A method and related device for identifying modal parameters of slender aircraft structure operation

Abstract

A method and a related device for identifying the operating modal parameters of a slender aircraft structure, comprising: measuring the vibration time domain response X at different positions of the slender aircraft structure through a vibration test, and expressing the vibration response into a third-order tensor X by using a segmentation operation ； The spectral analysis of the vibration time domain response is performed, and the number of active modes R of the structure is determined by searching the number of spectral peaks of the vibration response, and used as the rank of the tensor decomposition; the third-order tensor X is decomposed using the tensor decomposition model; the modal frequency modal parameters are obtained from the estimated source signal S. The proposed method can accurately identify the modal parameters of the slender aircraft structure under both positive and underdetermined conditions, and has good noise resistance and high computational efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of operating modal parameter identification, and relates to an operating modal parameter identification method for a slender aircraft structure and a related device. Background Art

[0002] As aircraft structures develop towards a high slenderness ratio, light weight and complexity, it is difficult to directly measure the loads on the structure in operation. In addition, due to the complex spatial structure, sensors can only be arranged at limited key positions, resulting in the measurement system being able to collect only a small amount of observation data, causing the practical problem of underdetermined modal parameter identification. Based on the above two aspects, it is of great significance to use limited sensor measurement data to identify hidden structural dynamic characteristic parameters, and then guide the structural design of slender aircraft and the modification of finite element models.

[0003] At present, most of the work results of blind source separation technology application in the identification of operational modal parameters are mainly focused on the study of overdetermined states, and the study of underdetermined states is relatively small. Moreover, each method has obvious limitations that cannot be solved, such as stringent requirements on the quality of source signal data, poor noise resistance, etc. Therefore, in view of the practical problem of operational modal parameter identification of slender aircraft structures, how to design an operational modal parameter identification method with higher identification accuracy and stronger engineering application capability is a technical problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide a method and a related device for identifying the operating modal parameters of a slender aircraft structure, so as to solve the problems of low computational efficiency and poor noise resistance in the prior art.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for identifying operating modal parameters of a slender aircraft structure, comprising:

[0007] The vibration time domain response X at different positions of the slender aircraft structure is measured through vibration tests, and the vibration response is expressed as a third-order tensor using a segmentation operation.

[0008] Perform spectrum analysis on the vibration time domain response, and determine the number of active modes R of the structure by searching the number of spectrum peaks of the vibration response, and use it as the rank of tensor decomposition;

[0009] Use the tensor decomposition model to decompose the third-order tensor Decompose to obtain a low-rank tensor with R sub-items of multilinear rank, and then convert the first mode sub-tensor A of each sub-item r With the second mode subtensor B rMultiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r As the column vector of the mixing matrix, the mixing matrix M and the source signal S are estimated, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response;

[0010] The modal frequency and modal parameters are obtained from the estimated source signal S.

[0011] Optionally, the modal frequency and modal parameters are obtained from the estimated source signal S by using single degree of freedom modal identification technology:

[0012] For free vibration, the modal frequency is identified using Fourier transform and Hilbert transform methods; for random vibration, it is necessary to use RDT technology to obtain the free decay signal of the single modal response in advance, and then use the same processing method as the free vibration case to identify the modal frequency.

[0013] Optionally, N vibration sensors are arranged on the surface of the slender aircraft structure to obtain the vibration time-domain response X of the structure under environmental excitation.

[0014] Optionally, according to the numerical relationship between the number of sensors N and the number of active modes M of the structure, the operation modal parameter identification problem can be divided into three subcategories: overdetermined, positively determined, and underdetermined. When the number of active modes of the structure is less than the number of sensors, it is an overdetermined blind source separation problem; when the number of active modes of the structure is equal to the number of sensors, it is a positively determined blind source separation problem. When the number of active modes of the structure is greater than the number of sensors, it is an underdetermined blind source separation problem.

