Dynamic modeling method for space deployable antenna system

Abstract

The invention belongs to the technical field of space flight and aviation, and relates to a space deployable antenna system dynamics modeling method comprising the following steps: using finite element simulation software to establish a space deployable antenna finite element model; correcting a linear substructure and a nonlinear hinge; after correction is completed, rigidity and mass matrixes are exported; performing first coordinate transformation on the linear substructure to complete order reduction of the linear substructure; second coordinate transformation is carried out, and all the linear substructures are fused and connected to obtain an overall structure kinematics equation; connecting the corrected linear substructure and the nonlinear hinge, analyzing dynamic response, constructing an input-output mapping agent model through data of restoring force and relative displacement at a connecting interface, and fusing an overall structure kinematics equation with the agent model to obtain a fused dynamic model; the dynamic response can be quickly predicted, computing resources are saved, and the analysis efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the field of aerospace technology, and in particular relates to a dynamic modeling method for a space deployable antenna system. Background Art

[0002] Aerospace is one of the main tools for humans to expand their range of activities. Over the past century, its design and manufacturing level has developed rapidly, and its application areas have continued to expand. In order to adapt to complex and diverse mission environments, the structure of aerospace is becoming larger, more complex, more sophisticated and more intelligent, which puts forward extremely high requirements on the safety, reliability and stability of engineering structures. When analyzing and designing aerospace structures, the dynamic characteristics of the structure must be considered.

[0003] With the rapid development of large-capacity computers and finite element software, finite element simulation has gradually become one of the efficient calculation methods for solving structural dynamics problems, and has been widely used in aerospace, machinery and other fields. However, for large and complex systems with nonlinear connection components, such as large space solid surface deployable antennas, which have the characteristics of large spatial dimensions, complex connections, and strong dynamic nonlinearity, and contain complex connection components such as deployment locking mechanisms, compression release devices, and drive mechanisms, the dynamic modeling method using only simplified assumptions cannot meet the mechanical performance evaluation of deployable antenna structures.

[0004] On the one hand, if linear approximate modeling is used, the mechanical properties of the nonlinear unit components in the solid deployable antenna structure will be ignored, which will affect the accuracy of the overall model and produce large errors; if the overall system is modeled with high precision, iterative solutions are required for nonlinear problems, which is very time-consuming and cannot predict the rapid response of the structure. On the other hand, the finite element model will be affected by modeling errors, such as inaccurate assumptions of boundary conditions, uncertainty in material model parameters, mesh size, and errors in structural static and dynamic test results, and there will be a certain degree of difference from the real structure, resulting in the finite element method being unable to accurately predict the dynamic characteristics of the real structure.

[0005] The substructure method was developed to analyze the mechanical properties of large complex systems. It is a divide-and-conquer idea. The free interface modal synthesis method in the substructure method has attracted the attention of many scholars in dealing with local nonlinear dynamics problems. The modal synthesis method solves the complex system by converting it from the physical space to the modal space, thereby achieving system order reduction. First, the complex system that is difficult or impossible to solve directly is decomposed into several subsystems that are easy to analyze, and then the mechanical properties of each subsystem are synthesized by a certain method to obtain the mechanical properties of the complete system. With the help of the idea of ​​the substructure method, the solid surface deployable antenna system with nonlinear connections can be divided into several linear substructures and nonlinear substructures.

[0006] For nonlinear substructures, the identification of traditional nonlinear systems is often difficult. The data-driven proxy model method processes and analyzes the dynamic data of nonlinear connection units, captures the nonlinear physical relationship in the input-output data, and then replaces the traditional mechanism for modeling. After the proxy model is successfully established, the nonlinear restoring force can be obtained by simply obtaining the response of the nonlinear connection position, which can effectively avoid the repeated and tedious identification process of the traditional method.

[0007] Finite element model correction technology mostly uses structural dynamic response data, including frequency, frequency response function, displacement, etc., to correct the model's parameters such as stiffness, mass, and boundary, so as to make 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, when the traditional finite element method is used to analyze the dynamic response of a system containing a space solid surface deployable antenna, the nonlinear simplification method has low accuracy, the full-order finite element method has large computational complexity, low computational efficiency, and there is a deviation between the model and the actual structure. There is an urgent need for a new method for quickly predicting the dynamic response of a space solid surface deployable antenna. The key lies in constructing a dynamic model of the space deployable antenna system that can respond quickly. Summary of the invention

[0009] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for dynamic modeling of a space deployable antenna system.

