A bridge modal parameter automatic identification method and system considering multi-channel information

Abstract

The application relates to a bridge modal parameter automatic identification method and system considering multi-channel information, which comprises the following steps: S1, generating a stability diagram by directly analyzing multi-channel monitoring signals by using COV-SSI, automatically extracting stable axes by combining a DBSCAN clustering algorithm, and realizing automatic identification of modal frequencies; S2, decomposing multi-channel monitoring data by using MvFIF to generate an intrinsic modal function (IMF) group with modal alignment characteristics; S3, calculating the instantaneous frequency and bandwidth of the IMF in step S2 by using HHT, screening out an IMF component containing a target modal frequency, and performing linear reconstruction; and S4, taking the multi-channel monitoring data after the reconstruction in step S3 as system input of the COV-SSI algorithm, calculating a system matrix and an output matrix, and calculating modal damping ratios by using eigenvalue decomposition; the method can consider the space-time correlation between multi-channel data, realize synchronous decomposition of multi-channel monitoring data, and realize automatic and accurate identification of structural modal parameters under different noise levels.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring and signal processing technology, and relates to an automatic identification method for bridge modal parameters that considers multi-channel information. In particular, it relates to an automatic identification method and system for bridge modal parameters that integrates multivariate fast iterative filtering (MvFIF) and DBSCAN clustering, as well as computer equipment and computer-readable storage media. Background Technology

[0002] The rapid growth of traffic flow in modern society, the increasing diversity of vehicle types, and the rising proportion of heavy-duty vehicles have made the load conditions on bridges more complex and severe. In recent years, natural disasters such as earthquakes, floods, and strong winds, as well as extreme events such as ship collisions and fires, have become more frequent. The interplay of changing traffic load conditions and various adverse events has led to accelerated degradation of bridge durability, a significant decrease in load-bearing capacity, and a gradual decline in structural resistance. Changes in the modal parameters of bridge structures (such as frequency, damping ratio, and mode shape) can reflect problems such as damage, fatigue, or aging. Therefore, accurate identification of modal parameters is of great significance for bridge damage diagnosis, condition assessment, and disaster prevention.

[0003] Operating state modal analysis (OMA) is a structural dynamics testing method based on environmental excitation. It can be performed while the structure is in its operational state, requiring no artificial excitation and not affecting the normal use of the structure. Therefore, this method is mainly applied to the modal analysis of large structures. OMA is mainly divided into three categories based on the identification domain: frequency domain method, time domain method, and time-frequency domain method. Among them, random subspace identification (SSI) is currently the most commonly used time-domain modal parameter identification method, widely applied in the operational modal analysis of large-scale civil infrastructure. However, in actual bridge monitoring scenarios, due to environmental factors and equipment limitations, the input data of SSI is inevitably affected by noise pollution.

[0004] Covariance Random Subspace Identification (COV-SSI) is a systematic identification method for modal parameters (such as frequency, damping ratio, and mode shape), commonly used in structural health monitoring and vibration analysis of bridges and buildings. Although COV-SSI theoretically incorporates a noise model, large measurement noise variance can cause noise components in the singular value decomposition of the covariance matrix to mask the true modal information, leading to biased modal parameter estimation. This directly affects the performance of SSI, especially the accuracy of modal damping ratio identification. Furthermore, the presence of noise alters the characteristics of the covariance matrix, resulting in spurious modes (i.e., noise points) in the stability map generated by SSI, in addition to the true modes of the structure. These noise points do not conform to the distribution patterns of normal modal characteristics, severely impacting the manual selection and extraction of physical modes on the stability map.

[0005] Therefore, how to accurately and automatically identify the modal parameters of bridge structures in complex multi-channel high-noise environments has become a key problem that needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, to address the problems of existing random subspace identification methods leading to deviations in modal parameter estimation, particularly affecting the accuracy of modal damping ratio identification, when the measurement noise variance is large, and the generation of spurious modes in the stability graph by noise interfering with the identification of true modes and impacting manual selection and extraction on the stability graph, this invention provides an automatic bridge modal parameter identification method and system that considers multi-channel information. This method can consider the spatiotemporal correlation between multi-channel data, achieving synchronous decomposition of multi-channel monitoring data; by effectively filtering and extracting useful information related to frequency-based structural modal parameters, it can accurately identify structural modal parameters under different noise levels; and it also automates the modal parameter extraction process, thereby avoiding subjective errors caused by manual intervention.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] An automatic identification method for bridge modal parameters considering multi-channel information includes the following steps:

[0009] S1. COV-SSI is used to directly analyze multi-channel monitoring signals to generate a stability map. Combined with the DBSCAN clustering algorithm, the stability axis is automatically extracted to achieve automatic identification of modal frequencies.

[0010] S2. Use MvFIF to decompose the multi-channel monitoring data to generate a set of intrinsic mode functions (IMFs) with mode alignment characteristics;

[0011] S3. Calculate the instantaneous frequency and bandwidth of the IMF in step S2 using HHT, filter out the IMF components containing the target modal frequency, and perform linear reconstruction.

[0012] S4. Use the multi-channel monitoring data reconstructed in step S3 as the system input of the COV-SSI algorithm, calculate the system matrix and output matrix, and use eigenvalue decomposition to calculate the modal damping ratio.

