Improved random subspace identification method based on MCKF and DBSCAN

Abstract

The invention relates to an improved random subspace identification method based on MCKF and DBSCAN, and belongs to the technical field of structure health monitoring and signal processing, the method comprises an MCKF noise reduction preprocessing module, a COV-SSI identification module and a DBSCAN clustering post-processing module, and the method comprises the following steps: S1, the COV-SSI identification module is used to directly analyze and measure a response signal, and the COV-SSI clustering post-processing module is used to process the response signal; estimating an initial system state matrix F and a measurement matrix H of the MCKF; s2, MCKF parameters are set in an MCKF noise reduction preprocessing module, and the MCKF noise reduction preprocessing module is used for achieving reduction of measurement noise in the measurement response signals in the step S1; s3, adopting a COV-SSI identification module to identify structural parameters, inputting the measurement response signal preprocessed in the step S2, and recalculating a system state matrix # imgabs0 # and a measurement matrix # imgabs1 # according to the step S1; s4, adopting a DBSCAN clustering post-processing module to perform mechanical energy clustering on a result identified in the step S3; measurement noise can be effectively reduced, data quality and signal quality are improved, and robustness and accuracy of modal parameter identification are improved.

Description

Technical Field

[0001] The 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 the core technology for health monitoring and safety assessment of engineering structures. It provides a key basis for structural damage diagnosis, performance degradation assessment and service life prediction by accurately analyzing the dynamic characteristics (such as natural frequency, damping ratio, and modal vibration shape) of complex structural systems (such as high-rise buildings, long-span bridges, and transmission tower line systems). During the service life, factors such as environmental excitation (such as earthquakes, waves, wind, etc.), material aging, and manufacturing defects may cause significant changes in physical parameters such as structural stiffness and damping, which directly affect the safety and durability of the structure. In this context, accurate identification of structural parameters is of great significance for structural health monitoring, damage diagnosis, and performance assessment.

[0003] The operational modal analysis (OMA) method has become the mainstream method for parameter identification due to its advantages of not requiring artificial excitation and avoiding structural damage. OMA usually includes two major methods, frequency domain and time domain, both of which have achieved remarkable success in identifying basic structural parameters. Among them, the random subspace identification (SSI) method is 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, the measurement noise of the sensor has a great impact on the quality of the response signal. This noise mainly comes from the inherent physical properties of the sensor and the interference of external environmental factors. There are two types of measurement noise, including Gaussian white noise (such as Johnson noise) and non-Gaussian colored noise (such as flicker noise). These noises not only increase the complexity of the signal, but may even mask the original characteristics of the signal, resulting in unsatisfactory parameter estimation, especially for the identification of structural damping. When the signal-to-noise ratio is low, the variability of the estimated parameters may increase significantly, thereby reducing the identification accuracy.

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

[0005] Therefore, how to achieve automatic high-precision identification of structural parameters in a complex noise environment is a technical problem that those skilled in the art need to solve at present, and there is an urgent need for a method that can achieve automatic high-precision identification of structural parameters in a complex noise environment. Summary of the Invention

[0006] In view of this, in order to solve the problem that it is difficult to achieve high-precision automatic identification of structural modal parameters under measurement noise and the poor applicability of the existing structural parameter identification method, the present invention provides an improved stochastic subspace identification method based on MCKF and DBSCAN, which can achieve high-precision automatic identification of structural modal parameters in Gaussian and non-Gaussian noise environments.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] An improved stochastic subspace identification method based on MCKF and DBSCAN, including an MCKF noise reduction preprocessing module, a COV-SSI identification module, and a DBSCAN clustering postprocessing module. The spatial identification method specifically includes the following steps:

[0009] S1. Use the COV-SSI identification module to directly analyze the measured response signal and estimate the initial system state matrix F and measurement matrix H of MCKF; specifically, it includes the following steps:

[0010] S11. According to the measured response signal , construct a Toeplitz matrix through the output covariance matrix:

[0011] (1)

[0012] Among them, , respectively represent the Toeplitz matrix and the output covariance matrix; in the formula , where , respectively represent the total time of the measured response signal and the measured response signal at time

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

[0014] (2)

[0015] In the formula and are orthonormal matrices;

[0016] S13. According to the singular value decomposition (SVD) result, construct the extended observable matrix and the controllability matrix It is expressed as:

[0017] (3)

