A micro-vibration full-link simulation analysis method for a space optical load

Abstract

This invention discloses a full-link simulation analysis method for micro-vibration of space optical payloads. This method selects the main contributing modes and local vibration modes of the mirrors by modal participation factors, constructs a reduced-order state-space dynamic model, and achieves efficient modeling of micro-vibration transmission. The nodal responses are obtained by solving the state-space equations, and structural deformation caused by temperature loads is introduced to comprehensively evaluate the impact of micro-vibration and thermal deformation on imaging. Based on the displacement responses of a small number of mirror observation nodes, rigid body displacements are quickly fitted and image point shifts are calculated. Through a step-by-step simulation process of "modal selection → reduced-order modeling → response analysis → displacement fitting → image shift calculation," the full-link analysis of the impact of micro-vibration on imaging quality is completed. This method significantly reduces the system's degrees of freedom and computational load while maintaining accuracy, providing an efficient and reliable solution for micro-vibration evaluation and structural optimization of high-resolution optical payloads.

Description

Technical Field

[0001] This invention relates to the field of integrated analysis technology of optical loads, and specifically to a full-link simulation analysis method for micro-vibration of space optical loads. Background Technology

[0002] As space optical remote sensing satellites develop towards higher resolution, larger aperture, and longer focal length, the impact of micro-vibrations generated during satellite operation in orbit is becoming increasingly prominent. Micro-vibrations refer to the minute reciprocating motions caused by components such as momentum wheels and solar array drive mechanisms during normal operation of spacecraft in orbit. Although the energy of these vibrations is small and will not cause structural damage, they can cause line-of-sight jitter in high-precision optical payloads, leading to a decrease in imaging quality and, in severe cases, even affecting the success or failure of the mission.

[0003] To analyze the impact of micro-vibrations on the imaging performance of optical systems, integrated analysis methods are typically employed, combining structural dynamics, optical design, and thermal analysis in a joint simulation. However, current integrated analyses rely on the collaborative work of multiple independent software programs (such as UG, ANSYS, SIGFIT, and ZEMAX), resulting in complex model exchange and data conversion processes, making the analysis cumbersome and inefficient. For example, in patents CN 120493611 A and CN 112487672 A, the structural analysis and optical calculation modules are independent, requiring manual export of mirror node displacement data and import into SigFit for calculation to fit the rigid body displacements of each mirror, resulting in a fragmented and inefficient process. Patent CN 106484984 B achieves coupled analysis of thermal and structural aspects, but still lacks an optical response analysis module, making it impossible to directly assess the impact of micro-vibrations on imaging quality. Furthermore, as the structural complexity and number of degrees of freedom of optical remote sensing cameras continue to increase, the computational load of traditional methods rises exponentially, increasing the demands on computational resources and human intervention. For example, patent CN 105659888 B requires the retention of hundreds of modal orders for response analysis. Under high-precision models, the modal matrix is ​​enormous (for a model with tens of millions of degrees of freedom, the data from the first 600 modal orders can reach approximately 6 billion matrix elements), resulting in a huge burden on storage and computation.

[0004] Therefore, there is an urgent need for an integrated simulation method for micro-vibration of space optical loads that can significantly reduce computational costs while ensuring accuracy, and achieve effective modeling and solution analysis of structural dynamics, temperature load effects and optical response. Summary of the Invention

[0005] To address the technical problems mentioned above, this invention avoids data transfer and format conversion between multiple software platforms through integrated simulation. By performing modal screening and fusion to reduce the model order, it overcomes the technical bottleneck of difficult multidisciplinary integrated analysis and low solution efficiency of micro-vibration of space optical payloads. This invention can provide practical technical support for the micro-vibration analysis and evaluation of space optical payloads.

[0006] This method models the vibration source, structure, thermal, and optical subsystems separately. First, a state-space method is used for structural dynamics modeling, and model order reduction is achieved through modal screening and fusion. Then, the vibration source disturbance signal is input into the state-space equations for solution, obtaining the structural dynamic response caused by micro-vibrations. Simultaneously, the nodal response under temperature load is calculated and superimposed with the dynamic response to obtain the comprehensive nodal displacement. Based on the obtained nodal displacements, rigid body displacements are fitted, and further image point migration analysis is performed. Finally, the integration of each subsystem is completed in programming software, providing an effective technical method for solving the simulation problem of micro-vibrations of space optical loads.