[0013] Furthermore, step S1 specifically includes the following steps:

[0014] S11. Constructing the discrete state model: The stochastic discrete-time state-space model of an n-degree-of-freedom system is expressed as follows:

[0015]

[0016] Where, x k ∈R 2n Let y be a discrete-time state vector.k ∈R l The output vector is given by l, where l is the number of measurement points and w is the number of measurement points. k ∈R 2n For process noise, v k ∈R l For measuring noise, A∈R 2n×2n Let C be a discrete state matrix, ∈ R. l×2n It is a discrete output matrix;

[0017] Based on the multi-channel monitoring signals, the measured structural response vector y at discrete time k is used. k Construct the Hankel matrix H, as shown in the following expression:

[0018]

[0019] Among them, y i ∈R l The Hankel matrix represents the sequence of output signals from each measuring point at time i. It has 2i rows and j columns and is divided into Yi blocks. p and Y f Two matrices, representing the "past" and the "future" respectively, each with i blocks of rows; parameter j represents the number of samples used to calculate the output covariance matrix, theoretically j→∞;

[0020] S12. Calculate the output covariance matrix: Estimate the output covariance matrix using a finite amount of data.

[0021]

[0022] S13. Construct the Toeplitz matrix: Construct the Toeplitz matrix based on the output covariance matrix in step S12, and further organize it to obtain the state-output covariance matrix;

[0023] Based on the multi-channel monitoring data from step S11, y k+1 The Toeplitz matrix is ​​constructed using the output covariance matrix, as shown in the following expression:

[0024]

[0025] Further simplification of the Toeplitz matrix yields:

[0026]

[0027] in, Representing the state-output covariance matrix, Equation (5) shows that the Toeplitz matrix can be decomposed into the generalized observable matrix T. i ∈R il×2n and extended controllable matrix Δ i ∈R2n×li Where n is the system order, l is the number of measurement points, and the generalized observable matrix T is observed. i It includes the system's state matrix A and output matrix C;

[0028] S14. Singular Value Decomposition: Perform singular value decomposition on the Toeplitz matrix in step S13 to obtain the system's state matrix A and output matrix C.

[0029] Combining formula (5) in step S13 with the singular value decomposition of the Toeplitz matrix, we can obtain:

[0030]

[0031] From formula (7), we can deduce that the output matrix C is equal to the first l rows of the generalized observable matrix;

[0032] Define T i Two submatrices T1 and T2:

[0033]

[0034] The system matrix A is obtained from formula (8) in step S14:

[0035] A = (T1) + T2(9)

[0036] in,() + Represents the pseudo-inverse of a matrix;

[0037] S15. Constructing a stability graph: Obtain the system matrix through matrix operations, perform eigenvalue decomposition on it, calculate the modal frequencies to identify modal parameters, and further screen poles to construct a stability graph;

[0038] Perform eigenvalue decomposition on system matrix A:

[0039] A=ψΛψ -1 (10)

[0040] Where Ψ is the discrete-time eigenvector matrix of the system, and Λ is the eigenvalue λ of the system. i The diagonal matrix formed;

[0041] The system frequency is derived from the following formula:

[0042]

[0043] in,(·) * f represents conjugation i The modal frequency;

[0044] Due to overestimation of the system order, the identification results often contain a large number of spurious modes. To help identify the true physical modes, a stability diagram is typically used to observe the changes in modal frequencies, damping ratios, and mode shapes at different model orders. The calculation formula is as follows:

[0045]

[0046]

[0047] (1-MAC(i,i+1))<∈ Φ (14)

[0048] In the formula, i represents the model order, and f, ξ, and Φ represent the modal frequencies, damping ratios, and mode shapes of each order, respectively; ∈ f ,∈ ξ ,∈ Φ These are the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance, respectively; MAC is the Modal Assurance Criterion; and the DBSCAN clustering algorithm is used to automatically extract the stability axis in the generated stability graph.

[0049] Furthermore, in step S15, when using the DBSCAN clustering algorithm to cluster the dataset, it is necessary to determine the distance parameter ε and the density parameter (MinPts). Currently, these two parameters in the DBSCAN clustering algorithm need to be set based on experience.

[0050] Furthermore, step S15 uses the DBSCAN clustering algorithm to automatically extract the stable axis. The specific steps are as follows:

[0051] S151. Screen the poles in the stability plot to ensure the authenticity of the data. The modal parameters should meet the following standards: 1) The modal damping ratio is always positive; 2) In practical engineering applications, the modal damping ratio is usually considered to be no more than 15%.

[0052] S152. Select the initial point from step S151 and calculate the number of points in its neighborhood: randomly select an unvisited frequency point from all poles in the stable graph, denoted as point P; calculate all points within the radius ε of point P, denoted as N(P); if the number of points in N(P) is less than MinPts, mark point P as a noise point; if the number of points in N(P) is not less than MinPts, then point P is the core point, and a new cluster starts from point P;

[0053] S153. Determine whether a point is a noise point or a core point based on the number of points in its neighborhood in step S152, and expand the cluster accordingly. Initialize all points in points P and N(P) into a new cluster, denoted as cluster C. Starting from the core point in cluster C, check its neighborhood in turn. For each core point Q in cluster C, check its neighborhood N(Q). If the number of points in N(Q) is not less than MinPts, add all points in N(Q) to cluster C. For each core point in its neighborhood, repeat the check of its neighborhood until cluster C can no longer be expanded.

[0054] S154. Repeat steps S151-S153 until all poles have been visited.

[0055] S155. The average frequency and average damping ratio of the poles in each cluster are used as representative values ​​of the data in the cluster.

