Method for testing unfolding state of large flexible solar wing based on dynamic modal decomposition

Abstract

The invention belongs to the field of spacecraft modal testing, and particularly relates to a modal testing method based on dynamic modal decomposition in an unfolded state of a large flexible solar wing, which comprises the following steps of: S1, exciting the solar wing by adopting a pre-tightening force release method, and synchronously acquiring displacement attenuation data of different positions of the solar wing through a plurality of laser displacement sensors in a testing device; s2, performing fast Fourier transform calculation on each group of displacement attenuation data, and processing all fast Fourier transform calculation results to generate an average frequency response curve; s3, processing the displacement data by adopting a Monte Carlo delay embedding dynamic mode decomposition algorithm to obtain Q groups of fundamental frequencies, damping ratios and vibration mode results; and S4, arithmetic average is carried out on Q groups of results, and a final fundamental frequency, a modal damping ratio and a vibration mode are output. According to the method, the modal parameters are identified by adopting the Monte Carlo dynamic modal decomposition method, the fundamental frequency, the modal damping ratio and the vibration mode of the unfolded state of the large flexible solar wing can be identified, and meanwhile, the reliability of an identification result is ensured.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft modal testing, and in particular to a testing method for the unfolding state of a large flexible solar wing based on dynamic modal decomposition. Background Art

[0002] The fundamental frequency of a solar wing's deployed sail is a key indicator of its structural dynamic properties, reflecting its natural vibration frequency when deployed. The fundamental frequency directly impacts the sail's stability and vibration resistance. A higher fundamental frequency generally indicates greater sail stiffness, enabling it to better withstand external disturbances (such as spacecraft maneuvers or vibrations in the space environment), thereby ensuring spacecraft reliability and functional accuracy.

[0003] As spacecraft demand for energy increases, the size of solar panels continues to increase to meet higher power output. However, the increase in panel area leads to a more dispersed mass distribution and a relatively reduced structural stiffness, which in turn causes the fundamental frequency to gradually decrease. For example, the fundamental frequency of the solar panels on the International Space Station is less than 0.1 Hz (Reference: Zang Xu, Wu Song, Guo Qiwei, et al. Modal analysis and fundamental frequency optimization of flexible solar panels on the space station [J]. Vibration and Shock, 2019, 38(7):5.). Accurately measuring the fundamental frequency of the solar panel in its deployed state plays an important role in the reliability development of spacecraft. However, the ultra-low fundamental frequency of large flexible solar panels makes testing difficult.

[0004] The traditional EMA (Experimental Modal Analysis) test method requires simultaneous measurement of excitation and response, and then calculates the frequency response function (FRF) to identify the natural frequency, damping ratio and vibration mode parameters of the FRF. The direct application of EMA modal test technology to the ultra-low fundamental frequency of large flexible solar wings has the following difficulties: (1) Usually, accelerometers are used to test the response, but the commonly used piezoelectric accelerometers cannot collect ultra-low frequency responses (such as below 0.5Hz). Capacitive accelerometers can collect ultra-low frequency responses, but the added mass of the sensor will also cause errors in the test; (2) The commonly used electromagnetic exciters and hammers have poor low-frequency excitation performance. Hydraulic large displacement exciters can excite ultra-low frequencies, but the added stiffness of the exciter will also cause errors in the test; (3) The preload release method is considered the most intuitive and reliable method, but its disadvantage is that it cannot obtain the modal vibration shape of the solar wing in the deployed state.

[0005] In summary, the existing methods for ultra-low fundamental frequency testing of large flexible solar wings in the unfolded state have various difficulties. Therefore, there is an urgent need for a new ultra-low fundamental frequency testing method for large flexible solar wings that can identify the accurate frequency, damping and vibration mode while being intuitive and reliable. Summary of the Invention

[0006] The purpose of the present invention is to provide an ultra-low fundamental frequency testing method for the unfolded state of a large flexible solar wing based on dynamic modal decomposition. The method combines a machine learning algorithm with a preload release method, realizes non-contact measurement, solves the influence of the additional mass of the sensor and the additional stiffness of the exciter, and solves the problem that the preload release method has no modal vibration shape.

