A modal identification method based on unsupervised optimization covariance stochastic subspace method

Abstract

The application discloses a modal identification method based on an unsupervised optimization covariance stochastic subspace method, and comprises the following steps: arranging vibration sensors on a to-be-measured structure with noise interference or weak excitation modes, and acquiring structural dynamic response data; calculating a covariance matrix and constructing a toply matrix; calculating an extended observable matrix and a controllable matrix based on the weighted toply matrix; defining a toply matrix row block number and a model order parameter range, and iteratively calculating a parameter optimization index; calculating a cumulative contribution rate based on a singular entropy increment of the toply matrix and determining a critical model order; calculating a cumulative parameter optimization index in an interval from a minimum model order to the critical model order under different toply matrix row block numbers, and determining an optimal parameter combination through an average minimum value; substituting the optimal parameter combination into a covariance stochastic subspace algorithm to identify a system matrix and calculate structural modal parameters; and automatically identifying each order physical mode from candidate modes by using a DBSCAN clustering method. The application further discloses a system and an electronic device.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics and operational modal analysis technology, and in particular to a modal identification method based on the unsupervised optimization covariance random subspace method. It is an unsupervised algorithm based on parameter optimization in the covariance-driven random subspace identification (SSI-Cov) method, which is used to improve the accuracy and robustness of modal parameter identification, thereby providing a scientific basis for structural health monitoring. Background Technology

[0002] In the field of structural health monitoring and condition assessment, accurate identification of structural modal parameters is crucial for ensuring the safe operation of infrastructure. The Stochastic Subspace Covariance-Covariance (SSI-Cov) method, as a parametric system identification method, is widely used in practical engineering due to its superior robustness and efficiency. Its accuracy primarily depends on two user-defined parameters: the model order. The number of row blocks of the Topulitz matrix (or Hankel matrix) On the one hand, the model order should theoretically be equal to the number of non-zero singular values ​​in the Toplitz matrix. However, in practical engineering, the presence of noise makes it difficult to determine the number of non-zero singular values. Therefore, a certain range of overestimated model orders is usually selected and substituted into SSI-Cov to identify the system, thus plotting the calculation results as a stability graph with frequency on the horizontal axis and model order on the vertical axis. A stable vertical polar axis formed at a certain frequency after calculations with multiple model orders is identified as a certain physical mode of the structure; otherwise, it is a spurious mode. However, an excessively high model order not only increases the computational load but also leads to a higher probability of spurious modes; an excessively low model order may result in mode omission or the misinterpretation of linear combinations of modes as a single identification mode, thus introducing identification bias. On the other hand, the number of rows in the Toplitz matrix... The magnitude of these parameters not only affects computational speed but also the accuracy of modal identification. Especially for the damping ratio, its significant uncertainty level is typically on the same order of magnitude as its estimated value, thus impacting the reliability of the identification results. Therefore, these input parameters severely influence the accuracy and reliability of the SSI-Cov method in identifying modes, making them crucial for applications such as state or damage assessment and health monitoring based on modal parameter changes or derived damage-sensitive indicators.

[0003] In recent years, structural operational modal analysis based on the Stochastic Subspace Identification (SSI) method has been widely applied. For example, patent application CN118673348A discloses a structural modal parameter identification method and system based on intelligent clustering of modal features; patent CN115200700B discloses a modal parameter identification method based on Welch's method and covariance stochastic subspace method; patent application CN116796615A discloses a structural modal parameter identification method based on stochastic subspace deep learning; patent application CN118820718A discloses a structural modal parameter identification method, system, and medium; and patent CN115357853B discloses an engineering structure modal parameter identification method based on fast stochastic subspace, etc. However, currently, the parameter settings of the SSI-Cov method mainly rely on the professional experience of technicians, making it difficult to avoid human intervention and subjectivity, which directly affects the accuracy and consistency of the modal identification results. Therefore, there is an urgent need to develop an SSI-Cov modal recognition method based on unsupervised optimization of key parameters to automatically determine the optimal model order and the number of rows and blocks in the Toplitz matrix, thereby eliminating the uncertainty caused by manual parameter tuning. Through unsupervised optimization algorithms, input parameters are intelligently screened and optimized, significantly improving the accuracy and robustness of the recognition results, and providing more reliable data support for subsequent damage assessment and health monitoring based on modal parameter recognition. Summary of the Invention

