Bridge structure modal parameter identification method

Abstract

The application relates to a bridge structure modal parameter identification method, which is based on a bridge structure micro-vibration video collected by a camera, fuses a variational mode decomposition (VMD), a phase-based video motion magnification (PBVM), a Gabor filter-based phase extraction method (GBP), an improved clustering algorithm (ICA) and an integrated covariance-driven stochastic subspace identification (SSI-Cov) and frequency domain decomposition (FDD) algorithm, and constructs a complete non-contact structure modal parameter identification system. In the absence of prior knowledge of the target frequency bandwidth, environmental noise interference and without obvious characteristic targets, the effective decoupling of multiple vibration modes of the bridge structure, the frequency domain feature extraction of small-amplitude vibration and the intelligent and automatic modal parameter extraction are realized, and the application belongs to the technical field of bridge structure health monitoring.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring technology, and specifically to a method for identifying bridge structural modal parameters. Background Technology

[0002] As the core of transportation infrastructure, bridges face increasingly prominent issues of structural aging and performance degradation with the passage of time. Structural health monitoring, which reflects the structural condition by acquiring modal parameters such as frequency, mode shape, and damping ratio, is a crucial means of ensuring bridge safety.

[0003] Existing modal parameter identification methods are mainly divided into two categories: contact and non-contact. Contact methods, such as accelerometers and displacement gauges, require the installation of a large number of sensors on the structural surface, resulting in complex installation, high cost, and limited measurement range, making them unsuitable for large or complex bridges. Among non-contact methods, laser Doppler (LDV) instruments offer high accuracy but are expensive, while RTK-GNSS systems have low sampling frequencies. Video-based motion amplification (PVM) technology has become a research hotspot due to its low cost and wide coverage. Among video-based methods, Linear EVM is prone to amplifying noise, while Phase-based PVM requires prior knowledge of the structural frequency bandwidth. Furthermore, existing methods have shortcomings in handling situations without obvious feature targets, environmental noise interference, and multi-modal decoupling. Specifically: the structural frequency bandwidth needs to be pre-set, resulting in poor adaptability; environmental noise interference leads to low accuracy in extracting minute vibrations; decoupling multiple modes of vibration is difficult, resulting in low automation; and reliance on feature points or target markers limits the applicability. Summary of the Invention

[0004] To address the technical problems existing in the prior art, the purpose of this invention is to provide a method for identifying modal parameters of bridge structures, thereby achieving effective decoupling of multiple vibration modes of bridge structures, extraction of frequency domain features of small amplitude vibrations, and intelligent and automated extraction of modal parameters.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for identifying modal parameters of a bridge structure includes the following steps: S1: Acquiring video of minute vibrations of the bridge structure using a camera; S2: Performing complex controllable pyramid decomposition on the vibration video to obtain image phase information of the bridge structure at different scales and orientations; S3: Processing the image phase information through variational mode decomposition, selecting multiple target modal vibrations from the image phase information, and then amplifying these modal vibrations using a phase-based video motion amplification method to achieve adaptive decoupling of multiple modal vibrations in the phase information, thereby obtaining image modal information; S4: Capturing visual features using a Gabor filter. The local frequency response of the characteristic signal is analyzed, and then the frequency domain dynamic features are extracted from the decoupled image modal information by analyzing the image phase information; S5: The K-means algorithm and the DBSCAN algorithm are combined to obtain a clustering algorithm, which is used to process the frequency domain dynamic features and remove background noise and interference from non-target signals; S6: The average phase difference of the target region after processing in S5 is input into the integrated modal extraction algorithm, and the modal parameters are adaptively identified through the integrated modal extraction algorithm; Among them, the modal extraction algorithm is a joint algorithm of covariance driven random subspace recognition SSI-Cov and frequency domain decomposition FDD.

[0007] As a preferred option, in step S2, the scale and orientation of the complex controllable pyramid decomposition vibration video are determined based on the resolution and frame rate of the vibration video. The decomposed complex subband response is constructed by a bandpass filter, and the frequency domain expression of the bandpass filter is a complex function containing scale response parameters and orientation response parameters.

[0008] As a preferred option, in step S3, the variational mode decomposition is divided into a variational optimization model, which is constrained by the modal frequency center and the convolution operation.

[0009] As a preferred option, in step S4, the frequency domain dynamic feature extraction method of the Gabor filter is to obtain local phase information by convolving a two-dimensional Gabor wavelet with the image. The parameters of the two-dimensional Gabor wavelet include direction, wavelength, aspect ratio, bandwidth and phase offset.

