A Dynamic Modeling Method for Space-Deployable Antenna Systems

Abstract

This invention belongs to the field of aerospace technology and relates to a dynamic modeling method for a space deployable antenna system. The method includes the following steps: establishing a finite element model of the space deployable antenna using finite element simulation software; correcting the linear substructures and nonlinear hinges; deriving the stiffness and mass matrices after correction; performing a first coordinate transformation on the linear substructures to reduce their order; performing a second coordinate transformation to fuse and connect the linear substructures to obtain the overall structural kinematic equations; connecting the corrected linear substructures and nonlinear hinges and analyzing the dynamic response; constructing an input-output mapping proxy model using data on restoring forces and relative displacements at the connection interfaces; and fusing the overall structural kinematic equations with the proxy model to obtain a fused dynamic model. This invention can quickly predict dynamic responses, save computational resources, and improve analysis efficiency.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a dynamic modeling method for space deployable antenna systems. Background Technology

[0002] Aerospace vehicles are one of the main tools for humankind to expand its range of activities. Over the past century, their design and manufacturing capabilities have developed rapidly, and their application areas have continuously expanded. To adapt to complex and diverse mission environments, aerospace vehicle structures are becoming increasingly larger, more complex, more sophisticated, and more intelligent, placing extremely high demands on the safety, reliability, and stability of engineering structures. Therefore, the dynamic characteristics of the structure must be considered when analyzing and designing aerospace vehicle structures.

[0003] With the rapid development of high-capacity computers and finite element software, finite element simulation has gradually become one of the most efficient computational methods for solving structural dynamics problems, and has been widely applied in aerospace, mechanical and other fields. However, for large and complex systems containing nonlinear connecting components, such as large space-based deployable solid-plane antennas, which are characterized by large spatial dimensions, complex connections, and strong dynamic nonlinearity, and contain complex connecting components such as deployment locking mechanisms, clamping release devices, and drive mechanisms, the dynamic modeling methods based on simplified assumptions alone cannot meet the requirements for evaluating the structural mechanical performance of deployable antennas.

[0004] On the one hand, if linear approximation modeling is used, the mechanical properties of nonlinear unit components in the solid-plane deployable antenna structure will be ignored, thus affecting the accuracy of the overall model and producing large errors. If high-precision modeling of the entire system is performed, iterative solutions are required for nonlinear problems, which is very time-consuming and cannot provide rapid response predictions for the structure. On the other hand, the finite element model is affected by modeling errors, such as inaccurate assumptions about boundary conditions, uncertainties in material model parameters, mesh size, and errors in static and dynamic test results, resulting in a certain degree of difference from the real structure. This leads to the finite element method being unable to accurately predict the dynamic characteristics of the real structure.

[0005] The substructure method, developed for analyzing the mechanical properties of large and complex systems, employs a divide-and-conquer approach. The free-interface modal synthesis method within the substructure method has attracted considerable attention in handling locally nonlinear dynamics problems. Modal synthesis solves complex systems by transforming them from physical space to modal space, thereby reducing the system's order. First, the complex system, which is difficult or impossible to solve directly, is decomposed into several easily analyzable subsystems. Then, the mechanical properties of each subsystem are synthesized using a specific method to obtain the mechanical properties of the complete system. Using the substructure method, a solid-plane deployable antenna system with nonlinear connections can be divided into several linear and nonlinear substructures.

[0006] Identifying nonlinear substructures in traditional nonlinear systems is often challenging. Data-driven surrogate modeling methods, by processing and analyzing the dynamic data of nonlinear connection units, capture the nonlinear physical relationships within the input-output data, thus replacing traditional mechanistic models for modeling. Once the surrogate model is successfully established, the nonlinear restoring force can be obtained simply by receiving the response at the nonlinear connection location, effectively avoiding the repetitive and tedious identification process of traditional methods.

[0007] Finite element model correction techniques mostly involve using structural dynamic response data, including frequency, frequency response function, displacement, etc., to correct parameters such as stiffness, mass, and boundary conditions of the model. This makes the dynamic characteristics of the finite element model as close as possible to the measured dynamic characteristics of the real structure. The corrected model can be used for structural response analysis, structural damage identification, structural health monitoring and safety assessment, and structural optimization design.