[0004] The purpose of this invention is to provide a modality recognition method and system based on the unsupervised optimization covariance random subspace method to address the shortcomings of existing technologies. Specifically, it addresses the problems of traditional covariance-driven random subspace identification (SSI-Cov) methods, such as reliance on human experience in parameter setting, susceptibility to noise interference, and inappropriate model order selection during modality recognition. This invention proposes a parameter optimization method based on sensitivity analysis. This method constructs a Toplitz matrix and calculates the extended observable matrix and the extended controllable matrix. Within a preset parameter range, it establishes parameter optimization indices and iteratively analyzes parameter combinations of the number of rows in the Toplitz matrix and the model order. Furthermore, it calculates the singular entropy increments corresponding to the singular values ​​of the Toplitz matrix and determines the critical model order based on the cumulative contribution rate of the singular entropy increments, thereby achieving adaptive determination of the model order. Based on this, it calculates the average value of the parameter optimization indices within the model order interval and selects the parameter combination corresponding to the average minimum value as the optimal parameters, achieving joint optimization of the number of rows in the Toplitz matrix and the model order. Finally, the optimized parameter combination is substituted into the covariance random subspace identification algorithm to solve the system matrix and calculate the structure's natural frequency, damping ratio, and mode shape, etc. The candidate modes are then automatically classified using the DBSCAN clustering method, thereby realizing the automatic identification of the physical modes of the structure under noisy conditions and improving the stability and reliability of mode identification.

[0005] The first aspect of this invention is to provide a modality recognition method based on the unsupervised optimization covariance random subspace method, comprising:

[0006] S1, Vibration sensors are placed on the structure under test where there is noise interference or weak excitation mode to obtain the structural dynamic response data of the structure under test;

[0007] S2, Calculate the covariance matrix based on the structural dynamic response data under the conditions of noise interference or weak excitation. , and by Constructing the Toplitz matrix ;

[0008] S3, based on the weighted Topelitz matrix Compute the extended observable matrix and extended controllable matrix ;

[0009] S4, Defines the number of row blocks in a Topulitz matrix. and model order The parameter range;

[0010] S5, within the preset number of rows and blocks of the Toplitz matrix. and model order Within the range of parameter combinations, iterate through and calculate parameter optimization indices. ;

[0011] S6, based on the Topulitz matrix The cumulative contribution rate of the singular entropy increment is calculated to determine the critical model order. ;

[0012] S7, Calculate the number of row blocks for different Toplitz matrices. In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; Select parameter optimization index within the model order range [ , The average minimum value is used as the optimal parameter combination. ;

[0013] S8, combining the optimized parameters The modal parameters are calculated by substituting them into the covariance random subspace algorithm and then automatically identifying each physical mode using DBSCAN clustering. The modal parameters include natural frequency, damping ratio, and mode shape coefficient.

[0014] Preferably, S2 includes:

[0015] S21, assuming the output data is ergodic under noise interference, calculate the covariance matrix based on the structural dynamic response. The covariance matrix Represented as equation (1):

[0016] (1);

[0017] In equation (1), , indicating arrangement One sensor A system of degrees of freedom at discrete time The observation vector, i.e., the acceleration, velocity, or displacement within the time history of the measured signal, where Indicates the length of the delay time; The sequence corresponding to the maximum sampling time utilized. Indicates matrix transpose;

[0018] S22, based on the covariance matrix Constructing the Toplitz matrix , expressed as equation (2):

[0019] (2);

[0020] In equation (2), It also corresponds to a matrix The number of rows and blocks.