[0010] As a preferred option, in step S5, the improved clustering algorithm specifically includes: A1: Initially dividing the frequency domain dynamic feature data using K-means to obtain K subsets, with the optimization objective being to minimize the sum of squared distances between each data point and the cluster centroid; A2: For each frequency domain dynamic feature data subset initially divided by K-means, the DBSCAN algorithm is used to identify the core points of the corresponding vibration modes, remove noise points, and aggregate target regions by setting a neighborhood radius based on the data distribution density and a minimum number of points based on the total data volume, thereby realizing the automatic extraction of the modal frequency domain feature interval region of interest in bridge structure vibration analysis.

[0011] As a preferred option, in step S6, the covariance-driven random subspace identification SSI-Cov algorithm constructs a block Hankel matrix of the response covariance matrix, extracts the orthogonal subspace through QR decomposition, performs singular value decomposition (SVD), obtains the natural frequency, damping ratio, and mode shape of the target object through eigenvalue decomposition, and selects stable modes by combining stability graph theory.

[0012] As a preferred option, in step S6, the FDD algorithm performs SVD decomposition on the structural response power spectral density matrix and uses the first singular vector corresponding to the peak frequency as the mode shape estimate.

[0013] As a preferred option, in step S3, the adaptive decoupling process is an adaptive mode selection mechanism based on variational mode decomposition, which automatically focuses on the vibration frequency components of the bridge structure.

[0014] As a preferred option, in step S5, the average phase difference of the target region is obtained by averaging the clustering results along the y-axis, and the displacement field information in the corresponding direction is calculated by combining the directional parameters of the Gabor filter.

[0015] As a preferred option, the modal parameters include natural frequency, mode shape, and damping ratio. The consistency between the identified modal parameters and the theoretical values ​​is evaluated by the Modal Assurance Criterion (MAC). The MAC value of the laboratory model test is not less than 0.89, and the MAC value of the field test is not less than 0.96.

[0016] The principle of this invention is as follows: Based on Variational Mode Decomposition (VMD) and Phase-Based Video Motion Amplification (PBVM), a civilian camera is used to acquire video of minor structural vibrations. This is combined with Gabor-based phase extraction (GBP) and an improved clustering algorithm (ICA) to suppress environmental noise and remove non-target signals. Furthermore, covariance-driven random subspace identification (SSI-Cov) and frequency domain decomposition (FDD) are integrated to achieve adaptive mode recognition. Laboratory experiments on an aluminum alloy arch model and on-site testing on a pedestrian bridge have verified that the modal information extracted by this method shows good consistency with the finite element simulation results. The modal guarantee criterion (MAC) values ​​exceed 0.89 and 0.96, respectively, improving the accuracy, robustness, and automation level of structural modal recognition. This avoids the need for extensive on-site sensor installation and provides a novel and practical solution for structural modal parameter identification in complex engineering environments.

[0017] In summary, the present invention has the following advantages:

[0018] Compared with existing technologies, this invention has the following advantages: non-contact measurement, requiring only a civilian camera for monitoring without the need for sensor installation, reducing on-site operational complexity, suitable for complex engineering environments, strong adaptability, automatic multimodal decoupling through variational mode decomposition (VMD), no need for prior knowledge of structural frequency bandwidth, suitable for structures with unknown dynamic characteristics, excellent anti-interference performance, combined with Gabor filtering phase method and improved clustering algorithm, effectively suppressing environmental noise, improving the accuracy of small vibration extraction, high recognition accuracy, integrating covariance-driven random subspace recognition (SSI-Cov) and frequency domain decomposition (FDD) algorithms, with a MAC value exceeding 0.89 in laboratory model tests and exceeding 0.96 in field tests, showing good consistency with finite element simulation results, and high automation, requiring no manual intervention from modal decoupling and noise removal to parameter extraction, significantly improving recognition efficiency. Attached Figure Description

[0019] Figure 1 This is a diagram of the APBVM-MI algorithm architecture.

[0020] Figure 2 The flowchart is for the Adaptive Phase Motion Amplification (APBVM) algorithm.

[0021] Figure 3 This is a schematic diagram of the laboratory aluminum alloy arch model.

[0022] Figure 4 The results of the finite element simulation of the arch model are shown in the figures: (a) Finite element model, (b) First mode shape, (c) Second mode shape, and (d) Third mode shape.