[0007] To achieve the above objectives, this invention provides a full-link simulation analysis method for micro-vibration of space optical loads, comprising the following steps:

[0008] A full-link simulation analysis method for micro-vibration of space optical loads includes the following steps:

[0009] S1. Construct a finite element model of the space optical payload structure and perform modal analysis to obtain the analysis results;

[0010] S2. Based on the analysis results, perform modal screening, construct and solve the reduced-order state-space equations, and obtain the structural response caused by micro-vibrations;

[0011] S3. Apply temperature load to the finite element model and perform thermal deformation analysis to obtain the structural response caused by the temperature load;

[0012] S4. Integrate the structural response caused by micro-vibration and the structural response caused by temperature load, and calculate the rigid body displacement of each mirror based on the observation node;

[0013] S5. Based on the rigid body displacement of each mirror, the image point offset is calculated through the optical model to complete the simulation analysis.

[0014] Preferably, S1 includes: constructing a finite element model of the space optical load structure, setting up modal analysis simulation and exporting a solution file; and obtaining the frequency diagonal matrix and mode shape matrix of the space optical load structure based on the solution file.

[0015] Preferably, S2 includes: screening the modes of the space optical load structure according to the mode shape matrix, extracting the main contributing modes and the local vibration modes of the mirror; and constructing a reduced-order state-space equation based on the screened modes.

[0016] Preferably, the steps for constructing the reduced-order state-space equations include:

[0017] Transform physical coordinates to modal coordinates based on the mode shape matrix;

[0018] State-space equations are established based on modal coordinates, and the system matrix, input matrix, and output matrix are determined.

[0019] Preferably, in step S2, the step of obtaining the structural response caused by micro-vibration includes:

[0020] A mathematical model of the micro-vibration source is established by superimposing sinusoidal components;

[0021] Using the micro-vibration source as the input signal to the state-space equation, the displacement of the response observation node is obtained by solving the equation. The obtained displacement is the structural response caused by the micro-vibration.

[0022] Preferably, in step S3, the step of obtaining the structural response caused by the temperature load includes:

[0023] A temperature load is applied to the finite element model to perform thermal deformation analysis;

[0024] The displacement of the response observation node is extracted from the thermal deformation analysis results, and the obtained displacement is the structural response caused by the temperature load.

[0025] Preferably, in step S4, the step of calculating the rigid body displacement of each reflector includes:

[0026] Three non-collinear nodes are selected on the mirror surface to calculate the rigid body displacement of the mirror.

[0027] Calculate the absolute coordinates of the nodes in the global coordinate system based on the node displacements caused by micro-vibrations and temperature loads.

[0028] The absolute coordinates are mapped to the local coordinate system of each mirror to obtain the relative coordinates;

[0029] The rigid body displacement of each reflector is calculated based on its relative coordinates.

[0030] Preferably, in step S5, the step of calculating the image point offset includes:

[0031] Obtain the optical sensitivity matrix of each mirror in the optical model;

[0032] Multiply the rigid body displacement of each mirror by the corresponding optical sensitivity matrix to obtain the image point offset caused by each mirror.

[0033] The total image point offset is obtained by summing the image point offsets caused by all the mirrors.

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

[0035] 1. This invention proposes a full-link simulation method for micro-vibration, which uses the state-space method to model the structural dynamics and integrates it with thermal deformation calculation and optical imaging analysis, realizing an automated simulation process of structural response → rigid body displacement → image point offset. This effectively solves the problems of complex analysis process and low solution efficiency in the multi-disciplinary coupling process of existing methods.

[0036] 2. This invention quantitatively evaluates the contribution of each mode to the overall vibration of the system based on the modal participation factor, selects the main modes, and considers the higher-order local vibration modes of the mirror for modal fusion to establish a reduced-order dynamic model that balances accuracy and efficiency. This solves the problem that current modal truncation methods cannot take into account both the low-order overall modes and the high-order local vibration modes of the mirror.

