A method and apparatus for underdetermined mode recognition based on a monocular camera

Abstract

The application provides a kind of underdetermined modal identification method and device based on monocular camera, belong to modal parameter identification technical field, method includes: using monocular camera to collect multiple images including all feature targets, according to image acquisition vibration response signal, when vibration response signal is time-invariant vibration response signal, reconstruct time-invariant vibration response signal into compressed sensing model, the ESTD dictionary obtained by training time-invariant vibration response signal, according to ESTD dictionary and compressed sensing model, modal identification of time-invariant vibration response signal is realized, when vibration response signal is time-invariant vibration response signal, time-varying vibration response signal is divided into a finite time-invariant vibration response signal using sliding window, combined with the idea of transfer learning to obtain strong sparse ESTD dictionary, and then the modal identification of time-varying vibration response signal is obtained.The application can solve the underdetermined modal identification under time-invariant structure and time-varying structure, and improve the identification speed and precision of underdetermined modal identification parameters.

Description

Technical Field

[0001] This invention belongs to the field of modal parameter recognition technology, specifically relating to an underdetermined modal recognition method and apparatus based on a monocular camera. Background Technology

[0002] In practical engineering applications, traditional methods for measuring structural parameters (such as mass, stiffness, and damping) are difficult to implement due to cost and the difficulty of installing instruments for measuring response signals. Furthermore, sensors can only be deployed at a limited number of critical locations for dynamic response measurements. This results in incomplete structural response measurement information, failing to meet the requirements for overdetermined and positive definite modes, and hindering the performance of structural dynamic modal analysis. The advantages of using a monocular camera to measure vibration signals include high cost-effectiveness, ease of setup and use, avoidance of complex calibration and object matching between multiple cameras, and the ability to provide displacement measurements with a significantly superior field of view compared to traditional physical sensors. Therefore, research on underdetermined modal analysis of time-varying structures based on monocular cameras is of great importance and urgency.

[0003] For time-varying structures, modal analysis methods can be divided into two categories: time-domain methods and time-frequency domain methods. Existing patent document CN104698837B, "A Method, Device, and Application for Identifying Modal Parameters of Time-varying Structures," achieves good results in identifying modal parameters of time-varying structures by combining a sliding window with limited memory principal component analysis. Patent document CN116776708B, "An Adaptive Identification Method, Device, Equipment, and Medium for Time-varying Modal Parameters," combines a sliding window with blind source separation and manifold learning. However, these methods are not suitable for underdetermined problems and can only identify modal parameters equal to or less than the number of sensors.

[0004] Regarding the underdetermined problem, the existing patent document CN112507606B, "Method for Identifying and Detecting Underdetermined Modal Parameters Based on RBF Networks", identifies modal parameters under time-invariant structures, but does not consider modal parameter identification under time-varying structures. Summary of the Invention

[0005] The purpose of this invention is to propose an underdetermined mode recognition method and device based on a monocular camera, which can solve the underdetermined mode recognition under time-invariant and time-varying structures, and improve the recognition speed and accuracy of underdetermined mode recognition parameters.

[0006] This invention is achieved through the following technical solution:

[0007] An underdetermined mode recognition method based on a monocular camera includes the following steps:

[0008] Step S1: Arrange a limited number of feature targets in the linear vibration system, use a monocular camera to acquire multiple images including all feature targets, determine the feature points in each image, and obtain the vibration response signal based on the feature points in the images at two adjacent time points. When the vibration response signal is a time-invariant vibration response signal, proceed to step S21; when the vibration response signal is a time-varying vibration response signal, proceed to step S31.

[0009] Step S21: Perform a short-time Fourier transform on the time-invariant vibration response signal and estimate the mode shape matrix using single-source point detection, then proceed to step S22;

[0010] Step S22: Based on the modal shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation, and then proceed to step S23;

[0011] Step S23: Train the time-invariant vibration response signal using the K-SVD dictionary learning method to obtain the ESTD dictionary. Based on the ESTD dictionary and the compressed sensing model, obtain the modal response through the sparse reconstruction algorithm. Based on the modal response, obtain the natural frequency and loss damping ratio of each mode shape to achieve modal identification of the time-invariant vibration response signal.

[0012] Step S31: Divide the time-varying vibration response signal into a finite number of time-invariant vibration response signals using a sliding window with a set window length. Perform short-time Fourier transform on the time-invariant vibration response signal in each sliding window window. Estimate the instantaneous mode shape corresponding to each time-invariant vibration response signal using single-source point detection. Reconstruct the compressed sensing model of the time-invariant vibration response signal in each sliding window window after underdetermined blind source separation. Proceed to step S32.

[0013] Step S32: For the time-invariant vibration response signal in the current sliding window, perform learning and training based on the K-SVD dictionary to obtain the corresponding strongly sparse ESTD dictionary. The training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window, and the initial dictionary for learning and training is the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window.

[0014] Step S33: Based on the strongly sparse ESTD dictionary and compressed sensing model corresponding to the time-invariant vibration response signal of the current sliding window, obtain the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window through the sparse reconstruction algorithm, and obtain the instantaneous natural frequency and instantaneous damping ratio of each mode shape corresponding to the time-invariant vibration response signal in the current sliding window based on the instantaneous modal response, and obtain the modal identification result corresponding to the time-invariant vibration response signal in the current sliding window;

[0015] Step S34: Repeat steps S32 to S33 until the modal identification results corresponding to the time-invariant vibration response signals in all sliding window windows are obtained.

[0016] Furthermore, in step S1, obtaining the vibration response signal specifically includes the following steps:

[0017] Step S11: Arrange several feature targets in the linear vibration system and use a monocular camera to acquire multiple images including all feature targets;

[0018] Step S12: For the current feature target, determine the feature points corresponding to the current feature target in each image using the Shi_Tomasi corner detection algorithm;

[0019] Step S13: Obtain the Euclidean distance between feature point pairs in images at two adjacent time points using the FLANN feature point matching algorithm, and retain feature point pairs corresponding to Euclidean distances less than the set distance threshold.