[0056] Furthermore, in step S2, when using MvFIF to decompose the multi-channel monitoring data, predefined parameters are employed, including weighting coefficients, stopping criteria, and the maximum number of iterations. Beneficial effects: Using predefined parameters can effectively decompose the signal and generate a set of intrinsic mode functions (IMFs) with excellent mode alignment characteristics.

[0057] Furthermore, the specific steps of step S2 are as follows:

[0058] S21. Determine the filter length: Use the rotation angle of the vector as it changes over time to determine a unique filter length;

[0059] For bridge multi-channel monitoring data with m channels: {x(t), t=1,2,...,N}={x1(t),x2(t),...,x m (t)} T T denotes transpose. The unique filter length L is determined by the rotation angle θ(t) of the vector x(t) over time, where θ(t) is defined as follows:

[0060]

[0061] The following formula is used to calculate the filter length L:

[0062]

[0063] Where N is the dimension of θ(t), k is the number of extreme points in θ(t), and ξ is a weighting parameter. By rounding a number to the nearest integer, the average scale of the highest frequency rotation in the embedded signal can be estimated.

[0064] S22. Iterative decomposition of the signal: Iterate according to the following formula until the difference between adjacent iterations meets the stopping criterion;

[0065]

[0066] In the formula, l represents the number of iterations. This represents the IMF of the i-th channel in step l. It is its corresponding Fourier transform, where I represents the identity matrix, diag(·) represents the diagonal matrix, and DFT represents the discrete Fourier transform;

[0067] The formula for the stopping criterion is:

[0068]

[0069] Where ||·||2 represents the Euclidean norm; when δ>0 and When (the set of natural numbers), formula (20) holds true;

[0070] The first IMF is obtained according to the following formula (20), and the newly generated IMF is subtracted from the current signal; then the above calculation steps are repeated until θ(t) < 2, and the final IMF group is obtained according to formula (21);

[0071]

[0072] IMF=IMF∪{x(t)}(21)

[0073] Where the initial value of IMF is 0, and iDFT represents the inverse Fourier transform;

[0074] At this point, the original m-dimensional monitoring signal has been simultaneously decomposed into multiple IMF groups:

[0075]

[0076]

[0077] Where K represents the signal x of each channel. i (t) represents the total number of IMFs (i.e., the number of decomposition layers), where k is the layer index of the IMF. k (t) represents the IMF array of the k-th layer.

[0078] Furthermore, step S3 specifically includes the following steps:

[0079] S31. Calculate instantaneous frequency and bandwidth: Calculate the instantaneous average frequency and bandwidth of each intrinsic mode function (IMF) using the Hilbert-Huang transform (HHT);

[0080] S32. Screening IMF components: Correlate the identified structural modal frequencies with the instantaneous frequency bandwidth of the IMF components, and retain the IMF components whose bandwidth fully contains the target modal frequencies.

[0081] S33. Linear Reconstruction: Perform linear reconstruction on the selected IMF to extract basic information about the dynamic characteristics of the captured structural modes.

[0082] Further, step S4 specifically involves: using the multi-channel monitoring data reconstructed in step S3 as the system input for the COV-SSI algorithm, and calculating the system matrix A and output matrix C according to formulas (1)-(10) in step S1, where the damping ratio ξ i Calculated using the following formula:

[0083]

[0084] in,(·) R Indicate the real part, ξ i The modal damping ratio;

[0085] Using formulas (12)-(14) in step S1, the poles corresponding to each mode of the stability diagram are obtained, and the average damping ratio is used as the final identification result.

[0086] An improved random subspace identification system based on multivariate mode decomposition fusion DBSCAN clustering includes a frequency identification module, a multivariate signal decomposition module, a frequency-based signal filtering and reconstruction module, and a damping ratio identification module.

[0087] The frequency identification module specifically identifies the modal frequencies of the bridge structure by analyzing multi-channel monitoring signals and combining them with the DBSCAN clustering algorithm, thus providing a foundation for subsequent modal parameter identification.

[0088] The multivariate signal decomposition module specifically uses MvFIF to decompose multi-channel monitoring data and extracts a set of intrinsic mode functions (IMFs) with excellent mode alignment characteristics in order to better process complex signals.

[0089] The frequency-based signal filtering and reconstruction module specifically works by filtering IMF components related to structural modal frequencies and performing linear reconstruction to extract basic information about capturing the dynamic characteristics of structural modes, thereby improving the signal-to-noise ratio and useful information content of the signal.

[0090] The damping ratio identification module specifically uses the reconstructed data as input to calculate the modal damping ratio, ultimately achieving accurate identification of the bridge structure's modal parameters and providing crucial data support for bridge damage diagnosis and condition assessment.

[0091] Simultaneously, a computer device is provided, including a processor and a memory. The memory is used to store a computer executable program. The processor reads part or all of the computer executable program from the memory and executes it. When the processor executes part or all of the computer executable program, it can realize the automatic identification method for bridge modal parameters considering multi-channel information of the present invention.

[0092] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the automatic identification method for bridge modal parameters that takes into account multi-channel information, as described in this invention.

[0093] The automatic identification method for bridge modal parameters that considers multi-channel information disclosed in this invention has the following beneficial effects:

[0094] 1. Improved modal parameter identification accuracy: Through multi-stage optimization processes such as frequency identification, multivariate signal decomposition, frequency-based signal filtering and reconstruction, and damping ratio identification, modal parameter information is gradually extracted and refined, ultimately obtaining high-precision modal frequency and damping ratio identification results.