[0007] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a testing method for the unfolded state of a large flexible solar wing based on dynamic modal decomposition, comprising the following steps:

[0008] S1: The preload release method is used to excite the solar panel, and multiple laser displacement sensors in the test device synchronously collect displacement attenuation data at different positions of the solar panel;

[0009] S2: Perform fast Fourier transform calculation on each set of displacement attenuation data, and perform arithmetic averaging on all fast Fourier transform calculation results to generate an average frequency response curve;

[0010] S3: Use the delayed embedded dynamic modal decomposition algorithm to process the displacement data. After decomposition, the fundamental frequency, damping ratio and vibration mode of the Q group are obtained;

[0011] S4: Perform arithmetic averaging on the Q group results and output the final fundamental frequency, modal damping ratio and vibration shape.

[0012] The test device includes: a sensor array, a microgravity simulation suspension device, a large flexible solar wing, a satellite simulation wall, a DC power supply, a data acquisition system and a bracket;

[0013] The microgravity simulation hanging device is used to hang a large flexible solar wing to simulate the microgravity environment in space; the large flexible solar wing is fixed to the satellite simulation wall;

[0014] Two crossbeams are provided in parallel on the bracket, and the crossbeams are located directly above the edge of the large flexible solar wing;

[0015] The sensor array includes: 8 laser displacement sensors; the 8 laser displacement sensors are evenly distributed on two beams directly above the unfolded plane of the large flexible solar wing, and each sensor maintains a constant non-contact distance from the surface of the solar wing; the number of laser displacement sensors on the two beams is equal; each laser displacement sensor is connected to a data acquisition system via a cable to transmit a displacement signal to the data acquisition system;

[0016] The DC power supply is used to power all laser displacement sensors;

[0017] Among them, the sensor array and the data acquisition system constitute a one-way transmission link for displacement data, and the DC power supply and the sensor array constitute an independent power supply link.

[0018] In step S1, the pre-tightening force release method is specifically as follows:

[0019] Apply a pre-tightening rope to the outer end of the large flexible solar wing and stretch it to a preset displacement, and then instantaneously release it to induce free decay oscillation of the solar wing;

[0020] Each laser displacement sensor synchronously records the displacement time-domain signal of the entire oscillation process at a sampling rate of ≥1 kHz to generate multiple sets of time-displacement sequence data.

[0021] Step S3 is specifically as follows:

[0022] S3-1: Divide the test displacement data into N groups on average, with each group having a data length of K and the total data length being NK, to obtain an augmented matrix D

[0030] , , , , , , k , , , k , , aug , ,

[0025] ,

[0024] , ,

[0023] , k ,

[0029] , aug ,

[0028] ,

[0031] ,

[0027] , ,

[0026] ;

[0023] S3-2: Define a moving data frame in the augmented matrix D aug ; The moving data frame moves in the augmented matrix D aug . The data matrix at the initial position of the moving data frame is D1. Move the window with a step size of m, and perform delayed embedding dynamic mode decomposition on the data within each window to obtain the eigenvalues and eigenvectors of the delayed embedding dynamic mode decomposition;<0000​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​The step S3-2 includes the following steps:

[0032] (1) Complete snapshot matrix Used for delayed embedding dynamic mode decomposition algorithm, applied to snapshot matrix via sliding window middle;

[0033] (2) The sliding window moves from index 1 to S, thus based on the matrix Construct snapshot matrix sub-block D aug The matrix is ​​arranged into the following two augmented matrices:

[0034]

[0035] Among them, X' is the future state and X is the current state;

[0036] (3) The relationship between the future state X' and the current state X is:

[0037] R=X'X +

[0038] Among them, X and X' are augmented matrices, X + The pseudo-inverse matrix of the matrix X is represented, and the matrix R is called the operator of the delayed embedded dynamic mode decomposition. The operator R of the delayed embedded dynamic mode decomposition is solved by the least squares method. The operator R is eigendecomposed to extract the eigenvectors and eigenvalues ​​of R.

