Bridge modal parameter automatic identification method and system considering multichannel information

Abstract

The invention relates to a bridge modal parameter automatic identification method and system considering multi-channel information, and the method comprises the following steps: S1, directly analyzing a multi-channel monitoring signal through COV-SSI, generating a stability diagram, and automatically extracting a stability axis in combination with a DBSCAN clustering algorithm, thereby achieving the automatic identification of a modal frequency; s2, performing signal decomposition on the multi-channel monitoring data by adopting MvFIF to generate an intrinsic mode function (IMF) group with a mode alignment characteristic; s3, the instantaneous frequency and bandwidth of the IMF in the step S2 are calculated through HHT, IMF components containing target modal frequency are screened out, and linear reconstruction is carried out; s4, taking the multi-channel monitoring data reconstructed in the step S3 as system input of a COV-SSI algorithm, calculating a system matrix and an output matrix, and calculating a modal damping ratio by utilizing eigenvalue decomposition; according to the method, the spatial-temporal correlation among multi-channel data can be considered, and synchronous decomposition of multi-channel monitoring data is realized; and automatic and accurate identification of the structural modal parameters under different noise levels can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge structural health monitoring and signal processing, and relates to a method for automatically identifying bridge modal parameters considering multi-channel information, in particular to a method and system for automatically identifying bridge modal parameters, a computer device, and a computer-readable storage medium that fuse multi-variate fast iterative filtering (MvFIF) and DBSCAN clustering. Background Art

[0002] In modern society, the traffic flow has increased rapidly, the vehicle types have become increasingly diverse, and the proportion of heavy-duty vehicles has been rising continuously. This has made the load conditions borne by 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 occurred frequently. The changes in traffic load conditions are intertwined with various adverse events, leading to problems such as accelerated deterioration of bridge durability, significant decline in load-bearing capacity, and gradual attenuation of structural resistance. The changes in the modal parameters (such as frequency, damping ratio, mode shape, etc.) of the bridge structure can reflect problems such as damage, fatigue, or aging. Therefore, accurately identifying modal parameters is of great significance for bridge damage diagnosis, condition assessment, and disaster prevention.

[0003] Operational modal analysis (OMA) is a structural dynamics testing method based on ambient excitation. It can be tested when the structure is in an operational state without artificial excitation and without 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: frequency domain method, time domain method, and time-frequency domain method according to the different identification domains. Among them, stochastic subspace identification (SSI) is the most commonly used time domain modal parameter identification method at present and is widely used 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 will inevitably be contaminated by noise.

[0004] Covariance stochastic subspace identification, that is, COV-SSI, is a system identification method for modal parameter identification (such as frequency, damping ratio, and mode shape). It is often used in structural health monitoring, vibration analysis of bridges and buildings. Although COV-SSI incorporates a noise model in theory, when the measurement noise variance is large, the noise components in the singular value decomposition of the covariance matrix will cover up the true modal information, resulting in deviations in modal parameter estimation, which directly affects the performance of SSI, especially the identification accuracy of modal damping ratio. At the same time, due to the existence of noise, the characteristics of the covariance matrix will be changed, resulting in the existence of false modes (i.e., noise points) in the stability diagram generated based on SSI in addition to the true modes of the structure. These noise points do not conform to the distribution law of normal modal characteristics, thus seriously affecting the manual selection and extraction of physical modes on the stability diagram.

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

[0006] In view of this, in order to solve the problems that the existing stochastic subspace identification may lead to deviations in modal parameter estimation when the measurement noise variance is large, especially the identification accuracy of modal damping ratio is greatly affected, and at the same time, the noise will generate false modes in the stabilization diagram, interfering with the identification of true modes and affecting the manual selection and extraction on the stability diagram, the present invention provides an automatic identification method and system for bridge modal parameters considering multi-channel information. This method can consider the spatio-temporal correlation between multi-channel data and realize the 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; at the same time, it also realizes the automation of modal parameter extraction, thus avoiding the subjective errors brought by manual intervention.

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

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

[0009] S1. Use COV-SSI to directly analyze multi-channel monitoring signals to generate a stabilization diagram, and combine the DBSCAN clustering algorithm to automatically extract the stable axis to achieve automatic identification of modal frequencies;

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

[0011] S3. Calculate the instantaneous frequency and bandwidth of the IMFs in step S2 through HHT, screen 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 calculate the modal damping ratio using eigenvalue decomposition.