[0008] In summary, traditional finite element methods for analyzing the dynamic response of space-fixed deployable antenna systems suffer from low accuracy of nonlinear simplification methods, high computational cost and low efficiency of full-order finite element methods, and deviations between the model and the actual structure. Therefore, a new method for rapid prediction of the dynamic response of space-fixed deployable antennas is urgently needed. The key lies in constructing a dynamic model of a space-fixed deployable antenna system that can respond quickly. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a dynamic modeling method for space deployable antenna systems.

[0010] To achieve the objectives of this invention, the following technical solutions are adopted.

[0011] A method for dynamic modeling of a space-deployable antenna system includes the following steps:

[0012] S1. Use finite element simulation software to establish a finite element model of the spatial deployable antenna, and define the material properties, boundary conditions, connection assignments, and mesh properties of the spatial deployable antenna.

[0013] The finite element model includes a dual-reflector linear substructure finite element model and a nonlinear hinge finite element model. The dual-reflector linear substructure finite element model is established by dividing the two reflectors into two linear substructures using finite element simulation software and using shell elements to create the two linear substructure finite element models.

[0014] The nonlinear hinge finite element model is constructed using finite element simulation software. The connection assignment between two linear substructures is set, and a hinge connector is selected to simulate the hinge connection between the two linear substructures.

[0015] S2. Modify the linear substructure finite element model and the nonlinear hinge finite element model; wherein:

[0016] The correction process of the linear substructure finite element model involves analyzing the finite element modes of the linear substructure to obtain the modal frequencies and mode shapes of the linear substructure, and performing modal vibration simulations or physical tests on the linear substructure to obtain the test modal frequencies and mode shapes of the linear substructure as correction parameters. An objective function is defined, and the elastic modulus and Poisson's ratio of the reflecting surface are selected as the parameters to be corrected in the objective function. The trust region method is selected as the optimization algorithm, and the elastic modulus and Poisson's ratio that minimize the objective function are obtained through iterative solution to correct the linear substructure finite element model.

[0017] The correction process of the nonlinear hinge finite element model involves performing finite element modal analysis on the nonlinear hinge to obtain the dynamic displacement response signal, and conducting vibration simulation or physical experiments on the reflecting surface connected by the gap hinge to obtain the output displacement response signal of each measuring point of the linear substructure as correction parameters. An objective function is defined, and the gap value and stiffness coefficient of the gap hinge are selected as parameters to be corrected. The trust region method is selected as the optimization algorithm, and the gap value and stiffness coefficient that minimize the objective function are obtained through iterative solution to correct the nonlinear hinge finite element model.

[0018] S3. After the linear substructure finite element model is corrected, derive the stiffness and mass matrices of the linear substructure, denoted as K. α ,K β and M α M β Using the free interface modal synthesis method, the linear substructure is subjected to a first coordinate transformation to reduce its order; then, a second coordinate transformation is performed to fuse and connect the linear substructures to obtain the overall structural kinematic equations with independent generalized coordinates.

[0019] S4. Connect the linear substructure finite element model and the nonlinear hinge finite element model after the correction in step S2, and perform dynamic response analysis. Using the data of restoring force and relative displacement at the connection interface, construct an input-output mapping proxy model using the radial basis function method. Fuse the overall structural kinematic equations obtained in step S3 with the input-output mapping proxy model to obtain a fused dynamic model.

[0020] As a further aspect of the present invention, the fusion dynamics model is used to predict the response of the space deployable antenna, and error analysis and computational efficiency comparison of the prediction results are carried out to verify the accuracy and efficiency of the fusion dynamics model.

[0021] As a preferred embodiment of the present invention, the verification process includes the following steps:

[0022] S31. Using the Newmark-β method, solve for the dynamic response of the fused dynamic model, where the initial parameters of Newmark-β are γ = 0.5 and β = 0.25; the initial state of the system is a stationary state, with initial displacement, velocity, and acceleration all being 0; the time step is 1 / 1000, and the total duration is 5s.

[0023] S32. Compare the error between the response prediction results of the fusion dynamics model and the experimental results, using R... 2 Quantifying the error using relative mean absolute error

[0024]

[0025]

[0026] Where n is the length of the response result data; y i The response reference value obtained from the experiment; The predicted response value obtained by the proposed method; The mean of the response reference values ​​is given; STD is the standard deviation of the response reference values; R is the mean of the response reference values. 2 The larger the value, the closer it is to 1; or the smaller the RAAE value, the closer it is to zero, the closer the result is to the reference value.

