Parameter identification method for reduced order model of large flexible structure based on ground test data

Abstract

The present application relates to the field of structural dynamics analysis and test technology, and particularly relates to a large flexible structure reduced order model parameter identification method based on ground test data, comprising the following steps: installing force sensors and exciters on a large flexible structure to be tested, and dispersively installing multiple acceleration sensors and strain sensors; applying excitation to the large flexible structure by the exciters, and recording the measurement values of the acceleration sensors, strain sensors and force sensors; converting the local acceleration signals to a global coordinate system, and integrating the global acceleration signals to obtain velocity signals and displacement signals; performing modal test on the large flexible structure to obtain modal information, inputting the global acceleration signals, velocity signals and displacement signals into a nonlinear structure reduced order model after modal conversion, and calculating the nonlinear stiffness coefficient by a least square method; the present application can improve the reliability and accuracy of the identification result.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics analysis and testing technology, specifically to a method for parameter identification of a reduced-order model of a large flexible structure based on ground test data. Background Technology

[0002] Modern aircraft design demands increasingly higher flight performance, leading to a growing focus on highly flexible aircraft, such as high-altitude long-endurance unmanned aerial vehicles (UAVs), large passenger aircraft, and large transport aircraft, becoming a key research area for major aviation nations. Due to the stringent requirements for flight performance, particularly range and endurance, highly flexible aircraft typically utilize a large wing aspect ratio to improve lift-to-drag ratio. Simultaneously, they increase the proportion of composite materials in their structural design. These factors result in relatively low structural weight and low stiffness, leading to significant structural deformation caused by aerodynamic loading and introducing geometrically nonlinear aeroelastic problems.

[0003] Accurate structural modeling is central to aeroelastic analysis. Nonlinear finite element analysis and large deformation beam theory are the two most commonly used methods for modeling large flexible structures in traditional geometrically nonlinear aeroelastic analysis. The former has good applicability to engineering models and can be applied to complex structural models, but it suffers from high degrees of freedom, poor convergence, and low computational efficiency. The latter offers high computational accuracy and efficiency, but can only be used for simple model analysis and cannot be directly applied to complex engineering objects. Nonlinear structural order reduction models are a method for modeling large flexible structures that can better balance solution efficiency, computational accuracy, and applicability to complex models. In nonlinear structural order reduction models, nonlinear stiffness is expressed as a generalized coordinate polynomial, and the reduced-order nonlinear structural model is obtained by solving for the nonlinear stiffness coefficients. In the past, the solution of nonlinear stiffness coefficients in reduced-order models of nonlinear structures has been based on simulation data from finite element model analysis. In Chinese patent CN112580241B, "A Nonlinear Aeroelastic Dynamic Response Analysis Method Based on a Reduced-Order Model of a Structure," the applicant first provides various static nonlinear finite element analysis examples and then combines regression analysis to solve for the nonlinear stiffness coefficients. In Chinese patent CN113536456B, "A Modeling Method for Reduced-Order Models of Large Flexible Structures Based on Dynamic Response Identification," the dynamic response data of the large flexible structure is first calculated, and then the nonlinear stiffness coefficients are discretely solved using this data. In the above studies, the nonlinear stiffness coefficients are all solved based on simulation data samples. Since the actual structure differs from the simulation model, errors are inevitably introduced during the establishment of the finite element model. Furthermore, establishing a corresponding finite element model before solving for the nonlinear stiffness coefficients increases the analysis time and difficulty. If parameter identification could be performed directly based on the original actual model, the results would be more accurate and reliable. Currently, there are no relevant methods or patents for this. Summary of the Invention

[0004] In view of the above problems, the present invention provides a method for parameter identification of a reduced-order model of a large flexible structure based on ground test data, which solves the technical problem that the calculation of nonlinear stiffness coefficients of a reduced-order model of a large flexible nonlinear structure must rely on simulation data and cannot be directly identified using test data in the prior art.