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

[0014] S11. Construct a discrete state model: a stochastic discrete-time state space model of an n-degree-of-freedom system, the expression is:

[0015]

[0016] where, x k ∈R 2n is the discrete-time state vector, yk ∈R l is the output vector, l is the number of measurement points, w k ∈R 2n is the process noise, v k ∈R l is the measurement noise, A ∈ R 2n×2n is the discrete state matrix, C ∈ R l×2n is the discrete output matrix;

[0017] According to the multi-channel monitoring signals, using the measured structural response vector y at discrete time k k construct the Hankel matrix H, and the expression is as follows:

[0018]

[0019] where, y i ∈R l represents the sequence formed by the output signals of each measurement point at the i-th time. The Hankel matrix has 2i block rows and j columns, and is divided into Y p and Y f two matrices, representing "past" and "future" respectively, and each matrix has i block rows; the parameter j represents the number of samples used to calculate the output covariance matrix, and theoretically j → ∞;

[0020] S12. Calculate the output covariance matrix: Estimate the output covariance matrix using the limited data quantity:

[0021]

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

[0023] According to the multi-channel monitoring data y in step S11 k+1 , construct the Toeplitz matrix using the output covariance matrix, and the expression is as follows:

[0024]

[0025] Further organize the Toeplitz matrix to obtain:

[0026]

[0027] where, represents the state-output covariance matrix. Formula (5) shows that the Toeplitz matrix can be decomposed into the generalized observable matrix T i ∈R il×2n and the 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 contains the state matrix A and output matrix C of the system;

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

[0029] Performing singular value decomposition on the Toeplitz matrix in combination with formula (5) in step S13 gives:

[0030]

[0031] It is obtained from formula (7) that the output matrix C is equal to the first l rows of the generalized observable matrix;

[0032] Define two sub - matrices T1 and T2 of T i :

[0033]

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

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

[0036] where, () + denotes the pseudo - inverse of the matrix;

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

[0038] Perform eigenvalue decomposition on the system matrix A:

[0039] A = ψΛψ -1 (10)

[0040] where, Ψ is the system discrete - time eigenvector matrix, and Λ is the diagonal matrix composed of the system eigenvalues λ i ;

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

[0042]

[0043] where, (·) * denotes the conjugate, and f i is the modal frequency;

[0044] Due to the overestimation of the system order, the identification results often contain a large number of spurious modes. Usually, the stabilization diagram is combined to observe the changes of modal frequencies, damping ratios, and modal shapes at different model orders to help identify the true physical modes. 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, f, ξ, and Φ represent the modal frequencies, damping ratios, and modal shapes of each order respectively; ∈ f 、∈ ξ 、∈ Φ are the characteristic frequency tolerance, damping ratio tolerance, and modal shape tolerance respectively; MAC is the Modal Assurance Criterion; the DBSCAN clustering algorithm is used to automatically extract the stable axis in the generated stabilization diagram.

[0049] Furthermore, in step S15, when using the DBSCAN clustering algorithm to cluster the data set, the distance parameter ε and the density parameter (MinPts) need to be determined. Currently, both of these two parameters in the DBSCAN clustering algorithm need to be set according to 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 stabilization diagram to ensure the authenticity of the data. Among them, the modal parameters should meet the following criteria: 1) The modal damping ratio is always positive. 2) In practical engineering applications, the modal damping ratio is usually considered not to exceed 15%.

[0052] S152. Select the initial point in step S151 and calculate the number of points in its neighborhood: Randomly select an unvisited frequency point from all the poles in the stabilization diagram and denote it as point P; Calculate all the points within the radius ε of point P and denote it 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 a core point, and start a new cluster with point P as the starting point;

[0053] S153. Determine whether the point is a noise point or a core point based on the number of points in the neighborhood in step S152, and expand the cluster based on this; initialize all points in point P and N(P) as a new cluster, denoted as cluster C; starting from the core points in cluster C, check their neighborhoods 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 the neighborhood, repeat checking its neighborhood until cluster C can no longer be expanded;

[0054] S154. Repeat the steps of S151 - S153 until all extreme points have been visited;

[0055] S155. Use the average frequency value and average damping ratio value of the extreme points in each cluster as the representative values of the data in the cluster.

[0056] Furthermore, when step S2 uses MvFIF to decompose the multi - channel monitoring data, predefined parameters are adopted, including a weight coefficient, a stopping criterion, and a maximum number of iterations. Beneficial effect: By adopting the predefined parameters, the signal can be effectively decomposed, and a set of intrinsic mode functions (IMFs) with excellent modal alignment characteristics can be generated.