[0027] S33. Under the same calculation conditions, compare the dynamic analysis time of the fused dynamic model and the finite element simulation model to verify the computational efficiency of the fused dynamic model.

[0028] As a preferred embodiment of the present invention, the correction process of the linear substructure finite element model includes the following steps:

[0029] S41. Perform finite element modal analysis on the two linear substructures respectively to obtain the modal frequencies and mode shapes of each linear substructure.

[0030] S42. Perform modal vibration simulation or physical experiment on the two linear substructures respectively, arrange excitation points and response measurement points, and obtain the response signal output by each measurement point of each linear substructure;

[0031] S43. Analyze the response signal using a cluster-based automatic working modal analysis method to obtain the test modal frequencies and mode shapes of each linear substructure;

[0032] S44. Set the objective function, using the modal frequencies and mode shapes of each linear substructure and the test modal frequencies and mode shapes of each linear substructure as correction parameters, and define the objective function as follows:

[0033]

[0034]

[0035] In the formula, ε Υ (r) represents the difference between the finite element modal parameters and the experimental analysis modal parameters; Let represent the i-th modal frequency obtained by the finite element method and the i-th modal frequency obtained by experimental analysis, respectively. Let represent the i-th mode shape obtained by the finite element method and the i-th mode shape obtained by experimental analysis, respectively; the vector form of multiple variables such as frequency and mode shape is used to consider the contribution of multiple variables to the same objective; W represents the different weighting coefficient matrix applied to each experimental frequency and mode shape of the structure, and r represents the parameter to be corrected;

[0036] S45. Select the elastic modulus and Poisson's ratio of the linear substructure as parameters to be corrected, select the trust region method as the optimization algorithm, and obtain the elastic modulus and Poisson's ratio that minimize the objective function through iterative solution.

[0037] As a preferred embodiment of the present invention, the correction process of the nonlinear hinge finite element model includes the following steps:

[0038] S51. Perform finite element modal analysis on the nonlinear hinge, set the gap value and stiffness coefficient, and perform implicit dynamic analysis to obtain the dynamic displacement response signal.

[0039] S52. Conduct vibration simulation or physical tests on the reflective surface with gap hinge connection, arrange excitation points and response measurement points, and obtain the output displacement response signals of each measurement point of the structure.

[0040] S53. Define the objective function for the experimental results and finite element method results of the structural dynamic response as follows:

[0041]

[0042] Among them, H Α H Ε t represents the dynamic response value obtained by the finite element method and the dynamic response value obtained by experimental measurement, respectively; r represents the time series and is the parameter to be corrected.

[0043] S54. Select the gap value and stiffness coefficient of the gap hinge as the parameters to be corrected, select the trust region method as the optimization algorithm, and obtain the gap value and stiffness coefficient that minimize the objective function through iterative solution.

[0044] As a preferred embodiment of the present invention, the process of establishing the kinematic equations of the overall structure includes the following steps:

[0045] S61. Perform eigenvalue decomposition on each linear substructure to obtain eigenvectors, and select the truncation order to obtain the preserved modes Φ.k ;

[0046] S62. Calculate the residual modes Ψ of the linear substructure based on whether it has rigid body modes. d ;

[0047] When the linear substructure does not contain rigid body modes

[0048]

[0049] in: B T The interface force projection matrix;

[0050] S63. When a linear substructure contains rigid body modes, the stiffness matrix is ​​a singular matrix and cannot be inverted. In engineering practice, a frequency-shifting method is often used to shift the frequency of the substructure stiffness matrix, thereby eliminating its singularity. The residual modes are then used to approximate higher-order truncated modes. The basic formula is as follows:

[0051]

[0052] in: Let K be the stiffness matrix after frequency shift, and M be the stiffness and mass matrices before frequency shift, respectively. τ is the frequency shift amount. The mode shapes of the structure remain unchanged before and after the frequency shift. Therefore, we obtain... Later according to Obtain the remaining modes;

[0053] S64. Determine the rigid and elastic connection properties of the degrees of freedom between each linear substructure, and distinguish the connection coordination conditions according to the connection properties, as shown below:

[0054]

[0055] Where: r represents the degree of freedom of rigid connection; e represents the degree of freedom of elastic connection; and δ represents the relative displacement.