[0095] 2. Highly efficient noise suppression: By synchronously decomposing multi-channel monitoring data through multivariate fast iterative filtering (MvFIF), noise can be effectively filtered while retaining useful information related to structural modal parameters. Under different noise levels, this method can accurately identify modal parameters, demonstrating excellent robustness and solving the problem of biased modal parameter estimation in traditional SSI methods under strong noise environments. By automatically extracting stable axes using the DBSCAN clustering algorithm, the true physical modes can be effectively identified, avoiding interference from spurious modes caused by noise on modal parameter identification and improving the accuracy of modal parameter identification.

[0096] 3. High degree of automation: Combined with the DBSCAN clustering algorithm, it can automatically extract the stability axis in the stability graph and realize the automatic identification of modal frequencies without manual intervention, reducing the subjective error caused by manual selection and extraction of modal parameters, and improving the identification efficiency and reliability; in the frequency-based signal screening and reconstruction stage, by calculating the instantaneous average frequency and bandwidth of each intrinsic mode function (IMF), the IMF components containing the target modal frequency are automatically screened out and linearly reconstructed, and the dynamic characteristic information of the structural modes is further extracted, realizing the automation of signal processing.

[0097] 4. Applicable to complex environments and various structures: This method can accurately and automatically identify the modal parameters of bridge structures in complex multi-channel high-noise environments, and is applicable to various practical bridge monitoring scenarios. It can be extended to other types of large structures, such as high-rise buildings, long-span bridges, and high arch dams, providing an effective technical means for health monitoring and condition assessment of various structures.

[0098] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0099] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0100] Figure 1 The flowchart of the automatic identification method for bridge modal parameters considering multi-channel information of the present invention is shown below;

[0101] Figure 2 This is a flowchart of step S1 in the automatic identification method for bridge modal parameters that considers multi-channel information in this invention;

[0102] Figure 3 The flowchart of steps S2 to S4 in the automatic identification method for bridge modal parameters considering multi-channel information of the present invention is shown below;

[0103] Figure 4 This is an overall view of the bridge in this embodiment;

[0104] Figure 5 This is a finite element model of a bridge in an embodiment of the present invention;

[0105] Figure 6 This is a schematic diagram of the measurement point arrangement in an embodiment of the present invention. Detailed Implementation

[0106] The following specific examples illustrate the implementation of the present invention. 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 embodiments, and 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.

[0107] like Figures 1-3 The method for automatic identification of bridge modal parameters considering multi-channel information, as shown, includes the following steps:

[0108] S1. COV-SSI is used to directly analyze multi-channel monitoring signals to generate a stability map. Combined with the DBSCAN clustering algorithm, the stability axis is automatically extracted to achieve automatic identification of modal frequencies.

[0109] Specifically:

[0110] S11. Constructing the discrete state model: The stochastic discrete-time state-space model of an n-degree-of-freedom system is expressed as follows:

[0111]

[0112] Where, x k ∈R 2n Let y be a discrete-time state vector. k ∈R l The output vector is given by l, where l is the number of measurement points and w is the number of measurement points. k ∈R 2n For process noise, v k ∈R l For measuring noise, A∈R 2n×2n Let C be a discrete state matrix, ∈ R. l×2n It is a discrete output matrix;

[0113] Based on the multi-channel monitoring signals, the measured structural response vector y at discrete time k is used. k Construct the Hankel matrix H, as shown in the following expression:

[0114]

[0115] Among them, y i ∈R l The Hankel matrix represents the sequence of output signals from each measuring point at time i. It has 2i rows and j columns and is divided into Yi blocks. p and Y f Two matrices, representing the "past" and the "future" respectively, each with i blocks of rows; parameter j represents the number of samples used to calculate the output covariance matrix, theoretically j→∞;

[0116] S12. Calculate the output covariance matrix: Estimate the output covariance matrix using a finite amount of data.

[0117]

[0118] S13. Construct the Toeplitz matrix: Construct the Toeplitz matrix based on the output covariance matrix in step S12, and further organize it to obtain the state-output covariance matrix;

[0119] Based on the multi-channel monitoring data from step S11, y k+1 The Toeplitz matrix is ​​constructed using the output covariance matrix, as shown in the following expression:

[0120]

[0121] Further simplification of the Toeplitz matrix yields:

[0122]

[0123] in, Representing the state-output covariance matrix, Equation (5) shows that the Toeplitz matrix can be decomposed into the generalized observable matrix T. i ∈R il×2n and extended controllable matrix Δ i ∈R 2n×li Where n is the system order, l is the number of measurement points, and the generalized observable matrix T is observed. i It includes the system's state matrix A and output matrix C;

[0124] S14. Singular Value Decomposition: Perform singular value decomposition on the Toeplitz matrix in step S13 to obtain the system's state matrix A and output matrix C.

