A verification method for inertial sensor correction based on finite element analysis model

Abstract

The present invention provides a verification method for inertial sensor correction based on a finite element analysis model, which adjusts the size of the test mass in the existing inertial sensor and the distance from the electrode plate to obtain an improved inertial sensor; using the finite element analysis model, the capacitance finite element simulation value and electrostatic force simulation value between the test mass and the electrode plate in the improved inertial sensor, as well as the capacitance gradient formed between the various components of the improved inertial sensor are obtained; according to the capacitance gradient, the corrected electrostatic force is obtained; so as to obtain an inertial sensor that meets the preset requirements for gravitational wave detection in space. The beneficial effect of the present invention is that the electrostatic force on the test mass in the improved inertial sensor is reduced, and the electrostatic force requirements for position control of the inertial sensor by injection electrodes are reduced.

Description

Technical Field

[0001] The present invention relates to the field of inertial sensors, and in particular to a verification method for inertial sensor correction based on a finite element analysis model. Background Art

[0002] General relativity is one of the most brilliant achievements of mankind in the field of natural science in the 20th century, and gravitational waves are the most important prediction of general relativity. Therefore, the detection of gravitational waves has important scientific significance for the development of physics. Since LIGO first detected gravitational waves in 2016, dozens of gravitational wave events have been discovered by ground-based gravitational wave detection equipment. However, ground-based detection equipment is affected by ground vibration noise and ambient temperature and cannot complete the detection of low-frequency gravitational waves below 1.0 Hz. Gravitational wave detectors in space can greatly reduce these effects, so they can make up for the shortcomings of ground detection range in this regard. In addition, space gravitational wave detection will open a new window for exploring the universe and lead mankind into a new era of gravitational wave astronomy.

[0003] The two most important technologies for space gravitational wave detectors are inertial sensing technology and space laser interferometry technology. The core technology of inertial sensing is to test the command probe that performs free fall in space, while the laser interferometry technology measures the distance between each test mass probe to record the distance change, thereby providing information about gravitational waves. The quality of inertial sensors is measured by the residual acceleration of the test mass probe. Currently, the most accurate result in the world was obtained by LISA Pathfinder (LPF) in 2016. However, LPF still has shortcomings in the low-frequency part. Summary of the invention

[0004] Gravitational waves are invisible signals. LISA is expected to launch three satellites into space, each carrying two inertial sensors. The three satellites form a triangular array. When there are no gravitational waves, the test mass and the satellite remain relatively still, and the lasers do not interfere. When the gravitational wave signal affects, the test mass shifts, and due to the coherence of light, the lasers on the three satellites interfere. In space, the laser is longer than on the ground, so the shift is easy to observe, but it is difficult to adjust the inertial sensor and other components in space. Therefore, it is necessary to analyze all the noises that may be received before launching to minimize the noise. After the LPF was launched in 2016, the data obtained showed that the high-frequency region has reached the accuracy requirement for detecting gravitational waves, but in the low-frequency region, due to the increasing influence of Brownian noise, the performance of LPF cannot meet the requirements for detecting gravitational wave signals. The problem that the inertial sensor of LPF is insufficient in the low-frequency part is to be solved by the present invention. In order to solve the above problems, the most direct method is to appropriately increase the size of the test mass (TM) and increase the distance between the electrode plate and TM, thereby improving the Brownian noise to reduce the acceleration noise introduced by the force noise. However, the above improvements mean that the noise of the inertial sensor needs to be redistributed, and higher requirements are also placed on external devices such as locking and releasing. The present invention provides a verification method for inertial sensor correction based on a finite element analysis model, which aims to verify the capacitance and capacitance gradient formed by the mass and the surrounding objects in the improved inertial sensor through finite element analysis calculation, so as to provide support for the smooth detection of gravitational waves, including the following steps:

[0005] S1: Adjust the size of the test mass in the existing inertial sensor and the distance between the test mass and the electrode plate, draw the improved three-dimensional model of the inertial sensor in Comsol physical field simulation software, perform meshing, set the electrostatic physical field, and obtain the finite element analysis model;

[0006] S2: Using Comsol multi-physics simulation software to simulate and calculate the finite element analysis model, and obtain the finite element simulation value of the capacitance and the electrostatic force simulation value between the test mass and the electrode plate in the improved inertial sensor;

[0007] S3: Based on the above method, several capacitance finite element simulation values ​​are obtained, and a capacitance curve is obtained by fitting with Matlab software. According to the capacitance curve, the capacitance gradient formed between the components of the improved inertial sensor is obtained. According to the capacitance gradient, the corrected electrostatic force of the improved inertial sensor in each degree of freedom is calculated;

[0008] S4: Compare the corrected electrostatic force obtained in step S3 with the electrostatic force simulation value in step S2 to determine whether the accuracy of the improved inertial sensor meets the preset requirements. If so, use the improved inertial sensor to detect gravitational waves. If not, return to step S1, adjust the inertial sensor again, and use the method of steps S1-4 to obtain an inertial sensor that meets the preset requirements for gravitational wave detection in space.

[0009] Furthermore, adjusting the position of the proof mass in the existing inertial sensor includes at least one of the six degrees of freedom, and the six degrees of freedom are translation of the proof mass along the X-axis, translation of the proof mass along the Y-axis, translation of the proof mass along the Z-axis, rotation of the proof mass along the X-axis, rotation of the proof mass along the Y-axis, and rotation of the proof mass along the Z-axis.

[0010] Furthermore, the slope of the capacitance curve is the capacitance gradient.

[0011] Furthermore, the formula for calculating the corrected electrostatic force is as follows:

[0012]

[0013] Where F represents the modified electrostatic force, q represents the generalized coordinates, i.e., the relative change of the coordinates of the test mass after it is moved and rotated along the three coordinate axes X, Y, and Z relative to the zero position, and V i represents the voltage on the ith electrode plate, V j represents the voltage on the jth electrode plate, V TM Indicates the voltage of the test mass, C EL,TM represents the capacitance of the electrode plates and the test mass, represents the capacitance gradient between the ith electrode plate and the test mass at a certain degree of freedom, represents the capacitance gradient between the test mass and the electrode frame, represents the capacitance gradient between the ith electrode plate and the electrode frame, represents the capacitance gradient between the i-th electrode plate and the j-th electrode plate.

[0014] Furthermore, the preset requirement refers to achieving the accuracy requirement of LISA for the inertial sensor in terms of electrostatics.

[0015] The beneficial effects of the technical solution provided by the present invention are as follows: the advantage of the present invention is that by increasing the spacing and the size of the test mass and analyzing the error between the finite element simulation value and the theoretical value, the electrostatic force on the test mass in the improved inertial sensor is reduced, thereby reducing the electrostatic force requirements applied to the position control of the inertial sensor by the injection electrode. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0017] Figure 1 The present invention is a flowchart of a method for verifying inertial sensor correction based on a finite element analysis model in an embodiment of the present invention.

[0018] Figure 2 is a perspective view of an inertial sensor in an embodiment of the present invention.

[0019] Figure 3 1 is an internal diagram of an inertial sensor in an embodiment of the present invention.

[0020] Figure 4 It is a cross-sectional view of electrodes and insulating rings in the X, Y, and Z directions in an embodiment of the present invention.

[0021] Figure 5 It is a Comsol finite element simulation modeling diagram in an embodiment of the present invention.

[0022] Figure 6 is a capacitance fitting curve diagram between electrode plates 1 and 2 and the inspection mass in an embodiment of the present invention.

[0023] Figure 7 is a capacitance fitting curve diagram between the electrode plates 1 and 2 and the electrode frame in an embodiment of the present invention.