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

[0019] S14. Calculate the initial system state matrix and the controllability matrix by expanding the observable matrix and the measurement matrix can be obtained through that is:

[0020] (4)

[0021] where represents the number of output channels; the symbol in the formula represents the pseudo-inverse;

[0022] S2. Set 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 use the MCKF noise reduction preprocessing module to reduce 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 measurement response signal preprocessed in the above step S2, and recalculate the system state matrix and the measurement matrix according to formulas 1-4 in step S1;

[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 system with degrees of freedom, its dynamic motion process can be described by the following discrete state space model:

[0027] (17)

[0028] In the formula is the discrete state vector at time point , represents the discrete output vector at time point , represents the discrete state vector at time point k + 1, , denote and with multiply respectively; and are denoted as process noise and output noise respectively, where their covariance matrices are defined as:

[0029] (18)

[0030] In the formula denotes 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, and the observation noise covariance matrix is a positive definite matrix;

[0031] The Hankel matrix is expressed as:

[0032] (19)

[0033] In the formula denotes the output signals of different sensors at time and , where the subscripts and denote 'past' and 'future' respectively.

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

[0035] S21. Calculate the prior state and covariance matrix: The prior state and the covariance matrix are calculated by the following formulas:

[0036] (5)

[0037] In the formula and denote the estimated state and covariance matrix at time respectively, denotes the process noise covariance matrix at time ;

[0038] S22. Update the estimated state: The initial estimated state and the error covariance matrix are set to 0 and I respectively. According to the measured response signal Update the estimated state ;

[0039] (6)

[0040] (7)

[0041] where denotes the Kalman gain matrix; and in Equation (7) are expressed as:

[0042] (8)

[0043] In the formula and are obtained by performing Cholesky decomposition on the prior covariance matrix and the measurement noise covariance matrix at the time step ; and are diagonal matrices defined by the following equations:

[0044] (9)

[0045] (10)

[0046] In the formula denotes the Gaussian kernel function with kernel bandwidth ; and respectively denote the -th element of and the -th row of and The expressions of

[0047] (11)

[0048] can be obtained by performing Cholesky decomposition on ;

[0049] S23. Update the estimated state: The estimated state is determined by iteratively solving the system of equations in Formulas 6 - 11. Then, the posterior error covariance is updated by the following equation:

[0050] (12)

[0051] S24. Iterative solution: Through the above formula 5 - 12 for iterative solution, MCKF realizes the extraction of measurement noise in the response signal. in the

[0052] Furthermore, step S3 is specifically as follows:

[0053] Discrete-time eigenvalues and modal shapes are defined as:

[0054] (13)

[0055] where is the eigenvector corresponding to the eigenvalue ; On this basis, the continuous-time poles of the system matrix are given by the following formula:

[0056] (14)

[0057] where represents the sampling time interval, represents the continuous-time poles of the system matrix;

[0058] According to formula (14), calculate the modal frequency and damping ratio which are expressed as:

[0059] (15)

[0060] (16).

[0061] Furthermore, step S4 specifically includes the following steps:

[0062] S41. Preprocess and normalize the frequency and damping data identified by the COV - SSI identification module, and ensure that the data 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 the neighborhood radius ε and the minimum number of clusters MinPts; Select an unvisited frequency and damping data point;

[0064] S43. Calculate the number of data points within 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. Expand the cluster from the core object using density accessibility;

[0066] S45. Repeat the above steps S3 - S4 until no further expansion is possible;

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

[0068] S47. Each cluster consists of a frequency and damping core point and its reachable points; then, the determined modal frequency and damping ratio are obtained through each cluster.

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

[0070] 1. An improved stochastic subspace identification method based on MCKF and DBSCAN disclosed by the present method directly analyzes the measured response signal by using the COV-SSI identification module, then reduces the measurement noise in the measured response signal by using the MCKF noise reduction preprocessing module, inputs the preprocessed measured response signal, and recalculates the system state matrix and the measurement matrix , and uses the DBSCAN clustering post-processing module to cluster the identification results, and obtains the determined modal frequency and damping ratio through each cluster; the high-precision automatic identification of structural modal parameters in Gaussian and non-Gaussian noise environments is realized through this method.