[0021] Preferably, S3 includes:

[0022] S31, Calculate the singular values, where the singular values ​​are equal to those derived from the Topulitz matrix. The number of singular values ​​obtained by the singular value decomposition is shown in equation (3):

[0023] (3);

[0024] In equation (3), and It is an orthogonal matrix. and It is an orthogonal matrix. It is a diagonal matrix;

[0025] S32, considering the modal weak excitation condition under noise interference or environmental excitation, the matrix... Multiplying by an invertible weighted matrix Multiply by an invertible weighted matrix Calculate the singular values ​​of the weighted Toplitz matrix and omit the zero singular values ​​to obtain the extended observable matrix. and extended controllable matrix As shown in equations (4) and (5) respectively:

[0026] (4);

[0027] (5);

[0028] In equations (4) and (5), Represents the pseudo-inverse of a matrix. and Assume there exists a lower triangular matrix. and ,but:

[0029] (6);

[0030] (7);

[0031] Invertible weighted matrix and invertible weighted matrix The calculation results are shown in equation (8):

[0032] , (8).

[0033] Preferably, S4 includes:

[0034] S41, Determine the number of row blocks of the Toplitz matrix based on the sampling frequency and the structural fundamental frequency. lower limit As shown in equation (9); the model order is determined based on the peak value of the power spectral density function. lower limit As shown in equation (10);

[0035] (9);

[0036] (10);

[0037] In the formula, This is the ratio of the sampling frequency to the fundamental frequency of the structure. The number of peaks in the power spectral density function of the structural dynamic response signal;

[0038] S42, based on equations (9) and (10) and constraints ≥ Determine the number of rows in the Toplitz matrix respectively upper limit and model order upper limit :

[0039] (11);

[0040] (12);

[0041] In the formula, and This is the parameter range magnification factor, typically ranging from 5 to 20.

[0042] Preferably, S5 includes:

[0043] Based on parameter { , The range of} Through equation (13), for each pair of parameters in the range { , } Optimize metrics The calculation; that is, the calculation of the extended observable matrix. and extended controllable matrix The product of condition numbers, :

[0044] (13);

[0045] In the formula, and Let represent the maximum singular value and the minimum non-zero singular value in the singular value decomposition of a matrix, respectively.

[0046] Preferably, S6 includes:

[0047] S61, for each parameter The constructed Toplitz matrix is ​​calculated according to equation (14). Singular entropy increment:

[0048] (14);

[0049] In the formula, Refers to the increase in singular entropy. and Pointer matrix eigenvalues.

[0050] S62, calculate the cumulative contribution rate of the singular entropy increment, including:

[0051] For each parameter The cumulative contribution rate of the singular entropy increment is calculated according to equation (15):

[0052] (15);

[0053] In the formula, This represents the cumulative contribution rate of the singular entropy increment corresponding to the first p singular values; This represents the singular entropy increment corresponding to the k-th singular value; Indicates the total number of singular values;

[0054] S63, Calculate the critical model order based on the cumulative contribution rate of singular entropy increments. ,include:

[0055] For different Value, when the cumulative contribution rate The first time the preset threshold was reached At that time, the corresponding model order p is determined as the critical model order. The threshold value range is: .

[0056] Preferably, S7 includes:

[0057] Calculate the number of rows in different Toplitz matrices In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; to improve the stability of evaluation results for different parameter combinations, the parameter optimization index is calculated within the model order range [ , The average minimum value is used as the optimal parameter. As shown in equation (16):

[0058] (16);

[0059] In the formula, It is the specified calculation based on step S63 The critical model order under the given value.

[0060] Preferably, S8 includes:

[0061] S81, using the optimized optimal parameters Identifying the system matrix includes: expressing the system matrix A as equation (17) as follows:

[0062] (17);

[0063] In equation (17), Observable matrix The former OK, for After The modal parameters of the discrete-time system are obtained from the system matrix A and the output matrix C, wherein the output matrix C is equal to the modal parameters in equation (4). The former OK;

[0064] S82, Determine the modal parameters, including:

[0065] (1) The system matrix A is decomposed by eigenvalues ​​to obtain equation (18):

[0066] (18);

[0067] In the formula, The system poles of the discrete-time system The diagonal matrix formed; The right eigenvectors of matrix A correspond to the continuous-time eigenvalues; while the continuous-time eigenvalues... and eigenvalues ​​in discrete states The following relationship is satisfied, as shown in equation (19):

[0068] (19);

[0069] In the formula, Indicates the sampling time interval;

[0070] (2) Determine the natural frequency of the system using equation (20). Damping ratio and mode shape coefficient ;

[0071] (20);

[0072] S83, based on the calculated two-dimensional data of frequency and damping ratio, automatically identifies each physical mode from candidate modes containing noise interference using DBSCAN clustering, where the two key parameters of DBSCAN are set as follows:

[0073] (twenty one);

[0074] In the formula, To minimize the number of clustered sample points, The clustering neighborhood radius, The number of frequencies calculated for the random subspace.