[0015] Optionally, the acquired vibration time domain response X is expressed as a third-order tensor by segmentation operation The spectrum analysis of the vibration time domain response X is performed, and the modal order R is determined by searching the number of spectrum peaks of the vibration response signal or using the stability diagram, which is used as the rank of the block term tensor decomposition.

[0016] Optionally, use rank-(L r ,L r ,1) Block term decomposition tensor decomposition model for third-order tensor To break it down:

[0017] rank-(L r ,L r ,1) is defined as follows: A tensor If it is represented as a series of rank-(L r ,L r,1) The form of the sum of factors, and the decomposition factors satisfy certain rank constraints, then this decomposition method is called rank-(L r ,L r ,1) Block item decomposition, the specific expression is as follows:

[0018]

[0019] in, All are full rank, Expressed as Formula (1) can also be expressed as:

[0020]

[0021] Among them, D r The rank is L r ;

[0022] The rank-(L r ,L r ,1) When the block term decomposition satisfies the following two conditions, its decomposition satisfies uniqueness:

[0023] (1)A r Right multiply the non-singular matrix Γ r Get the factor matrix B r Right multiplication Get the factor matrix

[0024] (2) Decomposition factors The product remains unchanged under any scaling, satisfying the scale change criterion.

[0025] Optional, rank-(L r ,L r ,1) The condition for the uniqueness of the block term decomposition is that both factor matrices A and B are column-full rank matrices and there are no collinear column vectors in C;

[0026] If the Kruskal rank of the factor matrix is ​​R, then rank-(L r ,L r ,1) The uniqueness condition of block term decomposition is expressed as:

[0027] r′ A +r′ B ≥R+2 (3)

[0028] In the formula, r′ A is the number of block submatrices; any r′ of matrix A A The set of block sub-matrices is a set of linearly independent columns; the following necessary conditions are further derived:

[0029]

[0030] In a second aspect, the present invention provides a system for identifying modal parameters of a slender aircraft structure, comprising:

[0031] A data acquisition module is used to measure the vibration time domain response X at different positions of the slender body aircraft structure through a vibration test, and express the vibration response into a third-order tensor χ by using a segmentation operation;

[0032] The spectrum analysis module is used to perform spectrum analysis on the vibration time domain response. The number of active modes R of the structure is determined by searching the number of spectrum peaks of the vibration response and used as the rank of tensor decomposition.

[0033] The decomposition module is used to decompose the third-order tensor χ using the tensor decomposition model to obtain a low-rank tensor with R sub-items of multilinear rank, and then convert the first mode sub-tensor A of each sub-item into r With the second mode subtensor B r Multiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r As the column vector of the mixing matrix, the mixing matrix M and the source signal S are estimated, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response;

[0034] The modal parameter acquisition module is used to obtain the modal frequency modal parameters from the estimated source signal S.

[0035] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of a method for identifying operating modal parameters of a slender aircraft structure when executing the computer program.

[0036] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a method for identifying operating modal parameters of a slender aircraft structure.

[0037] Compared with the prior art, the present invention has the following technical effects:

[0038] Aiming at the problem of modal parameter identification of slender aircraft structure, the present invention proposes an underdetermined modal parameter identification method based on tensor decomposition. The proposed method can accurately identify the modal parameters of slender aircraft structure under both positive and underdetermined conditions, and has good noise resistance and high computational efficiency. In addition, compared with other modal parameter identification methods, such as independent component analysis method and sparse component analysis method, the advantages of this method are also reflected in the relaxation of the assumption that the source signal satisfies statistical independence in the traditional independent component analysis method and the requirement that the source signal satisfies sufficient sparsity and more parameter adjustment requirements in the sparse component analysis method. Therefore, this method has better application capabilities in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the identification of the modal parameters of the slender body aircraft structure operation provided by the present invention;

[0040] Figure 2 It is a block item tensor decomposition flow chart provided by the present invention;

[0041] Figure 3 It is a solid rocket engine structure test site in an embodiment of the present invention;

[0042] Figure 4 is the estimated modal response and corresponding Fourier spectrum of the solid rocket motor in the underdetermined state in an embodiment of the present invention;