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

[0058] S21. Determine the filter length: Determine the unique filter length using the rotation angle of the vector changing with time;

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

[0060]

[0061] For the calculation of the filter length L, the following formula is used:

[0062]

[0063] where N is the dimension of θ(t), k is the number of extreme points in θ(t), ξ is a weight parameter, Round a number to the nearest integer. Through this process, the average scale of the highest - frequency rotation in the embedded signal can be estimated;

[0064] S22. Iteratively decompose the signal: Iterate according to the following formula until the difference between adjacent iterations satisfies the stopping criterion;

[0065]

[0066] In the formula, l represents the number of iterations, represents the IMF of the i-th channel at the l-th step, is its corresponding Fourier transform, 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 (the set of natural numbers), the formula (20) holds;

[0070] Obtain the first IMF according to the following formula (20), and subtract the newly generated IMF from the current signal; then repeat the above calculation steps until θ(t) < 2, and obtain the final IMF set according to the 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] So far, the original m-dimensional monitoring signal is simultaneously decomposed into multiple IMF sets:

[0075]

[0076]

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

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

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

[0080] S32. Screen IMF components: Associate the identified structural modal frequencies with the instantaneous frequency bandwidths of the IMF components, and retain the IMF components whose bandwidths fully contain the target modal frequencies;

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

[0082] Furthermore, step S4 is specifically as follows: Use the multi-channel monitoring data reconstructed in step S3 as the system input of the COV-SSI algorithm, and calculate the system matrix A and the output matrix C according to formulas (1)-(10) in step S1, where the damping ratio ξ i is calculated by the following formula:

[0083]

[0084] where, (·) R denotes the real part, and ξ i is the modal damping ratio;

[0085] Use formulas (12)-(14) in step S1 to obtain the poles corresponding to each order of the stable diagram, and use the average damping ratio as the final identification result.

[0086] An improved stochastic subspace identification system based on multi-modal decomposition fusion and DBSCAN clustering includes a frequency identification module, a multi-signal decomposition module, a frequency-based signal screening and reconstruction module, and a damping ratio identification module;

[0087] The frequency identification module is specifically as follows: Automatically identify the modal frequencies of the bridge structure by analyzing multi-channel monitoring signals and combining with the DBSCAN clustering algorithm, providing a basis for subsequent modal parameter identification;

[0088] The multi-signal decomposition module is specifically as follows: Use MvFIF to decompose multi-channel monitoring data, and extract a group of intrinsic mode functions (IMFs) with excellent modal alignment characteristics to better process complex signals;

[0089] The frequency-based signal screening and reconstruction module is specifically as follows: By screening the IMF components related to the structural modal frequencies and performing linear reconstruction, extract the basic information that captures the dynamic characteristics of the structural modes, improving the signal-to-noise ratio and the content of useful information of the signal;

[0090] The damping ratio identification module is specifically as follows: Use the reconstructed data as the input, calculate the modal damping ratio, and finally achieve accurate identification of the modal parameters of the bridge structure, providing key data support for the damage diagnosis and condition assessment of the bridge.

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

[0092] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, it can implement the automatic identification method for bridge modal parameters considering multi-channel information of the present invention.

[0093] The automatic identification method for bridge modal parameters considering multi-channel information disclosed by the present invention has the following beneficial effects:

[0094] 1. Improve the accuracy of modal parameter identification: Through multi-stage optimization processes such as frequency identification, multi-signal decomposition, frequency-based signal screening and reconstruction, and damping ratio identification, gradually extract and refine modal parameter information, and finally obtain high-precision modal frequency and damping ratio identification results.

[0095] 2. Have high-efficient noise suppression ability: Through multi-variate fast iterative filtering (MvFIF) to synchronously decompose multi-channel monitoring data, it can effectively filter noise while retaining useful information related to structural modal parameters; under different noise levels, this method can accurately identify modal parameters, showing excellent robustness, and solving the problem of deviation in modal parameter estimation of traditional SSI methods in strong noise environments; using the DBSCAN clustering algorithm to automatically extract stable axes can effectively identify true physical modes, avoiding the interference of false modes caused by noise to modal parameter identification and improving the accuracy of modal parameter identification.

[0096] 3. High degree of automation: Combining with the DBSCAN clustering algorithm, it can automatically extract stable axes in the stability diagram to achieve automatic identification of modal frequencies without manual intervention, reducing subjective errors brought by manual selection and extraction of modal parameters, and improving 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), automatically screen out the IMF components containing the target modal frequency and perform linear reconstruction to further extract structural modal dynamic characteristic information, 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 strong noise environments, and is applicable to various actual bridge monitoring scenarios; it can be extended and applied to other types of large structures, such as high-rise buildings, long-span bridges, high arch dams, etc., providing an effective technical means for the health monitoring and condition assessment of various structures.