[0071] 2. An improved stochastic subspace identification method based on MCKF and DBSCAN disclosed by the present method can effectively reduce the measurement noise and improve the data quality and signal quality by suppressing non-Gaussian noise through the MCKF noise reduction preprocessing module; through the COV-SSI identification module based on the covariance-driven stochastic subspace method, the system state matrix and the measurement matrix can be accurately estimated; through the DBSCAN clustering post-processing module, outliers are removed, and the robustness and accuracy of modal parameter identification are improved.

[0072] Other advantages, objectives and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. Description of the Drawings

[0073] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0074] Figure 1 is the flowchart of the improved stochastic subspace identification method based on MCKF and DBSCAN of the present invention;

[0075] Figure 2 is the 3-degree-of-freedom model diagram in this embodiment. Detailed Embodiment

[0076] The following describes the implementation manners of the present invention through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0077] Such as Figure 1 shown, an improved random subspace identification method based on MCKF and DBSCAN includes an MCKF noise reduction preprocessing module, a COV-SSI identification module, and a DBSCAN clustering postprocessing module. This space identification method specifically includes the following steps:

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

[0079] Specifically: For any system with degrees of freedom, its dynamic motion process can be described by the following discrete state space model:

[0080] (17)

[0081] In the formula is the discrete state vector at time point , represents the discrete output vector at time point , represents the discrete state vector at time point k + 1, , represents and are multiplied by respectively; and represent process noise and output noise respectively, and their covariance matrices are defined as:

[0082] (18)

[0083] In the formula represents 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, and the observation noise covariance matrix is a positive definite matrix;

[0084] The Hankel matrix is expressed as:

[0085] (19)

[0086] Wherein represents the output signals of different sensors at different times; the Hankel matrix can be expressed as the division of two components, i.e., and , where the subscripts and represent 'past' and 'future' respectively.

[0087] Specifically, it includes the following steps:

[0088] S11. According to the measurement response signal , construct a Toeplitz matrix through the output covariance matrix:

[0089] (1)

[0090] Wherein, , represent the Toeplitz matrix and the output covariance matrix respectively; in the formula , wherein , represent the total time of the measurement response signal and the measurement response signal at time

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

[0092] (2)

[0093] Wherein and are orthonormal matrices.

[0094] S13. Then, according to the singular value decomposition (SVD) result, construct the extended observable matrix and the controllability matrix expressed as:

[0095] (3)

[0096] Wherein is a non-singular matrix.

[0097] S14. Through the extended observable matrix and the controllability matrix , calculate the initial system state matrix and the measurement matrix can be obtained through Obtained, i.e.:

[0098] (4)

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

[0100] S2. Set 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 use the MCKF noise reduction preprocessing module to reduce the measurement noise in the measurement response signal in the above step S1.

[0101] Specifically, it includes the following steps:

[0102] S21. Calculate the prior state and covariance matrix: The prior state and the covariance matrix are calculated by the following formulas:

[0103] (5)

[0104] In the formula and respectively represent the estimated state and covariance matrix at time , represents the process noise covariance matrix at time .

[0105] S22. Update the estimated state: The initial estimated state and the initial covariance matrix are respectively set to 0 and I, and the estimated state is updated according to the measured response signal ;

[0106] (6)

[0107] (7)

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

[0109] (8)

[0110] In the formula and are respectively obtained by performing operations on the prior covariance matrix and the measurement noise covariance matrix at the time step obtained by performing Cholesky decomposition at and a diagonal matrix defined by the following equation:

[0111] (9)

[0112] (10)

[0113] where denotes a Gaussian kernel function with a kernel bandwidth of ; and respectively denote the th element of and the th row of ; the expressions of

[0114] (11)

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

[0116] S23. Update the estimated state: The estimated state is determined by iteratively solving the system of equations in Equation 6 - 11. Then, the posterior error covariance is updated by the following equation:

[0117] (12).

[0118] S24. Iterative solution: Through the above Equation 5 - 12 for iterative solution, MCKF realizes the extraction of measurement noise in the response signal .

[0119] S3. Use the COV - SSI identification module to identify the structural parameters (i.e., the modal frequencies and damping ratios of the system), input the measurement response signal pre - processed in Step S2 above, and recalculate the system state matrix and the measurement matrix according to Equation 1 - 4 in Step S1.

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

[0121] (13)

[0122] where is the one corresponding to the eigenvalue The eigenvector; on this basis, the continuous-time poles of the system matrix are given by the following formula:

[0123] (14)

[0124] where denotes the sampling time interval, denotes the continuous-time poles of the system matrix;

[0125] According to Equation (14), calculate the modal frequency and damping ratio which are expressed as:

[0126] (15)

[0127] (16).