[0037] 3. This invention uses state-space equations to solve the system. By changing parameters such as the system matrix, input matrix, and output matrix, it can be quickly adjusted for different structural models, excitation input positions, and observation positions without having to perform complex finite element modeling and simulation analysis again. Compared with traditional methods that rely on finite element software, it significantly reduces the simulation workload under multiple working conditions and multiple structural configurations and speeds up the simulation analysis. Attached Figure Description

[0038] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0040] Figure 2 This is a schematic diagram of the micro-vibration excitation signal;

[0041] Figure 3 Scatter plot of image point offset in the XY direction obtained from micro-vibration integrated simulation. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0043] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Example

[0045] To address the problems of existing technologies, this embodiment proposes the following solution: Based on a finite element model of a spatial optical load, modal analysis is performed to obtain dynamic parameters such as the modal matrix and modal frequency vector, which characterize the dynamic properties of the structure. Based on these dynamic parameters, a state-space equation is established starting from the vibration differential equation. The order of the state-space equation is reduced by combining the modal superposition principle and the modal participation factor. The flywheel disturbance force signal obtained experimentally is used as input, and the mirror node displacement is used as the output to solve the state-space equation. Simultaneously, a temperature load is applied to the finite element model to solve for the mirror node displacement caused by the temperature load. The mirror node displacement after coordinate transformation is used to fit the six-degree-of-freedom rigid body displacement of the mirror, which is then input into the optical model to solve for indices such as image point offset, effectively evaluating the impact of micro-vibrations on imaging quality.

[0046] The following will, in conjunction with this embodiment, explain in detail how the present invention solves the technical problems in practical work. The process is as follows: Figure 1 As shown:

[0047] S1. Construct a finite element model of the space optical payload structure and perform modal analysis to obtain the analysis results.

[0048] The finite element model of the space optical payload structure constructed in this embodiment includes the main load-bearing plate structure, primary mirror assembly, secondary mirror assembly, etc., and the materials, properties, and boundary conditions are set. Then, modal analysis simulation settings are performed, and a BDF format solution file is exported. The finite element software reads the BDF file, and after the solution is completed, an f06 format result file is automatically generated.

[0049] According to the writing specifications of f06 files, a parameter extraction function is written using programming software (such as MATLAB, Python, etc.). By querying keywords such as "REAL EIGENVALUES" in the f06 file, the data storage field is quickly located, thereby retrieving the frequency diagonal matrix. And mode matrix Among them, the frequency vector Composed of the first n eigenvalues, the mode shape matrix It consists of the first n order mode shape vectors.

[0050] S2. Based on the analysis results, construct and solve the state-space equations to obtain the structural response caused by micro-vibrations.

[0051] S201. First, based on the structural mode shape matrix obtained from the simulation, the modes of the system (the vibration analysis system composed of the space optical load structure) are screened, and the low-order modes that play a major role in the overall vibration of the structure and the local vibration modes of each mirror that may appear in the high-frequency band are extracted.

[0052] The modal participation factor is used to quantitatively assess the contribution of each mode to the overall vibration of the structure. The formula for calculating the modal participation factor is as follows:

[0053]

[0054] in, is the participation factor of the i-th mode; M is the mass matrix of the system; r is the displacement transformation vector; T represents the mode shape vector corresponding to the i-th mode; T represents the vector... Perform transpose operation. Select modal participation factor. Greater than the threshold The modal composition is the main contributing modal set.

[0055] Although the overall energy contribution of higher-order modes is relatively small, the local vibration modes of the mirrors appearing in the high-frequency band still have a significant impact on optical axis stability and image point offset. To avoid excessive truncation and loss of high-frequency mode shape information, the local vibration modes of each mirror are identified, forming a mirror local mode set.

[0056] The two modes are fused to form a complete effective modal shape matrix. :

[0057]

[0058] in, This represents the number of effective modes.

[0059] S202. Based on the state-space method, the system matrix is ​​solved using dynamic parameters, and the input and output matrices are determined by combining the excitation application nodes and response observation nodes, thus establishing the state-space equations.

[0060] Using the mode matrix, the physical coordinates x are transformed into modal coordinates ξ, and the two satisfy the following relationship:

[0061] .

[0062] Based on the aforementioned coordinate transformation, the forced vibration equation of an N-degree-of-freedom system is... This can be transformed into a differential equation with modal coordinates as variables:

[0063]

[0064] Wherein, the superscript "." represents the first derivative; ".." represents the second derivative; F represents the excitation force vector; This represents a frequency diagonal matrix.

[0065] The state variables are composed of modal coordinates and their first derivatives. Establish the state-space equations:

[0066]

[0067] Where y represents the output nodal displacement response signal; u represents the input excitation force signal; and t represents time.