[0056] S65. After obtaining the interface compatibility conditions, eliminate the non-independent generalized coordinate components between linear substructures to obtain the overall structural kinematic equations:

[0057]

[0058] Where: F is the external excitation experienced by the substructure, f βJ Let T be the interface restoring force, and T be the second coordinate transformation matrix.

[0059] As a preferred embodiment of the present invention, the process of establishing the fusion dynamics model includes the following steps:

[0060] S71. Perform implicit dynamic response analysis on the modified linear substructure-nonlinear hinge finite element model, set up multiple working conditions, change the excitation amplitude and type, and solve the dynamic response of the system under the action of multiple excitations.

[0061] S72. Extract the restoring force and relative displacement data at both ends of the nonlinear hinge, and use the radial basis function method to construct the mapping relationship between the restoring force and the relative displacement to obtain the nonlinear input-output mapping surrogate model;

[0062] S73. The linear substructure finite element model and the nonlinear input-output mapping proxy model are fused to obtain the fused dynamic model of the spatially deployable antenna.

[0063] Beneficial effects

[0064] 1. The present invention discloses a dynamic modeling method for a space deployable antenna system, which divides the solid-plane deployable antenna system into a linear substructure of the antenna reflector and a nonlinear substructure connected by hinges. The free interface mode synthesis method is used to perform coordinate transformation on the linear substructure, and the system is transformed from physical space to modal space for solution, thereby reducing the order of the system's degrees of freedom and ultimately improving the computational efficiency of the dynamic model.

[0065] 2. The present invention discloses a dynamic modeling method for a space deployable antenna system, which combines the ideas of substructure and model correction, and performs model correction on the antenna reflector substructure and the hinge nonlinear substructure respectively, thereby improving the accuracy of the finite element model;

[0066] 3. The present invention discloses a dynamic modeling method for a space deployable antenna system. By capturing the relationship between the restoring force and the relative displacement at both ends of a nonlinear hinge, and using a data-driven method, an input-output mapping model is obtained. The nonlinear substructure is then equivalent to a proxy model, which can effectively avoid the problem of low computational efficiency caused by repeated iterative solutions in traditional finite element simulation methods when dealing with nonlinear problems.

[0067] 4. The present invention discloses a dynamic modeling method for a space deployable antenna system. By using the concept of substructure, the space solid-surface deployable antenna system is modularized. Once the input-output surrogate model database is established, the dynamic response of the system can be predicted quickly and efficiently, which greatly saves computing resources and improves analysis efficiency. Attached Figure Description

[0068] Figure 1 This is a flowchart of the dynamic modeling method for the space deployable antenna system described in this invention;

[0069] Figure 2 A finite element model of a certain type of space deployable antenna, along with excitation points, response points, and boundary condition settings, is shown in the diagram.

[0070] Figure 3 The figure shows a comparison of the displacement, velocity, and acceleration identification results at response point 2 between the method described in this invention and the finite element simulation test. In the figure, the solid blue line represents the response identification result of the proposed method, and the dashed red line represents the finite element simulation test result. Detailed Implementation

[0071] The present invention will be further described in conjunction with the accompanying drawings and embodiments.

[0072] A fusion dynamics model of a certain type of space-based solid-surface deployable antenna system is performed, taking a dual-reflector system as an example. Figure 2 As shown in the table below. For the entire system, the reflective surface is a carbon fiber skin-aluminum honeycomb sandwich structure, with a single reflective surface size of 11m * 1.57m. Both the upper and lower skins are made of 0.3mm carbon fiber composite material, and the honeycomb core is a 5mm * 0.03mm aluminum honeycomb with a honeycomb thickness of 44.4mm. The mechanical property parameters of the reflective surface material are shown in the table below.

[0073] Table 1 Mechanical property parameters of antenna reflector material

[0074]

[0075] Step 1: Establish a finite element model of the space-based solid-plane deployable antenna using the finite element simulation method. Without loss of generality, a double-reflector structure will be used as an example for illustration. Figure 2 As shown, the deployable antenna is divided into linear reflector substructures α and β. Finite element models of the two substructures α and β are established using shell elements. In the "Properties" module, the properties of the skin and aluminum honeycomb materials shown in Table 1 are defined. In the "Interactions" module, a hinge connector is created using "Create Connection" to simulate the hinge. Substructures α and β are then connected together. Both substructures α and β contain 60 elements and 84 nodes, with each node having 6 degrees of freedom. Four nodes at the lower boundary of substructure α are fixed.