[0043] Figure 5 It is a modal vibration shape diagram of the solid rocket motor identified in the underdetermined state in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] The present invention provides a method for identifying the operating modal parameters of a slender aircraft structure. The time domain vibration displacement / velocity / acceleration response signals of the slender aircraft structure are collected by a vibration displacement / velocity / acceleration sensor, and the signals are substituted into a block tensor decomposition algorithm for operation to obtain a mixed matrix and a source signal, wherein the mixed matrix and the source signal correspond to a modal vibration shape matrix and a modal response, respectively, so as to obtain modal parameter information such as frequency and vibration shape of the slender aircraft structure. Compared with the existing methods, the proposed method has the advantages of high computational efficiency and good noise resistance.

[0046] The technical solution adopted by the present invention is:

[0047] The time-domain vibration displacement / velocity / acceleration response signal of the slender aircraft structure under environmental excitation is obtained; the time-domain vibration displacement / velocity / acceleration response signal is collected by a vibration displacement / velocity / acceleration sensor.

[0048] First, the vibration response of the slender aircraft structure is expressed as a third-order tensor form; then, the rank-(L r ,L r ,1) The tensor decomposition model decomposes the constructed third-order tensor, estimates the mixing matrix and extracts the source signal, where the source signal corresponds to the modal response, and the mixing matrix contains the modal vibration information; further processing of the modal response can obtain modal parameters such as frequency and damping ratio. The specific steps are as follows:

[0049] Firstly, the vibration time domain response X of different positions of the slender aircraft structure is measured through vibration tests, and the vibration response is expressed as a third-order tensor χ using a segmentation operation;

[0050] Furthermore, the spectrum analysis of the vibration time domain response is performed, and the number of active modes R of the structure is determined by searching the number of spectrum peaks of the vibration response, and used as the rank of tensor decomposition;

[0051] Furthermore, using rank-(L r ,L r ,1) The tensor decomposition model decomposes the third-order tensor χ to obtain a low-rank tensor with R sub-items of multilinear rank, and then converts the first mode sub-tensor A of each sub-item r With the second mode subtensor B r Multiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r As the column vector of the mixing matrix, the mixing matrix M and the source signal S are estimated, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response;

[0052] Finally, the modal parameters such as modal frequency are obtained from the estimated source signal S through single degree of freedom modal identification technology. For free vibration, the modal frequency is directly identified using Fourier transform and Hilbert transform methods; for random vibration, it is necessary to use RDT technology to obtain the free decay signal of the single modal response in advance, and then use the same processing method as the free vibration case to identify the modal frequency.

[0053] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 As shown, the method for identifying the operating modal parameters of a slender aircraft structure provided by the present invention comprises:

[0055] S1. Arrange N vibration sensors on the surface of the slender aircraft structure to obtain the time-domain vibration response signal X of the structure under environmental excitation. According to the numerical relationship between the number of sensors N and the number of active modes M of the structure, the operation modal parameter identification problem can be divided into three subcategories: overdetermined, positively determined, and underdetermined. When the number of active modes of the structure is less than the number of sensors, it is an overdetermined blind source separation problem; when the number of active modes of the structure is equal to the number of sensors, it is a positively determined blind source separation problem. When the number of active modes of the structure is greater than the number of sensors, it is an underdetermined blind source separation problem. The invention can accurately realize the operation modal parameter identification of the slender aircraft structure for all three types of sub-problems.

[0056] S2. By segmentation, the collected vibration time domain response X is expressed as a third-order tensor χ. The vibration time domain response X is subjected to spectrum analysis, and the modal order R is determined by searching the number of spectrum peaks of the vibration response signal or using a stability diagram, which is used as the rank of the block term tensor decomposition.

[0057] S3, using rank-(L r ,L r ,1) Block Term Decomposition (BTD) tensor decomposition model for third-order tensors Decompose to obtain a low-rank tensor with R sub-items of multilinear rank, and then convert the first mode sub-tensor A of each sub-item r With the second mode subtensor B r Multiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r It is regarded as the column vector of the mixing matrix, so as to estimate the mixing matrix M and the source signal S, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response.