[0039] (5) Calculate the natural frequency f according to the eigenvalue and eigenvector i and modal damping ratio

[0040] The step (3) is specifically:

[0041] (3-1) Perform truncated singular value decomposition on the matrix X and obtain X = U∑V * , U and V refer to the left singular matrix and right singular matrix of singular value decomposition, respectively, where V * represents the conjugate transpose of the matrix V;

[0042] For matrix X + Perform truncated singular value decomposition and get X + =V∑ -1 U * ;

[0043] (3-2) The projection matrix of the matrix R obtained by least squares fitting:

[0044]

[0045] Among them, U *is the conjugate transpose of the matrix U;

[0046] (3-3) The eigenvalue μ matrix is ​​obtained by eigenvalue decomposition, that is: Where w is The eigenvector of .

[0047] The mode corresponding to μ, that is, the eigenvector of the matrix R: φ=Uw=X'V∑ -1 w.

[0048] The step (4) is specifically:

[0049] The eigenvalue of the i-th delay embedded dynamic mode decomposition is expressed as μ i , its growth rate δ i and frequency w i for:

[0050]

[0051] Natural frequency f i and modal damping ratio Extract as follows:

[0052]

[0053] Among them, |s i | for s i The amplitude, Re(s i ) is s i The real part of .

[0054] The present invention has the following beneficial effects and advantages:

[0055] 1. This invention proposes an ultra-low fundamental frequency test device for a large-scale flexible solar wing in its unfolded state, which can measure the attenuation displacement of a solar wing in its unfolded state.

[0056] 2. This invention uses the preload release method and non-contact laser displacement sensor test data to perform fundamental frequency analysis, thus avoiding the influence of added mass and added stiffness on the fundamental frequency test results.

[0057] 3. The present invention uses the Monte Carlo dynamic modal decomposition method to identify modal parameters, which can identify the fundamental frequency, modal damping ratio and vibration shape of the large flexible solar wing in the unfolded state. The Monte Carlo method also ensures the reliability of the identification results. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic structural diagram of an ultra-low fundamental frequency testing device for a large-scale flexible solar wing in the unfolded state according to the present invention;

[0059] Figure 2Flowchart of the ultra-low fundamental frequency testing method for a large flexible solar wing in its unfolded state based on dynamic modal decomposition in the present invention;

[0060] Figure 3 The complete snapshot matrix defines the sliding window

[0061] Figure 4 Attenuation displacement data diagram of 8 laser displacement sensors in this embodiment;

[0062] Figure 5 Fundamental frequency analysis result diagram of this embodiment;

[0063] Figure 6 Damping ratio analysis result diagram of this embodiment;

[0064] Figure 7 Diagram of the mode shape analysis results of this embodiment;

[0065] Among them, 1 is laser displacement sensor No. 1, 2 is laser displacement sensor No. 2, 3 is laser displacement sensor No. 3, 4 is laser displacement sensor No. 4, 5 is laser displacement sensor No. 5, 6 is laser displacement sensor No. 6, 7 is laser displacement sensor No. 7, 8 is laser displacement sensor No. 8, 9 is the solar wing microgravity simulation suspension device, 10 is the large flexible solar wing, 11 is the satellite simulation wall, 12 is the DC power supply, 13 is the data acquisition system, and 14 is the bracket. DETAILED DESCRIPTION

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0067] like Figure 1 FIG. 1 shows an ultra-low fundamental frequency test device for a large flexible solar wing in its unfolded state. The test device of the present invention includes: a sensor array (laser displacement sensors 1-8), a microgravity simulation suspension device 9, a large flexible solar wing 10, a satellite simulation wall 11, a DC power supply 12, a data acquisition system 13, and a bracket 14.