[0005] This invention provides a method for parameter identification of a reduced-order model of a large flexible structure based on ground test data, comprising the following steps:

[0006] Step S1: Install force sensors on the large flexible structure to be tested, and install the force sensors on the exciter; install multiple acceleration sensors in a distributed manner on the large flexible structure to be tested, and install a strain sensor at the corresponding position of each acceleration sensor.

[0007] Step S2: Determine the excitation signal, apply the excitation signal to the large flexible structure using the exciter, and record the measured values ​​of the acceleration sensor, strain sensor and force sensor during the excitation time to obtain the local acceleration signal, strain signal and force signal respectively;

[0008] Step S3: Convert the local acceleration signal to the global coordinate system to obtain the global acceleration signal, and integrate the global acceleration signal to obtain the velocity signal and displacement signal;

[0009] Step S4: Conduct ground modal tests on the large flexible structure, measure the modal information of the large flexible structure, and convert the global acceleration signal, velocity signal and displacement signal into generalized acceleration response, generalized velocity response and generalized displacement response based on the modal information;

[0010] Step S5: Input the generalized acceleration response, generalized velocity response, and generalized displacement response into the nonlinear structural order reduction model, and calculate the nonlinear stiffness coefficient using the least squares method, which is then used as the identified model parameters.

[0011] Preferably, step S1 specifically includes:

[0012] Step S1-1: The large flexible structure has a clamping section. The clamping section of the large flexible structure is clamped on the tooling. A force sensor is attached to the root position of the large flexible structure. The force sensor is installed on the vibrator.

[0013] Step S1-2: Install 4 to 6 acceleration sensors in a distributed manner on the large flexible structure. At the location of each acceleration sensor, a strain sensor is installed. The strain sensor is a strain gauge or an optical fiber sensor.

[0014] Preferably, the step S1-2, wherein the dispersed installation of 4-6 acceleration sensors on the large flexible structure specifically includes:

[0015] Six accelerometers were installed at positions 40mm, 300mm, 500mm, 700mm, 900mm, and 980mm from the clamping section on the large flexible structure.

[0016] Preferably, step S2 specifically includes:

[0017] Step S2-1: Set a sinusoidal sweep frequency with a frequency step of 0.1Hz, and use a signal whose frequency range covers the first three natural frequencies of the large flexible structure as the excitation signal. Use the exciter to apply excitation to the large flexible structure with the excitation signal.

[0018] Step S2-2: The time period from the start of excitation to the achievement of steady-state response of the large flexible structure is taken as the excitation time. During the excitation time, the measured values ​​of the acceleration sensor, strain sensor and force sensor are recorded to obtain the local acceleration signal, strain signal and force signal respectively.

[0019] Preferably, step S3 specifically includes:

[0020] Step S3-1: Convert the strain signal into curvature The rotation angle θ(s) at various positions of the highly flexible structure is obtained from the curvature, and the calculation expression is as follows:

[0021]

[0022] Where θ(0) is the root position rotation angle of the large flexible structure, θ(0)=0; s is the arc length coordinate of the large flexible structure along the span, 0≤s≤1;

[0023] Step S3-2: Based on the rotation angle θ(s) at each position, the local acceleration signal is transformed into the global coordinate system, and the global acceleration signal calculation expression is obtained as follows:

[0024]

[0025] Where a y a z For global acceleration, a y1 a z1 Let θ be the local acceleration, and θ be the rotation angle of the current position of the flexible structure.

[0026] Step S3-3: Obtain the global acceleration response signal from the time-domain record in the global coordinate system. Given an initial excitation condition of 0, the velocity response signal can be obtained by performing a single time integration. The displacement response signal x can be obtained by performing a time integration on the velocity response signal.

[0027] Preferably, in step S4, the measured modal information of the large flexible structure is: Φ=[Φ1,Φ2,Φ3,…,Φ N ], where N is the total number of measurement modes.