[0125] Combining formula (5) in step S13 with the singular value decomposition of the Toeplitz matrix, we can obtain:

[0126]

[0127] From formula (7), we can deduce that the output matrix C is equal to the first l rows of the generalized observable matrix;

[0128] Define T i Two submatrices T1 and T2:

[0129]

[0130] The system matrix A is obtained from formula (8) in step S14:

[0131] A = (T1) + T2(9)

[0132] in,() + Represents the pseudo-inverse of a matrix;

[0133] S15. Constructing a stability graph: Obtain the system matrix through matrix operations, perform eigenvalue decomposition on it, calculate the modal frequencies to identify modal parameters, and further screen poles to construct a stability graph;

[0134] Perform eigenvalue decomposition on system matrix A:

[0135] A=ψΛψ -1 (10)

[0136] Where Ψ is the discrete-time eigenvector matrix of the system, and Λ is the eigenvalue λ of the system. i The diagonal matrix formed;

[0137] The system frequency is derived from the following formula:

[0138]

[0139] in,(·) * f represents conjugation i The modal frequency;

[0140] Due to overestimation of the system order, the identification results often contain a large number of spurious modes. To help identify the true physical modes, a stability diagram is typically used to observe the changes in modal frequencies, damping ratios, and mode shapes at different model orders. The calculation formula is as follows:

[0141]

[0142] (1-MAC(i,i+1))<∈ Φ (14)

[0143] In the formula, i represents the model order, and f, ξ, and Φ represent the modal frequencies, damping ratios, and mode shapes of each order, respectively; ∈ f ,∈ ξ ,∈ Φ These are the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance, respectively; MAC is the Modal Assurance Criterion; and the DBSCAN clustering algorithm is used to automatically extract the stability axis in the generated stability graph.

[0144] When using the DBSCAN clustering algorithm to cluster a dataset, the distance parameter ε and the density parameter (MinPts) need to be determined. Currently, these two parameters in the DBSCAN clustering algorithm need to be set based on experience.

[0145] Furthermore, step S15 uses the DBSCAN clustering algorithm to automatically extract the stable axis. The specific steps are as follows:

[0146] S151. Screen the poles in the stability plot to ensure the authenticity of the data. The modal parameters should meet the following standards: 1) The modal damping ratio is always positive; 2) In practical engineering applications, the modal damping ratio is usually considered to be no more than 15%.

[0147] S152. Select the initial point from step S151 and calculate the number of points in its neighborhood: randomly select an unvisited frequency point from all poles in the stable graph, denoted as point P; calculate all points within the radius ε of point P, denoted as N(P); if the number of points in N(P) is less than MinPts, mark point P as a noise point; if the number of points in N(P) is not less than MinPts, then point P is the core point, and a new cluster starts from point P;

[0148] S153. Determine whether a point is a noise point or a core point based on the number of points in its neighborhood in step S152, and expand the cluster accordingly. Initialize all points in points P and N(P) into a new cluster, denoted as cluster C. Starting from the core point in cluster C, check its neighborhood in turn. For each core point Q in cluster C, check its neighborhood N(Q). If the number of points in N(Q) is not less than MinPts, add all points in N(Q) to cluster C. For each core point in its neighborhood, repeat the check of its neighborhood until cluster C can no longer be expanded.

[0149] S154. Repeat steps S151-S153 until all poles have been visited.

[0150] S155. The average frequency and average damping ratio of the poles in each cluster are used as representative values ​​of the data in the cluster.

[0151] Furthermore, in step S2, when using MvFIF to decompose the multi-channel monitoring data, predefined parameters are employed, including weighting coefficients, stopping criteria, and the maximum number of iterations. Beneficial effects: Using predefined parameters can effectively decompose the signal and generate a set of intrinsic mode functions (IMFs) with excellent mode alignment characteristics.

[0152] S2. Use MvFIF to decompose the multi-channel monitoring data to generate a set of intrinsic mode functions (IMFs) with mode alignment characteristics.

[0153] The specific steps are as follows:

[0154] S21. Determine the filter length: Use the rotation angle of the vector as it changes over time to determine a unique filter length;

[0155] For bridge multi-channel monitoring data with m channels: {x(t), t=1,2,...,N}={x1(t),x2(t),...,x m (t)} T T denotes transpose. The unique filter length L is determined by the rotation angle θ(t) of the vector x(t) over time, where θ(t) is defined as follows:

[0156]

[0157] The following formula is used to calculate the filter length L:

[0158]

[0159] Where N is the dimension of θ(t), k is the number of extreme points in θ(t), and ξ is a weighting parameter. By rounding a number to the nearest integer, the average scale of the highest frequency rotation in the embedded signal can be estimated.

[0160] S22. Iterative decomposition of the signal: Iterate according to the following formula until the difference between adjacent iterations meets the stopping criterion;

[0161]

[0162] In the formula, l represents the number of iterations. This represents the IMF of the i-th channel in step l. It is its corresponding Fourier transform, where I represents the identity matrix, diag(·) represents the diagonal matrix, and DFT represents the discrete Fourier transform;

[0163] The formula for the stopping criterion is:

[0164]

[0165] Where ||·||2 represents the Euclidean norm; when δ>0 and When (the set of natural numbers), formula (20) holds true;

[0166] The first IMF is obtained according to the following formula (20), and the newly generated IMF is subtracted from the current signal; then the above calculation steps are repeated until θ(t) < 2, and the final IMF group is obtained according to formula (21);

[0167]

[0168] IMF=IMF∪{x(t)}(21)

[0169] Where the initial value of IMF is 0, and iDFT represents the inverse Fourier transform;

[0170] At this point, the original m-dimensional monitoring signal has been simultaneously decomposed into multiple IMF groups:

[0171]

[0172] Where K represents the signal x of each channel. i (t) represents the total number of IMFs (i.e., the number of decomposition layers), where k is the layer index of the IMF. k (t) represents the IMF array of the k-th layer.

[0173] S3. Calculate the instantaneous frequency and bandwidth of the IMF in step S2 using HHT, filter out the IMF components containing the target modal frequency, and perform linear reconstruction.

