimensional geometric model.

[0038] It is worth noting that the displacement of the test mass is calculated based on the baseline self-gravitational stiffness and the initial centroid coordinates, in order to quantify the degree of deviation of the test mass relative to the initial centroid coordinates and characterize the range of influence of the spacecraft's own gravity on the test mass.

[0039] In one embodiment, in step S3, a set of configuration parameters for the balancing mass is selected and constructed. A set of value constraints for the configuration parameters is generated based on the pre-acquired envelope geometry parameters of the inertial sensor. The installation conditions for the balancing mass are determined based on the separating axis theorem to filter out a qualified balancing mass configuration set. Specifically, this includes: Step S31: Select several balancing masses that are all in the shape of circular arc patches, extract the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, radial thickness, and the number of balancing masses that match each test mass for each balancing mass, and construct a set of configuration parameters; Step S32: Based on the pre-acquired inner diameter of the inner cylinder, axial installation height range, and circumferential angle range of the inertial sensor, generate a set of value constraints for the configuration parameter set, wherein the envelope geometric parameters include the inner diameter of the inner cylinder, the axial installation height range, and the circumferential angle range. Step S33: Based on the separation axis theorem, project the three-dimensional image of each balancing mass onto the two-dimensional projection range of the cylindrical mounting reference plane of the inertial sensor, so that the installation conditions are qualified when there is no overlap between any two balancing masses.

[0040] Specifically, several balancing masses in the form of arc-shaped patches are made of tungsten-copper alloy with high density, non-magnetic properties, low coefficient of thermal expansion, and easy machinability. They are installed inside the inertial sensor and in the cylindrical area of ​​the inertial sensor cavity around the inspection mass to achieve gravitational compensation for the inspection mass.

[0041] In one specific embodiment, in step S31, several balancing masses, all of which are in the form of circular arc patches, are selected. The circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, radial thickness, and the number of balancing masses matching each test mass are extracted for each balancing mass. A configuration parameter set is then constructed, specifically including: Step S311: Establish a cylindrical coordinate system with the central axis of the cylindrical region of the inertial sensor's inner cavity as the Z-axis, and pre-install any balancing mass in the cylindrical region with an arc patch configuration to determine the circumferential start angle and circumferential end angle. Step S312: Determine the axial top height and axial bottom height based on the axial boundary of the cylindrical region along the Z-axis; Step S313: Obtain the radial thickness of the balance mass and the number of balance masses matching each inspection mass to form a configuration parameter set. : In the formula: Represented as the first A balanced mass; Represented as the circumferential starting angle; Represented as the circumferential termination angle; This is expressed as the axial top height; This is expressed as the axial bottom height; Expressed as radial thickness; This is represented as the number of balanced masses that match each inspection quality.

[0042] Specifically, selecting any balancing mass with an arc-shaped patch configuration and pre-installing it in the cylindrical region involves defining the candidate placement area of ​​the balancing mass within the annular mounting space formed by the cylindrical surface of the inertial sensor cavity during the modeling stage. This only completes the preliminary definition of geometric placement and does not represent the completion of physical assembly. A cylindrical coordinate system is established in the cylindrical region with the cavity's central axis as the Z-axis. The circumferential angles are continuously distributed along the circumference of the cylinder. When the balancing mass is confined within the preset cylindrical region, it covers an arc segment along the circumference. The two endpoints of the patch's arc correspond to unique angle values ​​in the cylindrical coordinate system. The angles corresponding to the two endpoints are the circumferential start angle and circumferential end angle. Relying on the spatial calibration relationship of the circumferential angles in the cylindrical coordinate system, two sets of angle parameters can be directly and uniquely determined simply by defining the arc coverage area of ​​the balancing mass within the cylindrical region, completing the parameter definition without the need for physical machining and placement.

[0043] Furthermore, since the inertial sensor's internal cavity has insurmountable upper and lower axial boundaries along the Z-axis, these axial boundaries limit the maximum range within which the balancing mass can be arranged along the Z-direction. To prevent the balancing mass from exceeding the installation envelope and interfering with other components inside the inertial sensor, the axial bottom height of a single balancing mass must be set to a coordinate value within the lower boundary of the internal cavity, and the axial top height must be set to a coordinate value within the upper boundary of the internal cavity. By matching the Z-axis axial boundary of the cylindrical region, the upper and lower axial limit dimensions of the patch are defined. This constrains the axial geometric range of the balancing mass to be completely contained within the available axial installation range of the sensor, ensuring that the axial arrangement of the balancing mass is feasible for engineering assembly. The three-dimensional geometric profile of the balancing mass is obtained by matching the axial top height and axial bottom height with the circumferential start angle, circumferential end angle, and radial thickness.