[0098] Other advantages, objects, and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] In order to make the objects, technical solutions, and advantages of the present invention more clear, the present invention will be described in detail preferably with reference to the accompanying drawings, wherein:

[0100] Figure 1 is a flowchart of a method for automatically identifying bridge modal parameters considering multi-channel information according to the present invention;

[0101] Figure 2 is a flowchart of step S1 in the method for automatically identifying bridge modal parameters considering multi-channel information according to the present invention;

[0102] Figure 3 is a flowchart of steps S2 - S4 in the method for automatically identifying bridge modal parameters considering multi-channel information according to the present invention;

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

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

[0105] Figure 6 is a schematic diagram of the measuring point arrangement in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0106] The following describes the embodiments 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 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] As Figures 1 to 3 shown, a method for automatically identifying bridge modal parameters considering multi-channel information includes the following steps:

[0108] S1. Use COV-SSI to directly analyze multi-channel monitoring signals to generate a stability diagram, and combine the DBSCAN clustering algorithm to automatically extract the stable axis to achieve automatic identification of modal frequencies.

[0109] Specifically:

[0110] S11. Construct a discrete state model: The stochastic discrete-time state space model of an n-degree-of-freedom system, with the expression:

[0111]

[0112] where, \(x\) k \(\in\mathbb{R}\) 2n is the discrete-time state vector, \(y\) k \(\in\mathbb{R}\) l is the output vector, \(l\) is the number of measurement points, \(w\) k \(\in\mathbb{R}\) 2n is the process noise, \(v\) k \(\in\mathbb{R}\) l is the measurement noise, \(A\in\mathbb{R}\) 2n×2n is the discrete state matrix, \(C\in\mathbb{R}\) l×2n is the discrete output matrix;

[0113] According to the multi-channel monitoring signals, use the measured structural response vector \(y\) at discrete time \(k\) k to construct a Hankel matrix \(H\), with the expression as follows:

[0114]

[0115] where, \(y\) i \(\in\mathbb{R}\) l represents the sequence formed by the output signals of each measurement point at the \(i\)-th moment. The Hankel matrix has \(2i\) block rows and \(j\) columns, and is divided into \(Y\) p and \(Y\) f two matrices, representing "past" and "future" respectively, and each matrix has \(i\) block rows; The parameter \(j\) represents the number of samples used to calculate the output covariance matrix, and theoretically \(j\rightarrow\infty\);

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

[0117]

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

[0119] According to the multi-channel monitoring data \(y\) in step S11 k+1 , use the output covariance matrix to construct a Toeplitz matrix, with the expression as follows:

[0120]

[0121] Further organize the Toeplitz matrix to obtain:

[0122]

[0123] Among them, represents 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 the extended controllability matrix Δ i ∈R 2n×li , where n is the system order and l is the number of measurement points. It is observed that the generalized observable matrix T i contains the system 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 state matrix A and output matrix C;

[0125] Combining with equation (5) in step S13 to perform singular value decomposition on the Toeplitz matrix, we can get:

[0126]

[0127] It can be obtained from equation (7) that the output matrix C is equal to the first l rows of the generalized observable matrix;

[0128] Define two submatrices T1 and T2 of T i :

[0129]

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

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

[0132] where () + represents the pseudo-inverse of the matrix;

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

[0134] Perform eigenvalue decomposition on the system matrix A:

[0135] A = ψΛψ -1 (10)

[0136] where Ψ is the system discrete-time eigenvector matrix and Λ is the diagonal matrix composed of the system eigenvalues λ i ;

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

[0138]

[0139] where (·) * denotes conjugate, and f i is the modal frequency;

[0140] Due to the overestimation of the system order, the identification results often contain a large number of spurious modes. Usually, the changes of modal frequency, damping ratio, and modal shape at different model orders are observed by combining with the stabilization diagram to help identify the true physical modes. 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 frequency, damping ratio, and modal shape of each order respectively; ∈ f , ∈ ξ , ∈ Φ are the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance respectively; MAC is the Modal Assurance Criterion; the DBSCAN clustering algorithm is used to automatically extract the stable axis in the generated stabilization diagram.

[0144] Among them, when using the DBSCAN clustering algorithm to cluster the dataset, the distance parameter ε and the density parameter (MinPts) need to be determined. At present, both of these two parameters in the DBSCAN clustering algorithm need to be set according to 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 stabilization diagram to ensure the authenticity of the data. Among them, the modal parameters should meet the following criteria: 1) The modal damping ratio is always positive. 2) In practical engineering applications, it is usually considered that the modal damping ratio does not exceed 15%.

[0147] S152. Select the initial point in step S151 and calculate the number of points in its neighborhood: Randomly select an unvisited frequency point from all the poles in the stabilization diagram and denote it as point P; Calculate all the points within the radius ε of point P and denote it 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 a core point, and start a new cluster with point P as the starting point;

[0148] S153. Determine whether the point is a noise point or a core point based on the number of points in the neighborhood in step S152, and expand the cluster based on this; initialize all points in point P and N(P) as a new cluster, denoted as cluster C; starting from the core points in cluster C, check their neighborhoods 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 the neighborhood, repeat checking its neighborhood until cluster C can no longer be expanded.