[0023] Figure 5 Comparison images were selected for feature points: (a) LK optical flow method, (b) Gabor-based phase method.

[0024] Figure 6 The following are the vibration displacement time history and power spectrum diagrams of the arch structure: (a) measured displacement time history, (b) LK optical flow method displacement time history, (c) measured power spectrum, (d) LK optical flow method power spectrum, (e) phase method displacement time history, and (f) phase method power spectrum.

[0025] Figure 7 The images are the first frame of the vibration video and the decomposed modal video: (a) the original video, (b) the first-order mode, (c) the second-order mode, and (d) the third-order mode.

[0026] Figure 8 The results of the structural edge extraction are shown in blue for stationary edges and red for vibrating edges, (a) first-order mode, (b) second-order mode, and (c) third-order mode.

[0027] Figure 9This is a schematic diagram showing the location of video slices depicting the vibration of the arch structure.

[0028] Figure 10 The image shows a stitched image of video slices: (a) the original video, (b) the 12-18Hz frequency band, (c) the 30-35Hz frequency band, and (d) the 40-45Hz frequency band.

[0029] Figure 11 For comparison of clustering results, (a) initial K-means clustering, (b) final clustering.

[0030] Figure 12 Calculate the coordinate position for the phase difference: (a) the center position of the clustered image, and (b) the position calculated based on the phase difference information.

[0031] Figure 13 The time history curve of the average phase difference of the first mode.

[0032] Figure 14 The results are as follows: (a) Mode parameters extracted from Mode 1 video using SSI-cov; (b) Mode parameters extracted from Mode 1 video using FDD; (c) Power spectral density map of Mode 1 video.

[0033] Figure 15 This is a comparative analysis diagram of first-order mode shapes.

[0034] Figure 16 The time history curve is the average phase difference of the second-order mode.

[0035] Figure 17 The results are as follows: (a) Mode parameters extracted from Mode 2 video using the SSI-cov algorithm; (b) Mode parameters extracted from Mode 2 video using the FDD algorithm; (c) Power spectral density map generated from Mode 2 video.

[0036] Figure 18 This is a comparative analysis diagram of second-order mode shapes.

[0037] Figure 19 The time history curve of the average phase difference of the third mode

[0038] Figure 20 The results show the extraction of third-order mode parameters: (a) Mode parameters extracted from Mode 3 video using the SSI-cov algorithm; (b) Mode parameters extracted from Mode 3 video using the SSI-cov algorithm; and (c) Power spectral density map generated from Mode 3 video.

[0039] Figure 21 This is a comparative analysis diagram of the third-order mode shapes. Detailed Implementation

[0040] The present invention will now be described in further detail with reference to specific embodiments.

[0041] like Figures 1-21 As shown, this embodiment provides a bridge structure modal parameter identification method APBVM-MI, which includes the following steps: S1: Acquire minute vibration videos of the bridge structure using a camera; S2: Perform complex controllable pyramid decomposition on the vibration videos to obtain image phase information of the bridge structure at different scales and orientations; S3: Process the image phase information through variational mode decomposition, filter out multiple target modal vibrations from the image phase information, and then amplify these modal vibrations using a phase-based video motion amplification method to complete the adaptive decoupling of multiple modal vibrations in the phase information, thereby obtaining image modal information; S4: Use Gabo... The r-filter captures the local frequency response of the visual feature signal, and then extracts the frequency domain dynamic features from the decoupled image modal information by analyzing the image phase information; S5: The K-means algorithm and the DBSCAN algorithm are combined to obtain a clustering algorithm, which is used to process the frequency domain dynamic features and remove background noise and interference from non-target signals; S6: The average phase difference of the target region after processing in S5 is input into the integrated modal extraction algorithm, and the modal parameters are adaptively identified through the integrated modal extraction algorithm; Among them, the modal extraction algorithm is a joint algorithm of covariance-driven random subspace recognition SSI-Cov and frequency domain decomposition FDD.

[0042] Specifically, the camera is an existing civilian camera, which does not require the installation of a large number of sensors, reducing the complexity of on-site operation and making it suitable for non-contact monitoring in complex engineering environments.

[0043] Variational Mode Decomposition (VMD) and Phase-Based Video Motion Amplification (PBVM) effectively decouple structural multimodal vibrations without requiring prior knowledge of the target frequency bandwidth, thus improving adaptability to frequency domain feature extraction for small-amplitude vibrations. The Gabor-filtered phase extraction method GBP, combined with improved clustering algorithms K-means and DBSCAN, robustly suppresses environmental noise and effectively removes non-target signals, improving the quality of the extracted dynamic information. The integration of covariance-driven random subspace recognition (SSI-Cov) and frequency domain decomposition (FDD) enables adaptive modal recognition, enhancing the accuracy, robustness, and automation of structural modal recognition, and providing a reliable solution for structural modal parameter identification in complex engineering environments.