[0044] It is worth noting that the radial thickness is obtained by balancing the mass based on the pre-reserved assembly gap in the radial direction of the inertial sensor cavity and by selecting the corresponding standard machining thickness level.

[0045] Furthermore, the number of balance masses matching each inspection quality is obtained based on the number of pre-installed balance masses.

[0046] In one specific embodiment, in step S32, a set of constraint values ​​for the configuration parameter set is generated based on the pre-acquired inner diameter of the inertial sensor's inner cylinder, the axial installation height range, and the circumferential angle range. Specifically, this includes: Step S321: Based on the actual configuration data of the space gravitational wave detector, obtain the inner diameter of the inertial sensor's inner cylinder, the axial installation height range, and the circumferential angle range; Step S322: Based on the inner diameter of the inner cylinder, the axial installation height range, and the circumferential angle range, generate a set of constraint values ​​for the configuration parameter set: In the formula: and These represent the lower and upper limits of the configuration parameter set, respectively. , , , as well as These represent the upper limits of the values ​​for the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, and radial thickness, respectively. , , , as well as These represent the lower limits of the values ​​for the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, and radial thickness, respectively.

[0047] Specifically, the construction of the value constraint set can limit the reasonable value range of the configuration parameters of the balance mass, avoid generating installation space beyond the cylindrical region inside the inertial sensor cavity, ensure that the balance mass can be actually assembled and effectively suppress the measurement noise caused by the spacecraft's self-gravity disturbance.

[0048] In one specific embodiment, in step S33, based on the separating axis theorem, the three-dimensional image of each balancing mass is projected onto the two-dimensional projection range of the cylindrical mounting reference plane of the inertial sensor. When no two balancing mass projections overlap, the installation conditions are deemed qualified, thus obtaining a qualified balancing mass configuration set. Specifically, this includes: Step S331: Map each balancing mass to a three-dimensional reference coordinate system based on the balancing mass geometric parameters to obtain a three-dimensional image; Step S332: Project the three-dimensional image of each balance mass onto the two-dimensional projection range of the cylindrical mounting reference surface of the inertial sensor, and perform overlap detection on the projection ranges of any two balance mass projections according to the separation axis theorem to obtain the first overlap identifier Overlap1 and the second overlap identifier Overlap2. Step S333: When Overlap1=false and Overlap2=false, it is determined that any two balancing masses do not overlap, and the installation conditions are qualified, so as to obtain a qualified balancing mass configuration set.

[0049] Specifically, the dual-marker determination of the balance mass installation conditions based on the separation axis theorem can effectively constrain the geometric parameters of the balance mass, avoid misjudgment of interference states by a single mark, significantly reduce the computational workload of geometric conflicts, and achieve a good balance between the balance mass and the spacecraft layout. The geometric parameters of the balance mass are obtained by combining the actual construction data and configuration parameter set of the space gravitational wave detector to select a balance mass that can simultaneously meet the construction and compensation requirements.

[0050] In one embodiment, in step S4, a self-gravitational acceleration error objective function is constructed based on the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration; a self-gravitational stiffness error objective function is constructed based on the reference self-gravitational stiffness; and a balance mass physical mass objective function is constructed based on the qualified balance mass configuration set. Specifically, this includes: Step S41: Based on the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration, and based on the exterior point penalty function, construct the self-gravitational acceleration error objective function. : In the formula: This represents the distribution characteristics of the total mass of a spacecraft pre-installed with a balanced mass. This represents the self-gravitational acceleration experienced by the test mass after the balance mass is pre-installed; It represents the preset target value of the self-gravitational acceleration experienced by the i-th test mass; This represents the number of preset target values ​​for the self-gravitational acceleration of all inspection qualities; The linear weighting coefficient representing the self-gravitational acceleration deviation of each inspection quality; This represents the penalty weighting coefficient for the additional deviation after the self-gravitational acceleration deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Step S42: Construct the objective function of self-gravitational stiffness error based on the baseline self-gravitational stiffness and the exterior point penalty function. : In the formula: This represents the self-gravitational stiffness of the test mass calculated after the balance mass is pre-installed; It represents the preset target value of the self-gravitational stiffness experienced by the i-th test mass; The number of preset target values ​​for the self-gravitational stiffness of all inspected quality; Linear weighting coefficient for the self-gravitational stiffness deviation of each inspection quality; It is represented as the penalty weighting coefficient for the additional deviation after the self-gravitation stiffness deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Step S43: Based on the qualified balanced mass configuration set and according to the homogeneous firmware quality calculation formula, construct the balanced mass physical quality objective function. : In the formula: Material density expressed as equilibrium mass; Represented as the starting angle from the circumference To the circumferential termination angle Direction angle; R represents the radius of the inertial sensor.