[0020] Step S14: Calculate the angle between the direction vector formed by each feature point pair and the average direction vector. Retain feature point pairs with angles smaller than the set angle threshold. The average direction vector is calculated according to the formula... Calculate, where n' represents the number of feature point pairs retained in step S13. This represents the direction vector formed by the i'th pair of feature points;

[0021] Step S15: Calculate the distance between the feature point pairs retained in step S14, and calculate the average of all distances as the pixel displacement of the two adjacent images. Combine the timestamp information of the two adjacent images to obtain the displacement signal corresponding to the current feature target.

[0022] Step S16: Repeat steps S11 to S15 to obtain the displacement signals corresponding to each feature target, forming a vibration response signal.

[0023] Furthermore, step S21 includes the following steps:

[0024] Step S211, the time-invariant vibration response signal is expressed in modal coordinates as follows: ,in, , This represents the displacement signal corresponding to the i-th feature target, where n is the number of feature targets set. The modal shape matrix, Let m be the m-th mode shape, where m is the order of the mode shape. Here is the modal response matrix. Let [ ] be the modal response vector. T Indicates matrix transpose;

[0025] Step S212: Apply the short-time Fourier transform simultaneously to the modal coordinate representation to obtain the time-invariant vibration response signal in the time-frequency domain. ,in, and They are respectively and The result of the short-time Fourier transform;

[0026] Step S213, according to the formula Calculate the frequency energy of the time-invariant vibration response signal in the time-frequency domain, where, This represents the frequency energy corresponding to the displacement signal of the i-th feature target. This represents the frequency energy of the j-th mode shape. This represents the j-th mode shape corresponding to the i-th feature target;

[0027] Step S214: When the frequency f is within the frequency range At that time, The slope of the energy highest point at each frequency is calculated using a single-source detection method to obtain the modal shape matrix. ,in, f represents the set frequency threshold. j This represents the frequency value corresponding to the j-th frequency interval.

[0028] Furthermore, step S22 includes the following steps:

[0029] Step S221, Time-invariant vibration response signal The underdetermined blind source separation is represented as ,in, This is a hybrid matrix, where each column corresponds to the mode shape matrix. Each mode shape in the process, Represents the recovered source signal in the time domain;

[0030] Step S222: The reconstructed compressed sensing model is represented as follows: ,in, For the observation vector, For the mixed matrix A sparse matrix that satisfies the sparse field constraint. This represents the sparse representation of the source signal in the sparse domain.

[0031] Furthermore, in step S31, the time-invariant vibration response signal within the j'-th sliding window is represented in modal coordinates as follows: Where L represents the length of the sliding window, and j' represents the sliding window number. This is the midpoint of the sliding window. This represents the modal shape matrix of the time-invariant vibration response signal within the j'-th sliding window. Let represent the modal response matrix of the time-invariant vibration response signal within the j'-th sliding window.

[0032] Furthermore, in step S32, the modal identification result corresponding to the time-invariant vibration response signal in the previous sliding window includes the natural frequency and loss damping ratio of each mode. When the natural frequency of each mode corresponding to the time-invariant vibration response signal in the previous sliding window differs from the natural frequency of each mode corresponding to the time-invariant vibration response signal in the current sliding window by 1, the current sliding window is used as the first sliding window to re-enter step S32.

[0033] Furthermore, in step S33, the instantaneous natural frequency and loss damping ratio are extracted from the instantaneous modal response using single-degree-of-freedom technology.

[0034] This invention is also achieved through the following technical solutions:

[0035] An underdetermined modality recognition device based on a monocular camera, comprising:

[0036] Signal determination module: It is used to arrange a limited number of feature targets in a linear vibration system, use a monocular camera to acquire multiple images including all feature targets, determine the feature points in each image, and obtain the vibration response signal based on the feature points in the images at two adjacent time points, and determine whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal.

[0037] The time-invariant vibration response signal identification module performs short-time Fourier transform on the time-invariant vibration response signal and estimates the mode shape matrix using single-source point detection. Based on the mode shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation. The time-invariant vibration response signal is trained using the K-SVD dictionary learning method to obtain the ESTD dictionary. Based on the ESTD dictionary and the compressed sensing model, the modal response is obtained through a sparse reconstruction algorithm. Based on the modal response, the natural frequencies and loss damping ratios of each mode shape are obtained, thus realizing modal identification of the time-invariant vibration response signal.

[0038] The time-varying vibration response signal recognition module divides the time-varying vibration response signal into a finite number of time-invariant vibration response signals using a sliding window of a set window length. It performs a short-time Fourier transform on the time-invariant vibration response signal within each sliding window and estimates the instantaneous mode shape corresponding to each time-invariant vibration response signal using single-source point detection. After underdetermined blind source separation, it reconstructs a compressed sensing model for the time-invariant vibration response signal within each sliding window. For the time-invariant vibration response signal within the current sliding window, it performs training based on a K-SVD dictionary to obtain a corresponding strongly sparse ESTD dictionary. The training samples are the modal recognition results corresponding to the time-invariant vibration response signal within the previous sliding window. The initial dictionary for learning and training is the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window. Based on the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the current sliding window and the compressed sensing model, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained through a sparse reconstruction algorithm. Then, based on the instantaneous modal response, the instantaneous natural frequencies and instantaneous damping ratios of each mode shape corresponding to the time-invariant vibration response signal in the current sliding window are obtained, thus obtaining the modal identification result corresponding to the time-invariant vibration response signal in the current sliding window. This process is repeated until the modal identification results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

[0039] The present invention has the following beneficial effects:

[0040] 1. This invention first uses a monocular camera to acquire images of a feature target and obtains vibration response signals based on the acquired images. When the vibration response signal is time-invariant, a short-time Fourier transform is performed on the time-invariant vibration response signal, and the mode shape matrix is ​​estimated using single-source point detection. Based on the mode shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation. An ESTD dictionary is obtained by training the time-invariant vibration response signal using the K-SVD dictionary learning method. Based on the ESTD dictionary and the compressed sensing model, the modal response is obtained through a sparse reconstruction algorithm. Based on the modal response, the natural frequencies and loss damping ratios of each mode shape are obtained, thus realizing the time-invariant vibration response... Modal identification of the signal: When the vibration response signal is time-varying, it is divided into a finite number of time-invariant vibration response signals through a sliding window. Then, using the same method as for the time-invariant vibration response signals, the instantaneous modal model and compressed sensing model of the time-invariant vibration response signal within each sliding window are obtained. Next, the transfer learning approach is used to train the time-invariant vibration response signal within the sliding window based on the K-SVD dictionary to obtain the corresponding strongly sparse ESTD dictionary. Finally, based on the strongly sparse ESTD dictionary and the compressed sensing model, the modal identification results corresponding to the time-invariant vibration response signal within each sliding window are obtained, thus yielding the modal identification results of the time-varying vibration response signal. In this process, a monocular camera is used to acquire feature targets, and the vibration response signal is obtained from the acquired images. This avoids the shortcomings of existing technologies using sensors for measurement, such as incomplete structural response measurement information, inability to meet overdetermined and positive definite requirements, and difficulty in performing structural dynamics working modal analysis. Furthermore, it is cost-effective, easy to deploy, and has a significant field of view advantage. By combining sliding window and transfer learning methods, the time-invariant underdetermined modal analysis (TDM) method is extended to the time-varying underdetermined modal analysis method, thus solving the problem of underdetermined mode identification under both time-invariant and time-varying structures. For time-varying vibration response signals, when training the K-SVD dictionary to obtain the corresponding strongly sparse ESTD dictionary, the training samples are the modal identification results corresponding to the time-invariant vibration response signals in the previous sliding window, and the initial dictionary is the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signals in the previous sliding window. This reduces the dictionary training time and effectively improves the identification speed. When estimating mode shapes, since the frequency amplitude of environmental noise is low, the frequency energy of the noise is usually located at low coordinates (generally near 0). Therefore, the mode shapes estimated by the slope of the highest frequency energy point are less affected by Gaussian white noise and exhibit better robustness. Attached Figure Description

[0041] The present invention will now be described in further detail with reference to the accompanying drawings.

[0042] Figure 1 This is a flowchart of the time-varying vibration response signal mode identification provided by the present invention.

[0043] Figure 2 This is a detailed flowchart of the modal identification of time-varying vibration response signals provided by the present invention.

[0044] Figure 3 This is a schematic diagram of the training sample construction process based on transfer learning provided by the present invention.

[0045] Figure 4 This is a schematic diagram of the ESTD dictionary initialization process based on transfer learning provided by the present invention.

[0046] Figure 5 The flowchart is for the time-varying underdetermined working mode analysis method provided by the present invention.

[0047] Figure 6 This is a graph showing the variation of the correlation coefficient of the reconstructed modal response with sparsity provided by the present invention.

[0048] Figure 7 This is a schematic diagram of the time-varying three-degree-of-freedom spring oscillator model provided by the present invention.

[0049] Figure 8 This is a schematic diagram of Gaussian white noise excitation and three displacement response signals provided by the present invention.

[0050] Figure 9 This is a schematic diagram showing the values ​​of the theoretical natural frequency provided by this invention at various points in time.

[0051] Figure 10 These are schematic diagrams of the mode shapes at different time points provided by this invention. Detailed Implementation

[0052] like Figure 1 and Figure 2 As shown, the underdetermined modality recognition method based on a monocular camera includes the following steps:

[0053] Step S1: Arrange a limited number of feature targets in the linear vibration system, use a monocular camera to acquire multiple images including all feature targets, determine the feature points in each image, and obtain the vibration response signal based on the feature points in the images at two adjacent time points. When the vibration response signal is a time-invariant vibration response signal, proceed to step S21; when the vibration response signal is a time-varying vibration response signal, proceed to step S31.

[0054] More specifically, obtaining the vibration response signal includes the following steps:

[0055] Step S11: Arrange several feature targets in the linear vibration system, and use a monocular camera to acquire multiple images including all feature targets. In this embodiment, the linear vibration system is a bridge, the feature targets are attached to the bridge, and the monocular camera acquires images at 30 frames per second.

[0056] Step S12: For the current feature target, determine the feature points corresponding to the current feature target in each image using the Shi_Tomasi corner detection algorithm;

[0057] The expression for the Shi_Tomasi corner detection algorithm is as follows: , and The eigenvalues ​​of the autocorrelation matrix are calculated for each pixel. If R exceeds a set threshold, the point is identified as a corner point, and the corner point is a feature point.

[0058] Step S13: Obtain the Euclidean distance between feature point pairs in images at two adjacent time points using the FLANN feature point matching algorithm, and retain feature point pairs corresponding to Euclidean distances less than the set distance threshold.

[0059] According to the formula Calculate the Euclidean distance d from a feature point in one image to the K nearest feature points in the other image at two adjacent time points. 1i Let d represent the i-th feature point of one of the images. 2j This represents the j-th feature point of another image;

[0060] Step S14: Calculate the angle between the direction vector formed by each feature point pair and the average direction vector. Retain feature point pairs with angles smaller than the set angle threshold. The average direction vector is calculated according to the formula... Calculate, where n' represents the number of feature point pairs retained in step S13. This represents the direction vector formed by the i'th pair of feature points;

[0061] Step S15: Calculate the distance between the feature point pairs retained in step S14, and calculate the average of all distances as the pixel displacement of the two adjacent images. Combine the timestamp information of the two adjacent images to obtain the displacement signal corresponding to the current feature target.

[0062] Step S16: Repeat steps S11 to S15 to obtain the displacement signals corresponding to each feature target, forming a vibration response signal.

[0063] Step S21: Perform a short-time Fourier transform on the time-invariant vibration response signal and estimate the mode shape matrix using single-source point detection, then proceed to step S22;

[0064] Specifically, the steps include the following:

[0065] Step S211: The time-invariant vibration response signal is decomposed and represented in modal coordinates as follows: ,in, , This represents the displacement signal corresponding to the i-th feature target, where n is the number of feature targets set (n is less than the number of degrees of freedom), t represents time, and T represents the number of sampling points. This represents a matrix of dimension n×T within the real number range. The modal shape matrix, Let m be the vector of the m-th mode shape, where m is the order of the mode shape. To The modal response matrix obtained by decomposition Let [ ] be the modal response vector. T Indicates matrix transpose;

[0066] The meaning of underdetermined modal response is that m modal response signals are calculated using n observations. The natural frequencies of each modal response signal are not equal. After decoupling, their corresponding mode shapes are orthogonal to each other, and the modal responses are independent of each other. satisfy , satisfy , where n <m<n dof n dof The number of degrees of freedom.