[0028] Preferably, in step S4, the calculation expressions for converting the global acceleration signal, velocity signal, and displacement signal based on the modal information into the generalized acceleration response, generalized velocity response, and generalized displacement response are as follows:

[0029]

[0030]

[0031] in, To provide the generalized acceleration response corresponding to the i-th mode, For the velocity generalized response corresponding to the i-th mode, q i To represent the generalized displacement response corresponding to the i-th mode, Φ i Let i be the generalized mode vector of order i. For Φ i transpose, M is the structural mass matrix. i Let be the generalized mass of the i-th mode.

[0032] Preferably, step S5 specifically includes:

[0033] The dynamic equations of the discrete structure are constructed as follows:

[0034]

[0035] The Fourier transform of the discrete structure dynamics equations yields:

[0036]

[0037] For the discrete structure dynamics equations after Fourier transform, taking NK different frequency domain k values ​​yields NK equations, forming a system of equations, the expression of which is:

[0038]

[0039] The above equations are calculated using the least squares method to obtain the nonlinear stiffness coefficients. These are used as model parameters for identification.

[0040] Preferably, in step S5:

[0041] Set the total number of discrete time points NT to 2000; set the total number of frequency domain values ​​NK to 20, and take 20 different frequency domain k values ​​to obtain 20 equations, forming a system of equations. The 20 different frequency domain k values ​​are {0.1,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,7.0,8.0,9.0,10.0,15.0,20.0,25.0}.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] (1) The stiffness identification method of large flexible structure based on ground test data provided by the present invention, compared with the traditional structural reduced-order model parameter identification method, does not require the establishment of a finite element model and the completion of simulation analysis. Instead, it directly uses ground test data for parameter identification, which avoids the errors that may be caused by the simulation model and improves the reliability and accuracy of the identification results.

[0044] (2) In establishing a nonlinear structure order reduction model, the present invention uses linear modes as the order reduction basis, which improves the applicability of the model and can be more widely applied to different types of large flexible structures.

[0045] (3) The present invention utilizes the angle relationship to convert the measured local acceleration response signal into a global acceleration response signal, which further improves the accuracy of identification and ensures the precision of parameter identification results. Attached Figure Description

[0046] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0047] Figure 1 The flowchart illustrates the parameter identification method for a large flexible structure reduced-order model based on ground test data provided by this invention.

[0048] Figure 2 The flowchart for parameter identification of the nonlinear structure order reduction model of the present invention is provided for the present invention.

[0049] Figure 3 This is a schematic diagram of the actual installation of the force sensor provided by the present invention.

[0050] Figure 4 This is a schematic diagram of the distribution of acceleration measurement points provided by the present invention.

[0051] Figure 5 This is a schematic diagram of the actual installation of the accelerometer provided by the present invention.

[0052] Figure 6 This is a schematic diagram of the overall test apparatus provided by the present invention.

[0053] Figure 7 A schematic diagram of the wing aerodynamic model provided by the present invention. Detailed Implementation

[0054] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0055] This invention involves attaching accelerometers, strain gauges, or fiber optic sensors to a highly flexible structure. After clamping the flexible structure onto a fixture, a force sensor is attached to its root position. The force sensor is then mounted on a vibrator, and an excitation signal is applied. The acceleration response is measured, and the velocity and displacement signals are recovered through integration. Without finite element models or numerical simulation data, the nonlinear stiffness coefficient is calculated using the least squares method based on discrete-form dynamic equations. The method provided by this invention can be applied to the construction of dynamic models for geometrically nonlinear structures such as aerospace vehicle wing structures and cantilever beams.

[0056] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment, such as... Figure 1 , Figure 2 As shown, a method for parameter identification of a reduced-order model of a large flexible structure based on ground test data is disclosed. The specific implementation steps are as follows:

[0057] The first step is to prepare for ground testing.

[0058] The root of the large flexible structure to be measured is supported on the pre-designed and fabricated fixture. The support and installation should minimize the impact of gravity on the structure. After installation, force sensors are attached to the root of the model and mounted on the vibrator. The vibrator is fixed to a stable surface to prevent shaking during excitation. The vibrator is connected to the power amplifier and chassis, allowing the computer to send commands to the vibrator to excite the structure. The force sensors are connected to the modem and data acquisition chassis to convert digital signals to analog signals and transmit them to the terminal equipment.