[0024] Figure 8 is a capacitance fitting curve diagram between the electrode plates 3 and 5 and the inspection mass in an embodiment of the present invention.

[0025] Fig. 9 3 is a capacitance fitting curve diagram between the electrode plates 3 and 5 and the electrode frame in the embodiment of the present invention.

[0026] Fig.10 is a capacitance fitting curve diagram between the electrode plates 6 and 8 and the inspection mass in an embodiment of the present invention.

[0027] Fig.11 is a capacitance fitting curve diagram between the electrode plates 6 and 8 and the electrode frame in the embodiment of the present invention.

[0028] Fig.12 4 is a capacitance fitting curve diagram between the electrode plate rotating around the X-axis and the inspection mass in an embodiment of the present invention.

[0029] Fig.13 1 is a capacitance fitting curve diagram between the electrode plate and the electrode frame rotating around the X-axis in an embodiment of the present invention.

[0030] Fig.14 4 is a capacitance fitting curve diagram between the electrode plate rotating around the Y axis and the inspection mass in an embodiment of the present invention.

[0031] Fig.153 is a capacitance fitting curve diagram between the electrode plate and the electrode frame rotating around the Y axis in an embodiment of the present invention.

[0032] Fig.16 4 is a capacitance fitting curve diagram between the electrode plate rotating around the Z axis and the inspection mass in an embodiment of the present invention.

[0033] Fig.17 3 is a capacitance fitting curve diagram between the electrode plate and the electrode frame rotating around the Z axis in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0035] The embodiment of the present invention provides a verification method, device and storage device for inertial sensor correction based on a finite element analysis model. The size of the existing inertial sensor is 46mm*46mm*46mm, and the finite element analysis method is to simulate the improved inertial sensor correction electrostatic model using finite element simulation software.

[0036] Please refer to Figure 1 , Figure 1 : is a flow chart of a verification method for inertial sensor correction based on a finite element analysis model in an embodiment of the present invention, which specifically includes the following steps:

[0037] S1: Adjust the size of the proof mass in the existing inertial sensor and the distance from the electrode plate, draw the three-dimensional model of the improved inertial sensor in Comsol physical field simulation software, perform meshing, set the electrostatic physical field, and obtain a finite element analysis model; adjust the position of the proof mass in the existing inertial sensor to include at least one of the six degrees of freedom, the six degrees of freedom are: translation of the proof mass along the X-axis, translation of the proof mass along the Y-axis, translation of the proof mass along the Z-axis, rotation of the proof mass along the X-axis, rotation of the proof mass along the Y-axis, and rotation of the proof mass along the Z-axis.

[0038] S2: Using Comsol multi-physics simulation software to simulate and calculate the finite element analysis model, and obtain the finite element simulation value of the capacitance and the electrostatic force simulation value between the test mass and the electrode plate in the improved inertial sensor;

[0039] S3: Based on the above method, several capacitance finite element simulation values ​​are obtained, and the capacitance curve is fitted by Matlab software. The capacitance gradient formed between the components of the improved inertial sensor is obtained according to the capacitance curve. The slope of the capacitance curve is the capacitance gradient. According to the capacitance gradient, the corrected electrostatic force of the improved inertial sensor on each degree of freedom is calculated; the formula for calculating the corrected electrostatic force is as follows:

[0040]

[0041] Where F represents the modified electrostatic force, q represents the generalized coordinates, i.e., the relative change of the coordinates of the test mass after it is moved and rotated along the three coordinate axes X, Y, and Z relative to the zero position, and V i represents the voltage on the ith electrode plate, V j represents the voltage on the jth electrode plate, V TM Indicates the voltage of the test mass, C EL,TM represents the capacitance of the electrode plates and the test mass, represents the capacitance gradient between the ith electrode plate and the test mass at a certain degree of freedom, represents the capacitance gradient between the test mass and the electrode frame, represents the capacitance gradient between the ith electrode plate and the electrode frame, represents the capacitance gradient between the i-th electrode plate and the j-th electrode plate.