[0044] In step S2, the scale and orientation of the complex controllable pyramid decomposition of the vibration video are determined based on the resolution and frame rate of the vibration video. The decomposed complex subband response is constructed by a bandpass filter. The bandpass filter has the properties of spatial separability and directional adjustability. The frequency domain expression of the bandpass filter is a complex function containing scale response parameters and orientation response parameters.

[0045] In step S3, the variational mode decomposition is transformed into a variational optimization model. The variational optimization model uses the modal frequency center and convolution operation as constraints to decompose the image phase information into K intrinsic mode functions, thereby achieving automatic separation and amplification of multi-modes without the need to pre-set the frequency bandwidth of the structure.

[0046] Specifically, given a raw video image frame I(x,y,t), after complex controllable pyramid decomposition at each time frame t, it can be represented as a complex subband response R containing the low-frequency residual L0(x,y,t) and the responses R at each scale s = 1, 2, ..., S and each direction θ = 1, 2, ..., K. s,θ (x,y,t), that is:

[0047]

[0048] Pyramid stands for pyramid decomposition.

[0049] The pyramid subband response is as follows:

[0050] R s,θ (x,y,t)=I(x,y,t)*V s,θ (x,y) (2);

[0051] Among them, V s,θ (x,y) is a bandpass filter with spatially separable and directionally adjustable properties. Its frequency domain expression is:

[0052]

[0053] Where H s Controlling the scale response, G θ Control directional response. W x : Represents the spatial angular frequency along the x-direction, describing how quickly a signal / image changes in the horizontal direction. The larger the value, the "denseer" the texture and changes in the horizontal direction.

[0054] W y : Represents the spatial angular frequency along the y-direction, describing how fast the signal / image changes in the vertical direction. The larger the value, the more "dense" the change in the vertical direction.

[0055] To highlight the amplitude and phase, equation (2) is transformed into polar coordinates:

[0056]

[0057] in:

[0058] A s,θ (x,y,t)=|R s,θ(x,y,t)|,φ s,θ (x,y,t)=arg(R s,θ (x,y,t)) (5);

[0059] Furthermore, real-world signals often contain noise components. In phase motion amplification, as the amplification factor increases, the noise is shifted rather than amplified. Let the noise component be n(x,y,t), after passing through a bandpass filter V... s,θ After processing (x,y), it can be approximated as a high-frequency disturbance. s,θ (x,y,t), then:

[0060]

[0061] Local phase is highly sensitive to minute displacements. If a structural point in an image is displaced by a time factor F(x,y,t), the phase change satisfies a first-order approximation:

[0062]

[0063] Among them, K s,θ It is the local spatial frequency vector at that scale and direction.

[0064] For time series φ s,θ Perform variational mode decomposition (VMD) on (x,y,t), and let it be decomposed into K eigenmode functions u. k (x,y,t), then:

[0065]

[0066] Each mode function u k (x,y,t) can be optimized using variational methods:

[0067]

[0068] Where, ω k It represents the modal frequency center, and * indicates the convolution operation.

[0069] In step S3, these modal vibrations are amplified using a phase-based video motion amplification method. The specific steps are as follows: To amplify minute movements, it is only necessary to amplify the local phase changes in the time dimension:

[0070]

[0071] Where α is the amplification factor and t0 is the reference frame, the new complex response is constructed as follows:

[0072]

[0073] Finally, the image is reconstructed by merging the magnified responses of all scales and orientations with the low-frequency residual L0(x,y,t) through the inverse transformation of the complex controllable pyramid:

[0074]

[0075] Where P -1 This represents the inverse operation of the pyramid scheme.

[0076] In step S4, the phase extraction method of Gabor filtering is to obtain local phase information by convolving the two-dimensional Gabor wavelet with the image. The parameters of the two-dimensional Gabor wavelet include direction, wavelength, aspect ratio, bandwidth and phase offset. The phase difference between adjacent frames is proportional to the structural displacement, which can realize sub-pixel level micro-vibration detection.