[0059] Step 2: Install the structural measurement sensor.

[0060] Four to six acceleration sensors are installed on the flexible structure; testing ensures that the acceleration sensors can accurately measure and save the acceleration signals generated during the excitation vibration process; strain sensors are installed near the acceleration sensors to measure the strain signals; the strain sensors can be strain gauges or fiber optic sensors, etc.

[0061] Step 3: Excite the large flexible structure and record the acceleration response data.

[0062] By setting sinusoidal load signals of appropriate amplitude near the first three natural frequencies of a large flexible structure, the structure is made to undergo small to large deformations. Specifically, a specified frequency step size is set, and a sinusoidal sweep frequency excitation is input, with the frequency range covering the first three natural frequencies. During the excitation time, the time-domain acceleration response, strain signal, and force signal of the exciter from the structure to the steady-state response segment are recorded.

[0063] Step 4: Process the acceleration signal to the global coordinate system.

[0064] When a highly flexible structure is under large deformation, the accelerometer readings represent acceleration in the local structural coordinate system. To make the measured data suitable for parameter identification, the measured values ​​need to be transformed from the local coordinate system to the global coordinate system. This requires using strain gauges or fiber optic sensors to measure the strain signal and converting it into curvature. The rotation angle θ(s) at various positions of the flexible structure can be obtained, and then the acceleration signal value in the global coordinate system can be calculated. The calculation method depends on the actual structure and dimensions, and the expression is as follows:

[0065] a g =Aa(1)

[0066] Where a g Let A be the global acceleration signal value, A be the transformation matrix, which is a function of the rotation angle θ(s), and a be the measured local acceleration signal value of the structure.

[0067] Step 5: Integrate the acceleration signal to obtain the velocity and displacement response signals.

[0068] Acceleration response signal obtained from the time-domain record in the transformed global coordinate system Given an initial excitation condition of 0, the velocity response signal can be obtained by performing a single time integration. The displacement response signal x can be obtained by performing a time integration on the velocity response signal;

[0069] Step 6: Obtain the modal information of the structure and convert the response signal into a generalized response signal.

[0070] Modal information of a structure can be obtained using traditional ground-based modal testing methods. The structural modes measured in ground-based modal tests are Φ = [Φ1, Φ2, Φ3, ..., Φ...]. N ], Φ i Let be the i-th order generalized mode vector, and N be the total order of the measured modes. Based on this, the signals obtained in step 5 are converted into generalized modal response signals:

[0071]

[0072] in, To provide the generalized acceleration response corresponding to the i-th mode, For the velocity generalized response corresponding to the i-th mode, q i To represent the generalized displacement response corresponding to the i-th mode, Φ i Let i be the generalized mode vector of order i. For Φ i transpose, M is the structural mass matrix. i Let be the generalized mass of the i-th mode.

[0073] Step 7: Solve based on the nonlinear structural order reduction model to obtain the nonlinear stiffness coefficient.

[0074] The discrete form of the structural dynamics equations is as follows:

[0075]

[0076] Among them, M m Let q represent the generalized mass term of the m-th structural mode. m (j), q n (j), q l (j) and q p (j) represents the value of the generalized coordinate discrete sequence of the m, n, l, p-th structural modes at index j. For q m The second-order time differential of (j); K m The generalized stiffness term represents the m-th structural mode; The nonlinear stiffness term represents the product polynomial of the generalized coordinates of the nth and lth structural modes under the mth structural mode. F represents the nonlinear stiffness coefficient of the product polynomial of the generalized coordinates of the nth, lth, and pth structural modes under the mth structural mode. m (j) represents the value of the discrete sequence of modal force vectors of the m-th structural mode at index j, j∈{0,1,…,NT-1}, which represents the discrete time point sequence index, and NT represents the total number of discrete time points.