[0067] Step S212: Apply the short-time Fourier transform simultaneously to the modal coordinate representation to obtain the time-invariant vibration response signal in the time-frequency domain. -,Right now:

[0068]

[0069] in, and They are respectively and The result of the short-time Fourier transform, where f represents the frequency. This represents the result of the short-time Fourier transform corresponding to the vibration response signal measured by the i-th target;

[0070] Step S213: Based on the short-time Fourier transform, calculate the frequency energy (FE) after the short-time Fourier transform. The formula for calculating the frequency energy of the time-frequency domain vibration response signal is as follows: ,Right now: Calculate the frequency energy of the time-invariant vibration response signal in the time-frequency domain, where, This represents the frequency energy corresponding to the displacement signal of the i-th feature target. This represents the frequency energy of the j-th mode shape. This represents the j-th mode shape corresponding to the i-th feature target;

[0071] Step S214: When the frequency f is within the interval At that time, The slope of the energy highest point at each frequency is calculated using a single-source detection method to obtain the modal shape matrix. ,in, f represents the set frequency threshold. j This represents the frequency value corresponding to the j-th frequency interval.

[0072] Specifically, when the frequency of each modal response is greater than When this happens, the following formula can be obtained:

[0073] ,

[0074] When the vibration response signal is dominated by only a few frequency bands within a short period of time, that is, only within the frequency range... At that time, Thus, the formula is obtained. Since this formula is the same as the linear expression, the frequency-energy ratio of each modal response is consistent. Therefore, the mode shape can be estimated by calculating the slope of the energy highest point at each frequency using the Single-Source Points (SSP) technique. That is, to find the frequency peak corresponding to the highest energy point. .

[0075] Step S22: Based on the modal shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation, and then proceed to step S23;

[0076] Specifically, the steps include the following:

[0077] Step S221, Time-invariant vibration response signal Underdetermined blind source separation (UBSS) is represented as: ,Right now ,in, It is a mixture matrix, which is estimated by whitening the signal using the ICA algorithm. , Represents the mixture matrix The i-th column vector in the middle, Each column corresponds to the modal shape matrix. Each mode shape in the process, This represents the recovered source signal in the time domain, which will be estimated. Substitute into the formula get, Represents the i-th column vector in the estimation of the source signal in the time domain;

[0078] Step S222: The reconstructed compressed sensing model is represented as follows: ,Right now ,in, The observation vector is, i.e. transpose, For the mixed matrix A sparse matrix that satisfies the sparse domain constraint, i.e. yes diagonal matrix, , This is the sparse representation of the source signal in the sparse domain, i.e. The transpose of .

[0079] Step S23: The time-invariant vibration response signal is trained based on the K-SVD dictionary learning method to obtain the ESTD dictionary. Based on the ESTD dictionary and the compressed sensing model, the modal response is obtained through the sparse reconstruction algorithm. The natural frequency and loss damping ratio of each mode shape are extracted from the modal response using the single degree of freedom technique to realize the modal identification of the time-invariant vibration response signal.

[0080] The K-SVD (K-Singular Value Decomposition) algorithm aims to find an overcomplete dictionary (ESTD) and a sparse matrix X through an iterative process, such that Y ≈ DX, where Y is the input signal matrix, D is the ESTD dictionary matrix, and X is the sparse coefficient matrix. The algorithm's objective is to minimize the error between Y and DX while preserving the sparsity of X.

[0081] Step S31: Divide the time-varying vibration response signal into a finite number of time-invariant vibration response signals using a sliding window with a set window length. Perform short-time Fourier transform on the time-invariant vibration response signal in each sliding window window. Estimate the instantaneous mode shape corresponding to each time-invariant vibration response signal using single-source point detection. Reconstruct the compressed sensing model of the time-invariant vibration response signal in each sliding window window after underdetermined blind source separation. Proceed to step S32.

[0082] Specifically, the time-invariant vibration response signal within the j'-th sliding window is represented in modal coordinates as follows: Where L represents the length of the sliding window, j' represents the sliding window number, j'=1,2,…,L',…,T-L',+1, and L' is the duration of the time segment contained within each sliding window. The midpoint of the sliding window is used as the instantaneous modal parameter of the time-varying vibration response signal. This represents the modal shape matrix of the time-invariant vibration response signal within the j'-th sliding window. Let represent the modal response matrix of the time-invariant vibration response signal within the j'-th sliding window.

[0083] The time-invariant vibration response signal within each sliding window is subjected to short-time Fourier transform, and the instantaneous mode shape corresponding to each time-invariant vibration response signal is estimated using single-source point detection. The time-invariant vibration response signal within each sliding window is then reconstructed into a compressed sensing model after underdetermined blind source separation. The specific process is the same as the corresponding processing of the time-invariant vibration response signal mentioned above.

[0084] Step S32, as follows Figure 5 As shown, the time-invariant vibration response signal within the current sliding window is trained using a K-SVD dictionary to obtain the corresponding strongly sparse ESTD dictionary. During the K-SVD training of the ESTD dictionary, transfer learning is introduced. Due to the "short-term time-invariance" assumption of the sliding window, the modal parameters of the current sliding window are similar to those of the next sliding window. Therefore, as... Figure 3 As shown, during the transfer learning process, the training samples are the modal recognition results corresponding to the time-invariant vibration response signals within the previous sliding window. Unsupervised dictionary learning is achieved during each sliding window movement, such as... Figure 4 As shown, the initial dictionary for learning and training is the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window.

[0085] The time-invariant vibration response signal within the first sliding window undergoes the same training process as the time-invariant vibration response signal training described above (i.e., as described in step S23) when learning and training based on the K-SVD dictionary. The modal identification results corresponding to the time-invariant vibration response signal within the previous sliding window include the natural frequencies and loss damping ratios of each mode shape. When the natural frequencies of each mode shape corresponding to the time-invariant vibration response signal within the previous sliding window differ from the natural frequencies of each mode shape corresponding to the time-invariant vibration response signal within the current sliding window by 1, the current sliding window is used as the first sliding window to re-enter step S32 to prevent the accumulation of errors caused by transfer learning.