[0075] A second aspect of the present invention provides a modality recognition system based on the unsupervised optimization covariance random subspace method, for implementing the method of the first aspect, comprising:

[0076] The structural dynamic response acquisition module (101) is used to arrange vibration sensors on the structure under test where there is noise interference or weak excitation mode, wherein the vibration sensors are used to acquire the structural dynamic response data of the structure under test.

[0077] The Toplitz matrix construction module (102) is used to directly calculate the covariance matrix based on the structural dynamic response data. , and by Constructing the Toplitz matrix ;

[0078] The observable and controllable matrix calculation module (103) is used to calculate the observable and controllable matrices based on the weighted Toplitz matrix. Compute the extended observable matrix and extended controllable matrix ;

[0079] The parameter range definition module (104) is used to define the number of row blocks in the Toplitz matrix. and model order Scope;

[0080] The optimization index calculation module (105) is used to calculate the parameter optimization index within a preset parameter range;

[0081] The critical model order determination module (106) is used to calculate the weighted Toplitz matrix. The contribution rate of singular entropy increment is used to determine the critical model order. ;

[0082] The optimal parameter combination determination module (107) is used to calculate the number of row blocks for different Toplitz matrices. In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; Select parameter optimization index within the model order range [ , The average minimum value is used as the optimal parameter combination;

[0083] The modal automatic identification module (108) based on the optimized parameters is used to utilize the optimized optimal parameters. The system matrix is ​​identified and modal parameters are determined. DBSCAN clustering is used to automatically identify physical modes from candidate modes containing noise interference. The modal parameters include natural frequency, damping ratio and mode shape coefficient.

[0084] A third aspect of the present invention provides an electronic device including a processor and a memory, the memory storing a plurality of instructions, the processor being configured to read the instructions and execute the method as described in the first aspect.

[0085] A fourth aspect of the present invention provides a computer-readable storage medium storing a plurality of instructions which can be read by a processor and executed as described in the first aspect.

[0086] The beneficial effects of the methods and systems, electronic devices, and computer-readable storage media of the present invention are as follows:

[0087] In structural vibration environments with noise interference or weak excitation modes, a parameter optimization index is constructed by multiplying the condition number of the extended observable matrix and the extended controllable matrix. Within a preset parameter range, the number of rows and blocks in the Toplitz matrix and the model order are traversed and analyzed. Furthermore, the singular entropy increments corresponding to the singular values ​​of the Toplitz matrix are calculated, and the critical model order is determined based on the cumulative contribution rate of the singular entropy increments, thereby achieving adaptive determination of the model order. On this basis, by statistically analyzing the parameter optimization indexes within the model order interval and selecting the parameter combination corresponding to the average minimum value as the optimal parameters, the joint optimization of the number of rows and blocks in the Toplitz matrix and the model order is achieved. By utilizing optimized parameter combinations to perform covariance random subspace identification calculations and combining them with the DBSCAN clustering method to automatically classify and identify candidate modes, the system can stably identify modal parameters such as natural frequencies, damping ratios, and mode shapes of structures under noisy or weakly excited modal conditions. This significantly improves the automation and robustness of modal identification, avoids the dependence on empirical parameter selection and the uncertainty caused by overestimation of model order in traditional methods, and provides more reliable technical support for structural health monitoring and damage assessment. Attached Figure Description

[0088] To more clearly illustrate the technical solutions in the specific embodiments or related technologies of the present invention, the drawings used in the description of the specific embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0089] Figure 1 This is a flowchart of a modality recognition method based on the unsupervised optimization covariance random subspace method provided in an embodiment of the present invention;

[0090] Figure 2 This is a diagram illustrating the architecture of a modality recognition system based on the unsupervised optimization covariance random subspace method according to an embodiment of the present invention.