[0149] S154. Repeat the steps of S151 - S153 until all extreme points have been visited.

[0150] S155. Use the average frequency and average damping ratio of the extreme points in each cluster as the representative values of the data in the cluster.

[0151] Furthermore, when step S2 uses MvFIF to decompose the multi - channel monitoring data, predefined parameters are adopted, including a weight coefficient, a stopping criterion, and a maximum number of iterations. Beneficial effect: By adopting the predefined parameters, the signal can be effectively decomposed, and a group of intrinsic mode functions (IMFs) with excellent modal alignment characteristics can be generated.

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

[0153] The specific steps are as follows:

[0154] S21. Determine the filter length: Determine the unique filter length using the rotation angle of the vector varying with time.

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

[0156]

[0157] For the calculation of the filter length L, the following formula is adopted:

[0158]

[0159] where N is the dimension of θ(t), k is the number of extreme points in θ(t), and ξ is a weight parameter. Round a number to the nearest integer. Through this process, the average scale of the highest-frequency rotation in the embedded signal can be estimated;

[0160] S22. Iteratively decompose the signal: Iterate according to the following formula until the difference between adjacent iterations satisfies the stopping criterion;

[0161]

[0162] where l represents the number of iterations, represents the IMF of the i-th channel at the l-th step, is its corresponding Fourier transform, 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 (the set of natural numbers), formula (20) holds;

[0166] Obtain the first IMF according to the following formula (20), and subtract the newly generated IMF from the current signal; then repeat the above calculation steps until θ(t) < 2, and obtain the final IMF set 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] So far, the original m-dimensional monitoring signal is simultaneously decomposed into multiple IMF sets:

[0171]

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

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

[0174] Specifically, it includes the following steps:

[0175] S31. Calculate the instantaneous frequency and bandwidth: Use the Hilbert-Huang Transform (HHT) to calculate the instantaneous average frequency and bandwidth of each Intrinsic Mode Function (IMF).

[0176] S32. Screen the IMF components: Associate the identified structural modal frequencies with the instantaneous frequency bandwidth of the IMF components, and retain the IMF components whose bandwidths fully contain the target modal frequencies.

[0177] S33. Linear reconstruction: Perform linear reconstruction on the selected IMF to extract the basic information that captures the dynamic characteristics of the 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 calculate the modal damping ratio using eigenvalue decomposition.

[0179] Step S4 is specifically as follows: Use the multi-channel monitoring data reconstructed in step S3 as the system input of the COV-SSI algorithm, and calculate the system matrix A and output matrix C according to formulas (1)-(10) in step S1, where the damping ratio ξ i is calculated by the following formula:

[0180]

[0181] where (·) R represents the real part, and ξ i is the modal damping ratio;

[0182] Use formulas (12)-(14) in step S1 to obtain the poles corresponding to each order of the modal in the stability diagram, and use the average damping ratio as the final identification result.

[0183] An improved stochastic subspace identification system based on multi-modal decomposition fusion DBSCAN clustering includes a frequency identification module, a multi-signal decomposition module, a frequency-based signal screening and reconstruction module, and a damping ratio identification module;

[0184] The frequency identification module is specifically as follows: Automatically identify the modal frequencies of the bridge structure by analyzing the multi-channel monitoring signals and combining the DBSCAN clustering algorithm, providing a basis for subsequent modal parameter identification;

[0185] The multi-signal decomposition module is specifically as follows: Use MvFIF to decompose the multi-channel monitoring data, and extract a set of Intrinsic Mode Functions (IMFs) with excellent modal alignment characteristics to better process complex signals;

[0186] The frequency-based signal screening and reconstruction module is specifically as follows: By screening the IMF components related to the structural modal frequencies and performing linear reconstruction, extract the basic information that captures the dynamic characteristics of the structural modes, improving the signal-to-noise ratio and the content of useful information of the signal.

[0187] The damping ratio identification module specifically takes the reconstructed data as input, calculates the modal damping ratio, and finally realizes the accurate identification of the modal parameters of the bridge structure, providing key data support for the damage diagnosis and condition assessment of the bridge.

[0188] Embodiment

[0189] Taking the finite element model of Wuling Mountain Bridge as the research object. The overall view of the bridge is as Figure 4 shown; use Midas software to establish the finite element model of Wuling Mountain Bridge, as Figure 5 shown. 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 strands (selected from the database of software specification JTG04(S)), and the damping ratios of each material are set as follows: 0.05 for concrete and 0.02 for steel strands. The interaction between the structure and its support environment is simulated by setting boundary conditions. Specifically, the stay cables are fixed constraints with the bridge deck and the cable towers, the bottom pier bearings are fixed constraints, the translational degrees of freedom of the bearings on both sides of the bridge deck in the Y and Z directions are constrained, and the translational degree of freedom of the bearings at the connection between the pier and the bridge deck in the Y direction is constrained. Modal analysis is performed on the model, and the first six - order modal parameters of the structure are shown in Table 1.