[0174] Specifically, the following steps are included:

[0175] S31. Calculate instantaneous frequency and bandwidth: Calculate the instantaneous average frequency and bandwidth of each intrinsic mode function (IMF) using the Hilbert-Huang transform (HHT);

[0176] S32. Screening IMF components: Correlate the identified structural modal frequencies with the instantaneous frequency bandwidth of the IMF components, and retain the IMF components whose bandwidth fully contains the target modal frequencies.

[0177] S33. Linear Reconstruction: Perform linear reconstruction on the selected IMF to extract basic information about the dynamic characteristics of the captured structural modes.

[0178] S4. Use the multi-channel monitoring data reconstructed in step S3 as the system input of the COV-SSI algorithm, calculate the system matrix and output matrix, and use eigenvalue decomposition to calculate the modal damping ratio.

[0179] Step S4 specifically involves using the multi-channel monitoring data reconstructed in step S3 as the system input for the COV-SSI algorithm, and calculating the system matrix A and output matrix C according to formulas (1)-(10) in step S1, where the damping ratio ξ i Calculated using the following formula:

[0180]

[0181] in,(·) R Indicate the real part, ξ i The modal damping ratio;

[0182] Using formulas (12)-(14) in step S1, the poles corresponding to each mode of the stability diagram are obtained, and the average damping ratio is used as the final identification result.

[0183] An improved random subspace identification system based on multivariate mode decomposition fusion DBSCAN clustering includes a frequency identification module, a multivariate signal decomposition module, a frequency-based signal filtering and reconstruction module, and a damping ratio identification module.

[0184] The frequency identification module specifically identifies the modal frequencies of the bridge structure by analyzing multi-channel monitoring signals and combining them with the DBSCAN clustering algorithm, thus providing a foundation for subsequent modal parameter identification.

[0185] The multivariate signal decomposition module specifically uses MvFIF to decompose multi-channel monitoring data and extracts a set of intrinsic mode functions (IMFs) with excellent mode alignment characteristics in order to better process complex signals.

[0186] The frequency-based signal filtering and reconstruction module specifically works by filtering IMF components related to structural modal frequencies and performing linear reconstruction to extract basic information about capturing the dynamic characteristics of structural modes, thereby improving the signal-to-noise ratio and useful information content of the signal.

[0187] The damping ratio identification module specifically uses the reconstructed data as input to calculate the modal damping ratio, ultimately achieving accurate identification of the bridge structure's modal parameters and providing crucial data support for bridge damage diagnosis and condition assessment.

[0188] Example

[0189] The finite element model of the Wuling Mountain Bridge is used as the research object. The overall bridge diagram is shown below. Figure 4 As shown; a finite element model of the Wuling Mountain Bridge was created using Midas software, as follows. Figure 5 As shown in the figure, the model consists of 593 nodes and 419 elements, with a total length of 670 meters and a main span of 360 meters. The building materials include C40, C50, and C55 concrete (selected from the database of software specification JTG3362-18(RC)) and Wire1670 steel strand (selected from the database of software specification JTG04(S)). The damping ratios of each material are set as follows: concrete 0.05, steel strand 0.02. Boundary conditions are set to simulate the interaction between the structure and its supporting environment. Specifically, the stay cables are fixedly constrained with respect to the bridge deck and towers, the bottom pier supports are fixedly constrained, the translational degrees of freedom of the supports on both sides of the bridge deck in the Y and Z directions are constrained, and the translational degree of freedom of the supports at the connection between the piers and the bridge deck in the Y direction is constrained. Modal analysis is performed on the model, and the first six modal parameters of the structure are shown in Table 1.

[0190] Table 1: Modal parameters of each order in the finite element model

[0191]

[0192] The bridge deck was discretized into 101 nodes, and natural excitation was simulated using Gaussian white noise. Based on the optimal sensor placement strategy for cable-stayed bridges and considering the specific characteristics of the model, seven measurement points were arranged: one on each side span and five on the main span. All sensors were located on the centerline of the bridge deck, recording the vertical acceleration response for 1800 seconds at a sampling frequency of 20Hz. The sensor placement is as follows: Figure 6 As shown.

[0193] To account for the impact of measurement noise, we added Gaussian noise with signal-to-noise ratios (SNRs) of 1 dB, 5 dB, and 10 dB to the original data, thus achieving three different noise conditions. For each noise condition, 50 independent contaminated data samples were generated to ensure the statistical reliability of subsequent analyses.

[0194] A comprehensive statistical evaluation was conducted on all samples under different signal-to-noise ratio environments (1dB, 5dB, and 10dB SNR) to further verify the robustness of the method in accurately identifying the structural damping ratio. Under different signal-to-noise ratio (SNR) conditions, a consistent processing procedure and parameter configuration were adopted. The specific parameter settings are as follows: (1) The model order is assumed to be from 2 to 100; the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance are 0.02, 0.05, and 0.05, respectively; the number of blocks in the Toeplitz matrix is ​​380. (2) In MvFIF, the weight parameter ξ is 3.9, the stopping criterion δ is 0.002, and the maximum number of iterations is 200. (3) When identifying the frequency, the distance parameter ε of DBSCAN is 0.002, and the MinPts value is 25.

[0195] Statistical analysis was performed on 50 samples under each noise condition, and the error between the average result and the theoretical value is shown in Table 2. The table shows that the modal frequencies identified by all samples have high accuracy, with a maximum error of only 1.35%. This indicates that the modal frequencies are relatively insensitive to noise.