[0077] Specifically, a two-dimensional Gabor filter can be represented as:

[0078]

[0079] Where x′=xcosθ+ysinθ, y′=-xsinθ+ycosθ, θ is the direction, λ is the wavelength, γ is the aspect ratio, σ is the bandwidth, and ψ is the phase shift.

[0080] After convolving the image I(x,y) with a complex Gabor kernel, we get:

[0081] R(x,y,t)=I(x,y,t)*g(x,y)=A(x,y,t)e jφ(x,y,t) (14);

[0082] Where A(x,y,t) represents the local amplitude and φ(x,y,t) represents the local phase.

[0083] Representing minute motions as local phase differences:

[0084] δ(x,y,t)=(φ(x,y,t)-φ(x,y,0)) / k (15);

[0085] Where k is the mapping factor from Gabor's phase to the actual displacement, which can be obtained from the direction and wavelength:

[0086]

[0087] Select multiple directions θ i Multiple scales σ j Convolution is performed on each pair of parameters to obtain multiple responses:

[0088]

[0089] Where e is the base of the natural logarithm.

[0090] By combining different directions and scales, the local displacement field can be estimated by averaging or weighting.

[0091] In step S5, the improved clustering algorithm specifically includes:

[0092] A1: The frequency domain dynamic feature data is initially divided using K-means to obtain K subsets. The optimization objective is to minimize the sum of squared distances between each data point and the cluster centroid.

[0093] A2: For each frequency domain dynamic feature data subset initially divided by K-means, the DBSCAN algorithm is used. By setting the neighborhood radius based on the data distribution density and the minimum number of points based on the total amount of data, the core points of the corresponding vibration mode are identified, noise points are removed, and the target region is aggregated, thereby realizing the automatic extraction of the modal frequency domain feature interval region of interest in bridge structure vibration analysis.

[0094] Specifically, the improved clustering algorithm processes the peak frequency data of each pixel in the image twice, using K-means and density-based spatial clustering (DBSCAN). This solves the problems of inaccurate segmentation of irregularly shaped data and susceptibility to noise in non-interest regions when using K-means alone, as well as the problems of slow aggregation speed and parameter sensitivity when using DBSCAN alone.

[0095] (1) Initial K-means partitioning;

[0096] Given a dataset N = {x1, x2, ..., x...} n}, and divide it into K subsets {D1, D2, ..., D} using K-means. K The objective function is:

[0097]

[0098] Where c k Let P be the centroid of the k-th cluster, and let P be the weighted average of the different data points, calculated using the following formula:

[0099]

[0100] (2) DBSCAN local clustering;

[0101] In a K-means subcluster Dk, the neighborhood radius is ε, the minimum number of points in the neighborhood is MinPts, and for any data, x... i ∈D k Then the neighborhood is defined as:

[0102] N ε (x i )={xj ∈D k |Px j -x i P≤ε} (20);

[0103] If |N ε (x i If |≥MinPts, then determine x. i With density as the core point. Through density propagation, D k Divided into several sub-clusters {C k,1 C k,2 ,...}, and mark the set of noise points O.

[0104] The final output is the aggregated dataset:

[0105]

[0106] In step S6, the covariance-driven random subspace identification SSI-Cov algorithm constructs a block Hankel matrix of the response covariance matrix, extracts the orthogonal subspace through QR decomposition (a matrix decomposition method in linear algebra), performs singular value decomposition (SVD), obtains the natural frequency, damping ratio and mode shape of the target object through eigenvalue decomposition, and selects stable modes by combining stability graph theory.

[0107] In step S6, the FDD algorithm performs singular value decomposition (SVD) on the power spectral density matrix of the structural response and uses the first singular vector corresponding to the peak frequency as the mode shape estimate to achieve rapid preliminary identification of modal parameters.

[0108] Specifically, the Subspace Recognition Method (SSI-cov) constructs a response covariance matrix and combines orthogonal decomposition and singular value decomposition (SVD) techniques. SSI-cov effectively extracts the dynamic features of the target object and possesses strong noise resistance and frequency resolution capabilities. SVD, on the other hand, rapidly obtains key modal information through spectral analysis, offering high computational efficiency and making it suitable for preliminary modality screening. SSI-cov and SVD complement each other in their characteristics; SSI-cov provides accurate parameter estimation, while SVD enhances the intuitiveness and stability of feature identification.

[0109] (1) SSI-cov algorithm;

[0110] For a linear time-invariant target object with n degrees of freedom, and with external excitations treated as white noise, its discrete state equation is:

[0111]

[0112] Where x kLet y be the target object state vector at time k. k Let w be the target object's output vector at time k, A be the discrete state matrix of the target object, C be the output matrix of the target object, and w be the output vector of the target object. k ,v k These are process noise and observation noise, respectively.