[0068] The expressions for the four parameters in the state-space equations are as follows:

[0069]

[0070] Where 0 and I represent the zero matrix and identity matrix, respectively; Z represents the damping matrix; β represents the external force distribution vector, which contains the information of the nodes where the flywheel disturbance force acts; and γ represents the response observation vector, which contains the location information of the response observation nodes.

[0071] A mathematical model of the micro-vibration source is established using the superposition of sinusoidal components. The disturbance force of the micro-vibration source is as follows: Figure 2 As shown, the output signal is obtained by solving the state-space equation and using it as the input signal to solve the state-space equation. The displacement of the observation node under micro-vibration is obtained, and the obtained displacement is the structural response caused by micro-vibration.

[0072] S3. Apply temperature load to the finite element model and perform thermal deformation analysis to obtain the structural response caused by the temperature load.

[0073] Using the established finite element model of the space optical payload structure, a temperature load is applied, and finite element software (such as MSC.Nastran, ABAQUS, etc.) is used to calculate the structural thermal deformation under specific working conditions, obtaining the response observation node displacement caused by the temperature load. Based on the existing finite element model, a coefficient of thermal expansion is assigned to the material, and reference temperature and temperature load are set, exporting the solution file in BDF format.

[0074] The finite element method is used to solve the problem and generate an f06 result file. The nodal displacements under temperature load are then read from the file using programming software. The obtained displacements are the structural response caused by the temperature load.

[0075] S4. Combine the structural response caused by micro-vibration with the structural response caused by temperature load, and calculate the rigid body displacement of each reflector.

[0076] The nodal displacements under micro-vibration and temperature loads are summed. Based on the three-degree-of-freedom displacements of the observed nodes and their initial Cartesian coordinates, the absolute coordinates of the observed nodes in the global coordinate system are obtained. Based on the local coordinate systems of each mirror, the relative coordinates of the observed nodes with respect to their respective local coordinate systems are calculated using their absolute coordinates.

[0077] The total displacement of observation node i is composed of two superpositions:

[0078]

[0079] in, and These represent the nodal displacements under micro-vibration and temperature loads, respectively.

[0080] Set the initial coordinates of the observation node and nodal displacement Summing the results gives the absolute coordinates of the nodes in the global coordinate system:

[0081] .

[0082] For the j-th reflector, the absolute coordinates of the observation node are mapped to the local coordinate system of that reflector to obtain its relative coordinates. The absolute coordinates of node i... and relative coordinates with respect to the local coordinate system j The following relationship exists between them:

[0083]

[0084] in, Let be the direction cosine matrix (rotation matrix) of the j-th reflector from local to global. Let be the position of the origin of the local coordinate system of the j-th mirror in the global coordinate system.

[0085] For the j-th mirror, three representative observation nodes are selected on the mirror surface (usually nodes with non-collinear geometric layouts). The local coordinates of these three nodes at the initial time are as follows: , and The local coordinates at time t are respectively , and .

[0086] The coordinates of the geometric center of the mirror at the initial and current times are calculated based on the local coordinates of the three nodes as follows: , Then it is possible to obtain the three-degree-of-freedom translational displacement of the entire mirror. .

[0087] The unit normal vector of the mirror at the initial and current times is determined based on the positions of the three nodes. and :

[0088]

[0089] Project the two normal vectors onto the local coordinate system respectively. In the plane, the projection vector is obtained. and The angle between the projection vectors is the rotation angle of the mirror around the X-axis:

[0090] .

[0091] Similarly, project the normal vectors onto... and The rotation angles of the reflector around the Y and Z axes can be calculated, and the three rotation angles can be combined in sequence to obtain the rotational displacement vector of the reflector.

[0092] .

[0093] Integrating the translational and rotational displacements, we obtain the rigid body pose change vector of mirror j:

[0094] .

[0095] S5. Based on the rigid body displacement of each mirror, the image point offset is calculated through the optical model to complete the simulation analysis.

[0096] S501. Based on the relative coordinates of the observation node with respect to the local coordinate system, calculate the rigid body displacement of the reflector relative to the original local coordinate system, including three translational displacements and three rotational displacements.