[0077] Based on equation (5), a discrete Fourier transform is performed on it. The sequences after Fourier transform of the generalized coordinates are expressed as: Q m (k),Q n (k),Q l (k),Q p(k), where k is the frequency domain sequence index. Similarly, the second and third order terms of the generalized coordinates are also subjected to Discrete Fourier Transform, and the transformed sequences are represented as follows: and Performing a Discrete Fourier Transform on the generalized force, the resulting sequence is represented as f. m (k), the discrete dynamic equation after Fourier transform is:

[0078]

[0079] Among them, Q m (k),Q n (k),Q l (k),Q p (k) are respectively q m (j),q n (j),q l (j),q p (j) The value of the discrete Fourier transform of the corresponding sequence at index k. for The value of the discrete Fourier transform of the corresponding sequence at index k. Let k be the value of the discrete Fourier transform of the second-order term of the generalized coordinates at index k. f is the value of the discrete Fourier transform of the third-order term of the generalized coordinates at index k. m (k) is F m (j) The value of the discrete Fourier transform of the corresponding sequence at index k, k∈{k1,k2,...,k NK}, where NK is the total number of values ​​that can be taken in the frequency domain.

[0080] Taking NK different frequency domain values ​​of k yields NK equations forming a system of equations. The unknown nonlinear stiffness coefficient is then calculated using the least squares method. The least squares problem can be expressed as:

[0081]

[0082] After solving for the unknown nonlinear stiffness coefficient, the complete nonlinear structural dynamics equation can be obtained by substituting it into equation (5).

[0083] The following is a detailed description of the parameter identification method for large flexible structure order reduction model based on ground test data provided by the present invention through a specific embodiment.

[0084] like Figure 3As shown, this invention uses an aluminum steel plate ruler as a simulation component of a large flexible structure. The cross-sectional shape is a rectangle with a length of 35mm and a width of 1.5mm. The test section is 1000mm long. The test object is made of uniform material. Without the installation of other sensors and circuits, the bare weight of the rectangular beam is 0.407kg. After attaching various sensors, the total weight is 0.505kg.

[0085] Step 1: Preparing for Ground Testing

[0086] In this step, the large flexible structure has a clamping section, which is clamped onto a pre-set tooling, such as... Figure 3 As shown, a force sensor is attached 30mm from the clamping section and connected to the vibrator.

[0087] Step 2: Install the structural measurement sensor

[0088] like Figure 4 , Figure 5 As shown, a total of six accelerometers are installed at positions 40mm, 300mm, 500mm, 700mm, 900mm and 980mm away from the clamping section. Strain gauges or fiber optic sensors are installed near the accelerometers to measure the strain signals.

[0089] Step 3: Excite the flexible structure and record the acceleration response data.

[0090] Overall test apparatus such as Figure 6 As shown, a channel steel is fixed to the base by fixing bolts. The channel steel clamps a test steel ruler. The channel steel is a pre-set tooling, and the test steel ruler is a simulation component of a highly flexible structure. The control system generates excitation by controlling the exciter, applying excitation to the test steel ruler. The control system sets the excitation to a sinusoidal sweep excitation with a frequency step of 0.1 Hz, covering the first three natural frequencies. During the excitation time, the time-domain acceleration response and force signal of the structure to the steady-state response segment are recorded; a total of 2000 sets of valid data are obtained.

[0091] Step 4: Process the acceleration signal to the global coordinate system

[0092] Strain signals are obtained by measuring strain gauges or fiber optic sensors, and then converted into curvature. The rotation angle θ(s) at various positions of the highly flexible structure can be obtained using the following expression:

[0093]

[0094] Where θ(0) is the root position rotation angle, θ(0)=0; s is the arc length coordinate of the large flexible structure along the span, 0≤s≤1.

[0095] From the above equation, we can obtain the positional relationship between the local coordinate system and the global coordinate system at various locations of the large flexible structure. Since the large flexible beam is a two-dimensional structure under vertical loading, the acceleration can be further transformed into the global coordinate system:

[0096]

[0097] Where a y a z For global acceleration, a y1 a z1 The acceleration is measured locally, and θ is the rotation angle of the current position of the large flexible structure.

[0098] Step 5: Integrate the acceleration signal to obtain the velocity and displacement response signals.