[0010] In order to achieve the purpose of the present invention, the present invention is implemented by adopting the following technical solutions.

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

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

[0013] The finite element model includes a double-reflecting surface linear substructure finite element model and a nonlinear hinge finite element model, wherein: the double-reflecting surface linear substructure finite element model is to divide the two reflecting surfaces into two linear substructures by using finite element simulation software, and establish two linear substructure finite element models by shell elements;

[0014] The nonlinear hinge finite element model uses finite element simulation software to set the connection assignment between two linear substructures and select an articulated connector to simulate the hinge connection between the two linear substructures;

[0015] S2. Modifying 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 is to analyze the finite element mode of the linear substructure, obtain the modal frequency and vibration shape data of the linear substructure, perform modal vibration simulation or physical test on the linear substructure, obtain the test modal frequency and vibration shape data of the linear substructure as correction parameters, define the objective function, select the elastic modulus and Poisson's ratio of the reflection surface as the parameters to be corrected of the objective function, 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 to correct the linear substructure finite element model;

[0017] The correction process of the nonlinear hinge finite element model is to perform finite element modal analysis on the nonlinear hinge to obtain a dynamic displacement response signal and to conduct vibration simulation or physical test on the reflection surface connected by the gap hinge to obtain the output displacement response signal of each measuring point of the linear substructure as a correction parameter, define the objective function, 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 to correct the nonlinear hinge finite element model;

[0018] S3. After the linear substructure finite element model is modified, the stiffness and mass matrix of the linear substructure are derived and recorded as K α ,K β and M α ,M β ; Use the free interface modal synthesis method to perform the first coordinate transformation on the linear substructure to complete the order reduction of the linear substructure; then perform the second coordinate transformation on the linear substructure to merge 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 corrected in step S2, and perform dynamic response analysis. Use the data of restoring force and relative displacement at the connection interface and use the radial basis function method to construct an input-output mapping proxy model. Fusion the overall structural kinematic equation obtained in step S3 with the input-output mapping proxy model to obtain a fused dynamic model.

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

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

[0022] S31, using the Newmark-β method to solve the dynamic response of the fusion dynamic model, wherein the Newmark-β initial parameters γ = 0.5, β = 0.25; the initial state of the system is static, and the initial displacement, velocity, and acceleration are all 0; the time step is 1 / 1000, and the total duration is 5s;

[0023] S32, comparing the error between the predicted response result of the fusion dynamics model and the experimental result, using R 2 Quantify the error with the relative mean absolute error

[0024]

[0025]

[0026] Where n is the length of the response result data; y i is the response reference value obtained from the experiment; is the response prediction value obtained by the proposed method; is the mean of the response reference value; STD is the standard deviation of the response reference value; R 2 The larger the 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;

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

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

[0029] S41, performing finite element modal analysis on the two linear substructures respectively to obtain modal frequency and vibration shape data of each linear substructure;

[0030] S42, performing modal vibration simulation or physical test on the two linear substructures respectively, arranging excitation points and response measurement points, and obtaining response signals output by each measurement point of each linear substructure;

[0031] S43, analyzing the response signal using a clustering-based automatic working modal analysis method to obtain the test modal frequency and vibration shape data of each linear substructure;

[0032] S44, setting the objective function, using the modal frequency and vibration shape data of each linear substructure and the test modal frequency and vibration shape data of each linear substructure as correction parameters, and defining the objective function as:

[0033]

[0034]

[0035] In the formula, ε Υ (r) represents the difference between the finite element modal parameters and the experimental analysis modal parameters; They represent the i-th order modal frequency obtained by the finite element method and the i-th order modal frequency obtained by experimental analysis, respectively. They represent the i-th order modal vibration mode obtained by the finite element method and the i-th order modal vibration mode obtained by the experimental analysis respectively; multiple variables such as frequency and vibration mode are written in the form of vectors to consider the contribution of multiple variables to the same goal; W represents the different weight coefficient matrices applied to each order test frequency and vibration mode 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 the 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 solution of the present invention, the correction process of the nonlinear hinge finite element model includes the following steps:

[0038] S51, performing finite element modal analysis on the nonlinear hinge, setting the gap value and stiffness coefficient, and performing implicit dynamic analysis to obtain a dynamic displacement response signal;