[0113] The covariance matrix R of the target object response observed at time interval i i for:

[0114]

[0115] Target object state vector x k+1 For the output vector y k+1 The covariance matrix is:

[0116]

[0117] Substituting the target object state matrix (22) into equations (23) and (24), the covariance matrix R of the target object response can be obtained. i :

[0118] R i =CA i-1 G (25);

[0119] Construct the Hankel matrix from the above equation:

[0120]

[0121] To reduce computational data and eliminate the impact of duplicates on subsequent calculations, QR decomposition is performed to extract orthogonal subspaces.

[0122] H = QR (27);

[0123] Take the first r columns of Q, denoted as Q1, and then perform SVD decomposition on Q1:

[0124] Q1=UΣV T (28);

[0125] Where U is the orthogonal subspace of the target object, Σ is the singular value diagonal matrix, and V T It is a right singular vector.

[0126] Construct the observable matrix O of the target object i With target object matrix A:

[0127]

[0128] in,(·) + The table represents the pseudo-inverse matrix, and the parentheses can contain any matrix / vector that meets the dimension requirements. They represent O respectively i The upper and lower parts.

[0129] Finally, the eigenvalues ​​λ of the target object matrix A are calculated. k Decomposition can yield the natural frequency f of the target object. k Damping ratio ζ k And mode shape φ k :

[0130] AΦ=λ k Φ (31);

[0131]

[0132] φ k =CΦ (35);

[0133] Wherein, ∠λ k Let φ be the complex eigenvalue phase angle, and Φ be the eigenvector.

[0134] To determine the modal order of a target object, stability graph theory is introduced. This theory assumes that the target object may contain multiple modal orders and constructs multiple state-space models accordingly. After identifying the modal parameters of each model, the results are plotted on a single graph. If the natural frequency, damping ratio, and mode shape identified at a certain order are continuously stable within a set tolerance range, they are considered stable points, and the column formed by these points is called the stability axis.

[0135] Tolerance ranges are typically determined using the following formula:

[0136]

[0137] |1-MAC(i,i+1)|×100%<[ΔMAC] (38);

[0138]

[0139] The MAC (Modal Assurance Criterion) is called the modal confidence criterion. These are the theoretical values ​​of the modal parameters. These are the measured values ​​of the modal parameters.

[0140] (2) FDD algorithm;

[0141] In a multi-degree-of-freedom target object, assuming the excitation and structural response are x(t) and y(t) respectively, the output power spectral density function matrix of the structure can be obtained as:

[0142] G yy (jω)=H(jω)G xx(jω)H H (jω) (40);

[0143] Among them G xx (jω) is the input power spectral density matrix (PSD) of size r×r, G yy H(jω) is the m×m power spectral density matrix of the structural response, and H(jω) is the m×r structural frequency response matrix. H denot represents the complex conjugate transpose of a matrix, where j is the imaginary unit.

[0144] The structural frequency response matrix H(jω) can be expressed in residue form:

[0145]

[0146] In the formula, n is the number of modes, λ k R is the k-th order pole of the structure. k It is the residue matrix of order k, expressed as: in γ k Let be the nth-order mode shape vector and the modal participation coefficient vector of the structure, respectively. T ,(·) * These represent the transpose and conjugate of a matrix, respectively. The matrix within the parentheses can be any matrix or vector that can participate in the transpose and conjugate operations.

[0147] Assume the input excitation is white noise G xx (jω)=C, substituting formula (41) into formula (40) yields the structural response matrix:

[0148]

[0149] Multiplying and using the Heavisid fraction expansion theorem, we can further simplify and rearrange to obtain:

[0150]

[0151] Among them, B k With A k They are conjugate symmetric, A k To output the k-th residue matrix of the PSD, the expression is as follows:

[0152]

[0153] The contribution of the k-th mode to the residue matrix is ​​defined by the following equation:

[0154]

[0155] Where α k The k-th order pole λ of the structurek The negative number λ of the real part k =-α k +jω k Since the damping of the structure is generally small, the residue matrix is ​​proportional to the mode shape vector:

[0156]

[0157] Where d k A scalar constant at the k-th modal frequency ω k Under these conditions, usually one or two modes contribute significantly. Let the set of modes be represented as Sub(ω). Further simplification of equation (43) yields:

[0158]