[0068] A microgravity simulation hanging device 9 is used to hang a large flexible solar wing 10 to simulate the microgravity environment of space; the large flexible solar wing 10 is fixed to the satellite simulation wall 11;

[0069] Two parallel beams are provided on the bracket 14, and the beams are located directly above the edge of the large flexible solar wing 10;

[0070] The sensor array includes: 8 laser displacement sensors; the 8 laser displacement sensors are evenly distributed on two beams directly above the unfolding plane of the large flexible solar wing 10, and each sensor maintains a constant non-contact distance from the surface of the solar wing; the number of laser displacement sensors on the two beams is equal; each laser displacement sensor is connected to the data acquisition system 13 via a cable to transmit a displacement signal to the data acquisition system 13;

[0071] A DC power supply 12 is used to power all laser displacement sensors;

[0072] The sensor array and the data acquisition system 13 form a one-way transmission link for displacement data, and the DC power supply 12 and the sensor array form an independent power supply link.

[0073] like Figure 2 As shown in the figure, the present invention provides an ultra-low fundamental frequency testing method for a large flexible solar wing in the unfolded state based on dynamic modal decomposition.

[0074] The present invention provides a method for testing the unfolded state of a large flexible solar wing based on dynamic modal decomposition, comprising the following steps:

[0075] S1: The preload release method is used to excite the solar panel, and multiple laser displacement sensors in the test device synchronously collect displacement attenuation data at different positions of the solar panel;

[0076] A pre-tightened rope is applied to the outer end of the large flexible solar wing 10 and stretched to a preset displacement and then released instantaneously to induce free decay oscillation of the solar wing;

[0077] Each laser displacement sensor synchronously records the displacement time domain signal of the entire oscillation process at a sampling rate of ≥1kHz, generating multiple sets of time-displacement series data.

[0078] S2: Perform fast Fourier transform calculation on each set of displacement attenuation data, and perform arithmetic averaging on all fast Fourier transform calculation results to generate an average frequency response curve;

[0079] S3: Use the delayed embedded dynamic modal decomposition algorithm to process the displacement data. After decomposition, the fundamental frequency, damping ratio and vibration mode of the Q group are obtained;

[0080] S3-1: Divide the test displacement data into N groups, each group has a data length of K, and the total length of the data is NK, and obtain the augmented matrix D aug ;

[0081] S3-2: In the augmented matrix D aug The mobile data frame is defined in the augmented matrix D augPerform a movement. The data matrix at the initial position of the moving data frame is D1. Move the window with a step size of m, and perform delayed embedding dynamic mode decomposition on the data within each window to obtain the eigenvalues and eigenvectors of the delayed embedding dynamic mode decomposition.

[0082] S3-3: Repeat the decomposition Q = [(N - 1)K] / m times to obtain [(N - 1)K] / m groups of fundamental frequencies, damping ratios, and mode shape results.

[0083] S4: Perform arithmetic averaging on the Q groups of results and output the final fundamental frequency, modal damping ratio, and mode shape.

[0084] The method of the present invention is based on the delayed embedding dynamic mode decomposition algorithm, and an introduction to this algorithm is given.

[0085] To implement the delayed embedding dynamic mode decomposition, an augmented input matrix D1 is defined as follows:

[0086]

[0087] Then the augmented matrix is obtained, that is:

[0088]

[0089] Where, represents the state vector of an m-dimensional dynamic system at time t, x k = x(t k )(k = 1,...,K,...,NK) represents a set of snapshots equally spaced in time, and its time points are: t k = t1 + (k - 1)Δt, S(S < K) is the dimension of the delayed embedding, and D1 is the data matrix at the initial position of the moving data frame.

[0090] In the formula, represents the state vector of an m-dimensional dynamic system at time t, x k = x(t k )(k = 1,...,K) represents a set of snapshots equally spaced in time, and its time point is t k = t1 + (k - 1)Δt. K is the number of sample snapshots of the matrix D1, and S is the dimension of the delayed embedding where S(S < K).