[0086] Step S33: Based on the strongly sparse ESTD dictionary and compressed sensing model corresponding to the time-invariant vibration response signal of the current sliding window, obtain the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window through the sparse reconstruction algorithm, and obtain the instantaneous natural frequency and instantaneous damping ratio of each mode shape corresponding to the time-invariant vibration response signal in the current sliding window based on the instantaneous modal response, and obtain the modal identification result corresponding to the time-invariant vibration response signal in the current sliding window;

[0087] Specifically, the instantaneous natural frequency and loss damping ratio are extracted from the instantaneous modal response using a single degree of freedom technique.

[0088] Step S34: Repeat steps S32 to S33 until the modal identification results corresponding to the time-invariant vibration response signals in all sliding window windows are obtained.

[0089] The underdetermined modality recognition device based on a monocular camera includes:

[0090] Signal determination module: It is used to arrange a limited number of feature targets in a linear vibration system, use a monocular camera to acquire multiple images including all feature targets, determine the feature points in each image, and obtain the vibration response signal based on the feature points in the images at two adjacent time points, and determine whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal.

[0091] The time-invariant vibration response signal identification module performs short-time Fourier transform on the time-invariant vibration response signal and estimates the mode shape matrix using single-source point detection. Based on the mode shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation. The time-invariant vibration response signal is trained using the K-SVD dictionary learning method to obtain the ESTD dictionary. Based on the ESTD dictionary and the compressed sensing model, the modal response is obtained through a sparse reconstruction algorithm. Based on the modal response, the natural frequencies and loss damping ratios of each mode shape are obtained, thus realizing modal identification of the time-invariant vibration response signal.

[0092] The time-varying vibration response signal recognition module divides the time-varying vibration response signal into a finite number of time-invariant vibration response signals using a sliding window of a set window length. It performs a short-time Fourier transform on the time-invariant vibration response signal within each sliding window and estimates the instantaneous mode shape corresponding to each time-invariant vibration response signal using single-source point detection. After underdetermined blind source separation, it reconstructs a compressed sensing model for the time-invariant vibration response signal within each sliding window. For the time-invariant vibration response signal within the current sliding window, it performs training based on a K-SVD dictionary to obtain a corresponding strongly sparse ESTD dictionary. The training samples are the modal recognition results corresponding to the time-invariant vibration response signal within the previous sliding window. The initial dictionary for learning and training is the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window. Based on the strongly sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the current sliding window and the compressed sensing model, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained through a sparse reconstruction algorithm. Then, based on the instantaneous modal response, the instantaneous natural frequencies and instantaneous damping ratios of each mode shape corresponding to the time-invariant vibration response signal in the current sliding window are obtained, thus obtaining the modal identification result corresponding to the time-invariant vibration response signal in the current sliding window. This process is repeated until the modal identification results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

[0093] The process of determining the vibration response signal based on the acquired image, the time-invariant vibration response signal recognition module, and the time-varying vibration response signal recognition module are implemented through a memory and a processor. The memory stores the corresponding computer program, which can be executed by the processor to realize the above-mentioned underdetermined mode recognition method.

[0094] To verify the correctness and effectiveness of this invention, a five-degree-of-freedom mass-spring-damped model was established in Matlab / Simulink. The mechanical governing equations of the five-degree-of-freedom mass-spring-damped system are expressed as follows:

[0095] ,

[0096] Wherein, the mass matrix is ​​set as The stiffness coefficients are set to k1=0 and k 12 =800, k 24 =800, k 34 =2400, k 45 =3200, meaning the stiffness matrix is ​​set to: The damping matrix is ​​set to C = 0.5M + 0.0004K, the sampling frequency is set to 100Hz, and the initial velocity and displacement are set to... and .

[0097] In terms of parameter settings, the overlap interval of the short-time Fourier transform is set to 4. The cosine distance threshold in the frequency-energy method is a constant. The sample construction frame length for sparse dictionary learning is set to L=250, the overlap P=249, and the number of hierarchically coupled block sequences K=4. The number of iterations for K-SVD dictionary learning is 10.

[0098] Regarding evaluation methods and indicators, since the underdetermined working modal parameter identification methods are mainly divided into modal shape estimation and modal response reconstruction stages, and the existing methods have different research focuses, this invention compares the modal shape estimation method and the modal response reconstruction method with existing research methods.

[0099] 1) Use the Modal Assurance Criterion (MAC) method to evaluate the accuracy of mode shape identification: ;

[0100] in, This represents the i-th mode shape in the theory. The MAC value represents the i-th mode shape being identified. The closer the MAC value is to 1, the higher the identification accuracy.

[0101] 2) Define the correlation coefficient to evaluate the accuracy of the reconstructed modal coordinate response: ;

[0102] in, This represents the coordinate response of the j-th modal in the theory. This represents the reconstructed j-th modal coordinate response. The closer to 1, the higher the recognition accuracy.

[0103] 3) The natural frequency and damping ratio are compared with theoretical values ​​to evaluate its recognition accuracy.

[0104] The identification results for underdetermined conditions in the absence of measurement noise are as follows:

[0105] In the underdetermined case, the vibration response signals from channels 2 and 5 were used as inputs to compare the modal parameter identification effects of different methods. First, to determine the impact of sparsity on the modal response reconstruction accuracy in the underdetermined case, such as... Figure 6 The figure shows the correlation coefficients (average of the fifth order) of the reconstructed modal responses of the present invention (FEESTD) as a function of sparsity.

[0106] To verify the modal shape identification performance of the FEESTD method under underdetermined conditions, comparisons were made with SOBI (second-order blind identification algorithm), SCA-FCM (component analysis algorithm based on fuzzy C-means clustering), SCA-Kmeans (component analysis algorithm based on Kmeans clustering), and SCA-DBSCAN. M Modal modes identified by methods such as (based on an improved density space clustering component analysis algorithm). Table 1 shows a comparison of the MAC values ​​of the modal modes identified by different methods.