[0058] rank-(L r ,L r ,1) is defined as follows: A tensor If it can be expressed as a series of rank-(L r ,L r ,1) The form of the sum of factors, and the decomposition factors satisfy certain rank constraints, then this decomposition method is called rank-(L r ,L r ,1) Block item decomposition, the specific expression is as follows:

[0059]

[0060] in, All are full rank, It can be simply expressed as Formula (1) can also be expressed as:

[0061]

[0062] Among them, D r The rank is L r .

[0063] In the sense of permutation and scale transformation, block term decomposition is unique and has loose decomposition conditions. It is a universal decomposition model. r ,L r ,1) When the block term decomposition satisfies the following two conditions, its decomposition satisfies uniqueness:

[0064] (1)A r Right multiply the non-singular matrix Γ r Get the factor matrix B r Right multiplication Get the factor matrix

[0065] (2) Decomposition factors The product remains unchanged under any scaling, satisfying the scale change criterion.

[0066] For a third-order tensor, rank-(L r ,L r ,1) The condition for the uniqueness of the block term decomposition is that both factor matrices A and B are column-full rank matrices and there are no collinear column vectors in C.

[0067] If the Kruskal rank of the factor matrix is ​​R, then rank-(L r ,L r ,1) The uniqueness condition of block item decomposition can be expressed as:

[0068] r′ A +r′ B ≥R+2(3)

[0069] In the formula, r′ A is the number of block submatrices. Any r′ of matrix A A The set of block sub-matrices is a set of linearly independent columns. The following necessary conditions are further derived:

[0070]

[0071] The tensor decomposition blind source separation algorithm cited in this paper adopts the BTD model, assuming that before blind source separation, the collected signal has been denoised by certain preprocessing means, denoised as X=MS.

[0072] like Figure 2As shown, each row of the observed data matrix X is reshaped into a matrix and then stacked into a tensor The reshaped source appears in the first and second ways, and the mixed vector appears in the third way. If the reconstructed source allows a low-rank representation, thus achieving unique separation of the sources and identification of the mixed vector, the blind source separation problem can be reduced to the rank-(L r ,L r ,1) is the BTD block term decomposition problem.

[0073] S4. Through the single degree of freedom modal identification technology, modal parameters such as modal frequency are obtained from the above estimated source signal S. For free vibration, the modal frequency is directly identified using the Fourier transform and Hilbert transform methods; for random vibration, it is necessary to use the RDT technology to obtain the free decay signal of the single modal response in advance, and then use the same processing method as the free vibration case to identify the modal frequency.

[0074] Based on the above description, the present invention uses a solid rocket engine structure to illustrate the specific implementation process of the technical solution provided above. Figure 3 This is the solid rocket engine structure test site.

[0075] As a typical slender aircraft structure, the measured response data can be well used to verify and reflect the underdetermined modal parameter identification capability of the proposed method in practical engineering applications.

[0076] Experimental setup: (1) The experiment measures the acceleration response signal by hammering. The engine is suspended in the middle position without other constraints to simulate free boundary conditions. (2) Eight knocking points are arranged in each circle along the circumference of the engine. The shell is arranged in a circle every 50 cm, for a total of 10 circles. One circle of knocking points is arranged at the end of the nozzle, and a total of 88 points are arranged on the entire engine surface. They are numbered 1 to 88 in sequence. (3) The entire test system consists of six PCB-333B32 acceleration sensors, an LMS SCADAS III data acquisition and analysis system and a The hammer is connected to the input port of the LMS test instrument to collect input signals. (4) Six acceleration sensors are attached to the measuring points numbered 15, 17, 34, 48, 59, and 65 to collect acceleration responses. Figure 1 (5) Parameter setting: Complete parameter setting and engine modeling in Impact Test. The modal information of the engine structure is relatively complex, and in actual engineering, we generally pay more attention to the low-order modal information of the structure. Here, we are concerned about the frequency range within 300Hz, select the bandwidth as 512Hz, set the number of spectrum lines to 1024, and the sampling frequency to 2048Hz.