[0039] S52, conducting vibration simulation or physical test on the reflective surface with gap hinge connection, arranging excitation points and response measuring points, and obtaining output displacement response signals of each measuring point of the structure;

[0040] S53. Define the objective function of the test result value and the finite element method result value of the structural dynamic response as follows:

[0041]

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

[0043] S54, selecting the gap value and stiffness coefficient of the gap hinge as the parameters to be corrected, selecting the trust region method as the optimization algorithm, and obtaining 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 equation of the overall structure includes the following steps:

[0045] S61. Perform eigenvalue decomposition on each linear substructure to obtain eigenvectors respectively, and select the truncation order to obtain the retained mode Φk ;

[0046] S62. Calculate the residual mode Ψ of the linear substructure according to whether the linear substructure has a rigid body mode d ;

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

[0048]

[0049] in: B T is 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, the frequency shift method is often used to perform frequency shift processing on the substructure stiffness matrix to eliminate the singularity of the substructure stiffness matrix. After that, the residual mode is still used to approximate the high-order truncated mode. Its basic formula is

[0051]

[0052] in: is the stiffness matrix after frequency shift, K and M are the stiffness matrix and mass matrix before frequency shift, τ is the frequency shift amount; before and after frequency shift, the vibration mode of the structure remains unchanged; get After that, according to Get the remaining modes;

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

[0054]

[0055] Among them: r represents the rigid connection degree of freedom; e represents the elastic connection degree of freedom, δ represents the relative displacement;

[0056] S65. After obtaining the interface coordination conditions, eliminate the dependent generalized coordinate components between the linear substructures and obtain the kinematic equation of the overall structure:

[0057]

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

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

[0060] S71. Perform implicit dynamic response analysis on the modified linear substructure-nonlinear hinge finite element model, set 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, extracting the restoring force and relative displacement data at both ends of the nonlinear hinge, constructing a mapping relationship between the restoring force and the relative displacement using a radial basis function method, and obtaining a nonlinear input-output mapping proxy model;

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

[0063] Beneficial Effects

[0064] 1. A method for dynamic modeling of a space deployable antenna system disclosed in the present invention divides the solid surface deployable antenna system into a linear substructure of the antenna reflector surface and a nonlinear substructure of the hinge connection, uses a free interface modal synthesis method to perform coordinate transformation on the linear substructure, and converts the system from physical space to modal space for solution, thereby achieving a reduction in the degree of freedom of the system, and ultimately improving the computational efficiency of the dynamic model;

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

[0066] 3. The present invention discloses a method for dynamic modeling of a spatial deployable antenna system. By capturing the relationship between the restoring force and relative displacement at both ends of a nonlinear hinge, an input-output mapping model is obtained using a data-driven method, and then the nonlinear substructure is equivalent to a proxy model. This method 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 method for dynamic modeling of a space deployable antenna system, which modularizes the space solid surface deployable antenna system through the idea of ​​substructure. Once the input-output proxy model database is established, the system's dynamic response prediction can be performed quickly and efficiently, which greatly saves computing resources and improves analysis efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A flow chart of the method for dynamic modeling of a space deployable antenna system according to the present invention;

[0069] Figure 2 It is a finite element model of a certain type of spatially deployable antenna, as well as a diagram illustrating the setting of excitation points, response points, and boundary conditions;

[0070] Figure 3 This is a comparison chart of the displacement, velocity and acceleration identification results of the method of the present invention and the finite element simulation test at the response point 2, wherein: the blue solid line is the identification response result of the proposed method, and the red dotted line is the finite element simulation test result. DETAILED DESCRIPTION

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

[0072] The fusion dynamics modeling of a certain type of space solid surface deployable antenna system is carried out, taking the double reflection surface as an example. Figure 2 As shown. For the entire system, the reflective surface is a carbon fiber skin-aluminum honeycomb sandwich structure. The size of a single reflective surface is 11m*1.57m. Its upper and lower skins are both 0.3mm carbon fiber composite materials, and the honeycomb core is 5mm*0.03mm aluminum honeycomb with a honeycomb thickness of 44.4mm. The mechanical properties of the reflective surface material are shown in the following table.