[0196] Table 2: Frequency identification results under different operating conditions

[0197]

[0198] When identifying modal frequencies, COV-SSI, EMD-SSI, and the method proposed in this invention all exhibit different characteristics. COV-SSI shows significant sensitivity to noise contamination: while all modal damping ratios remain within ±5% error range under high signal-to-noise ratio conditions, its accuracy drops sharply at low signal-to-noise ratio levels, with the first mode damping ratio error reaching as high as 16%. Although EMD-SSI can partially mitigate noise interference, its filtering effect is still limited by its decomposition characteristics. In contrast, MvFIF-SSI demonstrates superior robustness, consistently obtaining reliable damping ratio estimates under various noise conditions. All modal errors remain within ±5%, confirming the effectiveness of the method proposed in this invention in noise suppression and its ability to reduce noise-induced disturbances during covariance matrix decomposition, thereby improving the accuracy of modal parameter estimation. See Table 3 for details, with 50 samples for each operating condition.

[0199] Table 3: Comparison of damping ratio identification results using different methods (50 samples)

[0200]

[0201] Table 4 lists the coefficient of variation (CV) of the damping ratio determined using various methods at different noise levels (50 samples per condition). The results show that the proposed method achieves the minimum CV value under most modal orders and noise conditions, indicating that the proposed method has significant advantages in reducing data dispersion compared to the unfiltered method and the EMD-SSI processing method.

[0202] Table 4: Comparison of coefficients of variation for different methods of identifying damping ratio (50 samples)

[0203]

[0204] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for automatic identification of bridge modal parameters considering multi-channel information, characterized in that, Includes the following steps: S1. COV-SSI is used to directly analyze multi-channel monitoring signals to generate a stability map. Combined with the DBSCAN clustering algorithm, the stability axis is automatically extracted to achieve automatic identification of modal frequencies. S2. Use MvFIF to decompose the multi-channel monitoring data to generate an intrinsic mode function set with mode alignment characteristics; The specific steps of step S2 are as follows: S21. Determine the filter length: Use the rotation angle of the vector as it changes over time to determine a unique filter length; For the number of measurement points is Bridge multi-channel monitoring data: T represents transpose, using vectors Rotation angle changing over time Determine the unique filter length ,in The definition is as follows: （15） For filter length The calculation uses the following formula: （16） in, Represents a sequence The number of data points contained in it yes The number of extreme points It is a weight parameter. By rounding a number to the nearest integer, the average scale of the highest frequency rotation in the embedded signal can be estimated. S22. Iterative decomposition of the signal: Iterate according to the following formula until the difference between adjacent iterations meets the stopping criterion; （17） In the formula, Indicates the number of iterations. Indicates the first The first channel in the The IMF's steps yes The corresponding Fourier transform, Represents the identity matrix. Denotes a diagonal matrix; DFT stands for Discrete Fourier Transform. The formula for the stopping criterion is: （18） in, Denotes the Euclidean norm; when and , When the set is the set of natural numbers, formula (18) holds true; The first IMF is obtained according to the following formula (19), and the newly generated IMF is subtracted from the current signal; then the above calculation steps are repeated until... The final IMF group is obtained according to formula (21); （19） （20） （21） The initial value of the IMF is 0. Indicates the inverse Fourier transform; Thus, the original The monitoring signal is simultaneously decomposed into multiple IMF groups: （22） （23） （24） in, Indicates the signal of each channel The total number of IMFs is the number of decomposition layers. It is the IMF's layer index. Indicates the first IMF array of the layer S3. Calculate the instantaneous frequency and bandwidth of the IMF in step S2 using HHT, filter out the IMF components containing the target modal frequency, and perform linear reconstruction. S4. Using the reconstructed multi-channel monitoring data from step S3 as the system input for the COV-SSI algorithm, calculate the system matrix and output matrix, and use eigenvalue decomposition to calculate the modal damping ratio; use the DBSCAN clustering algorithm to automatically extract the stability axis. The specific steps are as follows: S151. Screen the poles in the stability plot to ensure the authenticity of the data. The modal parameters should meet the following standards: 1) The modal damping ratio is always positive; 2) The modal damping ratio does not exceed 15%. S152. Select the initial point from step S151 and calculate the number of points in its neighborhood: Randomly select an unvisited frequency point from all poles of the stability graph, and denote it as point. ; Calculation points radius All points within the range are denoted as ;if If the number of points in the data is less than the density parameter MinPts, then the points will be... Mark as noise point; if If the number of points in the array is not less than MinPts, then the points... With the core point, with points Start a new cluster from the beginning; S153. Based on the number of points in the neighborhood obtained in step S152, determine whether the point is a noise point or a core point, and expand the cluster accordingly; then... and All points in the cluster are initialized to a new cluster, denoted as cluster . From cluster Starting from the core point, examine its neighborhood sequentially; for clusters Core point of each point Check its neighborhood ;if If the number of points in the array is not less than MinPts, then... Add all points to the cluster In the middle; for each core point within its neighborhood, repeatedly check its neighborhood until a cluster is reached. It cannot be expanded further; S154. Repeat steps S151-S153 until all poles have been visited. S155. The average frequency and average damping ratio of the poles in each cluster are used as representative values ​​of the data in the cluster.

