An improved random subspace identification method based on MCKF and DBSCAN

Abstract

The application relates to an improved random subspace identification method based on MCKF and DBSCAN, and belongs to the technical field of structural health monitoring and signal processing, which comprises an MCKF denoising pretreatment module, a COV-SSI identification module and a DBSCAN clustering post-processing module, and comprises the following steps: S1, directly analyzing a measurement response signal by using the COV-SSI identification module to estimate an initial system state matrix F and a measurement matrix H of MCKF; S2, setting parameters of MCKF in the MCKF denoising pretreatment module, and realizing the reduction of measurement noise in the measurement response signal in step S1 by using the MCKF denoising pretreatment module; S3, identifying structural parameters by using the COV-SSI identification module, inputting the measurement response signal pretreated in step S2, and recalculating the system state matrix and the measurement matrix according to step S1; and S4, adopting the DBSCAN clustering post-processing module to cluster the result identified in step S3; the method can effectively reduce measurement noise, improve data quality and signal quality, and improve the robustness and accuracy of modal parameter identification.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring and signal processing, and relates to an improved random subspace identification method based on MCKF and DBSCAN. Background Art

[0002] Structural parameter identification is a core technology for health monitoring and safety assessment of engineering structures. By accurately analyzing the dynamic characteristics (e.g., natural frequencies, damping ratios, and modal shapes) of complex structural systems (such as high-rise buildings, long-span bridges, and transmission tower-line systems), it provides a key basis for structural damage diagnosis, performance degradation assessment, and service life prediction. During the service life of a structure, factors such as environmental excitation (e.g., earthquakes, waves, and wind), material aging, and manufacturing defects can cause significant changes in physical parameters such as structural stiffness and damping, directly impacting the safety and durability of the structure. In this context, accurate identification of structural parameters is crucial for structural health monitoring, damage diagnosis, and performance assessment.

[0003] OMA (Operational Modal Analysis) has become a mainstream method for parameter identification, thanks to its advantages of eliminating the need for artificial excitation and avoiding structural damage. OMA generally encompasses two main approaches: frequency-domain and time-domain methods. Both have achieved significant success in identifying basic structural parameters. Among these, stochastic subspace identification (SSI) is highly favored for its high accuracy and stability. The performance of SSI is closely related to the quality of the response signal. However, in practical applications, sensor measurement noise significantly impacts the quality of the response signal. This noise primarily stems from the inherent physical properties of the sensor and interference from external environmental factors. There are two types of measurement noise: Gaussian white noise (such as Johnson noise) and non-Gaussian colored noise (such as flicker noise). These noises not only increase signal complexity but can even mask the original signal characteristics, leading to suboptimal parameter estimation, particularly for identifying structural damping. When the signal-to-noise ratio is low, the variability of the estimated parameters can significantly increase, thereby reducing identification accuracy.

[0004] The Maximum Correlation Entropy Kalman Filter (MCKF) is an algorithm for estimating the state of dynamic systems, commonly used in target tracking, navigation systems, and signal processing. DBSCAN is a density-based clustering algorithm that can partition regions of sufficiently high density into clusters and can handle noisy data. Covariance Random Subspace Identification (COV-SSI) is a system identification method for modal parameter identification (such as frequency, damping ratio, and mode shape). It is commonly used in structural health monitoring and vibration analysis of bridges and buildings. However, for COV-SSI, measurement noise inevitably produces some spurious modes, which seriously affect the manual selection and extraction of physical modes on stability diagrams.

[0005] Therefore, how to realize automatic high-precision identification of structural parameters in a complex noise environment is a technical problem to be solved by those skilled in the art at present, and there is an urgent need for a method capable of realizing automatic high-precision identification of structural parameters in a complex noise environment. SUMMARY

[0006] Therefore, in order to solve the problem that the existing structural parameter identification method is difficult to realize high-precision automatic identification of structural modal parameters in a measurement noise environment and has poor applicability, the application provides an improved random subspace identification method based on MCKF and DBSCAN, which can realize high-precision automatic identification of structural modal parameters in a Gaussian and non-Gaussian noise environment.