[0051] Specifically, the physical mass and material density of the equilibrium mass were obtained through actual configuration data of the space gravitational wave detector.

[0052] By simultaneously constructing objective functions for self-gravitational acceleration error, self-gravitational stiffness error, and equilibrium mass physical mass, the multi-axial self-gravitational acceleration deviation of each test mass is simultaneously managed. This improves the problems of gravitational coupling caused by complex spacecraft configurations and noise exceeding limits in other directions due to single-axis optimization, and adapts the quantitative constraints of the compensation mass physical mass to the spacecraft engineering layout constraints.

[0053] In one embodiment, in step S5, several candidate solutions for equilibrium mass configurations are generated based on a multi-objective genetic algorithm. A first optimization model is then constructed and used to optimize these candidate solutions to output a differentiated feasible solution set with elite feasible solutions. Specifically, this includes: Step S51: Generate several candidate solutions for balanced quality configurations based on the elite feasible non-dominated sorting genetic algorithm; Step S52: Based on the objective function of self-gravitational acceleration error, the objective function of self-gravitational stiffness error, the set of value constraints, and the qualified equilibrium mass configuration set function, construct the first optimization model: Step S53: The elite feasible non-dominated sorting genetic algorithm with g-domination improved sorting logic is used to iteratively optimize several balanced quality configuration candidate solutions to select elite candidate solutions. The elite candidate solutions and non-elite candidate solutions are stored in a hierarchical manner to output a differentiated feasible solution set.

[0054] Specifically, by setting each candidate solution for a balance mass configuration to include the configuration parameter set and spatial installation coordinates of each balance mass within it, a complete representation of the geometric dimensions and installation information of the balance mass in each candidate solution for a balance mass configuration is formed, which facilitates direct substitution into the first optimization model to achieve the output of differentiated feasible solution sets.

[0055] In one specific embodiment, in step S53, an elite feasible non-dominated sorting genetic algorithm based on g-dominant improved sorting logic is used to iteratively optimize several balanced quality configuration candidate solutions to select elite candidate solutions. The elite candidate solutions and non-elite candidate solutions are then stored hierarchically to output a differentiated feasible solution set. Specifically, this includes: Based on the preset reference point of the g-dominated improved sorting logic, when the objective functions of self-gravitational acceleration error and self-gravitational stiffness error are both ≤0, the corresponding equilibrium mass configuration candidate solutions fall into the preferred range and are defined as elite candidate solutions. Iterative optimization is performed on several candidate solutions for equilibrium mass configurations, and elite and non-elite candidate solutions are stored hierarchically to output a differentiated feasible solution set.

[0056] Specifically, this invention innovatively uses an elite feasible non-dominated sorting genetic algorithm that introduces g-domination improved sorting logic. When iteratively optimizing candidate solutions for balanced mass configurations, it first defines a preference range where both the objective function of self-gravitational acceleration error and the objective function of self-gravitational stiffness error are ≤0 based on the g-domination preset reference point. Candidate solutions that fall within the preference range and whose objective functions of self-gravitational acceleration error and self-gravitational stiffness error are all satisfied are directly classified as elite feasible solutions.

[0057] The remaining candidate solutions are then further stratified and screened according to the dominance relationship of the elite feasible non-dominated sorting genetic algorithm. Through population crossover, mutation, and multiple rounds of iteration to update the layout parameters of the candidate solutions, the algorithm continuously expands and retains qualified solutions with differentiated layouts. This ensures that all elite feasible solutions satisfy the self-gravity performance constraint, and based on the selection condition that the self-gravity acceleration error objective function and the self-gravity stiffness error objective function are <0, it retains the performance margin relative to the qualified threshold equal to the preset reference point 0. It also avoids the defects of traditional elite feasible non-dominated sorting genetic algorithms, such as the loss of elite candidate solutions within the preference range and the homogeneous distribution of the solution set, so as to output a differentiated feasible solution set with elite feasible solutions.