[0042] S4: Compare the corrected electrostatic force obtained in step S3 with the electrostatic force simulation value in step S2, and judge whether the accuracy of the improved inertial sensor meets the preset requirements. If so, use the improved inertial sensor to detect gravitational waves. If not, return to step S1, adjust the inertial sensor again, and use the method of steps S1-4 to obtain an inertial sensor that meets the preset requirements for gravitational wave detection in space. If the corrected electrostatic force is greater than or less than the electrostatic force simulation value, it means that in addition to the capacitance gradient between the test mass and the electrode plate, other capacitance gradients also have a certain influence on the electrostatic force on the test mass. If the corrected electrostatic force is equal to the electrostatic force simulation value, it means that it is only affected by the capacitance gradient between the test mass and the electrode plate, and is not affected by other capacitances. The comparison here is to correct the shortcomings of the data processing method. If the electrostatic force only considers the simulation value, the deviation is large, and the influence of other capacitance gradients needs to be considered, so it is necessary to obtain a corrected electrostatic force for correction. It can be said that it is optimal to use the corrected electrostatic force to adjust the inertial sensor. Relying on theoretical values ​​to adjust will cause a large deviation in the detection data, resulting in low measurement accuracy. The preset requirement is to meet the accuracy requirements of the European Space Gravitational Wave Program (LISA) for inertial sensors in terms of electrostatics, and the residual electrostatic disturbance index is about 0.4×10 -15 m / s 2 / Hz 1 / 2 .

[0043] like Figure 2As shown, the new inertial sensor includes a test mass, 18 electrode plates, an electrode frame and 6 insulating rings. The test mass is at the center, the 18 electrode plates are around the test mass, and the electrode frame is the middle part between the outermost solid line and the dotted line. The test mass is a cubic gold block and is the main part of the inertial sensor. The laser of the laser interferometer technology shines on the test mass. When the test mass is offset, the laser will cause interference. There are six insulating rings in an inertial sensor, which are located in the normal direction of the six faces of the test mass. They are all the remaining parts of a rectangular electrode plate after the corresponding sensing electrodes and injection electrodes are dug out.

[0044] The electrode frame has a side length of 80mm, with six circular holes on each of the six faces. The radius of the circular holes is consistent with the circular holes on the insulating ring, and the height passes through the six faces of the frame. A 70mm×70mm×70mm cube area is hollowed out in the center of the electrode frame, and the inspection mass is placed in the center. The inspection mass size is 50mm×50mm×50mm. Figure 3 This is an exploded view of the inertial sensor frame. Figure 4The cross-sections of the electrodes and their insulating rings in three directions. The electrode plates 1 and 2 in the X-axis direction are composed of a 14.5mm×36mm×2mm sensing electrode plate and a 14.5mm×36mm×3mm molybdenum insulating plate. The sensing electrode is close to the inspection mass, with a distance of 5mm from the inspection mass, and is surrounded by a 50mm×50mm×5mm insulating ring. A circular hole with a radius of 3mm and a height of 5mm is left in the center of the ring. The electrode plate 3 and the electrode plate 5 in the Y-axis direction are both composed of a 7.1mm×38.2mm×3.1mm sensing electrode plate and a 7.1mm×38.2mm×3mm molybdenum insulating plate. The sensing electrode is close to the inspection mass and the distance from the inspection mass is 3.9mm. The electrode plate 4 is composed of an injection electrode plate of 16mm×38.2mm×2mm and a 16mm×38.2mm×3mm molybdenum insulating plate. The injection electrode is close to the inspection mass and the distance from the inspection mass is 5mm. A circular hole with a radius of 3mm and a height of 5mm is dug in the center of the electrode plate, and the outside is surrounded by an insulating ring of 16mm×38.2mm×6.1mm. The electrode plates 6 and 8 in the Z-axis direction are composed of a 6.5mm×37mm×2.5mm sensing electrode plate and a 6.5mm×37mm×3mm molybdenum insulating plate. The sensing electrode is close to the inspection mass and the distance from the inspection mass is 4.5mm. The electrode plates 7 and 9 are composed of a 16mm×12mm×2mm injection electrode plate and a 16mm×12mm×3mm molybdenum insulating plate. The injection electrode is close to the inspection mass and the distance from the inspection mass is 5mm. It is surrounded by a 46mm×46mm×5.5mm insulating ring. A circular hole with a radius of 5mm and a height of 5mm is dug out in the center of the ring. The electrode plate area in all insulating rings is hollowed out along the length and width of the electrode plate in the four directions, and the normal direction is penetrated. The role of the sensing electrode is to detect the position of the inspection mass through capacitance, and the role of the injection electrode is to achieve the motion signal of the inspection mass in each degree of freedom by applying the injection voltage. Ideally, the potential on the insulating ring and the insulating plate is always 0.