[0091] The complete snapshot matrix of the augmented input matrix D1 is used for delayed embedding DMD and is applied to the snapshot matrix through a sliding window as Figure 3 shown.

[0092] In the formula, the sliding window moves from index 1 to S, thereby constructing sub-blocks of the snapshot matrix based on the matrix ​Therefore, formula (1) D aug The matrices are arranged into the following two augmented matrices:

[0093]

[0094] The goal of the delayed embedded dynamic mode decomposition method is to find the relationship between the future state X' and the current state X, which is given by the following formula:

[0095] X'=RX (4)

[0096] so:

[0097] R=X'X + (5)

[0098] Where X and X' are augmented matrices, X + represents the pseudo-inverse matrix of the matrix X. The matrix R is called the delayed embedding DMD operator. The eigenmode and eigenvalue of the delayed embedding DMD are defined as the eigenvector and eigenvalue of the matrix R.

[0099] First, perform truncated singular value decomposition on the matrix X and obtain X=U∑V * , U and V refer to the left singular matrix and right singular matrix of singular value decomposition, respectively, where V * represents the conjugate transpose (Hermitian transpose) of the matrix V. The pseudo-inverse matrix can be calculated as follows:

[0100] X + =V∑ -1 U * (6)

[0101] Where U * is the conjugate transpose of the matrix U.

[0102] The projection matrix of the matrix R obtained by least squares fitting is:

[0103]

[0104] The eigenvalues ​​μ of the delayed embedded dynamic modal decomposition are obtained by performing eigenvalue decomposition.

[0105]

[0106] Where w is The eigenvector of . The mode corresponding to μ is:

[0107] φ=Uw=X'V∑ -1 w (9)

[0108] It is worth noting that these DMD modes are the eigenvectors of the matrix R, as shown below:

[0109]

[0110] Denote the i-th delayed embedded DMD eigenvalue as μ i , its growth rate δ i and frequency w i It is given by the following formula:

[0111]

[0112] Therefore, the natural frequency f i and modal damping ratio It can be extracted as follows:

[0113]

[0114] Among them, |s i | for s i The amplitude, Re(s i ) is s i The real part of .

[0115] Example 1:

[0116] like Figure 1 The embodiment of the ultra-low fundamental frequency test device for a large-scale flexible solar wing in the unfolded state mainly includes four steps:

[0117] Step 1: During the test, a line is used to pull a certain distance from the outer end of the large flexible solar wing 10 and then released to allow the specimen to oscillate freely and decay. Eight laser displacement sensors 1-8 test the displacement decay of different positions of the solar wing and obtain eight sets of displacement data, such as Figure 4 As shown;

[0118] Step 2: Perform FFT calculation on the 8 sets of displacement data respectively, and perform average processing to obtain the average frequency response curve, such as Figure 5 As shown;

[0119] Step 3: Divide the test displacement data into N groups, each with a data length of K and a total data length of NK, to obtain the augmented matrix D aug ,in represents the displacement vector of a p-dimensional dynamic system at time t. In this paper, there are 8 displacement sensors, so p = 8;

[0120] Step 4: In the augmented matrix D aug The mobile data frame is defined in the augmented matrix D aug Move, define the data frame to move a distance m each time, and each time it moves, the data in the data frame is subjected to a delayed embedded dynamic modal decomposition algorithm analysis, and ultimately [(N-1)K] / m groups of fundamental frequencies, fundamental frequency damping ratios, and vibration modes can be obtained, such as Figure 5 As shown in the frequency response curve, 100 sets of identified fundamental frequencies are shown. Figure 6 The figure shows the modal damping ratios at 100 fundamental frequencies;

[0121] Step 5: Perform average calculation on 100 groups of fundamental frequencies, modal damping ratios and vibration shapes, as shown in the following example: Figure 7 The figure shows the vibration mode of a large flexible solar wing at its fundamental frequency.