[0077] Experimental process: After completing the relevant settings of the experimental equipment and LMS software, a hammering signal was applied to each of the 88 measuring points using a force hammer. Each measuring point was hammered 5 times, and the average value was taken as the response of that point.

[0078] Experimental results: The natural frequencies of each order within the first 300 Hz obtained from the experiment are shown in Table 1.

[0079] To verify the ability of the proposed method to solve problems in the underdetermined state, in this embodiment, four groups of channel data at the 67 measuring points were selected, and their acceleration response signals were collected. They were substituted into the algorithm for processing, and the processed signals were subjected to a fast Fourier transform to extract the frequency information of each order. The frequency identification results were compared with the identification results of the stochastic subspace method and the PolyMAX method in the LMS software. It was found that the frequency errors of each order were within 1%, and the identification results were accurate. The frequency extraction diagram and the comparison results are respectively as Figure 4 shown in and Table 1.

[0080] Table 1

[0081]

[0082] In this invention, the Modal Assurance Criterion (MAC) was introduced for structural dynamic characteristic analysis to evaluate the accuracy of the modal shape identification results. The mathematical meaning of MAC is the angle size between two groups of modal vectors in the spatial range. For the same vibration mode, its expression is:

[0083]

[0084] where represents the theoretical value of the i-th order vibration mode, represents the identified value of the i-th order vibration mode. The value range of MAC is [0, 1]. The closer the MAC value is to 1, the higher the similarity degree of the two vectors, and the more accurate the identification result. Generally, it is considered that when MAC > 0.9, it means that the two groups of vibration modes are related; when 0.05 < MAC < 0.9, it means that the two groups of vibration modes are partially related; when MAC < 0.05, it means that the two groups of vibration modes are completely unrelated.

[0085] The vibration modes of each order were extracted, the MAC values with the stochastic subspace method were calculated, and normalization processing was performed. The modal shape identification value images and the identification results of the stochastic subspace method images were compared. The comparison results are as Figure 5 shown in and Table 2.

[0086] Table 2

[0087]

[0088] In this embodiment, for the solid rocket engine, a typical slender aircraft structure, when the number of acceleration sensors is less than the number of active modes of the structure, the data signal is processed to extract the structural frequency and vibration mode information, and the results are compared with other methods such as the random subspace method to verify the algorithm accuracy. The results show that the proposed method can accurately identify the modal parameter information of the slender aircraft structure under the underdetermined state.

[0089] This article uses specific examples to illustrate the principles and implementation methods of the present invention, and the examples are only to help understand the method and core ideas of the present invention. For those of ordinary skill in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes, and the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for identifying the operating modal parameters of a slender aircraft structure, characterized in that: include: The vibration time domain response X at different positions of the slender aircraft structure is measured through vibration tests, and the vibration response is expressed as a third-order tensor using a segmentation operation. Perform spectrum analysis on the vibration time domain response, and determine the number of active modes R of the structure by searching the number of spectrum peaks of the vibration response, and use it as the rank of tensor decomposition; Use the tensor decomposition model to decompose the third-order tensor Decompose to obtain a low-rank tensor with R sub-items of multilinear rank, and then convert the first mode sub-tensor A of each sub-item r With the second mode subtensor B r Multiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r As the column vector of the mixing matrix, the mixing matrix M and the source signal S are estimated, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response; The modal frequency and modal parameters are obtained from the estimated source signal S.

2. The method for identifying the operating modal parameters of a slender aircraft structure according to claim 1, characterized in that: Through the single degree of freedom modal identification technology, the modal frequency modal parameters are obtained from the estimated source signal S: For free vibration, the modal frequency is identified using Fourier transform and Hilbert transform methods; for random vibration, it is necessary to use RDT technology to obtain the free decay signal of the single modal response in advance, and then use the same processing method as the free vibration case to identify the modal frequency.