[0076] Step 2: Conduct modal vibration tests on the antenna reflector. In this example, simulation tests are used instead of physical tests. The modal frequencies and mode shapes of the linear substructure of the antenna reflector are obtained using a cluster-based automatic working modal analysis method. Correction parameters, objective functions, and optimization algorithms are set to correct the finite element model of the linear substructure of the reflector.

[0077] Step 2.1: Perform finite element modal analysis on the antenna reflector substructures α and β respectively to obtain their respective modal frequencies and mode shapes.

[0078] Step 2.2: Conduct modal vibration simulation tests on the antenna reflector substructures α and β, where the reflector skin E... 11E =265e9 Pa, Poisson's ratio εE =0.246, excitation points and response measurement points are arranged to obtain the output response signals of each measurement point of the structure.

[0079] Step 2.3: Using a cluster-based automatic operating modal analysis method, the experimental response data is processed and analyzed to obtain the experimental modal frequencies and mode shapes of the antenna reflector substructures α and β.

[0080] Step 2.4: Set the objective function, using frequency and mode shape as correction parameters. The objective function is then: ε Υ (r) represents the difference between the finite element modal parameters and the experimental modal parameters. W represents the weighting coefficient matrix for each experimental frequency and mode shape of the structure, and r represents the parameter to be corrected.

[0081] Step 2.5: Select the elastic modulus E of the antenna reflector skin. 11 Using Poisson's ratio ε as the parameter to be corrected, the trust region method is chosen as the optimization algorithm. Through iterative solution, the corrected elastic modulus E is finally obtained, which minimizes the objective function J(r). 11A =265e9 Pa, Poisson's ratio ε A =0.246.

[0082] Step 3: After the linear finite element model is corrected, derive the stiffness and mass matrices of the linear substructure of the antenna reflector, denoted as K. α ,K β and M α M β Using the free interface modal synthesis method, the antenna reflector substructure is subjected to a first coordinate transformation to reduce the order of the linear substructure. After a second coordinate transformation, the substructures are fused and connected to obtain the overall structural kinematic equations with independent generalized coordinates.

[0083] Step 3.1: Calculate the K values ​​of the antenna reflector substructures α and β obtained in Step 2. α M α K β M β Eigenvalue decomposition is performed to obtain its eigenvectors. A truncation order of 50 is chosen to obtain the low-order preserved modes Φ. αk Φ βk .

[0084] Step 3.2: The linear substructure α does not contain rigid body modes, so the equation can be directly used. Its residual mode Ψ was calculated. αd The linear substructure β contains rigid body modes. First, the frequency shifting method is used to analyze K... β Frequency shifting is performed by an amount of 0.01. After frequency shifting, the result is then... The residual modes Ψ of substructure β were calculated. βd .

[0085] Step 3.3: Obtain the preserved mode Φ αk Φ βk and the remaining mode Ψ αd Ψ βd Then, the first coordinate transformation is performed to reduce the order of the substructure.

[0086] Step 3.4: The antenna reflector substructure satisfies the compatibility condition at the interface connection, requiring the elimination of non-independent components between generalized coordinates. The interface is hinged; therefore, the degree of freedom of rotation about the y-axis is elastic, while the remaining degrees of freedom are rigid. Distinguishing between the rigid and elastic degrees of freedom in the compatibility condition, the interface compatibility condition is:

[0087] u αJr =u βJr (10)

[0088] u αJe =u βJe +δ

[0089] f αJ =-f βJ

[0090] Where: r represents the degree of freedom of rigid connection; e represents the degree of freedom of elastic connection; and δ represents the relative displacement.

[0091] Step 3.5: After obtaining the displacement compatibility conditions, eliminate the non-independent generalized coordinate components between substructures to obtain the fused dynamic equations.

[0092]

[0093] Where F is the external excitation experienced by the substructure, f βJ Let T be the interface restoring force, and T be the second coordinate transformation matrix.

[0094] Step 4: Conduct vibration tests on the antenna reflector with gapped hinge connections to obtain structural dynamic response data. Set correction parameters, objective functions, and optimization algorithms to correct the nonlinear hinge finite element model.