[0159] At discrete frequency ω=ω i The following is an SVD decomposition of the structural response power spectral density matrix:

[0160]

[0161] Where matrix U i =[u i1 ,u i2 ,L,u im ] is a vector containing singular vector u ij The unitary matrix should have a peak value in the spectrum, and the frequency corresponding to the peak value is the i-th natural frequency ω. i Thus, the first singular vector of equation (48) is the estimated value of the i-th mode shape of the structure:

[0162]

[0163] In step S3, the adaptive decoupling process is achieved through an adaptive mode selection mechanism based on variational mode decomposition. This mechanism automatically focuses on the main vibration frequency components of the bridge structure without requiring manual intervention in setting the frequency bandwidth.

[0164] In step S5, the average phase difference of the target region is obtained by averaging the clustering results along the y-axis, and the displacement field information in the corresponding direction is calculated by combining the directional parameters of the Gabor filter.

[0165] Modal parameters include natural frequency, mode shape, and damping ratio. The consistency between the identified modal parameters and theoretical values ​​is evaluated using the Modal Assurance Criterion (MAC). The MAC value for laboratory model tests is not less than 0.89, and the MAC value for field tests is not less than 0.96.

[0166] Specific application examples:

[0167] like Figure 2-12 As shown, 1. Laboratory test verification:

[0168] The test subject was an aluminum alloy arch model, hinged at both ends, with a span of 80cm and a rise of 25cm. Material parameters included an elastic modulus of 200GPa, Poisson's ratio of 0.3, and a density of 7900kg / m³. 3 The test equipment included a Sony ZV-E10 camera with a CMOS sensor, a maximum resolution of 6000×4000 pixels, and a frame rate of 120fps; and an NDI-3D optical measurement sensor with an accuracy of 20μm and a measurement range of 1.5-4.5m.

[0169] The experimental process was as follows: (1) The arch model was struck with a rubber hammer to induce free vibration. Simultaneously, vibration video with a resolution of 1920×1080 and a frame rate of 100fps was collected, along with NDI displacement data (displacement measurement data collected by NDI (North Digital Company) related equipment) with a sampling frequency of 100Hz.

[0170] (2). The video is decomposed into 3rd-order modal video by adaptive phase motion amplification using the APBVM-MI algorithm;

[0171] (3). The Canny operator was used to extract the edges of the bridge structure in both the vibration and static states to verify the modal adaptive decoupling effect;

[0172] (4). The phase difference is extracted by the phase method of Gabor filtering, and after processing by the improved clustering algorithm, the input covariance drives the joint algorithm of random subspace recognition SSI-Cov and frequency domain decomposition FDD.

[0173] (5). The results showed that the theoretical FEM values ​​for the first-order frequency of 14.45Hz were 14.49Hz, the theoretical FEM values ​​for the second-order frequency of 30.86Hz were 29.7Hz, and the theoretical FEM values ​​for the third-order frequency of 42.58Hz were 40.5Hz. The average MAC value was 0.891, which was highly consistent with the measured and finite element results.

[0174] 2. For example Figure 2-12 As shown, on-site testing verified the results. The test object was a pedestrian overpass, a simply supported beam structure with a span of 15m. The test conditions involved using natural environmental excitation to induce vibrations from pedestrian loads, and video was captured using a civilian camera. The results showed that the MAC value between the modal parameters extracted by the method in this embodiment and the finite element simulation results exceeded 0.96, verifying the applicability of the method in practical engineering.

[0175] 3. Compared with the pyramid-based LK optical flow method, the Gabor filter phase method of this invention does not rely on textures or manual markings, making it suitable for regions without obvious features. The integrated modal recognition algorithm reduces frequency recognition error by 10%-15% compared to single methods, and significantly improves mode shape matching. Specifically, while the pyramid-based LK optical flow method has advantages such as high accuracy, sub-pixel level accuracy, adaptability to large-amplitude movements, and good stability in displacement recognition, it relies on obvious textures or manual markings and is greatly affected by the quality of feature point extraction. However, the Gabor-based phase method does not rely on textures or markings, is suitable for regions without obvious features, and has similarly high accuracy, but is more suitable for scenarios with small vibrations. Furthermore, it does not require feature point coordinate extraction, resulting in relatively weaker spatial adaptability.