[0058] In one embodiment, in step S6, a second optimization model is constructed based on the differentiated feasible solution set, and the differentiated feasible solution set is optimized using a multi-operator difference algorithm to output the configuration of the equilibrium mass to be compensated. Each feasible solution in the differentiated feasible solution set includes a configuration parameter set, spatial installation coordinates, and the total mass of all equilibrium masses within it, specifically including: Step S61: Construct a second optimization model based on the differentiated feasible solution set: Step S62: Adaptively iteratively optimize the differentiated feasible solution set using the multi-operator difference algorithm, and select the feasible solution whose objective function of self-gravitational acceleration error and objective function of gravitational stiffness error are both ≤0 and whose total mass of all equilibrium masses is minimized as the equilibrium mass configuration to be compensated.

[0059] Specifically, embodiments of the present invention utilize a differentiated feasible solution set with performance margin as the initial population. A multi-operator differential evolution algorithm is used to perform lightweight optimization under the premise that both the objective functions of self-gravitational acceleration error and gravitational stiffness error are ≤0 throughout the entire process. The reserved performance margin is fully utilized to adjust the configuration parameters and spatial coordinates of the balance mass, selecting the feasible solution that satisfies the compensation performance and minimizes the total mass. This solution is defined as the balance mass configuration to be compensated, reducing the disturbance of the spacecraft's self-gravity to the test mass. The performance margin provides adjustment space for subsequent weight reduction, thereby reducing the overall weight and lowering launch costs.

[0060] It is worth noting that all algorithms described above in the embodiments of the present invention that are not further elaborated are existing technologies, and therefore, the present invention will not elaborate further here. Although one or more embodiments of the present invention have been described above, those skilled in the art should understand that the present invention can be implemented in any other form without departing from its spirit and scope. Therefore, the embodiments described above are illustrative and not restrictive, and many modifications and substitutions will be obvious to those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A self-gravitational compensation method for space gravitational wave detection, characterized in that, include: Establish a finite element discrete model and output the finite element node parameters. Calculate the gravitational reference value of the spacecraft's gravity on the verification mass based on the finite element node parameters and the universal gravitation formula. Obtain the mass and dimensional parameters of the inspection mass, and calculate the reference self-gravitational acceleration, reference self-gravitational angular acceleration, and reference self-gravitational stiffness experienced by the inspection mass; A set of configuration parameters for the balancing mass is selected and constructed. The set of value constraints for the configuration parameter set is generated based on the envelope geometry parameters of the pre-acquired inertial sensor. The installation conditions of the balancing mass are determined based on the separation axis theorem to screen out a qualified balancing mass configuration set. A self-gravitational acceleration error objective function is constructed based on the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration. A self-gravitational stiffness error objective function is constructed based on the reference self-gravitational stiffness. Finally, a balance mass physical mass objective function is constructed based on the qualified balance mass configuration set. A number of candidate solutions for equilibrium mass configurations are generated based on a multi-objective genetic algorithm to construct a first optimization model. The multi-objective genetic algorithm is then used to optimize the candidate solutions for equilibrium mass configurations to output a differentiated set of feasible solutions with elite feasible solutions. Each candidate solution for equilibrium mass configuration includes the configuration parameter set and spatial installation coordinates of each equilibrium mass within it. A second optimization model is constructed based on the differentiated feasible solution set, and the differentiated feasible solution set is optimized by the multi-operator difference algorithm to output the configuration of the balance mass to be compensated. Each feasible solution in the differentiated feasible solution set includes the configuration parameter set, spatial installation coordinates, and the total mass of all balance masses within it.

2. The self-gravitational compensation method for space gravitational wave detection according to claim 1, characterized in that, The process of establishing a finite element discrete model and outputting finite element node parameters, and calculating the gravitational benchmark value of the spacecraft's gravitational force on the verification mass based on the finite element node parameters and the universal gravitation formula, specifically includes: Construct a three-dimensional geometric model of the space gravitational wave detector and obtain the original parameter set. Based on the FEM and the original parameter set, establish a finite element discrete model and output the finite element node parameters. Based on the finite element node parameters and the universal gravitation formula, the gravitational reference value of the spacecraft's gravity on the test mass is calculated.