[0122] This paper proposes a method and dedicated device for testing ultra-low fundamental frequencies (<0.1 Hz) of large flexible solar wings in their deployed state, addressing three major challenges in traditional experimental modal analysis (EMA) in ultra-low frequency measurements:

[0123] Sensor limitations: Traditional accelerometers cannot capture ultra-low frequency responses, and contact measurements introduce additional mass errors.

[0124] Excitation bottleneck: The low-frequency performance of the shaker is insufficient, and the additional stiffness interferes with the structural authenticity;

[0125] Missing vibration mode: The preload release method cannot obtain the modal vibration mode.

[0126] Combined with the above embodiment 1, the present invention has been improved in terms of accuracy:

[0127] The laser displacement sensor achieves micron-level displacement resolution and can measure amplitudes as low as centimeters (such as 0.1Hz oscillation); the Monte Carlo DMD processes ultra-low frequency attenuation signals (0.01–0.5Hz).

[0128] The present invention has engineering applicability:

[0129] Non-contact measurement eliminates the added mass / stiffness effect; the preload release method does not require external excitation equipment and is easy and reliable to operate; the algorithm automatically identifies complex vibration modes (such as the first-order bending mode of the solar wing).

[0130] And in Example 1, as Figure 4-6 As shown in the figure, by comparing simulation with experiment, the fundamental frequency identification error is less than 2%, and the degree of consistency of vibration mode reconstruction is greater than 95%.

[0131] The present invention provides an on-orbit precision modal testing method for the solar panels of ultra-large spacecraft (such as space stations and deep space probes), ensures the dynamic stability design of the structure, and directly serves the safety and life prediction of the spacecraft.

[0132] Those skilled in the art will understand that the above description is only a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of the present disclosure may be combined or coupled in various ways, even if such a combination or coupling is not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

[0133] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include such changes and modifications as fall within the scope of the claims and their equivalents.

Claims

1. A testing method for the deployment state of a large flexible solar wing based on dynamic modal decomposition, characterized in that: The following steps are involved: S1: The preload release method is used to excite the solar panel, and multiple laser displacement sensors in the test device synchronously collect displacement attenuation data at different positions of the solar panel; S2: Perform fast Fourier transform calculation on each set of displacement attenuation data, and perform arithmetic averaging on all fast Fourier transform calculation results to generate an average frequency response curve; S3: The displacement data is processed using the Monte Carlo delay embedding dynamic modal decomposition algorithm. After decomposition, the fundamental frequency, damping ratio and vibration mode of the Q group are obtained. S4: Perform arithmetic averaging on the Q group results and output the final fundamental frequency, modal damping ratio and vibration shape.

2. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 1 is characterized in that: The test device comprises: a sensor array, a microgravity simulation suspension device (9), a large flexible solar wing (10), a satellite simulation wall (11), a DC power supply (12), a data acquisition system (13) and a bracket (14); The microgravity simulation hanging device (9) is used to hang a large flexible solar wing (10) to simulate a space microgravity environment; the large flexible solar wing (10) is fixed to a satellite simulation wall (11); Two crossbeams are provided in parallel on the bracket (14), and the crossbeams are located directly above the edge of the large flexible solar wing (10); The sensor array comprises: 8 laser displacement sensors; the 8 laser displacement sensors are evenly distributed on two beams directly above the unfolding plane of the large flexible solar wing (10), and each sensor maintains a constant non-contact distance with the surface of the solar wing; the number of laser displacement sensors on the two beams is equal; each of the laser displacement sensors is connected to a data acquisition system (13) via a cable to transmit a displacement signal to the data acquisition system (13); The DC power supply (12) is used to supply power to all laser displacement sensors; The sensor array and the data acquisition system (13) form a one-way transmission link for displacement data, and the DC power supply (12) and the sensor array form an independent power supply link.

3. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 1, characterized in that: In step S1, the preload release method is specifically as follows: A pre-tightened rope is applied to the outer end of a large flexible solar wing (10), stretched to a preset displacement, and then released instantaneously to induce free decay oscillation of the solar wing; Each laser displacement sensor synchronously records the displacement time domain signal of the entire oscillation process at a sampling rate of ≥1kHz, generating multiple sets of time-displacement series data.

4. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 1, characterized in that: The step S3 is specifically as follows: S3-1: Divide the test displacement data into N groups, each with a data length of K and a total data length of NK, to obtain the augmented matrix D aug ; S3-2: In the augmented matrix D aug The mobile data frame is defined in the augmented matrix D aug Move the data frame, the data matrix at the initial position is D1, move the window with a step size of m, perform delayed embedded dynamic mode decomposition on the data in each window, and obtain the eigenvalues ​​and eigenvectors of delayed embedded dynamic mode decomposition; S3-3: Repeat the decomposition Q = [(N-1)K] / m times to obtain [(N-1)K] / m groups of fundamental frequency, damping ratio and mode shape results.

5. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 4 is characterized in that: In step S3-1, the moving step length m of the sliding window satisfies 1≤m≤K / 2; The length K of each sub-data set covers at least 10 fundamental frequency oscillation periods; The number of groups N is ≥ 20 to ensure the validity of Monte Carlo statistics.

6. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 4, characterized in that: In step S3-1, the augmented matrix is ​​obtained, specifically: Among them, represents the state vector of an m-dimensional dynamic system at time t, x k = x(t k )(k = 1,...,K,...,NK) represents a set of equally spaced snapshots in time, and their time points are: t k = t1 + (k - 1)Δt, S (S < K) is the dimension of delay embedding, and D1 is the data matrix at the initial position of the moving data frame.

7. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 4, characterized in that: The step S3-2, taking the data matrix D1 at the initial position of the mobile data frame as an example, includes the following steps: (1) Complete snapshot matrix in D1 Used for delayed embedding dynamic mode decomposition algorithm, applied to snapshot matrix via sliding window middle; (2) The sliding window moves from index 1 to S, thus based on the matrix Construct snapshot matrix sub-block D aug The matrix is ​​arranged into the following two augmented matrices: Among them, X' is the future state matrix, X is the current state matrix; (3) The relationship between the future state X' and the current state X is: R=X'X + where X + The pseudo-inverse matrix of the matrix X is represented, and the matrix R is called the operator of the delayed embedded dynamic mode decomposition. The operator R of the delayed embedded dynamic mode decomposition is solved by the least squares method. The operator R is eigendecomposed to extract the eigenvectors and eigenvalues ​​of R. (4) Calculate the natural frequency f according to the eigenvalue and eigenvector i and modal damping ratio 8. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 7, characterized in that: The step (3) is specifically: (3-1) Perform truncated singular value decomposition on the matrix X and obtain X = U∑V * , U and V refer to the left singular matrix and right singular matrix of singular value decomposition, respectively, where V * represents the conjugate transpose of the matrix V; For matrix X + Perform truncated singular value decomposition and get X + =V∑ -1 U * ; (3-2) The projection matrix of the matrix R obtained by least squares fitting: Among them, U * is the conjugate transpose of the matrix U; (3-3) The eigenvalue μ matrix is ​​obtained by eigenvalue decomposition, that is: Where w is The eigenvector of . The mode corresponding to μ, that is, the eigenvector of the matrix R: φ=Uw=X'V∑ -1 w.

9. The method for testing the deployment state of a large flexible solar wing based on dynamic modal decomposition according to claim 7, characterized in that: The step (4) is specifically: The eigenvalue of the i-th delay embedded dynamic mode decomposition is expressed as μ i , its growth rate δ i and frequency w i for: Natural frequency f i and modal damping ratio Extract as follows: Among them, |s i | for s i The amplitude, Re(s i ) is s i The real part of .

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