[0176] In summary, the method of this invention achieves non-contact, high-precision, and automated extraction of bridge structural modal parameters by integrating adaptive phase motion amplification, improved clustering, and integrated modal recognition technologies. This method improves the accuracy of structural modal recognition, with the MAC value of the modal guarantee criterion exceeding 0.89 in aluminum alloy arch model tests and 0.96 in pedestrian bridge field tests, respectively. It enhances the robustness of recognition, effectively suppressing environmental noise and non-target signal interference. It realizes an intelligent process for multimodal decoupling, feature extraction, and modal recognition. It avoids the installation of numerous sensors on-site, reducing operational complexity and making it suitable for complex engineering environments. Experiments and field tests demonstrate that this method effectively overcomes the bottlenecks of existing technologies and provides a practical solution for structural health monitoring in complex engineering environments.

[0177] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for identifying modal parameters of bridge structures, characterized in that, Includes the following steps: S1: Capture minute vibration videos of the bridge structure using a camera; S2: Perform complex controllable pyramid decomposition on the vibration video to obtain image phase information of the bridge structure at different scales and directions; S3: The image phase information is processed by variational mode decomposition. After multiple target modal vibrations are selected from the image phase information, these modal vibrations are amplified by the phase-based video motion amplification method to complete the adaptive decoupling of multiple modal vibrations in the phase information and obtain the image modal information. S4: Capture the local frequency response of visual feature signals through Gabor filters, and then extract frequency domain dynamic features from the decoupled image modal information by analyzing the image phase information; S5: The K-means algorithm and the DBSCAN algorithm are combined to obtain a clustering algorithm. The clustering algorithm is used to process the dynamic features in the frequency domain and remove background noise and interference from signals that are not the target of the study. S6: Input the average phase difference of the target region after processing in S5 into the integrated mode extraction algorithm, and adaptively identify the mode parameters through the integrated mode extraction algorithm; wherein, the mode extraction algorithm is a joint algorithm of covariance-driven random subspace identification SSI-Cov and frequency domain decomposition FDD.

2. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S2, the scale and orientation of the complex controllable pyramid decomposed vibration video are determined based on the resolution and frame rate of the vibration video. The decomposed complex subband response is constructed by a bandpass filter, and the frequency domain expression of the bandpass filter is a complex function containing scale response parameters and orientation response parameters.

3. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S3, the variational mode decomposes into a variational optimization model, which is constrained by the mode frequency center and the convolution operation.

4. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S4, the frequency domain dynamic feature extraction method of Gabor filter is to obtain local phase information by convolving two-dimensional Gabor wavelets with the image. The parameters of two-dimensional Gabor wavelets include direction, wavelength, aspect ratio, bandwidth and phase offset.

5. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S5, the improved clustering algorithm specifically includes: A1: The frequency domain dynamic feature data is initially divided using K-means to obtain K subsets. The optimization objective is to minimize the sum of squared distances between each data point and the cluster centroid. A2: For each frequency domain dynamic feature data subset initially divided by K-means, the DBSCAN algorithm is used. By setting the neighborhood radius based on the data distribution density and the minimum number of points based on the total amount of data, the core points of the corresponding vibration mode are identified, noise points are removed, and the target region is aggregated, thereby realizing the automatic extraction of the modal frequency domain feature interval region of interest in bridge structure vibration analysis.

6. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S6, the covariance-driven random subspace identification SSI-Cov algorithm constructs a block Hankel matrix of the response covariance matrix, extracts the orthogonal subspace through QR decomposition, performs singular value decomposition (SVD), obtains the natural frequency, damping ratio, and mode shape of the target object through eigenvalue decomposition, and selects stable modes by combining stability graph theory.

7. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S6, the FDD algorithm performs SVD decomposition on the power spectral density matrix of the structural response and uses the first singular vector corresponding to the peak frequency as the mode shape estimate.

8. The method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S3, the adaptive decoupling process is achieved through an adaptive mode selection mechanism based on variational mode decomposition. This adaptive mode selection mechanism automatically focuses on the vibration frequency components of the bridge structure.

9. A method for identifying bridge structural modal parameters according to claim 1, characterized in that: In step S5, the average phase difference of the target region is obtained by averaging the clustering results along the y-axis, and the displacement field information in the corresponding direction is calculated by combining the directional parameters of the Gabor filter.

10. A method for identifying bridge structural modal parameters according to claim 1, characterized in that: Modal parameters include natural frequency, mode shape, and damping ratio. The consistency between the identified modal parameters and theoretical values ​​is evaluated using the Modal Assurance Criterion (MAC). The MAC value for laboratory model tests is not less than 0.89, and the MAC value for field tests is not less than 0.96.

Images