[0107] Table 1

[0108]

[0109] To verify the modal response recognition performance of the FEESTD method under underdetermined conditions, the modal response recognition performance was compared with that of DCTCS (DCT Discrete Cosine Transform combined with CS Compressed Sensing), ESTD, MTD (The Mixture-Trained Dictionary), SCA (Independent Component Analysis), SOBI (Second-Order Blind Recognition Algorithm), NUBSS (Novel UBSS), and ADCS (Adaptive Dictionary Compression Sensing). Table 1 shows the recognition results for SCA-DBSCAN. M Clustering results are better, therefore DBSCAN is used for SCA. M The FEESTD clustering algorithm has a sparsity set to 30. Tables 2-4 show the modal response correlation coefficients reconstructed by different methods, as well as the identified natural frequencies and damping ratios. Table 5 shows the time cost of different methods.

[0110] Table 2 Comparison of modal response correlation coefficients reconstructed by different methods when n=2.

[0111]

[0112] Table 3. Comparison of intrinsic frequencies identified by different methods with theoretical values ​​when n=2.

[0113]

[0114] Table 4. Comparison of damping ratios identified by different methods with theoretical values ​​when n=2.

[0115]

[0116] Table 5. Time cost of different methods when n=2.

[0117]

[0118] Identification results of underdetermined conditions under added measurement noise:

[0119] To test the noise resistance of different methods, Gaussian white noise with different signal-to-noise ratios was added to the response signal under underdetermined conditions. SCA-FCM, SCA-Kmeans, and SCA-DBSCAN were compared separately. M The MAC values ​​of the modal shapes identified by FEESTD are shown in Table 6. The correlation coefficients of the modal responses reconstructed by SCA (using DBSCANM clustering algorithm), DCTCS, NUBSS, ADCS and FEESTD methods are compared respectively, as shown in Table 7.

[0120] Table 6 Comparison of MAC values ​​of identified modal shapes under different noise conditions

[0121]

[0122] Table 7. Comparison of correlation coefficients of reconstructed modal responses under different noise conditions.

[0123]

[0124] As shown in Tables 1-4, under underdetermined conditions, the SOBI method can only identify modal parameters equal to the number of sensors. The modal parameter identification effects of DCTCS, ESTD, and MTD methods are poor. FEESTD can identify higher-order modes than the number of sensors and has higher identification accuracy than clustering-based methods such as SCA and ADCS.

[0125] As can be seen from the identification results in Tables 6 and 7, under noisy conditions, the accuracy of the estimated mode shapes and reconstructed modal responses by various methods will decrease with the increase of noise. However, FEESTD has higher identification accuracy, indicating that the FEESTD method has better robustness in both mode shape estimation and modal response reconstruction.

[0126] To verify the correctness and effectiveness of the FEESTD-based linear time-varying underdetermined working mode analysis method, a three-degree-of-freedom spring oscillator with a linear time-varying structure was used, where the mass matrix changes with time.

[0127] like Figure 7 The three-degree-of-freedom spring oscillator system shown consists of three blocks, three springs, and three dampers connected in series. The initial displacement and velocity of the three blocks are all 0. The damping ratio of the three dampers is c1=c2=c3=0.01Ns / m, and their stiffness is k1=k2=k3=1000N / m. The masses of blocks m2 and m3 are 1kg. The mass of block m1 changes with time as follows:

[0128] ,

[0129] For the three-degree-of-freedom spring oscillator experiment, the response signal was obtained through simulation using MATLAB / Newmark-β. The sampling frequency was 40Hz, and the number of sampling points was T=2000s. The Gaussian white noise excitation applied to object m_1 and the simulated response signal are as follows: Figure 8 As shown.

[0130] The theoretical natural frequency mode shape was obtained by simulation using the undamped finite element method. The values ​​of the natural frequency at various time points are as follows: Figure 9 As shown, mode shapes were selected at t=56.425s, t=695.75s, t=1335.075s, and t=1974.4s, and the mode shape diagrams were plotted as follows. Figure 10 As shown.

[0131] Parameter settings: To simulate underdetermined conditions, response signals acquired from channels 1 and 3 are used as inputs. The sliding window length is set to 1024. The overlap interval of the short-time Fourier transform is set to 4. The cosine distance threshold constant ε in the frequency-energy method is 0.004. The planning method for SCA uses the L1 norm minimization method.

[0132] The modal confidence criterion (MAC) was used to evaluate the mode shape identification accuracy within each window, and the number of windows with a MAC value less than 0.8 was counted. The identified natural frequencies within each window were compared with the theoretical values, and the number of windows with a difference greater than 1 between the identified and theoretical natural frequency values ​​was counted to evaluate the accuracy of natural frequency identification.

[0133] The results of time-varying underdetermined instantaneous modal parameter identification under noise-free conditions are as follows:

[0134] (1) Instantaneous mode shape recognition effect

[0135] To verify the modal shape recognition performance of the proposed method MWTL-FEESTD (FEESTD with sliding window transfer learning) under time-varying underdetermined structures, comparisons were made with MW-SOBI (second-order blind sliding window recognition), MW-SCA-FCM (sliding window SCA based on FCM clustering), MW-SCA-Kmeans (sliding window SCA based on Kmeans clustering), and MW-SCA-DBSCAN. M The modal shapes were identified using methods such as (sliding window SCA based on improved DBSCAN clustering). To more intuitively demonstrate the effect of different comparison methods on the MAC values ​​of the modal shapes, Table 8 shows the number of time points where the MAC of the modal shapes identified by different comparison methods was <0.8.

[0136] Table 8 Number of time points for MAC values ​​of unidentified modal shapes by different methods

[0137]

[0138] (2) Instantaneous natural frequency recognition effect

[0139] To verify the performance of the proposed MWTL-FEESTD method in identifying intrinsic frequencies under time-varying structural underdetermined conditions and its time overhead before and after incorporating transfer learning, comparisons were made with MW-SOBI and MW-SCA (using DBSCAN clustering algorithm). M The intrinsic frequencies identified by methods such as MW-FEESTD (sliding window frequency energy and ESTD dictionary method without transfer learning) are shown in Table 9. The number of times when different methods failed to identify intrinsic frequencies is also shown in Table 10. The time cost of different methods throughout the time-varying period is compared.