[0095] Step 4.1: Using finite element simulation software, set the connection assignment between antenna reflectors α and β, select the "hinged" connector to simulate the hinge connection between the antenna reflectors, and set the gap value e. A =0.02 rad, stiffness coefficient K A = 500 N·m / rad, and implicit dynamic analysis was performed to obtain the dynamic displacement response signal H. Α (t,r).

[0096] Step 4.2: Conduct a vibration test on the antenna reflector with the gap hinge connection. In this example, a simulation test is used instead of a physical test, and the actual value e of the gap hinge is set. E =0.005 rad, stiffness coefficient K E =1000 N·m / rad, excitation points and response measurement points are arranged, and the output displacement response signal H of each measurement point of the structure is obtained. Ε (t).

[0097] Step 4.3: Define the experimental test values ​​of the structural dynamic response and the objective function of the finite element method as follows:

[0098]

[0099] Among them, H Α H Ε t represents the dynamic response value obtained by the finite element method and the dynamic response value obtained by experimental measurement, respectively. r represents the time series and r is the parameter to be corrected.

[0100] Step 4.4: Select the clearance value e and stiffness coefficient K of the clearance hinge as the parameters to be corrected, and choose the trust region method as the optimization algorithm. Through iterative solution, the objective function J(r) is finally minimized. After correction, e A =0.005 rad, stiffness coefficient K A = 1000 N·m / rad.

[0101] Step 5: Connect the finite element models corrected in Steps 2 and 4 and perform dynamic response analysis. Using the data of restoring force and relative displacement at the connection interface, construct an input-output mapping proxy model using the radial basis function method. Finally, obtain the fused dynamic model according to Step 3.

[0102] Step 5.1: Connect the corrected antenna reflector-gap hinge finite element model, establish a "dynamic implicit" analysis step with a time of 5s and an increment step size of 0.001; in the "Load" module, perform calculations on a cosine excitation with an amplitude of 100N and an angular frequency of 20rad / s at the excitation point. Change the excitation magnitude and perform 10 analysis steps respectively, then export the restoring force and relative displacement data at both ends of the connector.

[0103] Step 5.2: Extract the restoring force and relative displacement data at both ends of the gap hinge, and use the radial basis function method to construct the mapping relationship between the restoring force and the relative displacement, finally obtaining the gap nonlinear input-output mapping surrogate model.

[0104] Step 5.3: After obtaining the nonlinear surrogate model, according to Step 3, the linear substructure of the reflector surface is fused with the nonlinear surrogate model to obtain the fused dynamic model of the space solid-surface deployable antenna system.

[0105] Step 6: After obtaining the fused dynamic model, the response of the solid-plane deployable antenna system is predicted, and the error analysis and computational efficiency comparison of the prediction results are carried out to verify the accuracy and efficiency of the dynamic modeling method of this invention.

[0106] Step 6.1: Using the Newmark-β method, solve for the system response of the fused dynamic model of the solid-plane deployable antenna system obtained in Step 5, where the Newmark-β initial parameters are γ = 0.5 and β = 0.25; the external excitation is a cosine excitation with an amplitude of 100N and an angular frequency of 20rad / s; the initial state of the system is a stationary state with initial displacement, velocity, and acceleration all being 0; the time step is 1 / 1000 and the total duration is 5s.

[0107] Step 6.2: Compare the response error at response point 2 between the predicted response result of the dynamic model of the proposed method and the simulation test result. Figure 3 As shown, using R 2 The error is quantified by comparing the relative mean absolute error, as shown in Table 2.

[0108] Table 2 Error Table of Fusion Dynamics Model and Experimental Results for Space Solid Deployable Antenna

[0109]

[0110] By calculating R using two methods 2 Compared to the RAAE value, since velocity and acceleration are obtained recursively from displacement using the Newmark format, the errors in acceleration and velocity are slightly higher than the errors in displacement. The response error R between the method proposed in this invention and the experimental results... 2 The values ​​are all above 0.97, which shows that the method proposed in this invention can perform high-precision response prediction for space-based solid-surface deployable antenna systems.

[0111] Step 6.3: Under the same calculation conditions, the time for dynamic response calculation using the dynamic modeling method proposed in this invention is 20.72s, while the calculation using finite element simulation software takes 1625s under the same working conditions. It can be seen that the method proposed in this invention improves the efficiency of dynamic modeling and response prediction of the system while ensuring the accuracy of response prediction, reduces the calculation cost, and is beneficial to the analysis and iterative design of the structure, which has great engineering significance.