2. The automatic identification method for bridge modal parameters considering multi-channel information as described in claim 1, characterized in that, Step S1 specifically includes the following steps: S11. Construct a discrete state model: The stochastic discrete-time state-space model of a system with degrees of freedom is expressed as follows: （1） in, It is a discrete-time state vector. For monitoring data, For the number of measurement points, For process noise, To measure noise, For the discrete system matrix, It is a discrete output matrix; Based on multi-channel monitoring signals, using discrete real-time monitoring data Constructing the Hankel matrix The expression is as follows: （2） in, Indicates the first The sequence of output signals from each measuring point at time t, the Hankel matrix has a total of Each block row and The columns are divided into and Two matrices, representing the "past" and "future" respectively, each matrix having... One block of lines; parameters This represents the number of samples used to calculate the output covariance matrix, theoretically... ; S12. Calculate the output covariance matrix: Estimate the output covariance matrix using a finite amount of data. （3）； S13. Construct the Toeplitz matrix: Construct the Toeplitz matrix based on the output covariance matrix in step S12, and further organize it to obtain the state-output covariance matrix; Based on the multi-channel monitoring data in step S11 The Toeplitz matrix is ​​constructed using the output covariance matrix, as shown in the following expression: （4） Further simplification of the Toeplitz matrix yields: （5） in, Representing the state-output covariance matrix, Equation (5) shows that the Toeplitz matrix can be decomposed into a generalized observable matrix. and extended controllable matrix ,in For system order, The number of measurement points is used to observe the generalized observable matrix. Includes system matrix and output matrix ; S14. Singular Value Decomposition: Perform singular value decomposition on the Toeplitz matrix from step S13 to obtain the system matrix. and output matrix ; Combining formula (5) in step S13 with the singular value decomposition of the Toeplitz matrix, we can obtain: （6） （7） The output matrix is ​​obtained from formula (7). Equal to the front of the generalized observable matrix OK; definition Two submatrices and : （8）； The system matrix is ​​obtained from formula (8) in step S14. : （9） in, Represents the pseudo-inverse of a matrix; S15. Constructing a stability graph: Obtain the system matrix through matrix operations, perform eigenvalue decomposition on it, calculate the modal frequencies to identify modal parameters, and further screen poles to construct a stability graph; For system matrix Perform eigenvalue decomposition: （10） in, Let be the discrete-time eigenvector matrix of the system. For the first eigenvalues The diagonal matrix formed; The system frequency is derived from the following formula: （11） in, Indicates conjugate. The modal frequency; By combining stability diagrams to observe the changes in modal frequencies, damping ratios, and mode shapes at different model orders, the true physical modes can be identified. The calculation formula is as follows: （12） （13） （14） In the formula, Indicates the model order. , , These represent the modal frequencies, damping ratios, and mode shapes for each order, respectively. , , These are the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance, respectively; MAC is the modal guarantee criterion; and the DBSCAN clustering algorithm is used to automatically extract the stability axis in the generated stability diagram.

3. The automatic identification method for bridge modal parameters considering multi-channel information as described in claim 1, characterized in that, When performing signal decomposition on multi-channel monitoring data using MvFIF in step S2, predefined parameters are used, including weighting coefficients, stopping criteria, and maximum number of iterations.

4. The automatic identification method for bridge modal parameters considering multi-channel information as described in claim 1, characterized in that, Step S3 specifically includes the following steps: S31. Calculate instantaneous frequency and bandwidth: Calculate the instantaneous average frequency and bandwidth of each intrinsic mode function (IMF) using the Hilbert-Huang transform (HHT); S32. Screening IMF components: Correlate the identified structural modal frequencies with the instantaneous frequency bandwidth of the IMF components, and retain the IMF components whose bandwidth fully contains the target modal frequencies. S33. Linear Reconstruction: Perform linear reconstruction on the selected IMF to extract basic information about the dynamic characteristics of the captured structural modes.

5. The automatic identification method for bridge modal parameters considering multi-channel information as described in claim 2, characterized in that, Step S4 specifically involves using the multi-channel monitoring data reconstructed in step S3 as the system input for the COV-SSI algorithm, and calculating the system matrix according to formulas (1)-(10) in step S1. and output matrix The damping ratio Calculated using the following formula: （25） in, Indicates the real part, The modal damping ratio is used; using formulas (12)-(14) in step S1, the poles corresponding to each mode of the stability diagram are obtained, and the average damping ratio is used as the final identification result.

6. A recognition system for implementing the automatic bridge modal parameter recognition method considering multi-channel information as described in any one of claims 1-5, characterized in that, It includes a frequency identification module, a multi-element signal decomposition module, a frequency-based signal filtering and reconstruction module, and a damping ratio identification module; The frequency identification module specifically identifies the modal frequencies of the bridge structure by analyzing multi-channel monitoring signals and combining them with the DBSCAN clustering algorithm, thus providing a foundation for subsequent modal parameter identification. The multivariate signal decomposition module specifically uses MvFIF to decompose multi-channel monitoring data and extract intrinsic mode function sets with excellent mode alignment characteristics in order to better process complex signals. The frequency-based signal filtering and reconstruction module specifically works by filtering IMF components related to structural modal frequencies and performing linear reconstruction to extract basic information about capturing the dynamic characteristics of structural modes, thereby improving the signal-to-noise ratio and useful information content of the signal. The damping ratio identification module specifically uses the reconstructed data as input to calculate the modal damping ratio, ultimately achieving accurate identification of the bridge structure's modal parameters and providing crucial data support for bridge damage diagnosis and condition assessment.

7. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and when the processor executes part or all of the computer-executable program, it is able to implement the automatic identification method for bridge modal parameters considering multi-channel information as described in any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the automatic identification method for bridge modal parameters considering multi-channel information as described in any one of claims 1-5.

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