3. The self-gravitational compensation method for space gravitational wave detection according to claim 2, characterized in that, The process of obtaining the mass and dimensional parameters of the inspection mass, and calculating the reference self-gravitational linear acceleration, reference self-gravitational angular acceleration, and reference self-gravitational stiffness of the inspection mass based on the gravitational reference value, specifically includes: Let the reference self-gravitational acceleration be... Obtain the quality value of the inspection and set it as... According to the gravitational reference value ,get: Let the reference self-gravitational angular acceleration be Obtain the dimensional values ​​of the inspection quality on the X, Y, and Z axes and set them as... , and Based on the Euler equations, the following calculations were performed: In the formula: , and These represent the angular accelerations on the X, Y, and Z axes of the i-th grid node corresponding to the inspection quality, respectively. Let the component of the gravitational reference value in the e direction be... Let K be the reference self-gravitational stiffness in the j-direction, then: In the formula: e and All are represented as the X-axis, Y-axis, or Z-axis; This represents the initial centroid coordinates for quality inspection. It represents the displacement of the inspection mass along the X-axis, Y-axis, or Z-axis.

4. The self-gravitational compensation method for space gravitational wave detection according to claim 3, characterized in that, The selection and construction of the configuration parameter set for the balancing mass involves generating a set of value constraints for the configuration parameter set based on the pre-acquired envelope geometry parameters of the inertial sensor, and determining the installation conditions of the balancing mass based on the separating axis theorem to screen out a qualified balancing mass configuration set. Specifically, this includes: Several balancing masses with circular arc patch configurations are selected, and the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, radial thickness, and the number of balancing masses matching each test mass are extracted for each balancing mass, and a configuration parameter set is constructed. generating a value constraint set for the configuration parameter set according to the pre-obtained inner cavity cylinder inner diameter, axial installation height range and circumferential angle range of the inertial sensor, wherein the envelope geometric parameters include the inner cavity cylinder inner diameter, the axial installation height range and the circumferential angle range; projecting the three-dimensional image of each balance mass onto the two-dimensional projection interval of the cylindrical installation reference plane of the inertial sensor based on the separating axis theorem, so as to determine that the installation condition is qualified when there is no overlap between any two balance masses.

5. The self-gravitational compensation method for space gravitational wave detection according to claim 4, characterized in that, selecting a number of balance masses all in the form of arc patch configuration, extracting the circumferential start angle, circumferential end angle, axial top height, axial bottom height, radial thickness of each balance mass, and the number of balance masses matched with each test mass, and constructing a configuration parameter set, which specifically includes: taking the central axis of the inner cavity cylindrical region of the inertial sensor as the Z axis, establishing a cylindrical coordinate system, pre-installing any balance mass in the arc patch configuration in the cylindrical region, so as to determine the circumferential start angle and the circumferential end angle; determining the axial top height and the axial bottom height according to the axial boundary of the cylindrical region along the Z axis; Obtain the radial thickness of the balance mass and the number of balance masses matching each inspection mass to form a configuration parameter set. : in the formula: Represented as the first A balanced mass; Represented as the circumferential starting angle; Represented as the circumferential termination angle; This is expressed as the axial top height; This is expressed as the axial bottom height; Expressed as radial thickness; This is represented as the number of balanced masses that match each inspection quality.

6. The self-gravitational compensation method for space gravitational wave detection according to claim 5, characterized in that, generating a value constraint set for the configuration parameter set according to the pre-obtained inner cavity cylinder inner diameter, axial installation height range and circumferential angle range of the inertial sensor, which specifically includes: acquiring the inner cavity cylinder inner diameter, axial installation height range and circumferential angle range of the inertial sensor based on the actual configuration data of the space gravitational wave detector; generating the value constraint set of the configuration parameter set according to the inner cavity cylinder inner diameter, the axial installation height range and the circumferential angle range: in the formula: and These represent the lower and upper limits of the configuration parameter set, respectively. , , , as well as These represent the upper limits of the values ​​for the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, and radial thickness, respectively. , , , as well as These represent the lower limits of the values ​​for the circumferential starting angle, circumferential ending angle, axial top height, axial bottom height, and radial thickness, respectively.