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

[0191]

[0192] The bridge deck is discretized into 101 nodes, and natural excitation is simulated by Gaussian white noise. According to the optimal sensor layout strategy for cable - stayed bridges and considering the specific characteristics of the model, a total of seven measurement points are arranged: one at each side span and five at the main span. All sensors are located on the center line of the bridge deck, and the vertical acceleration responses are recorded for 1800 seconds at a sampling frequency of 20Hz. The layout of the sensor measurement points is as Figure 6 shown.

[0193] To consider the influence of measurement noise, Gaussian noise with signal - to - noise ratios (SNRs) of 1dB, 5dB, and 10dB respectively is added to the original data, thus realizing three different noise conditions. For each noise condition, 50 independent contaminated data samples are generated to ensure the statistical reliability of subsequent analysis.

[0194] Comprehensive statistical evaluations were conducted on all samples in different signal-to-noise ratio environments (1 dB, 5 dB, and 10 dB SNR) to further verify the robustness of the method in accurately identifying the structural damping ratio; consistent processing procedures and parameter configurations were adopted under different signal-to-noise ratio (SNR) conditions; the specific parameter settings are as follows: (1) The model order was assumed to range from 2 to 100; the tolerances for characteristic frequency, damping ratio, and mode shape were 0.02, 0.05, and 0.05, respectively; the number of block rows of the Toeplitz matrix was set to 380. (2) In MvFIF, the weight parameter ξ was 3.9, the stopping criterion δ was 0.002, and the maximum number of iterations was 200. (3) When identifying frequencies, the distance parameter ε value of DBSCAN was 0.002, and the MinPts value was 25.

[0195] Statistical analyses were performed on 50 groups of samples under each noise condition, and the errors between the average results and the theoretical values are shown in Table 2. As can be seen from the table, the modal frequencies identified for all samples are highly accurate, with a maximum error of only 1.35%. This indicates that the modal frequencies are less sensitive to noise.

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

[0197]

[0198] When COV-SSI, EMD-SSI, and the method proposed in the present invention are used to identify modal frequencies, COV-SSI shows obvious sensitivity to noise pollution: Although all modal damping ratios can maintain an error range of ±5% under high signal-to-noise ratio conditions, at low signal-to-noise ratio levels, its accuracy drops significantly, and the error of the first modal damping ratio is as high as 16%. Although EMD-SSI can partially reduce noise interference, its filtering effect is still limited by the decomposition characteristics. In contrast, MvFIF-SSI shows excellent robustness and can continuously obtain reliable damping ratio estimates under different noise conditions. All modal errors are kept within ±5%, which confirms the effectiveness of the method proposed in the present invention in noise suppression and its ability to reduce noise-induced perturbations during the covariance matrix decomposition process, thereby improving the accuracy of modal parameter estimation. For specific reference, see Table 3, with 50 samples for each working condition.

[0199] Table 3: Comparison of damping ratio identification results by 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 for each working condition). The results show that, for most modal orders and noise conditions, the proposed method can obtain the minimum CV value, indicating that the method proposed in the present invention has significant superiority in reducing data discreteness compared with the unfiltered method and the EMD-SSI processing method.

[0202] Table 4: Comparison of the coefficient of variation of damping ratio identified by different methods (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 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 purpose and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. An automatic identification method for bridge modal parameters considering multi-channel information, characterized in that, It includes the following steps: S1. Use COV-SSI to directly analyze multi-channel monitoring signals to generate a stability diagram, combine the DBSCAN clustering algorithm to automatically extract the stable axis, and achieve automatic identification of modal frequencies; S2. Use MvFIF to decompose multi-channel monitoring data to generate a group of intrinsic mode functions (IMFs) with modal alignment characteristics; S3. Calculate the instantaneous frequency and bandwidth of the IMFs in step S2 through HHT, screen out the IMF components containing the target modal frequency and perform linear reconstruction; 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 calculate the modal damping ratio using eigenvalue decomposition.