[0007] To achieve the above purpose, the application provides the following technical scheme:

[0008] An improved random subspace identification method based on MCKF and DBSCAN, comprising an MCKF noise reduction preprocessing module, a COV-SSI identification module and a DBSCAN clustering post-processing module, the space identification method specifically comprises the following steps:

[0009] S1, the COV-SSI identification module is used to directly analyze the measurement response signal, and the initial system state matrix F and the measurement matrix H of the MCKF are estimated; specifically comprising the following steps:

[0010] S11, according to the measurement response signal , the Toeplitz matrix is constructed by the output covariance matrix:

[0011] (1)

[0012] Wherein, , respectively represent the Toeplitz matrix and the output covariance matrix; in the formula , wherein , respectively represent the total time of the measurement response signal and the measurement response signal at time

[0013] S12, singular value decomposition (SVD) is used to decompose the Toeplitz matrix, that is:

[0014] (2)

[0015] In the formula, and are orthogonal normalized matrices;

[0016] S13, according to the singular value decomposition (SVD) result, the extended observable matrix and the controllability matrix Expressed as:

[0017] (3)

[0018] In the formula is a non-singular matrix;

[0019] S14. By extending the observable matrix and the controllability matrix , calculate the initial system state matrix and the measurement matrix Available through Obtain, that is:

[0020] (4)

[0021] in, Indicates the number of output channels; where represents pseudo-inverse;

[0022] S2, in the MCKF noise reduction preprocessing module, the parameters of MCKF are set, including the initial estimated state, the initial error covariance matrix, the process noise covariance matrix and the measurement noise covariance matrix, and then the MCKF noise reduction preprocessing module is utilized to realize the reduction of the measurement noise in the measurement response signal in the above step S1;

[0023] S3, use the COV-SSI identification module to identify the structural parameters (i.e., the modal frequency and damping ratio of the system), input the measured response signal after pre-processing in step S2 above, and recalculate the system state matrix according to formulas 1-4 in step S1 and the measurement matrix ;

[0024] S4. Use the DBSCAN clustering post-processing module to cluster the results identified in step S3.

[0025] Furthermore, step S1 also includes:

[0026] For any one with For a system with 1 degree of freedom, its dynamic motion process can be described by the discrete state space model given below:

[0027] (17)

[0028] In the formula For time point The discrete state vector of Indicates a time point The discrete output vector of Represented as the discrete state vector at time point k+1, 、 express and and Multiply them separately; and They are denoted as process noise and output noise respectively, where their covariance matrix is ​​defined as:

[0029] (18)

[0030] In the formula Represents an operation to obtain an expected value; is the Kronecker delta function; and are any two time points; the process noise covariance matrix is a non-negative definite matrix, the observation noise covariance matrix is a positive definite matrix;

[0031] The Hankel matrix is ​​expressed as:

[0032] (19)

[0033] In the formula express The output signals of different sensors at different times; the Hankel matrix can be expressed as the division of two components, that is, and , where the subscript and They represent 'past' and 'future' respectively.

[0034] Furthermore, step S2 specifically includes the following steps:

[0035] S21. Calculate the prior state and covariance matrix: Prior state and the covariance matrix Calculated by the following formula:

[0036] (5)

[0037] In the formula and Respectively indicate time The estimated state and covariance matrix of , Indicates time The process noise covariance matrix at ;

[0038] S22. Update estimated state: initial estimated state and the error covariance matrix Set to 0 and I respectively, according to the measured response signal Update estimate status ;

[0039] (6)

[0040] (7)

[0041] in represents the Kalman gain matrix; in formula (7) and Expressed as:

[0042] (8)

[0043] In the formula and By respectively analyzing the prior covariance matrix and the measurement noise covariance matrix At time step Perform Cholesky decomposition at and The diagonal matrix defined by the following equation:

[0044] (9)

[0045] (10)

[0046] In the formula The kernel bandwidth is Gaussian kernel function; and Respectively No. elements and No. OK; and The expression is:

[0047] (11)

[0048] Can be achieved by The Cholesky decomposition of is obtained;

[0049] S23. Update estimated status: estimated status Determine by iteratively solving equations 6-11, then, the posterior error covariance Updated by the following equation:

[0050] (12)

[0051] S24, Iterative solution: MCKF realizes the response signal by iterative solution of the above formulas 5-12 The extraction of the measurement noise.