[0073] Table 1 Mechanical properties parameters of antenna reflector materials

[0074]

[0075] Step 1: Use the finite element simulation method to establish a finite element model of the space solid surface deployable antenna. Without loss of generality, a double reflector structure is used as an example. Figure 2 As shown. The deployable antenna is divided into linear substructures α and β of the reflector surface. The 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 respectively. In the "Interaction" module, "Create Connection" is used to establish a Hinge connector to simulate the hinge. The substructures α and β are connected together. Each substructure α and β contains 60 units and 84 nodes. Each node has 6 degrees of freedom, and the 4 nodes at the lower boundary of the substructure α are fixed.

[0076] Step 2: Conduct a modal vibration test on the antenna reflector surface. In this case, a simulation test is used instead of a physical test. The modal frequency and vibration shape data of the linear substructure of the antenna reflector surface are obtained using an automatic working modal analysis method based on clustering. The correction parameters, objective function, and optimization algorithm are set to correct the finite element model of the linear substructure of the reflector surface.

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

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

[0079] Step 2.3: Use the clustering-based automatic working modal analysis method to process and analyze the test response data to obtain the test modal frequencies and vibration shapes of the antenna reflector substructures α and β.

[0080] Step 2.4: Set the objective function, with frequency and vibration mode as correction parameters, then the objective function is ε Υ (r) represents the difference between the finite element modal parameters and the experimental modal parameters. W represents the weight coefficient matrix for each test frequency and vibration mode 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 , Poisson's ratio ε as the parameters to be corrected, and the trust region method is selected as the optimization algorithm. Through iterative solution, the objective function J(r) is minimized, and the corrected elastic modulus Ε 11A =265e9 Pa, Poisson's ratio ε A =0.246.

[0082] Step 3: After the linear finite element model is modified, the stiffness and mass matrix of the linear substructure of the antenna reflector are derived and recorded as K α ,K β and M α ,M β The free interface modal synthesis method is used to perform the first coordinate transformation on the antenna reflector substructure to complete the order reduction of the linear substructure; after the second coordinate transformation on the antenna reflector linear substructure, the substructures are fused and docked to obtain the overall structural kinematic equations with independent generalized coordinates.

[0083] Step 3.1: Substitute the K values ​​of antenna reflector substructures α and β obtained in step 2 α ,M α , K β ,M β Perform eigenvalue decomposition to obtain the eigenvectors respectively, select the truncation order as 50, and obtain the low-order retained mode Φ αk , Φ βk .

[0084] Step 3.2: The linear substructure α does not contain rigid body modes, so directly use the formula The residual mode Ψ is calculated αd ; The linear substructure β contains rigid body modes. First, the frequency shift method is used to β Perform frequency shift processing, the frequency shift amount is 0.01, and then according to The residual mode Ψ of the substructure β is calculated βd .

[0085] Step 3.3: Get the preserved mode Φ αk , Φ βk And the residual mode Ψ αd ,Ψ βd After that, the first coordinate transformation is performed to complete the order reduction of the substructure.

[0086] Step 3.4: The antenna reflector substructure satisfies the coordination condition at the interface connection, and the dependent components between generalized coordinates need to be eliminated. The connection interface is hinged, so the degree of freedom of rotation around the y-axis is an elastic connection, and the remaining degrees of freedom are rigid connections. Distinguishing the rigid-elastic degrees of freedom in the coordination condition, the interface coordination condition is

[0087] u αJr =u βJr (10)

[0088] u αJe =u βJe +δ

[0089] f αJ =-f βJ

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

[0091] Step 3.5: After obtaining the displacement coordination conditions, eliminate the non-independent generalized coordinate components between the substructures and obtain the fused dynamic equation

[0092]

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

[0094] Step 4: Conduct a vibration test on the antenna reflector surface with a gap hinge connection to obtain the structural dynamic response data, set the correction parameters, objective function and optimization algorithm, and perform model correction on the nonlinear hinge finite element model.

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

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

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

[0098]

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

[0100] Step 4.4: Select the gap value e and stiffness coefficient K of the gap hinge as the parameters to be corrected, select the trust region method as the optimization algorithm, and solve iteratively to minimize the objective function J(r). After correction, e A =0.005rad, stiffness coefficient K A =1000N·m / rad.

[0101] Step 5: Connect the finite element models corrected in step 2 and step 4 and perform dynamic response analysis. By connecting the data of restoring force and relative displacement at the interface, use the radial basis function method to construct an input-output mapping proxy model, and finally obtain the fusion dynamic model according to step 3.