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

[0129] Specifically, it includes the following steps:

[0130] S41. Preprocess and normalize the frequency and damping data identified by the COV-SSI identification module, and ensure that the data 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;

[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 within 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. Expand the cluster from the core object using density accessibility;

[0134] S45. Repeat the above steps S3 - S4 until no further expansion is possible;

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

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

[0137] Refer to Figure 2 shown in the example of a 3-degree-of-freedom structure. The mass and stiffness matrices of the model are defined as follows:

[0138] (20)

[0139] wherein and .

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

[0141] Table 1: Dynamic parameters of the 3 - degree - of - freedom model

[0142]

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

[0144] (21)

[0145] wherein , and represent the acceleration, velocity, and displacement of the system respectively; is the external load. In this embodiment, white - noise input excitation with a power of is used as an example.

[0146] Equation (21) is numerically solved by the fourth - order Runge - Kutta method. The structural displacement response is continuously collected at a sampling frequency of 100 Hz for 630 seconds. To simulate the influence of actual measurement noise, a noise model is adopted, and the noise signal is superimposed on the displacement response. Two noise - interference scenarios are included in the experimental design: Case 1 is Gaussian white noise, and Case 2 is non - Gaussian colored noise (generated by low - pass filtering non - Gaussian white noise). For the two scenarios, three noise levels are set respectively, and the amplitude ratio (NSA) of the noise signal to the original signal is 0.10, 0.20, and 0.30 in sequence. 100 groups of displacement signals contaminated by noise are generated for each noise level for statistical analysis.

[0147] After generating the noise - contaminated signals, the traditional COV - SSI method, the KF - SSI method (i.e., the combination of Kalman filtering and COV - SSI), and the method of the present invention are respectively used to identify the modal frequencies and damping ratios. The parameter settings of each method are as follows: (1) The block row number of the Hankel matrix is set to 300, and the system order N is taken as 50 (i.e., N = 50); (2) The stable - pole evaluation tolerances for frequency, damping ratio, and modal shape are respectively set to 0.02, 0.05, and 0.05; (3) The minimum number of clustering points (MinPts) and the maximum neighborhood radius of the DBSCAN algorithm are respectively set to 10 and 0.01.

[0148] Case 1: Gaussian white noise

[0149] When identifying modal frequencies, COV-SSI, KF-SSI, and the method proposed in the present invention all maintain a high degree of consistency under different noise levels, and the identification accuracy is satisfactory. When identifying the damping ratio, the COV-SSI method shows obvious sensitivity to the noise level, and its error is even as high as 30%. In contrast, the method proposed in the present invention and the KF-SSI method show significant robustness to measurement noise. Under different noise levels, both methods can provide high-precision damping ratio identification results, and their estimation errors are stable at about 5%, showing significant superiority in suppressing Gaussian white measurement noise.

[0150] Specifically, refer to the comparison of modal frequencies and damping ratios of different methods under Gaussian white measurement noise shown in Table 2 and Table 3.

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

[0152] Table 2:

[0153]

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

[0155] Table 3:

[0156]

[0157] Case 2: Non-Gaussian colored noise

[0158] The modal frequencies identified by COV-SSI, KF-SSI, and the method proposed in the present invention are basically the same under various noise levels, and the identification of modal frequencies has strong robustness to the interference of non-Gaussian colored noise. However, in terms of identifying damping, the COV-SSI method shows relatively large identification errors under various noise levels, and these errors are more significant compared with those under Gaussian white noise conditions. For the KF-SSI method, it does not show obvious advantages in improving the damping ratio identification accuracy, and even in some cases, the damping ratio identification error of KF-SSI exceeds that of COV-SSI. In contrast, the method proposed in the present invention can significantly improve the identification accuracy of the damping ratio, and basically achieves an identification error within 10%, showing significant superiority in dealing with non-Gaussian colored measurement noise.

[0159] Specifically, refer to the comparison of modal frequencies and damping ratios of different methods under non-Gaussian colored measurement noise shown in Table 4 and Table 5.