[0052] Further, step S3 specifically comprises:

[0053] Discrete-time eigenvalues And modal shape Defined as:

[0054] (13)

[0055] Where Is the eigenvector corresponding to the eigenvalue On this basis, the continuous-time pole of the system matrix is given by:

[0056] (14)

[0057] Where Denotes the sampling time interval, Denotes the continuous-time pole of the system matrix;

[0058] According to formula 14, the modal frequency And the damping ratio Of the system are expressed as:

[0059] (15)

[0060] (16).

[0061] Further, step S4 specifically comprises the following steps:

[0062] S41, The frequency and damping data identified by the COV-SSI identification module are preprocessed, normalized, and ensured to meet the following two conditions: a) The damping ratio of the physical mode must be positive; b) In practical applications, high-damping modes with a damping ratio exceeding 10% rarely occur;

[0063] S42, Set the parameters of DBSCAN, including neighborhood radius ε and minimum cluster number MinPts; select an unvisited frequency and damping data point;

[0064] S43, Calculate the number of data points in its ε neighborhood, if the number is greater than or equal to MinPts, mark it as a core object; otherwise, mark it as a noise point;

[0065] S44, Use density accessibility to expand clusters from core objects;

[0066] S45, Repeat steps S3-S4 above until it cannot be expanded;

[0067] S46. Mark all unvisited points as noise;

[0068] S47. Each cluster consists of frequency and damping core points and their reachable points; then, the determined modal frequencies and damping ratios are obtained through each cluster.

[0069] The beneficial effects of the present invention are:

[0070] 1. This method discloses an improved random subspace identification method based on MCKF and DBSCAN, which uses the COV-SSI identification module to directly analyze the measurement response signal, and then uses the MCKF noise reduction preprocessing module to reduce the measurement noise in the measurement response signal. The preprocessed measurement response signal is input and the system state matrix is ​​recalculated. and the measurement matrix The DBSCAN clustering post-processing module is used to cluster the identification results, and the determined modal frequency and damping ratio are obtained through each cluster; this method realizes high-precision automatic identification of structural modal parameters in Gaussian and non-Gaussian noise environments.

[0071] 2. This method discloses an improved random subspace identification method based on MCKF and DBSCAN. The MCKF noise reduction preprocessing module is used to suppress non-Gaussian noise, which can effectively reduce measurement noise and improve data quality and signal quality. The COV-SSI identification module uses a covariance-driven random subspace method to accurately estimate the system state matrix and measurement matrix. The DBSCAN clustering post-processing module removes outliers and improves the robustness and accuracy of modal parameter identification.

[0072] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0074] Figure 1 Flowchart of the improved random subspace identification method based on MCKF and DBSCAN of the present invention;

[0075] Figure 2 This is a 3-DOF model diagram in this embodiment. DETAILED DESCRIPTION

[0076] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0077] like Figure 1 An improved random subspace identification method based on MCKF and DBSCAN is shown, including an MCKF noise reduction preprocessing module, a COV-SSI identification module and a DBSCAN clustering post-processing module. The spatial identification method specifically includes the following steps:

[0078] S1. Use the COV-SSI identification module to directly analyze the measurement response signal and estimate the initial system state matrix F and measurement matrix H of the MCKF.

[0079] Specifically: For any one with For a system with 1 degree of freedom, its dynamic motion process can be described by the discrete state space model given below:

[0080] (17)

[0081] In the formula For time point The discrete state vector of Indicates a time point The discrete output vector of Represented as the discrete state vector at time point k+1, 、 express and and Multiply them separately; and They are denoted as process noise and output noise respectively, where their covariance matrix is ​​defined as:

[0082] (18)

[0083] In the formula Represents an operation to obtain an expected value; is the Kronecker delta function; and are any two time points; the process noise covariance matrix is a non-negative definite matrix, the observation noise covariance matrix is a positive definite matrix;

[0084] The Hankel matrix is ​​expressed as:

[0085] (19)

[0086] In the formula express The output signals of different sensors at different times; the Hankel matrix can be expressed as the division of two components, that is, and , where the subscript and They represent 'past' and 'future' respectively.

[0087] The specific steps include:

[0088] S11, according to the measurement response signal , construct the Toeplitz matrix by outputting the covariance matrix:

[0089] (1)

[0090] in, 、 Represent the Toeplitz matrix and output covariance matrix respectively; where ,in 、 Represent the total time and time of measuring the response signal respectively The response signal is measured at all times.

[0091] S12. Use singular value decomposition (SVD) to decompose the Toeplitz matrix, that is:

[0092] (2)

[0093] In the formula and is an orthonormalized matrix.