[0102] Step 5.1: Connect the modified antenna reflector-gap hinge finite element model, establish a "dynamic implicit" analysis step, with a time of 5s and an incremental step size of 0.001; in the "load" module, solve the cosine excitation with an amplitude of 100N and an angular frequency of 20rad / s at the excitation point. Change the excitation size, perform 10 analysis steps respectively, and derive 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, use the radial basis function method to construct the mapping relationship between the restoring force and the relative displacement, and finally obtain the gap nonlinear input-output mapping agent model.

[0104] Step 5.3: After the nonlinear proxy model is obtained, according to step 3, the linear substructure of the reflection surface is fused with the nonlinear proxy model to obtain the fused dynamic model of the spatial solid surface deployable antenna system.

[0105] Step 6: After obtaining the fusion dynamic model, the response of the solid surface 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 the present invention.

[0106] Step 6.1: Use the Newmark-β method to solve the system response of the fusion dynamic model of the solid surface deployable antenna system obtained in step 5, where the initial parameters of Newmark-β are γ=0.5, 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 static, and the initial displacement, velocity, and acceleration are all 0; the time step is 1 / 1000, and the total duration is 5s.

[0107] Step 6.2: Compare the response error of the dynamic model response prediction result of the method proposed in the present invention with the response error of the simulation test result at the response point 2, such as Figure 3 As shown, using R 2 The error is quantified with the relative mean absolute error, as shown in Table 2

[0108] Table 2 Error table of space solid surface deployable antenna fusion dynamics model and test results

[0109]

[0110] By calculating two methods R 2 Compared with the RAAE value, since the velocity and acceleration are recursively obtained from the displacement using the Newmark format, the acceleration and velocity errors are slightly higher than the displacement errors. 2 The values ​​are all above 0.97, which shows that the method proposed in the present invention can perform high-precision response prediction on the space fixed surface deployable antenna system.

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

[0112] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A method for dynamic modeling of a space deployable antenna system, characterized by: The steps include: S1. Use finite element simulation software to establish a finite element model of the space deployable antenna, and define the material properties, boundary conditions, connection assignments, and mesh properties of the space deployable antenna; The finite element model includes a double-reflecting surface linear substructure finite element model and a nonlinear hinge finite element model, wherein: the double-reflecting surface linear substructure finite element model is to divide the two reflecting surfaces into two linear substructures by using finite element simulation software, and establish two linear substructure finite element models by shell elements; The nonlinear hinge finite element model uses finite element simulation software to set the connection assignment between two linear substructures and select an articulated connector to simulate the hinge connection between the two linear substructures; S2. Modifying the linear substructure finite element model and the nonlinear hinge finite element model; wherein: The correction process of the linear substructure finite element model is to analyze the finite element mode of the linear substructure, obtain the modal frequency and vibration shape data of the linear substructure, perform modal vibration simulation or physical test on the linear substructure, obtain the test modal frequency and vibration shape data of the linear substructure as correction parameters, define the objective function, select the elastic modulus and Poisson's ratio of the reflection surface as the parameters to be corrected of the objective function, 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 to correct the linear substructure finite element model; The correction process of the nonlinear hinge finite element model is to perform finite element modal analysis on the nonlinear hinge to obtain a dynamic displacement response signal and to conduct vibration simulation or physical test on the reflection surface connected by the gap hinge to obtain the output displacement response signal of each measuring point of the linear substructure as a correction parameter, define the objective function, 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 to correct the nonlinear hinge finite element model; S3. After the linear substructure finite element model is modified, the stiffness and mass matrix of the linear substructure are derived and recorded as K α ,K β and M α ,M β ; Use the free interface modal synthesis method to perform the first coordinate transformation on the linear substructure to complete the order reduction of the linear substructure; then perform the second coordinate transformation on the linear substructure to merge 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 corrected in step S2, and perform dynamic response analysis. Use the data of restoring force and relative displacement at the connection interface and use the radial basis function method to construct an input-output mapping proxy model. Fusion the overall structural kinematic equation 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 fusion dynamics model is used to predict the response of the space deployable antenna, and the error analysis and computational efficiency comparison of the prediction results are carried out to verify the accuracy and efficiency of the fusion 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 to solve the dynamic response of the fusion dynamic model, wherein the Newmark-β initial parameters γ = 0.5, β = 0.25; the initial state of the system is static, and the initial displacement, velocity, and acceleration are all 0; the time step is 1 / 1000, and the total duration is 5s; S32, comparing the error between the predicted result of the fusion dynamics model response and the experimental result, using R 2 Quantify the error with the relative mean absolute error Among them, n is the length of the response result data; y i is the response reference value obtained from the experiment; is the response prediction value obtained by the proposed method; 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 result is closer to the reference value; S33. Under the same calculation conditions, compare the dynamic analysis time of the fusion dynamics model and the finite element simulation model to verify the calculation efficiency of the fusion dynamics model.