[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 shows the comparison of 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 not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An improved random subspace identification method based on MCKF and DBSCAN, characterized in that, It includes an MCKF noise reduction preprocessing module, a COV-SSI identification module, and a DBSCAN clustering postprocessing module, and includes the following steps: S1. Use the COV-SSI identification module to directly analyze the measured response signal and estimate the initial system state matrix F and measurement matrix H of MCKF; specifically: S11. Construct a Toeplitz matrix from the output covariance matrix according to the measured response signal , as follows: （1） Among them, and represent a Toeplitz matrix and an output covariance matrix respectively; in the formula , where and represent the total time of the measured response signal and the measured response signal at the time S12. Use singular value decomposition to decompose the Toeplitz matrix, that is: （2） wherein and are orthonormal matrices; S13. Construct an extended observable matrix based on the singular value decomposition result and the controllability matrix which is expressed as: （3） where is a non-singular matrix; S14. By expanding the observable matrix and the controllability matrix , calculate the initial system state matrix and the measurement matrix Obtained by , that is: （4） Among them, represents the number of output channels; in the formula, the symbol represents the pseudo-inverse; S2. Set the parameters of MCKF in the MCKF noise reduction preprocessing module, including the initial estimated state, initial error covariance matrix, process noise covariance matrix, and measurement noise covariance matrix, and then use the MCKF noise reduction preprocessing module to reduce the measurement noise in the measurement response signal in step S1; S3. Use the COV-SSI identification module to identify structural parameters, such as the modal frequency and damping ratio of the system. Based on the measured response signal preprocessed in step S2, recalculate the system state matrix according to Formula 1-4 in step S1 and the measurement matrix ; S4. Use the DBSCAN clustering postprocessing module to cluster the results identified in step S3.

2. An improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that, Step S1 further includes: For any system with degrees of freedom, its dynamic motion process is described by the discrete state space model given below: （17） where is the discrete state vector at time point , represents the discrete output vector at time point , is expressed as the discrete state vector at time point k + 1 , represents and are multiplied by respectively; and represent process noise and output noise respectively, and their covariance matrices are defined as: （18） where denotes 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, and the observation noise covariance matrix is a positive definite matrix; The Hankel matrix is expressed as: （19） In the formula represents 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 subscripts and represent 'past' and 'future' respectively.

3. An improved random subspace identification method based on MCKF and DBSCAN as claimed in claim 1, characterized in that, Step S2 includes the following steps: S21. Calculate the prior state and covariance matrix: The prior state and covariance matrix are calculated by the following formula: （5） where and represent the estimated state and covariance matrix at time respectively, and represents the process noise covariance matrix at time ; S22. Update the estimated state: the initial estimated state and the initial covariance matrix are respectively set to 0 and I, and update the estimated state according to the measured response signal ; ; （6） （7） Among them represents the Kalman gain matrix; in formula (7), and are expressed as: （8） where and are obtained by performing Cholesky decomposition on the prior covariance matrix and the measurement noise covariance matrix at the time step respectively; and are diagonal matrices defined by the following equations: （9） （10） where denotes a Gaussian kernel function with a kernel bandwidth of ; and respectively denote the -th element of and the -th row of ; the expressions of and are as follows: （11） can be obtained by implementing Cholesky decomposition of; S23. Update the estimated state: the estimated state is determined by iteratively solving the system of equations in Formula 6 - 11. Then, the posterior error covariance is updated by the following equation: （12） S24. Iterative solution: By iteratively solving using the formula 5 - 12, MCKF realizes the extraction of measurement noise in the response signal. in the response signal.

4. An improved random subspace identification method based on MCKF and DBSCAN according to claim 1, characterized in that, Step S3 is specifically: Discrete-time eigenvalues and mode shapes are defined as: （13） where is the eigenvector corresponding to the eigenvalue ; based on this, the continuous-time poles of the system matrix are given by the following formula: （14） where represents the sampling time interval, represents the continuous-time poles of the system matrix; Calculate the modal frequency of the system according to Equation 14 and damping ratio which are expressed as: （15） （16）。 5. An improved random subspace identification method based on MCKF and DBSCAN as claimed in claim 1, characterized in that, Step S4 includes the following steps: S41. Preprocess and normalize the frequency and damping data identified by the COV-SSI identification module, and ensure that the data 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; 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 within 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. Expand the cluster from the core object using density accessibility; S45. Repeat the above steps S3 - S4 until no further expansion is possible; S46. Mark all unvisited points as noise; S47. Each cluster consists of the frequency and damping core points and their reachable points; then, the determined modal frequency and damping ratio are obtained through each cluster.

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