[0094] S13. Then, based on the singular value decomposition (SVD) results, the extended observable matrix is ​​constructed and the controllability matrix Expressed as:

[0095] (3)

[0096] In the formula is a non-singular matrix.

[0097] S14. By extending the observable matrix and the controllability matrix , calculate the initial system state matrix and the measurement matrix Available through Obtain, that is:

[0098] (4)

[0099] in, Indicates the number of output channels; where the symbol represents the pseudo-inverse.

[0100] S2. Setting the MCKF parameters in the MCKF noise reduction preprocessing module, including the initial estimated state, the initial error covariance matrix, the process noise covariance matrix, and the measurement noise covariance matrix, and then using the MCKF noise reduction preprocessing module to achieve the reduction of the measurement noise in the measurement response signal in step S1 above.

[0101] It specifically includes the following steps:

[0102] S21. Calculate the prior state and covariance matrix: Prior state and covariance matrix Calculated by the following formula:

[0103] (5)

[0104] In the formula and Respectively indicate time The estimated state and covariance matrix of , Indicates time The process noise covariance matrix at .

[0105] S22. Update estimated state: initial estimated state and the initial covariance matrix Set to 0 and I respectively, according to the measured response signal Update estimate status ;

[0106] (6)

[0107] (7)

[0108] in represents the Kalman gain matrix; in formula (7) and Expressed as:

[0109] (8)

[0110] In the formula and By respectively analyzing the prior covariance matrix and the measurement noise covariance matrix At time step by Cholesky decomposition at the step; and a diagonal matrix defined by the following equation:

[0111] (9)

[0112] (10)

[0113] where denotes a Gaussian kernel function with kernel bandwidth ; and denote the th element of and the th row of , respectively; and are expressed as:

[0114] (11)

[0115] can be obtained by implementing Cholesky decomposition of .

[0116] S23, updating the estimated state: the estimated state is determined by solving the equation group formula 6-11 iteratively, and then the posterior error covariance is updated by the following equation:

[0117] (12).

[0118] S24, iterative solution: by solving the above formula 5-12 iteratively, the MCKF realizes the extraction of the measurement noise in the response signal .

[0119] S3, identify the structural parameters (i.e. the modal frequency and damping ratio of the system) by using the COV-SSI identification module, input the measurement response signal preprocessed in the above step S2, and recalculate the system state matrix and the measurement matrix according to the formula 1-4 in step S1.

[0120] The discrete-time eigenvalues and modal shapes are defined as:

[0121] (13)

[0122] where is the eigenvalue corresponding to the eigenvalue On this basis, the continuous-time poles of the system matrix are given by:

[0123] (14)

[0124] In the formula represents the sampling time interval, represents the continuous-time poles of the system matrix;

[0125] According to formula 14, calculate the modal frequency of the system and damping ratio Expressed as:

[0126] (15)

[0127] (16).

[0128] S4. Use the DBSCAN clustering post-processing module to cluster the results identified in step S3.

[0129] The specific steps include:

[0130] S41. Preprocess and normalize the frequency and damping data identified by the COV-SSI identification module, and ensure that the data meets the following two conditions: a) the damping ratio of the physical mode must be positive; b) high-damping modes with a damping ratio exceeding 10% rarely occur in practical applications;

[0131] S42. Set the parameters of DBSCAN, including the neighborhood radius ε and the minimum number of clusters MinPts; select an unvisited frequency and damping data point;

[0132] S43, calculate the number of data points in its ε neighborhood, if the number is greater than or equal to MinPts, mark it as a core object; otherwise, mark it as a noise point;

[0133] S44, using density accessibility to expand clusters from core objects;

[0134] S45, repeat the above steps S3-S4 until it cannot be expanded;

[0135] S46. Mark all unvisited points as noise;

[0136] S47. Each cluster consists of frequency and damping core points and their reachable points; then, the determined modal frequencies and damping ratios are obtained through each cluster.

[0137] Reference Figure 2 As shown, a 3-DOF structure is used as an example. The mass and stiffness matrices of the model are defined as follows:

[0138] (20)

[0139] In the formula and .