[0045] To analyze the capacitance between the sensing electrode and the test mass, it is assumed that the electrode frame is vacuum, and the initial potentials of the test mass and the electrode frame are both 0. Apply +1V and -1V voltages to the two sensing electrodes 1 and 2 on the X axis, +2V and -2V voltages to the two sensing electrodes 3 and 5 on the Y axis, +3V and -3V voltages to the two sensing electrodes 6 and 8 on the Z axis, and the initial potentials of the remaining electrode plates are all 0. Figure 5 This is a finite element simulation modeling diagram. The inertial sensor is divided into several small grids through the finite element analysis model. The partial differential equation is solved on the small grids, similar to solving pi. The finer the division, the higher the accuracy, but the longer the time. The capacitance between each electrode plate and the inspection mass measured by finite element simulation is shown in Table 1:

[0046] Table 1. Finite Element Analysis Model Capacitance (Nominal TM Location and Orientation)

[0047]

[0048] Among them, CEL1,TM is actually C(EL1,TM), which means that the two poles of the inertial capacitor are composed of electrode plate 1 and TM, TM is the abbreviation of test mass, and EH is the electrode frame. The parameters in the brackets indicate the capacitor type of the test mass, which are the capacitance in the x direction, the capacitance in the y direction and the sensing electrode, the capacitance in the z direction and the sensing electrode, the capacitance in the y direction and the injection electrode, and the capacitance in the z direction and the injection electrode. Ctot represents the total capacitance of the test mass to which each electrode plate and electrode frame are subjected.

[0049] CTM-EH is the capacitance between the inspection mass and the frame, and CTM is the sum of all capacitances. By comparison, it can be found that there is a certain error between the simulated data and the theoretical value. This is because the parallel plate model in the theoretical value ignores the edge field effect of the electrode, thereby ignoring the increase in the effective area and underestimating the capacitance. Although the edge effect can be effectively reduced by adding insulating rings and insulating plates around the electrode plate in the design, this influence still exists. The finite element analysis model can accurately calculate the capacitance value in the inertial sensor.

[0050] In addition, this method also calculates the electrostatic force and torque. Unlike the capacitor, the electrostatic force value obtained by finite element simulation is much lower than the theoretical value, as shown in Table 2:

[0051] Table 2. Current FEA Model Electrostatic Forces and Torques (Nominal TM Positions and Directions)

[0052]

[0053] In Table 2, the six degrees of freedom represent: translation of the inspection mass along the X-axis, translation of the inspection mass along the Y-axis, translation of the inspection mass along the Z-axis, rotation of the inspection mass along the X-axis, rotation of the inspection mass along the Y-axis, and rotation of the inspection mass along the Z-axis, i.e., movement and rotation in three different directions.