2. The automatic identification method for bridge modal parameters considering multi-channel information according to claim 1, wherein, Step S1 specifically includes the following steps: S11. Construct a discrete state model: The stochastic discrete-time state space model of an n-degree-of-freedom system, and the expression is: where x k ∈R 2n is the discrete-time state vector, y k ∈R l is the output vector, l is the number of measurement points, w k ∈R 2n is the process noise, v k ∈R l is the measurement noise, A ∈ R 2n×2n is the discrete state matrix, C ∈ R l×2n is the discrete output matrix; Based on the multi-channel monitoring signals, the measured structural response vector y at discrete time instant k is used k to construct a Hankel matrix H, whose expression is as follows: where y i ∈R l represents the sequence formed by the output signals of each measurement point at the i-th moment. The Hankel matrix has 2i block rows and j columns, and is divided into Y p and Y f two matrices, representing "past" and "future" respectively, and each matrix has i block rows; the parameter j represents the number of samples used to calculate the output covariance matrix, and theoretically j→∞; S12. Calculate the output covariance matrix: Estimate the output covariance matrix using a finite number of data; S13. Construct a Toeplitz matrix: Based on the output covariance matrix in step S12, construct a Toeplitz matrix, and further organize it to obtain the state-output covariance matrix; According to the multi-channel monitoring data y in step S11 k+1 , a Toeplitz matrix is constructed using the output covariance matrix, and the expression is as follows: Further organizing the Toeplitz matrix gives: Among them, denotes 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 the extended controllability matrix Δ i ∈R 2n×li , where n is the system order and l is the number of measurement points. It is observed that the generalized observable matrix T i contains the system state matrix A and output matrix C; S14. Singular value decomposition: Perform singular value decomposition on the Toeplitz matrix in step S13 to obtain the system state matrix A and output matrix C; Combined with formula (5) in step S13, performing singular value decomposition on the Toeplitz matrix gives: It can be obtained from formula (7) that the output matrix C is equal to the first l rows of the generalized observable matrix; Define T i with two submatrices T1 and T2: The system matrix A is obtained from formula (8) in step S14: A = (T1) + T2 (9) where, () + denotes the pseudo-inverse of a matrix; S15. Construct a stability diagram: Obtain the system matrix through matrix operations, perform eigenvalue decomposition on it, calculate the modal frequencies to identify modal parameters, and further preliminarily screen the poles to construct a stability diagram; Perform eigenvalue decomposition on the system matrix A: A = ψΛψ -1 (10) where Ψ is the system discrete-time eigenvector matrix, and Λ is the diagonal matrix composed of the system eigenvalues λ i ; The frequency of the system is obtained from the following formula: Among them, (·) * represents conjugation, and f i is the modal frequency; Combined with observing the changes of modal frequencies, damping ratios, and modal shapes at different model orders in the stability diagram, identify the true physical modes, and the calculation formula is as follows: (1 - MAC(i, i + 1)) < ∈ Φ (14) where \(i\) represents the model order, and \(f\), \(\xi\), and \(\varPhi\) represent the modal frequency, damping ratio, and modal shape of each order respectively; \(\in\) f and \(\in\) ξ and \(\in\) Φ are the characteristic frequency tolerance, damping ratio tolerance, and mode shape tolerance respectively; MAC is the modal assurance criterion; the DBSCAN clustering algorithm is used to automatically extract the stable axis in the generated stability diagram.

3. The automatic identification method for bridge modal parameters considering multi-channel information according to claim 2, characterized in that In step S15, when using the DBSCAN clustering algorithm to cluster the data set, it is necessary to determine the distance parameter ε and density parameter (MinPts), and use the DBSCAN clustering algorithm to automatically extract the stable axis. The specific steps are as follows: S151. Screen the poles in the stability diagram to ensure the authenticity of the data. Among them, the modal parameters should meet the following criteria: 1) The modal damping ratio is always positive; 2) In practical engineering applications, it is usually considered that the modal damping ratio does not exceed 15%; S152. Select the initial point in step S151 and calculate the number of points in its neighborhood: Randomly select an unvisited frequency point from all the poles in the stability diagram and denote it as point P; Calculate all the points within the radius ε of point P and denote it 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 a core point, and start a new cluster with point P as the starting point; S153. Determine whether the point is a noise point or a core point based on the number of points in the neighborhood in step S152, and expand the cluster based on this; Initialize all points in point P and N(P) as a new cluster, denoted as cluster C; Starting from the core points in cluster C, check their neighborhoods 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 the neighborhood, repeat checking its neighborhood until cluster C can no longer be expanded; S154. Repeat the steps of S151 - S153 until all extreme points have been visited; S155. Use the average frequency and average damping ratio of the extreme points in each cluster as the representative values of the data in the cluster.

4. The automatic bridge modal parameter identification method considering multi-channel information according to claim 1, characterized in that When step S2 uses MvFIF to perform signal decomposition on multi-channel monitoring data, predefined parameters are adopted, including weight coefficients, stopping criteria, and maximum number of iterations.