[0140] Table 1 shows the natural frequencies (modal frequencies) and damping ratios corresponding to each mode extracted from the mass and stiffness matrix:

[0141] Table 1: Kinetic parameters of the 3-DOF model

[0142]

[0143] The dynamic response of the structure can be obtained by solving the system's equation of motion. Under a given external load, the system equation can be expressed as:

[0144] (twenty one)

[0145] In the formula 、 and denote the acceleration, velocity and displacement of the system respectively; is the external load. In this embodiment, the power used is The white noise input stimulus of is used as an example.

[0146] Equation 21 was numerically solved using the fourth-order Runge-Kutta method. The structural displacement response was sampled for 630 seconds at a sampling frequency of 100 Hz. To simulate the effects of actual measurement noise, a noise model was used to superimpose the noise signal onto the displacement response. The experimental design included two noise interference scenarios: Case 1 used Gaussian white noise, and Case 2 used non-Gaussian colored noise (generated by low-pass filtering non-Gaussian white noise). Three noise levels were set for each scenario, with the noise signal to original signal amplitude ratio (NSA) being 0.10, 0.20, and 0.30, respectively. One hundred noise-contaminated displacement signals were generated for each noise level for statistical analysis.

[0147] After generating a noise-contaminated signal, the modal frequencies and damping ratios were identified using the conventional COV-SSI method, the KF-SSI method (i.e., a combination of Kalman filtering and COV-SSI), and the proposed method. The parameters of each method were set as follows: (1) the number of block rows of the Hankel matrix was set to 300, and the system order N was taken as 50 (i.e., N = 50); (2) the stable pole evaluation tolerances for frequency, damping ratio, and modal shape were set to 0.02, 0.05, and 0.05, respectively; and (3) the minimum number of cluster points (MinPts) and the maximum neighborhood radius of the DBSCAN algorithm were set to 10 and 0.01, respectively.

[0148] Case 1: Gaussian white noise

[0149] The COV-SSI, KF-SSI and the method proposed in the present application all maintain high consistency in identifying modal frequencies under different noise levels, and the identification accuracy is satisfactory. The COV-SSI method exhibits obvious sensitivity to noise levels in identifying damping ratios, and the error is even as high as 30%. In contrast, the method proposed in the present application and the KF-SSI method exhibit significant robustness to measurement noise. Under different noise levels, both methods can provide high-precision damping ratio identification results, with an estimation error of about 5%, and exhibit significant superiority in suppressing Gaussian white measurement noise.

[0150] For reference, Table 2 and Table 3 show the modal frequency comparison and damping ratio comparison of different methods under Gaussian white measurement noise.

[0151] Table 2 is the modal frequency comparison of different methods under Gaussian white measurement noise, as follows:

[0152] Table 2:

[0153]

[0154] Table 3 is the damping ratio comparison of different methods under Gaussian white measurement noise, as follows:

[0155] Table 3:

[0156]

[0157] Case 2: Non-Gaussian colored noise

[0158] The COV-SSI, KF-SSI and the method proposed in the present application all maintain high consistency in identifying modal frequencies under different noise levels, and the identification accuracy is satisfactory. The COV-SSI method exhibits obvious sensitivity to noise levels in identifying damping ratios, and the error is even as high as 30%. In contrast, the method proposed in the present application and the KF-SSI method exhibit significant robustness to measurement noise. Under different noise levels, both methods can provide high-precision damping ratio identification results, with an estimation error of about 5%, and exhibit significant superiority in suppressing Gaussian white measurement noise.

[0159] For reference, Table 4 and Table 5 show the modal frequency comparison and damping ratio comparison of different methods under non-Gaussian colored measurement noise.

[0160] Table 4 shows the comparison of modal frequencies of different methods under non-Gaussian colored measurement noise, as follows:

[0161] Table 4:

[0162]

[0163] Table 5 compares the damping ratios of different methods under non-Gaussian colored measurement noise, as follows:

[0164] Table 5:

[0165]