[0097] S502. Establish an optical model in optical software (such as ZEMAX, Code V, etc.) to obtain the optical sensitivity matrix of each mirror. Multiply the rigid body displacement vector by the optical sensitivity matrix to obtain the image point offset in two directions, and plot a scatter plot of the image point offset in the XY directions as shown below. Figure 3 As shown.

[0098] By applying small unit displacement (1 micrometer) and small unit angle (1 arcsecond) perturbations to the j-th mirror along different directions, the image point offset is solved using software simulation. This process is repeated 6 times to obtain the complete sensitivity matrix. .

[0099] Multiplying the sensitivity matrix of the j-th mirror by the rigid body pose change vector yields the image displacement corresponding to the j-th mirror:

[0100] .

[0101] The total image point offset is obtained by summing the image point offsets caused by each mirror:

[0102] .

[0103] Based on the coupled calculation of the rigid body displacement of each mirror and the optical sensitivity matrix, the total offset of the image point on the imaging plane is finally obtained, thereby realizing a quantitative assessment of the full-link impact of space optical payloads on imaging performance under the combined effects of micro-vibration and temperature loads. At this point, the full-link simulation analysis of micro-vibration of the space optical payload is complete, providing a reliable basis for the subsequent optimization design of the optical system and on-orbit performance prediction.

[0104] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A full-link simulation analysis method for micro-vibration of space optical loads, characterized in that, Includes the following steps: S1. Construct a finite element model of the space optical payload structure and perform modal analysis to obtain the analysis results; S2. Based on the analysis results, perform modal screening, construct and solve the reduced-order state-space equations, and obtain the structural response caused by micro-vibrations; S3. Apply temperature load to the finite element model and perform thermal deformation analysis to obtain the structural response caused by the temperature load; S4. Integrate the structural response caused by micro-vibration and the structural response caused by temperature load, and calculate the rigid body displacement of each mirror based on the observation node; In step S4, the step of calculating the rigid body displacement of each reflector includes: selecting three non-collinear nodes on the mirror surface to calculate the rigid body displacement of the reflector; calculating the absolute coordinates of the nodes in the global coordinate system based on the node displacements caused by micro-vibration and temperature loads; mapping the absolute coordinates to the local coordinate system of each reflector to obtain the relative coordinates; and calculating the rigid body displacement of each reflector based on the relative coordinates. S5. Based on the rigid body displacement of each mirror, calculate the image point offset using the optical model to complete the simulation analysis; the steps for calculating the image point offset in S5 include: obtaining the optical sensitivity matrix of each mirror in the optical model; multiplying the rigid body displacement of each mirror by the corresponding optical sensitivity matrix to obtain the image point offset caused by each mirror; summing the image point offsets caused by all mirrors to obtain the total image point offset.

2. The method for full-link simulation analysis of micro-vibration of space optical loads according to claim 1, characterized in that, S1 includes: constructing a finite element model of the space optical load structure, setting up modal analysis simulation and exporting the solution file; and obtaining the frequency diagonal matrix and mode shape matrix of the space optical load structure based on the solution file.

3. The full-link simulation analysis method for micro-vibration of space optical loads according to claim 2, characterized in that, S2 includes: screening the modes of the space optical load structure according to the mode shape matrix, extracting the main contributing modes and the local vibration modes of the mirror; and constructing a reduced-order state-space equation based on the screened modes.

4. The full-link simulation analysis method for micro-vibration of space optical loads according to claim 3, characterized in that, The steps to construct a reduced-order state-space equation include: Transform physical coordinates to modal coordinates based on the mode shape matrix; State-space equations are established based on modal coordinates, and the system matrix, input matrix, and output matrix are determined.

5. The method for full-link simulation analysis of micro-vibration of space optical loads according to claim 1, characterized in that, In step S2, the step of obtaining the structural response caused by micro-vibration includes: A mathematical model of the micro-vibration source is established by superimposing sinusoidal components; Using the micro-vibration source as the input signal to the state-space equation, the displacement of the response observation node is obtained by solving the equation. The obtained displacement is the structural response caused by the micro-vibration.

6. The full-link simulation analysis method for micro-vibration of space optical loads according to claim 1, characterized in that, In step S3, the step of obtaining the structural response caused by temperature load includes: A temperature load is applied to the finite element model to perform thermal deformation analysis; The displacement of the response observation node is extracted from the thermal deformation analysis results, and the obtained displacement is the structural response caused by the temperature load.

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