[0112] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for dynamic modeling of a space-deployable antenna system, characterized in that: Includes the following steps: S1. Use finite element simulation software to establish a finite element model of the spatial deployable antenna, and define the material properties, boundary conditions, connection assignments, and mesh properties of the spatial deployable antenna. The finite element model includes a dual-reflector linear substructure finite element model and a nonlinear hinge finite element model. The dual-reflector linear substructure finite element model is established by dividing the two reflectors into two linear substructures using finite element simulation software and using shell elements to create the two linear substructure finite element models. The nonlinear hinge finite element model is constructed using finite element simulation software. The connection assignment between two linear substructures is set, and a hinge connector is selected to simulate the hinge connection between the two linear substructures. S2. Modify the linear substructure finite element model and the nonlinear hinge finite element model; wherein: The correction process of the linear substructure finite element model involves analyzing the finite element modes of the linear substructure to obtain the modal frequencies and mode shapes of the linear substructure, and performing modal vibration simulations or physical tests on the linear substructure to obtain the test modal frequencies and mode shapes of the linear substructure as correction parameters. An objective function is defined, and the elastic modulus and Poisson's ratio of the reflecting surface are selected as the parameters to be corrected in the objective function. The trust region method is selected as the optimization algorithm, and the elastic modulus and Poisson's ratio that minimize the objective function are obtained through iterative solution to correct the linear substructure finite element model. The correction process of the nonlinear hinge finite element model involves performing finite element modal analysis on the nonlinear hinge to obtain the dynamic displacement response signal, and conducting vibration simulation or physical experiments on the reflecting surface connected by the gap hinge to obtain the output displacement response signal of each measuring point of the linear substructure as correction parameters. An objective function is defined, and the gap value and stiffness coefficient of the gap hinge are selected as parameters to be corrected. The trust region method is selected as the optimization algorithm, and the gap value and stiffness coefficient that minimize the objective function are obtained through iterative solution to correct the nonlinear hinge finite element model. S3. After the linear substructure finite element model is corrected, derive the stiffness and mass matrices of the linear substructure, denoted as K. α ,K β and M α M β Using the free interface modal synthesis method, the linear substructure is subjected to a first coordinate transformation to reduce its order; then, a second coordinate transformation is performed to fuse and connect the linear substructures to obtain the overall structural kinematic equations with independent generalized coordinates. S4. Connect the linear substructure finite element model and the nonlinear hinge finite element model after the correction in step S2, and perform dynamic response analysis. Using the data of restoring force and relative displacement at the connection interface, construct an input-output mapping proxy model using the radial basis function method. Fuse the overall structural kinematic equations obtained in step S3 with the input-output mapping proxy model to obtain a fused dynamic model.

2. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The fused dynamics model was used to predict the response of a space deployable antenna, and error analysis and computational efficiency comparison of the prediction results were carried out to verify the accuracy and efficiency of the fused dynamics model.

3. The method for dynamic modeling of a space deployable antenna system according to claim 2, characterized in that: The verification process includes the following steps: S31. Using the Newmark-β method, solve for the dynamic response of the fused dynamic model, where the initial parameters of Newmark-β are γ = 0.5 and β = 0.25; the initial state of the system is a stationary state, with initial displacement, velocity, and acceleration all being 0; the time step is 1 / 1000, and the total duration is 5s. S32. Compare the error between the response prediction results of the fusion dynamics model and the experimental results, using R... 2 Quantifying the error using relative mean absolute error Where n is the length of the response result data; y i The response reference value obtained from the experiment; The predicted response value obtained by the proposed method; R² is the mean of the response reference value; STD is the standard deviation of the response reference value; the larger the R² value, the closer it is to 1, or the smaller the RAAE value, the closer it is to zero, indicating that the obtained result is closer to the reference value. S33. Under the same calculation conditions, compare the dynamic analysis time of the fused dynamic model and the finite element simulation model to verify the computational efficiency of the fused dynamic model.

4. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The correction process for the linear substructure finite element model includes the following steps: S41. Perform finite element modal analysis on the two linear substructures respectively to obtain the modal frequencies and mode shapes of each linear substructure. S42. Perform modal vibration simulation or physical experiment on the two linear substructures respectively, arrange excitation points and response measurement points, and obtain the response signal output by each measurement point of each linear substructure; S43. Analyze the response signal using a cluster-based automatic working modal analysis method to obtain the test modal frequencies and mode shapes of each linear substructure; S44. Set the objective function, using the modal frequencies and mode shapes of each linear substructure and the test modal frequencies and mode shapes of each linear substructure as correction parameters, and define the objective function as follows: In the formula, ε Υ (r) represents the difference between the finite element modal parameters and the experimental analysis modal parameters; Let represent the i-th modal frequency obtained by the finite element method and the i-th modal frequency obtained by experimental analysis, respectively. Let i represent the i-th mode shape obtained by the finite element method and the i-th mode shape obtained by experimental analysis, respectively; the contribution of multiple variables such as frequency and mode shape to the same objective is considered by writing multiple variables as vectors. W represents the different weighting coefficient matrix applied to each test frequency and mode shape of the structure, and r represents the parameter to be corrected; S45. Select the elastic modulus and Poisson's ratio of the linear substructure as parameters to be corrected, select the trust region method as the optimization algorithm, and obtain the elastic modulus and Poisson's ratio that minimize the objective function through iterative solution.

5. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The correction process of the nonlinear hinge finite element model includes the following steps: S51. Perform finite element modal analysis on the nonlinear hinge, set the gap value and stiffness coefficient, and perform implicit dynamic analysis to obtain the dynamic displacement response signal. S52. Conduct vibration simulation or physical tests on the reflective surface with gap hinge connection, arrange excitation points and response measurement points, and obtain the output displacement response signals of each measurement point of the structure. S53. Define the objective function for the experimental results and finite element method results of the structural dynamic response as follows: Among them, H Α H Ε t represents the dynamic response value obtained by the finite element method and the dynamic response value obtained by experimental measurement, respectively; r represents the time series and is the parameter to be corrected. S54. Select the gap value and stiffness coefficient of the gap hinge as the parameters to be corrected, select the trust region method as the optimization algorithm, and obtain the gap value and stiffness coefficient that minimize the objective function through iterative solution.

6. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The process of establishing the kinematic equations of the overall structure includes the following steps: S61. Perform eigenvalue decomposition on each linear substructure to obtain eigenvectors, and select the truncation order to obtain the preserved modes Φ. k ; S62. Calculate the residual modes Ψ of the linear substructure based on whether it has rigid body modes. d ; When the linear substructure does not contain rigid body modes in: B T The interface force projection matrix; S63. When a linear substructure contains rigid body modes, the stiffness matrix is ​​a singular matrix and cannot be inverted. In engineering practice, a frequency-shifting method is often used to shift the frequency of the substructure stiffness matrix, thereby eliminating its singularity. The residual modes are then used to approximate higher-order truncated modes. The basic formula is as follows: in: Let K be the stiffness matrix after frequency shift, and M be the stiffness and mass matrices before frequency shift, respectively. τ is the frequency shift amount. The mode shapes of the structure remain unchanged before and after the frequency shift. Therefore, we obtain... Later according to Obtain the remaining modes; S64. Determine the rigid and elastic connection properties of the degrees of freedom between each linear substructure, and distinguish the connection coordination conditions according to the connection properties, as shown below: Where: r represents the degree of freedom of rigid connection; e represents the degree of freedom of elastic connection; and δ represents the relative displacement. S65. After obtaining the interface compatibility conditions, eliminate the non-independent generalized coordinate components between linear substructures to obtain the overall structural kinematic equations: Where: F is the external excitation experienced by the substructure, f βJ Let T be the interface restoring force, and T be the second coordinate transformation matrix.

7. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The process of establishing the fusion dynamics model includes the following steps: S71. Perform implicit dynamic response analysis on the modified linear substructure-nonlinear hinge finite element model, set up multiple working conditions, change the excitation amplitude and type, and solve the dynamic response of the system under the action of multiple excitations. S72. Extract the restoring force and relative displacement data at both ends of the nonlinear hinge, and use the radial basis function method to construct the mapping relationship between the restoring force and the relative displacement to obtain the nonlinear input-output mapping surrogate model; S73. The linear substructure finite element model and the nonlinear input-output mapping proxy model are fused to obtain the fused dynamic model of the spatially deployable antenna.

Images