[0054] As can be seen from the table, the largest gap reached 51.46%. The theoretical value is based on an electrostatic model approximated by infinite non-parallel plate capacitance, which calculates the capacitance between the electrode plate and the test mass. The model ignores the remaining additional capacitance, such as the capacitance between the electrodes and the capacitance between the electrode and the frame. Therefore, a finite element simulation calculation was also performed on the capacitance gradient formed between the various components of the improved inertial sensor.

[0055] Taking the X degree of freedom as an example, by moving the inspection mass along the X direction by ±0.2mm, the capacitance finite element simulation value at each spacing is recorded. The capacitance finite element simulation value is the capacitance between the inspection mass and the electrode plate when it is stationary at zero position. The capacitance gradient simulation value under this degree of freedom can be obtained by fitting. Among them, the capacitance fitting curve between electrode plates 1 and 2 and the inspection mass is as follows Figure 6 As shown, the capacitance fitting curve between electrode plates 1 and 2 and the electrode frame is as follows Figure 7 As shown in the figure, the capacitance in the capacitance fitting curve refers to the change curve of the capacitance between the electrode plate and the inspection mass when the inspection mass is moved and rotated under six degrees of freedom, which is a series of capacitance finite element simulation values. The specific values ​​of the capacitance gradient in the X direction of the finite element simulation are shown in Table 3:

[0056] Table 3. Capacitance gradient in the X direction of finite element simulation

[0057]

[0058]

[0059] From Table 3, we can see that the capacitance gradient between the electrode and the surrounding frame has an opposite sign to the capacitance gradient between the electrode and the inspection mass, which may be the reason why the electrostatic force simulation value is lower than the theoretical value. The blank indicates that the theoretical value cannot be calculated.

[0060] Similarly, based on the above results, the capacitance when the mass moves ±0.2mm along the Y and Z directions is analyzed by finite element simulation, and the fitting results are: Figure 8 The fitting curve diagram of the electrode plates 3 and 5 and the test mass capacitance is shown in FIG. Fig. 9 The fitting curve diagram of the capacitance between the electrode plates 3 and 5 and the electrode frame is shown in FIG. Fig.10 The fitting curve diagram of the electrode plates 6 and 8 and the test mass capacitance is shown in FIG. Fig.11 The capacitance fitting curve diagram between the electrode plates 6 and 8 and the electrode frame is shown in Table 4. When the inspection mass moves, the data of capacitance and capacitance gradient in each direction are shown in Table 4:

[0061] Table 4. Data of capacitance and capacitance gradient in each direction when the test mass moves

[0062]

[0063] At the same time, the capacitance when the mass rotates ±2mrad around the X, Y, and Z axes is tested by finite element simulation analysis, and the fitting results are: Fig.12 The fitting curve diagram of the main electrode plates 3 and 5 and the test mass capacitance when rotating around the X axis is shown in FIG. Fig.13 The fitting curve diagram of the main electrode plates 3 and 5 and the electrode frame capacitance when rotating around the X-axis is shown in FIG. Fig.14The fitting curve diagram of the main electrode plates 6 and 8 and the capacitance of the inspection mass when rotating about the Y axis is shown in FIG. Fig.15 The fitting curve diagram of the main electrode plates 6 and 8 and the electrode frame capacitance when rotating around the Y axis is shown in FIG. Fig.16 The fitting curve diagram of the main electrode plates 1 and 2 and the capacitance of the inspection mass when rotating about the Z axis is shown in FIG. Fig.17 The fitting curve diagram of the capacitance of the main electrode plates 1 and 2 and the electrode frame when rotating around the Z axis is shown in Table 5. When the inspection mass rotates, the capacitance gradient data in each direction are shown in Table 5:

[0064] Table 5. Capacitance gradient data when the test mass rotates

[0065]

[0066]

[0067] The capacitance gradient simulation values ​​in Table 4 are calculated using formula (1) to obtain the corrected electrostatic force after considering multiple additional capacitances, as shown in Table 6:

[0068] Table 6. Corrected capacitance gradient and electrostatic force

[0069]

[0070] It can be seen from this that the edge effect of the capacitor generated by the electrode plate and the frame does need to be considered, and the corrected electrostatic force and torque are closer to the simulation values.