[0091] Figure 3 This represents the power spectral density of the structural response in the numerical example of Embodiment 1 of the present invention.

[0092] Figure 4 This refers to the 7-DOF mass-spring-damping system in Embodiment 1 of the present invention.

[0093] Figure 5The critical model order determined based on the cumulative contribution rate of singular entropy increment in Embodiment 1 of the present invention;

[0094] Figure 6 These are the parameter optimization indices calculated under different parameter combinations in Embodiment 1 of the present invention;

[0095] Figure 7 This is a frequency-damping ratio result diagram automatically identified based on optimal parameters in Embodiment 1 of the present invention;

[0096] Figure 8 This is a structural diagram of an electronic device provided according to an embodiment of the present invention. Detailed Implementation

[0097] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0098] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0099] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0100] Example 1

[0101] like Figure 1 As shown in the figure, this embodiment provides a flowchart of a modality recognition method based on the unsupervised optimization covariance random subspace method; as follows... Figure 2 As shown, this second embodiment provides a modality recognition system based on the unsupervised optimization covariance random subspace method, which is used to implement the method of the first embodiment.

[0102] In Example 1, a multi-degree-of-freedom structural dynamics model is constructed for algorithm verification. This model is a seven-degree-of-freedom mass-spring-damped system (see...). Figure 3 This model is used to simulate the structural vibration response under environmental excitation conditions. In the model, the mass of each layer is taken as a uniform unit mass, the inter-layer stiffness is set to the same stiffness coefficient, and the system damping matrix is ​​established using a Rayleigh damping model. During the simulation, random excitation is applied to each degree of freedom to simulate environmental loads. Specifically, Gaussian white noise with a mean of 0 and a variance of 1 is generated using the MATLAB platform as the input excitation signal, and the response of the dynamic system is calculated using a linear system simulation function. Simultaneously, to simulate measurement noise present in actual engineering tests, random noise of a certain intensity is superimposed on the system output signal to obtain structural response data closer to actual working conditions. The system response is recorded in the form of acceleration. Based on sampling theory, the response of each degree of freedom of the structure is discretely sampled at a fixed sampling frequency, and a response sequence is continuously recorded for a relatively long period to obtain sufficient dynamic response data yi(t) for subsequent modal identification calculations. In this embodiment, the sampling frequency is set to 5Hz, and the sampling duration is 3000s, thus obtaining the acceleration response time history data of each measuring point.

[0103] The specific implementation steps for structural modal parameter identification are described below:

[0104] Based on the output response signals of each layer We obtained structural dynamic response data under environmental excitation.

[0105] The covariance matrix is ​​directly calculated based on the dynamic response data under noisy conditions. And by Constructing the Toplitz matrix .

[0106] According to the weighted Topplitz matrix Compute the extended observable matrix and extended controllable matrix .

[0107] Based on the response spectrum results containing 10dB noise interference ( Figure 4 The fundamental frequency of this numerical model The frequency is 0.105 Hz, and there are at least 6 distinct peaks. =6), and therefore according to the formula The lower limit of the model order is determined to be 12. Based on... The minimum number of rows in the Topulitz matrix can be set. The value is 25. Furthermore, the peak of the 7th mode is submerged under noise interference, forming a typical weakly excited mode.

[0108] Determine the parameters { , The range of values ​​for} is Two of the parameters and The increments are set to 5 and 4 respectively.

[0109] Calculate each parameter combination { , The optimization metrics under}

[0110] According to the weighting matrix The cumulative contribution rate of singular entropy increment (threshold) ), to obtain different Critical model order at value ( Figure 5 ).

[0111] The optimal parameters automatically determined by the corresponding algorithm of this invention are { =50, =38}( Figure 6 ).

[0112] Based on DBSCAN clustering, the physical modes of the structure are automatically identified, and the final frequency-damping ratio diagram is obtained. Figure 7 ).

[0113] Table 1 lists the theoretical and identified modes of the numerical model, including the frequencies, damping ratios, and relative error statistics of the first seven identified modes compared to their theoretical values. The results show that the errors in frequency and mode shape are extremely small (average errors of 0.001 and 0.004, respectively), and the average error in damping ratio is 0.148.