[0140] Table 9 Number of time points where natural frequencies were not identified by different methods

[0141]

[0142] Table 10 Time Costs of Different Methods

[0143]

[0144] To verify the effects of adding transfer learning in the construction of training samples and the initialization of adaptive dictionary, the recognition performance and time cost of intrinsic frequencies before and after adding transfer learning were compared. The comparison results are shown in Table 11.

[0145] Table 11 Recognition accuracy and time cost before and after adding transfer learning

[0146]

[0147] In practical engineering, signals are frequently interfered with by external noise; therefore, the robustness of working mode parameter analysis algorithms is of great importance. To test the noise resistance of different methods, Gaussian white noise with a signal-to-noise ratio of 15 dB was added to the response signal under time-varying underdetermined conditions. In this embodiment, the results of the instantaneous mode parameter identification under time-varying underdetermined conditions with added measurement noise are as follows:

[0148] (1) Instantaneous mode shape recognition effect

[0149] To verify the modal shape identification performance of MWTL-FEESTD under noisy conditions, Table 12 shows the statistical results for MW-SOBI, MW-SCA-FCM, MW-SCA-Kmeans, and MW-SCA-DBSCAN. M The number of time points at which the modal MAC is less than 0.8, as identified by methods such as [method name missing].

[0150] Table 12 Number of time points for MAC values ​​of unidentified modal shapes by different methods

[0151]

[0152] (2) Instantaneous natural frequency recognition effect

[0153] To verify the intrinsic frequency identification performance of MWTL-FEESTD under noisy conditions, Table 13 shows the statistical results of MW-SOBI and MW-SCA (clustering algorithm: DBSCAN). M The number of moments when the inherent frequency was not identified by methods such as MW-FEESTD.

[0154] Table 13 Number of time points where natural frequencies were not identified by different methods under noisy conditions

[0155]

[0156] As shown in Tables 8 and 9, when the input response signal has only two channels, MW-SOBI can only identify second-order modal parameters. This method can only solve the problem of identifying time-varying structural modal parameters under positive definite and overdetermined conditions. MWTL-FEESTD and MW-SCA methods based on different clustering algorithms can both identify third-order modal parameters well, but MWTL-FEESTD has a better recognition effect than MW-SCA methods based on different clustering algorithms.

[0157] Table 10 shows that the MWTL-FEESTD method with transfer learning has a lower time cost than the MW-FEESTD method without transfer learning, and its time cost is similar to that of the MW-SCA method. Table 11 shows that incorporating transfer learning during the training sample construction process improves the accuracy of modality parameter recognition and increases the method's recognition speed. Furthermore, incorporating transfer learning during the ESTD dictionary initialization process effectively improves the method's recognition speed.

[0158] As can be seen from the identification results in Tables 12 and 13, the MW-SCA and MW-SOBI methods have more unidentified time points due to the influence of noise in identifying mode shapes and natural frequencies. In contrast, the MWTL-FEESTD method has fewer unidentified time points than other methods, indicating that this method misses fewer modes and has better noise immunity.

[0159] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0160] In estimating mode shapes, this invention takes into account the low frequency amplitude of ambient noise, where the frequency energy of the noise is usually located at the low coordinate (generally near 0). Therefore, the mode shapes estimated by the slope at the highest frequency energy point are less affected by Gaussian white noise and exhibit better robustness.

[0161] This invention employs a dictionary learning method based on transfer learning, which can quickly converge to a specified error, thereby reducing the training time of dictionary learning, lowering the time complexity of the method, and effectively improving the recognition speed of modal parameters.

[0162] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made in accordance with the scope of the patent application and the contents of the specification of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A method for underdetermined modal identification based on monocular camera, characterized in that: Comprising the following steps: Step S1, defining a plurality of feature targets in a linear vibration system, acquiring a plurality of images comprising all the feature targets by using a monocular camera, determining feature points in each image respectively, and obtaining a vibration response signal according to the feature points in the images of two adjacent time instants, entering step S21 when the vibration response signal is a time-invariant vibration response signal, and entering step S31 when the vibration response signal is a time-varying vibration response signal; Step S21, performing short-time Fourier transform on the time-invariant vibration response signal, and obtaining a modal shape matrix by using single-source point detection estimation, and entering step S22; Step S22, according to the modal shape matrix, reconstructing the time-invariant vibration response signal into a compressed sensing model after underdetermined blind source separation, and entering step S23; Step S23, training the time-invariant vibration response signal based on a K-SVD dictionary learning method to obtain an ESTD dictionary, obtaining a modal response through a sparse reconstruction algorithm according to the ESTD dictionary and the compressed sensing model, and obtaining an inherent frequency and a loss damping ratio of each order modal shape according to the modal response, so as to realize modal identification of the time-invariant vibration response signal; Step S31, dividing the time-varying vibration response signal into a plurality of time-invariant vibration response signals by using a sliding window with a set window length, performing short-time Fourier transform on the time-invariant vibration response signal in each sliding window, obtaining an instantaneous modal shape corresponding to each time-invariant vibration response signal by using single-source point detection estimation, and reconstructing the time-invariant vibration response signal in each sliding window into a compressed sensing model after underdetermined blind source separation, and entering step S32; Step S32, learning and training a K-SVD dictionary based on the time-invariant vibration response signal in the current sliding window to obtain a corresponding strong sparse ESTD dictionary, wherein the sample for learning and training is the modal identification result corresponding to the time-invariant vibration response signal in the previous sliding window, and the initialized dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window; Step S33, obtaining an instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window through a sparse reconstruction algorithm according to the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the current sliding window and the compressed sensing model, and obtaining an instantaneous inherent frequency and an instantaneous damping ratio of each order modal shape corresponding to the time-invariant vibration response signal in the current sliding window according to the instantaneous modal response, so as to obtain a modal identification result corresponding to the time-invariant vibration response signal in the current sliding window; Step S34, repeating steps S32 to S33 until the modal identification results corresponding to the time-invariant vibration response signals in all the sliding windows are obtained; The modal identification result corresponding to the time-invariant vibration response signal in the last sliding window in the step S32 includes the natural frequency and loss damping ratio of each order modal vibration mode, and when the natural frequency of each order modal vibration mode corresponding to the time-invariant vibration response signal in the last sliding window is different from the natural frequency of each order modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window by 1, the current sliding window is taken as the first sliding window to re-enter the step S32.