[0099] The global acceleration response signal obtained from the time-domain record in the transformed global coordinate system Given an initial excitation condition of 0, the velocity response signal can be obtained by performing a single time integration. The displacement response signal x can be obtained by performing a time integration on the velocity response signal;

[0100] Step 6: Obtain the modal information of the structure and convert the response signal into a generalized response signal.

[0101] Ground modal tests were conducted using traditional modal ground testing methods. The structural modes measured during the ground modal tests were Φ=[Φ1,Φ2,Φ3,…,Φ…]. N In this embodiment, the first 6 modes are selected, i.e., N=6. The modal information is shown in Table 1:

[0102] Table 1

[0103]

[0104]

[0105] Based on this, the signal obtained in step 5 is converted into a generalized modal response signal:

[0106]

[0107] Step 7: Solve based on the nonlinear structural order reduction model to obtain the nonlinear stiffness coefficient.

[0108] The discrete form of the structural dynamics equations is as follows:

[0109]

[0110] For j∈{0,1,…,NT-1}, the total number of discrete time points NT is set to 2000.

[0111] Based on equation (13), the discrete dynamic equation after Fourier transform is:

[0112]

[0113] Where, for k∈{k1,k2,...,k NK The total number of frequency domain values ​​NK is set to 20. Taking 20 different frequency domain k values ​​yields 20 equations forming a system of equations. The unknown nonlinear stiffness coefficient is then calculated using the least squares method. Twenty different frequency domain k values ​​are taken as {0.1,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,7.0,8.0,9.0,10.0,15.0,20.0,25.0}. After solving for the unknown nonlinear stiffness coefficient, the complete nonlinear structural dynamics equation can be obtained by substituting it into equation (13).

[0114] This invention avoids the need to establish a finite element model and dynamic simulation when solving for parameters of a reduced-order model of a real large flexible structure. It directly utilizes ground-based testing techniques for solution and identification, thus avoiding modeling errors. This invention is of great significance in practical dynamic analysis and aircraft design applications.

[0115] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0116] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for parameter identification of a reduced-order model of a large flexible structure based on ground test data, characterized in that, Includes the following steps: Step S1: Install force sensors on the large flexible structure to be tested and connect the force sensors to the exciter; install multiple acceleration sensors in a distributed manner on the large flexible structure to be tested, and install a strain sensor at the corresponding location of each acceleration sensor. Step S2: Determine the excitation signal, apply the excitation signal to the large flexible structure using the exciter, and record the measured values ​​of the acceleration sensor, strain sensor and force sensor during the excitation time to obtain the local acceleration signal, strain signal and force signal respectively; Step S3: Combine the strain signal with the local acceleration signal and convert it to the global coordinate system to obtain the global acceleration signal. Integrate the global acceleration signal to obtain the velocity signal and displacement signal. Step S4: Conduct ground modal tests on the large flexible structure, measure the modal information of the large flexible structure, and convert the global acceleration signal, velocity signal and displacement signal into generalized acceleration response, generalized velocity response and generalized displacement response based on the modal information; Step S5: Input the generalized acceleration response, generalized velocity response, and generalized displacement response into the nonlinear structural order reduction model, and calculate the nonlinear stiffness coefficient using the least squares method, which is then used as the identified model parameters.

2. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 1, characterized in that, Step S1 specifically includes: Step S1-1: The large flexible structure has a clamping section. The clamping section of the large flexible structure is clamped on the tooling. A force sensor is attached to the root position of the large flexible structure and connected to the vibrator. Step S1-2: Install 4 to 6 acceleration sensors in a distributed manner on the large flexible structure. At the location of each acceleration sensor, a strain sensor is installed. The strain sensor is a strain gauge or an optical fiber sensor.

3. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 2, characterized in that... In step S1-2, the specific steps of distributing 4-6 acceleration sensors on the large flexible structure include: Six accelerometers were installed at positions 40mm, 300mm, 500mm, 700mm, 900mm, and 980mm from the clamping section on the large flexible structure.

4. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 3, characterized in that, Step S2 specifically includes: Step S2-1: Set a sinusoidal sweep frequency with a frequency step of 0.1Hz, and use a signal whose frequency range covers the first three natural frequencies of the large flexible structure as the excitation signal. Use the exciter to apply excitation to the large flexible structure with the excitation signal. Step S2-2: The time period from the start of excitation to the achievement of steady-state response of the large flexible structure is taken as the excitation time. During the excitation time, the measured values ​​of the acceleration sensor, strain sensor and force sensor are recorded to obtain the local acceleration signal, strain signal and force signal respectively.

5. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 4, characterized in that, Step S3 specifically includes: Step S3-1: Convert the strain signal into curvature The rotation angle at various positions of the large flexible structure is obtained from the curvature. The calculation expression is: in, The corner is located at the root of the large flexible structure. =0; Let be the arc length coordinates along the span of the large flexible structure. ; Step S3-2: Based on the angles at each of the aforementioned positions The local acceleration signal is transformed into the global coordinate system, and the global acceleration signal calculation expression is obtained as follows: in , For global acceleration, , For local acceleration, This represents the current rotation angle of the highly flexible structure. Step S3-3: Obtain the global acceleration response signal from the time-domain record in the global coordinate system. Given an initial excitation condition of 0, the velocity response signal can be obtained by performing a single time integration. The displacement response signal can be obtained by performing a time integration on the velocity response signal. .

6. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 5, characterized in that... In step S4, the measured modal information of the highly flexible structure is as follows: ,in, To measure the total modal order.

7. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 6, characterized in that... In step S4, the calculation expressions for converting the global acceleration signal, velocity signal, and displacement signal into a generalized acceleration response, a generalized velocity response, and a generalized displacement response based on the modal information are as follows: in, To provide the generalized acceleration response corresponding to the i-th mode, For the velocity generalized response corresponding to the i-th mode, For the displacement generalized response corresponding to the i-th mode, Let i be the generalized mode vector of order i. for transpose, The structural mass matrix, Let be the generalized mass of the i-th mode.

8. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 7, characterized in that, Step S5 specifically includes: The dynamic equations of the discrete structure are constructed as follows: in, Indicates the first The generalized mass term of the first-order structural modes, , , and They represent the first The generalized coordinate discrete sequence of the order structure modes in the index The value at; Indicates the first The generalized stiffness term of the structural modes; Indicates the first The first structural mode Generalized coordinates of the first-order structural modes and the first-order structural modes The nonlinear stiffness term of the product polynomial of the generalized coordinates of the structural modes. Indicates the first The first structural mode Generalized coordinates of the first-order structural modes, the first Generalized coordinates of the first-order structural modes and the first-order structural modes The nonlinear stiffness coefficients of the product polynomial of the generalized coordinates of the structural modes. Indicates the first Discrete sequence of modal force vectors of the first-order structural modes in the index The value at that location, , representing a discrete-time point sequence index. Represents the total number of discrete time points; The Fourier transform of the discrete structure dynamics equations yields: in, They are respectively , , , The discrete Fourier transform of the corresponding sequence at the index The value at that location, for The discrete Fourier transform of the corresponding sequence at the index The value at that location, The discrete Fourier transform of the second-order terms of the generalized coordinates at the index The value at that location, The discrete Fourier transform of the third-order terms of the generalized coordinates at the index The value at that location, for The discrete Fourier transform of the corresponding sequence at the index The value at that location, , This represents the total number of values ​​that can be taken in the frequency domain. For the discrete structure dynamics equations after Fourier transform, take Different frequency domains Value, get These equations form a system of equations, expressed as follows: The above equations are calculated using the least squares method to obtain the nonlinear stiffness coefficients. , which serve as model parameters for identification.

9. The method for parameter identification of a large flexible structure reduced-order model based on ground test data according to claim 8, characterized in that, In step S5: The total number of discrete time points Set the total number of frequency domain values ​​to 2000. Set it to 20, take Different frequency domains Worth it These equations form a system of equations, including 20 different frequency domains. The value is taken as .

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