[0114] Table 1

[0115]

[0116] The present invention also provides a memory that stores multiple instructions for implementing the method as described in Embodiment 1.

[0117] like Figure 8 As shown, the present invention also provides an electronic device, including a processor 301 and a memory 302 connected to the processor 301. The memory 302 stores a plurality of instructions, which can be loaded and executed by the processor to enable the processor to perform the method as described in Embodiment 1.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modality recognition method based on unsupervised optimization of covariance random subspace, characterized in that, include: S1, Vibration sensors are placed on the structure under test where there is noise interference or weak excitation mode to obtain the structural dynamic response data of the structure under test; S2, Calculate the covariance matrix based on the structural dynamic response data under the conditions of noise interference or weak excitation. , and by Constructing the Toplitz matrix ; S3, based on the weighted Topelitz matrix Compute the extended observable matrix and extended controllable matrix ; S4, Defines the number of row blocks in a Topulitz matrix. and model order The parameter range; S5, within the preset number of rows and blocks of the Toplitz matrix. and model order Within the range of parameter combinations, iterate through and calculate parameter optimization indices. ; S6, based on the Topulitz matrix The cumulative contribution rate of the singular entropy increment is calculated to determine the critical model order. ; S7, Calculate the number of row blocks for different Toplitz matrices. In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; Select parameter optimization index within the model order range [ , The average minimum value is used as the optimal parameter combination. ; S8, combining the optimized parameters The modal parameters are calculated by substituting them into the covariance random subspace algorithm and then automatically identifying each physical mode using DBSCAN clustering. The modal parameters include natural frequency, damping ratio, and mode shape coefficient.

2. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 1, characterized in that, S2 includes: S21, assuming the output data is ergodic under noise interference, calculate the covariance matrix based on the structural dynamic response. The covariance matrix Represented as equation (1): （1）； In equation (1), , indicating arrangement One sensor A system of degrees of freedom at discrete time The observation vector, i.e., the acceleration, velocity, or displacement within the time history of the measured signal, where Indicates the length of the delay time; The sequence corresponding to the maximum sampling time utilized. Indicates matrix transpose; S22, based on the covariance matrix Constructing the Toplitz matrix , expressed as equation (2): （2）； In equation (2), It also corresponds to a matrix The number of rows and blocks.

3. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 2, characterized in that, S3 includes: S31, Calculate the singular values, where the singular values ​​are equal to those derived from the Topulitz matrix. The number of singular values ​​obtained by the singular value decomposition is shown in equation (3): （3）； In equation (3), and It is an orthogonal matrix. and It is an orthogonal matrix. It is a diagonal matrix; S32, considering the modal weak excitation condition under noise interference or environmental excitation, the matrix... Multiplying by an invertible weighted matrix Multiply by an invertible weighted matrix Calculate the singular values ​​of the weighted Toplitz matrix and omit the zero singular values ​​to obtain the extended observable matrix. and extended controllable matrix As shown in equations (4) and (5) respectively: （4）； （5）； In equations (4) and (5), Represents the pseudo-inverse of a matrix. and Assume there exists a lower triangular matrix. and ,but: （6）； （7）； Invertible weighted matrix and invertible weighted matrix The calculation results are shown in equation (8): , （8）。 4. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 3, characterized in that, S4 includes: S41, Determine the number of row blocks of the Topulitz matrix based on the sampling frequency and the structural fundamental frequency. lower limit As shown in equation (9); the model order is determined based on the peak value of the power spectral density function. lower limit As shown in equation (10); （9）； （10）； In the formula, This is the ratio of the sampling frequency to the fundamental frequency of the structure. The number of peaks in the power spectral density function of the structural dynamic response signal; S42, based on equations (9) and (10) and constraints ≥ Determine the number of rows in the Toplitz matrix respectively upper limit and model order upper limit : （11）； （12）； In the formula, and This is the parameter range magnification factor.

5. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 4, characterized in that, S5 includes: Based on parameter { , The range of} Through equation (13), for each pair of parameters in the range { , } Optimize metrics The calculation; that is, the calculation of the extended observable matrix. and extended controllable matrix The product of condition numbers, : （13）； In the formula, and Let represent the maximum singular value and the minimum non-zero singular value in the singular value decomposition of a matrix, respectively.

6. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 5, characterized in that, S6 includes: S61, for each parameter The constructed Toplitz matrix is ​​calculated according to equation (14). Singular entropy increment: （14）； In the formula, Refers to the singular entropy increment. and Pointer matrix eigenvalues; S62, calculate the cumulative contribution rate of the singular entropy increment, including: For each parameter The cumulative contribution rate of the singular entropy increment is calculated according to equation (15): （15）； In the formula, This represents the cumulative contribution rate of the singular entropy increment corresponding to the first p singular values; This represents the singular entropy increment corresponding to the k-th singular value; This represents the total number of singular values; S63, Calculate the critical model order based on the cumulative contribution rate of singular entropy increments. ,include: For different Value, when the cumulative contribution rate The first time the preset threshold was reached At that time, the corresponding model order p is determined as the critical model order. The threshold value range is: .

7. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 6, characterized in that, S7 includes: Calculate the number of rows in different Toplitz matrices In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; to improve the stability of evaluation results for different parameter combinations, the parameter optimization index is calculated within the model order range [ , The average minimum value is used as the optimal parameter. As shown in equation (16): （16）； In the formula, It is the specified calculation based on step S63 The critical model order under the given value.

8. The modality recognition method based on the unsupervised optimization covariance random subspace method according to claim 7, characterized in that, S8 includes: S81, using the optimized parameters Identifying the system matrix includes: expressing the system matrix A as equation (17) as follows: （17）； In equation (17), Observable matrix The former OK, for After The modal parameters of the discrete-time system are obtained from the system matrix A and the output matrix C, wherein the output matrix C is equal to the modal parameters in equation (4). The former OK; S82, Determine the modal parameters, including: decomposing the system matrix A using eigenvalues ​​and further determining the system's natural frequencies. Damping ratio and mode shape coefficient ; S83, based on the calculated two-dimensional data of frequency and damping ratio, automatically identifies each physical mode from candidate modes containing noise interference using DBSCAN clustering, where the two key parameters of DBSCAN are set as follows: （18）； In the formula, To minimize the number of clustered sample points, The clustering neighborhood radius, The number of frequencies calculated for the random subspace.

9. A modal recognition system based on the unsupervised optimization covariance random subspace method, used to implement the method described in any one of claims 1-8, characterized in that, include: The structural dynamic response acquisition module (101) is used to arrange vibration sensors on the structure under test where there is noise interference or weak excitation mode, wherein the vibration sensors are used to acquire the structural dynamic response data of the structure under test. The Toplitz matrix construction module (102) is used to directly calculate the covariance matrix based on the structural dynamic response data. , and by Constructing the Toplitz matrix ; The observable and controllable matrix calculation module (103) is used to calculate the observable and controllable matrices based on the weighted Toplitz matrix. Compute the extended observable matrix and extended controllable matrix ; The parameter range definition module (104) is used to define the number of row blocks in the Toplitz matrix. and model order Scope; The optimization index calculation module (105) is used to calculate the parameter optimization index within a preset parameter range; The critical model order determination module (106) is used to calculate the weighted Toplitz matrix. The contribution rate of singular entropy increment is used to determine the critical model order. ; The optimal parameter combination determination module (107) is used to calculate the number of row blocks for different Toplitz matrices. In the case of minimum model order To the critical model order Cumulative parameter optimization index Value; Select parameter optimization index within the model order range [ , The average minimum value is used as the optimal parameter combination; The modal automatic identification module (108) based on the optimized parameters is used to utilize the optimized optimal parameters. The system matrix is ​​identified and modal parameters are determined. DBSCAN clustering is used to automatically identify physical modes from candidate modes containing noise interference. The modal parameters include natural frequency, damping ratio and mode shape coefficient.

10. An electronic device comprising a processor and a memory, the memory storing a plurality of instructions, the processor being configured to read the instructions and execute the method as claimed in any one of claims 1-8.

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