4. The method for dynamic modeling of a space deployable antenna system according to claim 1, characterized in that: The modification process of the linear substructure finite element model comprises the following steps: S41, performing finite element modal analysis on the two linear substructures respectively to obtain modal frequency and vibration shape data of each linear substructure; S42, performing modal vibration simulation or physical test on the two linear substructures respectively, arranging excitation points and response measurement points, and obtaining response signals output by each measurement point of each linear substructure; S43, analyzing the response signal using a clustering-based automatic working modal analysis method to obtain the test modal frequency and vibration shape data of each linear substructure; S44, setting the objective function, using the modal frequency and vibration shape data of each linear substructure and the test modal frequency and vibration shape data of each linear substructure as correction parameters, and defining the objective function as: In the formula, ε Υ (r) represents the difference between the finite element modal parameters and the experimental analysis modal parameters; They represent the i-th order modal frequency obtained by the finite element method and the i-th order modal frequency obtained by experimental analysis, respectively. Respectively represent the i-th order modal vibration mode obtained by the finite element method and the i-th order modal vibration mode obtained by experimental analysis; write multiple variables such as frequency and vibration mode into vector form to consider the contribution of multiple variables to the same target; W represents the different weight coefficient matrices applied to each test frequency and vibration mode 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 the 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, performing finite element modal analysis on the nonlinear hinge, setting the gap value and stiffness coefficient, and performing implicit dynamic analysis to obtain a dynamic displacement response signal; S52, conducting vibration simulation or physical test on the reflective surface with gap hinge connection, arranging excitation points and response measuring points, and obtaining output displacement response signals of each measuring point of the structure; S53. Define the objective function of the test result value and the finite element method result value of the structural dynamic response as follows: Among them, H Α , H Ε They represent the dynamic response values ​​obtained by the finite element method and the dynamic response values ​​obtained by experimental measurement, t represents the time series, and r is the parameter to be corrected; S54, selecting the gap value and stiffness coefficient of the gap hinge as the parameters to be corrected, selecting the trust region method as the optimization algorithm, and obtaining 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 equation of the overall structure includes the following steps: S61. Perform eigenvalue decomposition on each linear substructure to obtain eigenvectors respectively, and select the truncation order to obtain the retained mode Φ k ; S62. Calculate the residual mode Ψ of the linear substructure according to whether the linear substructure has a rigid body mode d ; When the linear substructure does not contain rigid body modes in: B T is 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, the frequency shift method is often used to perform frequency shift processing on the substructure stiffness matrix to eliminate the singularity of the substructure stiffness matrix. After that, the residual mode is still used to approximate the high-order truncated mode. Its basic formula is in: is the stiffness matrix after frequency shift, K and M are the stiffness matrix and mass matrix before frequency shift, τ is the frequency shift amount; before and after frequency shift, the vibration mode of the structure remains unchanged; get After that, according to Get the remaining modes; S64. Determine the rigid and elastic connection properties of the connection degrees of freedom between the linear substructures, and distinguish the connection coordination conditions according to the connection properties, as shown below: Among them: r represents the rigid connection degree of freedom; e represents the elastic connection degree of freedom, δ represents the relative displacement; S65. After obtaining the interface coordination conditions, eliminate the dependent generalized coordinate components between the linear substructures and obtain the kinematic equation of the overall structure: Where: F is the external excitation of the substructure, f βJ is the interface restoring force, and T is 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 multiple working conditions, change the excitation amplitude and type, and solve the dynamic response of the system under the action of multiple excitations; S72, extracting the restoring force and relative displacement data at both ends of the nonlinear hinge, constructing a mapping relationship between the restoring force and the relative displacement using a radial basis function method, and obtaining a nonlinear input-output mapping proxy model; S73. The linear substructure finite element model is fused with the nonlinear input-output mapping proxy model to obtain a fused dynamic model of the spatially deployable antenna.

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