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. An improved random subspace identification method based on MCKF and DBSCAN, characterized by: It includes the MCKF noise reduction pre-processing module, the COV-SSI identification module and the DBSCAN clustering post-processing module, and includes the following steps: S1. Use the COV-SSI identification module to directly analyze the measurement response signal and estimate the initial system state matrix F and measurement matrix H of the MCKF; specifically: S11, according to the measurement response signal , construct the Toeplitz matrix by outputting the covariance matrix: （1） in, 、 Represent the Toeplitz matrix and output covariance matrix respectively; where ,in 、 Represent the total time and time of measuring the response signal respectively Measure the response signal at all times; S12. Use singular value decomposition to decompose the Toeplitz matrix, that is: （2） In the formula and is an orthonormalized matrix; S13. Construct an extended observable matrix based on the singular value decomposition results and the controllability matrix Expressed as: （3） In the formula is a non-singular matrix; S14. By extending the observable matrix and the controllability matrix , calculate the initial system state matrix and the measurement matrix pass Obtain, that is: （4） in, Indicates the number of output channels; where represents pseudo-inverse; S2, setting the parameters of MCKF in the MCKF noise reduction preprocessing module, including the initial estimated state, the initial error covariance matrix, the process noise covariance matrix and the measurement noise covariance matrix, and then utilizing the MCKF noise reduction preprocessing module to realize the reduction of the measurement noise in the measurement response signal of step S1; S3, using the COV-SSI identification module to identify structural parameters, namely the modal frequency and damping ratio of the system, based on the measured response signal pre-processed in step S2, recalculate the system state matrix according to formulas 1-4 in step S1 and the measurement matrix ; S4. Clustering the results identified in step S3 using a DBSCAN clustering post-processing module.

2. The improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that: The step S1 further includes: For any one with For a system with 1 degree of freedom, its dynamic motion process is described by the discrete state space model given below: （17） In the formula For time point The discrete state vector of Indicates a time point The discrete output vector of Represented as the discrete state vector at time point k+1, 、 express and and Multiply them separately; and They are denoted as process noise and output noise respectively, where their covariance matrix is ​​defined as: （18） In the formula Indicates the operation of taking the expected value; is the Kronecker delta function; and are any two time points; the process noise covariance matrix is a non-negative definite matrix, the observation noise covariance matrix is a positive definite matrix; The Hankel matrix is ​​expressed as: （19） In the formula express The output signals of different sensors at different times; the Hankel matrix is ​​expressed as the division of two components, that is, and , where the subscript and They represent 'past' and 'future' respectively.

3. The improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that: The step S2 comprises the following steps: S21. Calculate the prior state and covariance matrix: Prior state and covariance matrix Calculated by the following formula: （5） In the formula and Respectively indicate time The estimated state and covariance matrix of Indicates time The process noise covariance matrix at ; S22. Update estimated state: initial estimated state and the initial covariance matrix Set to 0 and I respectively, according to the measured response signal Update estimate status ; （6） （7） in represents the Kalman gain matrix; in formula (7) and Expressed as: （8） In the formula and By respectively analyzing the prior covariance matrix and the measurement noise covariance matrix At time step Perform Cholesky decomposition at and The diagonal matrix defined by the following equation: （9） （10） In the formula The kernel bandwidth is Gaussian kernel function; and Respectively No. elements and No. OK; and The expression is: （11） By achieving The Cholesky decomposition of is obtained; S23. Update estimated status: estimated status Determine by iteratively solving equations 6-11, then, the posterior error covariance Updated by the following equation: （12） S24, iterative solution Through the iterative solution of formula 5-12, MCKF realizes the response signal Extraction of measurement noise.

4. The improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that: The step S3 is specifically as follows: Discrete-time eigenvalues and mode shapes Defined as: （13） In the formula is the eigenvalue corresponding to On this basis, the continuous-time poles of the system matrix are given by: （14） In the formula represents the sampling time interval, represents the continuous-time poles of the system matrix; According to formula 14, calculate the modal frequency of the system and damping ratio Expressed as: （15） （16）。 5. The improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that: The step S4 comprises the following steps: S41. Preprocess and normalize the frequency and damping data identified by the COV-SSI identification module, and ensure that the data meets the following two conditions: a) the damping ratio of the physical mode must be positive; b) high-damping modes with a damping ratio exceeding 10% rarely occur in practical applications; S42. Set the parameters of DBSCAN, including the neighborhood radius ε and the minimum number of clusters MinPts; select an unvisited frequency and damping data point; S43, calculate the number of data points in its ε neighborhood, if the number is greater than or equal to MinPts, mark it as a core object; otherwise, mark it as a noise point; S44, using density accessibility to expand clusters from core objects; S45, repeat the above steps S3-S4 until it cannot be expanded; S46. Mark all unvisited points as noise; S47. Each cluster consists of frequency and damping core points and their reachable points; then, the determined modal frequencies and damping ratios are obtained through each cluster.

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