2. The method of claim 1, wherein: In the step S1, the acquisition of the vibration response signal specifically includes the following steps: In step S11, a plurality of characteristic targets are arranged in the linear vibration system, and a plurality of images including all the characteristic targets are captured by using a monocular camera; In step S12, for a current characteristic target, feature points corresponding to the current characteristic target in each image are determined by using a Shi_Tomasi corner detection algorithm respectively; In step S13, the Euclidean distances between the feature point pairs in the images of two adjacent time points are obtained by using a FLANN feature point matching algorithm, and the feature point pairs corresponding to the Euclidean distances less than a set distance threshold are retained; Step S14, respectively calculate the included angle between the direction vector formed by each feature point pair and the average direction vector, and retain the feature point pair corresponding to the included angle less than the set included angle threshold, wherein the average direction vector is calculated according to the formula Calculate, n' represents the number of feature point pairs retained in step S13, indicates the direction vector formed by the i'th feature point pair. In step S15, the distances between the retained feature point pairs in step S14 are calculated respectively, and the average of all the distances is taken as the pixel displacement of the two adjacent images, and the displacement signal corresponding to the current characteristic target is obtained by combining the time stamp information of the two adjacent images; In step S16, steps S11 to S15 are repeated to obtain the displacement signals corresponding to the characteristic targets, and the vibration response signal is formed.

3. The method of claim 2, wherein: The step S21 includes the following steps: Step S211, the time-invariant vibration response signal is expressed in modal coordinates as wherein, , denotes the displacement signal corresponding to the i-th characteristic target, n is the number of characteristic targets set, is a modal mode shape matrix, is the m-th order modal mode shape, m is the order of the modal mode shape, is a modal response matrix, is a modal response vector, T denotes matrix transposition; Step S212, the short-time Fourier transform is simultaneously applied to the modal coordinate representation to obtain a time-invariant vibration response signal in the time-frequency domain as wherein, and are respectively the results of the short-time Fourier transform of and . Step S213, calculating the frequency energy of the time-invariant vibration response signal in the time-frequency domain according to the formula , wherein, represents the frequency energy corresponding to the displacement signal corresponding to the i-th characteristic target, represents the frequency energy of the j-th modal shape, represents the j-th modal shape corresponding to the i-th characteristic target. Step S214, when the frequency f is in the frequency interval , the slope of the highest energy point on each frequency is calculated by using the single-source point detection method to obtain the modal shape matrix , where , and represents the set frequency threshold, f k represents the frequency value corresponding to the kth frequency interval.

4. The method of claim 3, wherein: The step S22 includes the following steps: Step S221, time-invariant vibration response signal underdetermined blind source separation is represented as wherein, is a mixing matrix, each column of which corresponds to each order modal shape in the modal shape matrix denotes the recovered source signals in the time domain;​ Step S222, the reconstructed compressed sensing model is represented as wherein, is an observation vector, is a mixing matrix is a sparse matrix under the sparse domain constraint condition, is a sparse representation of the source signal in the sparse domain.

5. The method of claim 4, wherein: In the step S31, the time-invariant vibration response signal in the j'th sliding window is expressed in modal coordinates as where L denotes the sliding window length, j' denotes the sliding window number, is the middle time of the sliding window, denotes the modal shape matrix of the time-invariant vibration response signal in the j'th sliding window, denotes the modal response matrix of the time-invariant vibration response signal in the j'th sliding window.

6. The method of claim 5, wherein: In the step S33, the instantaneous natural frequency and loss damping ratio are extracted from the instantaneous modal response by using a single degree of freedom technology. 7.A monocular camera based underdetermined modal identification device, characterized in that: It includes: The signal determination module is used for arranging a plurality of characteristic targets in the linear vibration system, capturing a plurality of images including all the characteristic targets by using a monocular camera, determining feature points in each image respectively, and acquiring a vibration response signal according to the feature points in the images of two adjacent time points, and judging whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal; The time-invariant vibration response signal identification module is used for performing short-time Fourier transform on the time-invariant vibration response signal, and estimating a modal vibration mode matrix by using a single source point detection; the time-invariant vibration response signal is reconstructed into a compressed sensing model after underdetermined blind source separation according to the modal vibration mode matrix; the ESTD dictionary is obtained by training the time-invariant vibration response signal based on the K-SVD dictionary learning method, the modal response is obtained by the sparse reconstruction algorithm according to the ESTD dictionary and the compressed sensing model, and the natural frequency and loss damping ratio of each order modal vibration mode are obtained according to the modal response, so as to realize the modal identification of the time-invariant vibration response signal. The time-varying vibration response signal identification module is used for dividing the time-varying vibration response signal into a limited number of time-invariant vibration response signals by using a sliding window with a set window length, performing short-time Fourier transform on the time-invariant vibration response signal in each sliding window, respectively, and using single-source point detection estimation to obtain the instantaneous modal shape corresponding to each time-invariant vibration response signal, and using underdetermined blind source separation to reconstruct the time-invariant vibration response signal in each sliding window into a compressed sensing model; for the time-invariant vibration response signal in the current sliding window, learning and training based on the K-SVD dictionary are performed to obtain the corresponding strong sparse ESTD dictionary, the sample for learning and training is the modal recognition result corresponding to the time-invariant vibration response signal in the previous sliding window, the initialized dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window, and the modal recognition result corresponding to the time-invariant vibration response signal in the previous sliding window includes the natural frequency and loss damping ratio of each order modal shape; when the natural frequency of each order modal shape corresponding to the time-invariant vibration response signal in the previous sliding window is different from the natural frequency of each order modal shape corresponding to the time-invariant vibration response signal in the current sliding window by 1, the current sliding window is regarded as the first sliding window and learning and training based on the K-SVD dictionary are performed again; According to the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the current sliding window and the compressed sensing model, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained through a sparse reconstruction algorithm, and the instantaneous natural frequency and instantaneous damping ratio of each order modal shape corresponding to the time-invariant vibration response signal in the current sliding window are obtained according to the instantaneous modal response, so as to obtain the modal recognition result corresponding to the time-invariant vibration response signal in the current sliding window; the process is repeated continuously until the modal recognition result corresponding to the time-invariant vibration response signal in all sliding windows is obtained.

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