5. The automatic identification method for bridge modal parameters considering multi-channel information according to claim 1, characterized in that The specific steps of step S2 are as follows: S21. Determine the filter length: Determine the unique filter length using the rotation angle of the vector changing with time; For the multi-channel monitoring data of a bridge with \(m\) channels: \(\{x(t), t = 1, 2, \ldots, N\} = \{x_1(t), x_2(t), \ldots, x_m(t)\}\), where \(T\) represents the transpose. The unique filter length \(L\) is determined by the rotation angle \(\theta(t)\) of the vector \(x(t)\) varying with time, and \(\theta(t)\) is defined as follows: m (t)} T , where \(T\) represents the transpose. The unique filter length \(L\) is determined by the rotation angle \(\theta(t)\) of the vector \(x(t)\) varying with time, and \(\theta(t)\) is defined as follows: For the calculation of the filter length L, the following formula is used: where N is the dimension of θ(t), k is the number of extreme points in θ(t), and ξ 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 through this process. S22. Iteratively decompose the signal: Perform iteration according to the following formula until the difference between adjacent iterations meets the stopping criteria; where \(l\) represents the number of iterations, denotes the IMF of the \(i\)-th channel at the \(l\)-th step, is its corresponding Fourier transform, \(I\) represents the identity matrix, \(diag(·)\) represents the diagonal matrix, and DFT represents the discrete Fourier transform; The formula for the stopping criteria is: where, ||·||2 represents the Euclidean norm; when δ > 0 and (the set of natural numbers), the formula (20) holds; Obtain the first IMF according to the following formula (20), and subtract the newly generated IMF from the current signal; Then repeat the above calculation steps until θ(t) < 2, and obtain the final IMF group according to formula (21); IMF = IMF ∪ {x(t)} (21) Among them, the initial value of IMF is 0, and iDFT represents the inverse Fourier transform; So far, the original m-dimensional monitoring signal is simultaneously decomposed into multiple IMF groups: Among them, K represents the total number of IMFs (i.e., the decomposition layer number) of each channel signal x i (t), k is the layer index of the IMF, and IMF k (t) represents the IMF array of the k-th layer.

6. The automatic identification method for bridge modal parameters considering multi-channel information according to claim 1, characterized in that Step S3 specifically includes the following steps: S31. Calculate the instantaneous frequency and bandwidth: Use the Hilbert-Huang transform (HHT) to calculate the instantaneous average frequency and bandwidth of each intrinsic mode function (IMF); S32. Screen the IMF components: Associate 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 the basic information capturing the dynamic characteristics of the structural modal.

7. The automatic identification method for bridge modal parameters considering multi-channel information according to claim 1, characterized in that Step S4 is specifically as follows: Use the multi-channel monitoring data reconstructed in step S3 as the system input of the COV-SSI algorithm, and calculate the system matrix A and the output matrix C according to formulas (1)-(10) in step S1, where the damping ratio ξ i is calculated by the following formula: where, (·) R represents the real part, and ξ i is the modal damping ratio; using the formulas (12)-(14) in step S1, the poles corresponding to each order of mode in the stability diagram are obtained, and the average damping ratio is used as the final identification result.

8. An improved random subspace identification system based on multi-modal decomposition fusion and DBSCAN clustering, characterized in that, Including a frequency identification module, a multi-signal decomposition module, a frequency-based signal screening and reconstruction module, and a damping ratio identification module; The frequency identification module is specifically: By analyzing the multi-channel monitoring signal and combining with the DBSCAN clustering algorithm, automatically identify the modal frequencies of the bridge structure, providing a basis for subsequent modal parameter identification; The multi-signal decomposition module is specifically: Use MvFIF to decompose the multi-channel monitoring data, and extract the intrinsic mode function (IMF) group with excellent modal alignment characteristics to better process complex signals; The frequency-based signal screening and reconstruction module is specifically: By screening the IMF components related to the structural modal frequencies and performing linear reconstruction, extract the basic information capturing the dynamic characteristics of the structural modal, improving the signal-to-noise ratio and the content of useful information of the signal; The damping ratio identification module specifically: takes the reconstructed data as input, calculates the modal damping ratio, and finally realizes the accurate identification of the modal parameters of the bridge structure, providing key data support for the damage diagnosis and condition assessment of the bridge.

9. A computer device, characterized in that, It includes a processor and a memory. The memory is used to store computer-executable programs. The processor reads part or all of the computer-executable programs from the memory and executes them. When the processor executes part or all of the computer-executable programs, it can implement the automatic identification method of bridge modal parameters considering multi-channel information according to any one of claims 1-7.

10. A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, it can implement the automatic identification method of bridge modal parameters considering multi-channel information according to any one of claims 1-7.

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