3. The method for identifying the operating modal parameters of a slender aircraft structure according to claim 1, characterized in that: N vibration sensors are arranged on the surface of the slender aircraft structure to obtain the vibration time domain response X of the structure under environmental excitation.

4. The method for identifying the operating modal parameters of a slender aircraft structure according to claim 3, characterized in that: According to the numerical relationship between the number of sensors N and the number of active modes M of the structure, the operating modal parameter identification problem can be divided into three subcategories: overdetermined, positively determined and underdetermined. When the number of active modes of the structure is less than the number of sensors, it is an overdetermined blind source separation problem; when the number of active modes of the structure is equal to the number of sensors, it is a positively determined blind source separation problem; when the number of active modes of the structure is greater than the number of sensors, it is an underdetermined blind source separation problem.

5. The method for identifying the operating modal parameters of a slender aircraft structure according to claim 1, characterized in that: Through the segmentation operation, the collected vibration time domain response X is expressed as a third-order tensor The spectrum analysis of the vibration time domain response X is performed, and the modal order R is determined by searching the number of spectrum peaks of the vibration response signal or using the stability diagram, which is used as the rank of the block term tensor decomposition.

6. The method for identifying the operating modal parameters of a slender aircraft structure according to claim 1, characterized in that: Using rank-(L r ,L r ,1) Block term decomposition tensor decomposition model for third-order tensor To break it down: rank-(L r ,L r ,1) is defined as follows: A tensor If it is represented as a series of rank-(L r ,L r ,1) The form of the sum of factors, and the decomposition factors satisfy certain rank constraints, then this decomposition method is called rank-(L r ,L r ,1) Block item decomposition, the specific expression is as follows: in, All are full rank, Expressed as Formula (1) can also be expressed as: Among them, D r The rank is L r ; The rank-(L r ,L r ,1) When the block term decomposition satisfies the following two conditions, its decomposition satisfies uniqueness: (1)A r Right multiply the non-singular matrix Γ r Get the factor matrix B r Right multiplication Get the factor matrix (2) Decomposition factors The product remains unchanged even when scaled arbitrarily, satisfying the scale change criterion.

7. A method for identifying the operating modal parameters of a slender aircraft structure according to claim 6, characterized in that: rank-(L r ,L r ,1) The condition for the uniqueness of the block term decomposition is that the factor matrices A and B are both column-full rank matrices and there are no collinear column vectors in C; If the Kruskal rank of the factor matrix is ​​R, then rank-(L r ,L r ,1) The uniqueness condition of block term decomposition is expressed as: r′ A +r′ B ≥R+2 (3) In the formula, r′ A is the number of block submatrices; any r′ of matrix A A The set of block sub-matrices is a set of linearly independent columns; the following necessary conditions are further derived:

8. A slender aircraft structure operation modal parameter identification system, characterized in that: include: The data acquisition module is used to measure the vibration time domain response X at different positions of the slender aircraft structure through vibration tests, and express the vibration response as a third-order tensor using a segmentation operation The spectrum analysis module is used to perform spectrum analysis on the vibration time domain response. The number of active modes R of the structure is determined by searching the number of spectrum peaks of the vibration response and used as the rank of tensor decomposition. Decomposition module, used to decompose third-order tensors using tensor decomposition models Decompose to obtain a low-rank tensor with R sub-items of multilinear rank, and then convert the first mode sub-tensor A of each sub-item r With the second mode subtensor B r Multiply to obtain the low-rank matrix representation of each source signal The source signal vector is reconstructed by desegmentation operation, and the third mode subtensor c of each sub-item is r As the column vector of the mixing matrix, the mixing matrix M and the source signal S are estimated, where the mixing matrix corresponds to the modal vibration matrix and the source signal corresponds to the modal response; The modal parameter acquisition module is used to obtain the modal frequency modal parameters from the estimated source signal S.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for identifying the operating modal parameters of a slender aircraft structure as claimed in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for identifying the operating modal parameters of a slender aircraft structure as claimed in any one of claims 1 to 7 are implemented.

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