7. The self-gravitational compensation method for space gravitational wave detection according to claim 6, characterized in that, the step of projecting the three-dimensional image of each balance mass onto the two-dimensional projection interval of the cylindrical installation reference plane of the inertial sensor based on the separating axis theorem, so as to determine that the installation condition is qualified when there is no overlap between the projections of any two balance masses, to screen out a qualified balance mass configuration set, specifically includes: mapping each balance mass into the three-dimensional reference coordinate system based on the geometric parameters of the balance mass, so as to obtain a three-dimensional image; projecting the three-dimensional image of each balance mass onto the two-dimensional projection interval of the cylindrical installation reference plane of the inertial sensor, and performing overlap detection on the projection intervals of the projections of any two balance masses according to the separating axis theorem, to obtain a first overlap identifier Overlap1 and a second overlap identifier Overlap2; when Overlap1=false and Overlap2=false, it is determined that any two balance masses do not overlap, then the installation condition is qualified, so as to screen out the qualified balance mass configuration set.

8. The self-gravitational compensation method for space gravitational wave detection according to claim 7, characterized in that, the step of constructing the self-gravitational acceleration error objective function according to the reference self-gravitational linear acceleration and the reference self-gravitational angular acceleration, constructing the self-gravitational stiffness error objective function based on the reference self-gravitational stiffness, and constructing the balance mass physical mass objective function based on the qualified balance mass configuration set, specifically includes: Based on the baseline self-gravitational linear acceleration and the baseline self-gravitational angular acceleration, and based on the exterior point penalty function, a self-gravitational acceleration error objective function is constructed. : In the formula: This represents the distribution characteristics of the total mass of a spacecraft pre-installed with a balanced mass. This represents the self-gravitational acceleration experienced by the test mass after the balance mass is pre-installed; It represents the preset target value of the self-gravitational acceleration experienced by the i-th test mass; This represents the number of preset target values ​​for the self-gravitational acceleration of all inspection qualities; The linear weighting coefficient representing the self-gravitational acceleration deviation of each inspection quality; This represents the penalty weighting coefficient for the additional deviation after the self-gravitational acceleration deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Based on the baseline self-gravitational stiffness, and using the exterior point penalty function, an objective function for the self-gravitational stiffness error is constructed. : In the formula: This represents the self-gravitational stiffness of the test mass calculated after the balance mass is pre-installed; It represents the preset target value of the self-gravitational stiffness experienced by the i-th test mass; The number of preset target values ​​for the self-gravitational stiffness of all inspected quality; Linear weighting coefficient for the self-gravitational stiffness deviation of each inspection quality; It is represented as the penalty weighting coefficient for the additional deviation after the self-gravitation stiffness deviation of each inspection quality exceeds the preset target value; It represents the weighting coefficient corresponding to the self-gravitational acceleration of the i-th test quality; Based on a qualified balanced mass configuration set and according to the homogeneous firmware quality calculation formula, a balanced mass physical mass objective function is constructed. : in the formula: Material density expressed as equilibrium mass; Represented as the starting angle from the circumference To the circumferential termination angle Direction angle; R represents the radius of the inertial sensor.

9. The self-gravitational compensation method for space gravitational wave detection according to claim 8, characterized in that, the step of generating a number of balance mass configuration candidate solutions based on a multi-objective genetic algorithm, constructing and optimizing the number of balance mass configuration candidate solutions through a first optimization model, so as to output a differentiated feasible solution set with elite feasible solutions, specifically includes: Based on the elite feasible non-dominated sorting genetic algorithm, several candidate solutions for balanced quality configurations are generated. Based on the objective functions of self-gravitational acceleration error, self-gravitational stiffness error, value constraint set, and qualified equilibrium mass configuration set function, the first optimization model is constructed as follows: An elite feasible non-dominated sorting genetic algorithm with g-domination improved sorting logic is adopted to iteratively optimize several balanced quality configuration candidate solutions to select elite candidate solutions. Elite candidate solutions and non-elite candidate solutions are stored hierarchically to output a differentiated feasible solution set.

10. The self-gravitational compensation method for space gravitational wave detection according to claim 9, characterized in that, The second optimization model is constructed based on the differentiated feasible solution set, and the differentiated feasible solution set is optimized using a multi-operator difference algorithm to output the configuration of the equilibrium mass to be compensated. Each feasible solution in the differentiated feasible solution set includes a configuration parameter set, spatial installation coordinates, and the total mass of all equilibrium masses within it, specifically including: Construct a second optimization model based on the differentiated feasible solution set: The differentiated feasible solution set is adaptively iteratively optimized using a multi-operator difference algorithm. The feasible solution with the minimum total mass of all equilibrium masses within it, whose objective functions of self-gravitational acceleration error and gravitational stiffness error are both ≤0, is defined as the equilibrium mass configuration to be compensated.

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