[0071] Table 7. Corrected capacitance gradient and electrostatic torque

[0072]

[0073] Through verification of this embodiment, it can be seen that the size of the proof mass is enlarged from 46 mm to 50 mm, and the distance between the sensing electrode and the proof mass is enlarged by 1 mm. After the enlargement, the capacitance and capacitance gradient of the inertial sensor are optimal.

[0074] The beneficial effects of the present invention are as follows: the advantages of the present invention are that by increasing the spacing and the size of the test mass and analyzing the error between the finite element simulation value and the theoretical value, the electrostatic force on the test mass in the improved inertial sensor is reduced, thereby reducing the electrostatic force requirements applied to the position control of the inertial sensor by the injection electrode.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A verification method for inertial sensor correction based on a finite element analysis model, the inertial sensor comprising a test mass, a plurality of electrode plates, an electrode frame and a plurality of insulating rings, characterized in that: The following steps are involved: S1: Adjust the size of the test mass in the existing inertial sensor and the distance between the test mass and the electrode plate, draw the improved three-dimensional model of the inertial sensor in Comsol physical field simulation software, perform meshing, set the electrostatic physical field, and obtain the finite element analysis model; S2: Using Comsol multi-physics simulation software to simulate and calculate the finite element analysis model, and obtain the finite element simulation value of the capacitance and the electrostatic force simulation value between the test mass and the electrode plate in the improved inertial sensor; S3: Based on the above method, several capacitance finite element simulation values ​​are obtained, and a capacitance curve is obtained by fitting with Matlab software. According to the capacitance curve, the capacitance gradient formed between the components of the improved inertial sensor is obtained. According to the capacitance gradient, the corrected electrostatic force of the improved inertial sensor in each degree of freedom is calculated; The formula for calculating the modified electrostatic force is as follows: Where F represents the modified electrostatic force, q represents the generalized coordinates, i.e., the relative change of the coordinates of the test mass after it is moved and rotated along the three coordinate axes X, Y, and Z relative to the zero position, and V i represents the voltage on the ith electrode plate, V j represents the voltage on the jth electrode plate, V TM Indicates the voltage of the test mass, C EL,TM represents the capacitance between the electrode plates and the test mass, represents the capacitance gradient between the ith electrode plate and the test mass at a certain degree of freedom, represents the capacitance gradient between the test mass and the electrode frame, represents the capacitance gradient between the ith electrode plate and the electrode frame, represents the capacitance gradient between the i-th electrode plate and the j-th electrode plate; S4: Compare the corrected electrostatic force obtained in step S3 with the electrostatic force simulation value in step S2 to determine whether the accuracy of the improved inertial sensor meets the preset requirements. If so, use the improved inertial sensor to detect gravitational waves. If not, return to step S1, adjust the inertial sensor again, and use the method of steps S1-4 to obtain an inertial sensor that meets the preset requirements for gravitational wave detection in space.

2. The method for verifying inertial sensor correction based on a finite element analysis model as claimed in claim 1, characterized in that: In step S1, adjusting the position of the proof mass in the existing inertial sensor includes at least one of the six degrees of freedom, and the six degrees of freedom are translation of the proof mass along the X-axis, translation of the proof mass along the Y-axis, translation of the proof mass along the Z-axis, rotation of the proof mass along the X-axis, rotation of the proof mass along the Y-axis, and rotation of the proof mass along the Z-axis.

3. The verification method for inertial sensor correction based on finite element analysis model as claimed in claim 1, characterized in that: In step S3, the slope of the capacitance curve is the capacitance gradient.

4. The verification method for inertial sensor correction based on finite element analysis model as claimed in claim 1, characterized in that: The preset requirement in step S4 refers to meeting the accuracy requirement of LISA on the inertial sensor in terms of electrostatics.

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