Underdetermined modal identification method and device based on monocular camera

Abstract

The invention provides an underdetermined modal identification method and device based on a monocular camera, and belongs to the technical field of modal parameter identification, and the method comprises the steps: collecting a plurality of images comprising all feature targets through the monocular camera, obtaining a vibration response signal according to the images, and when the vibration response signal is a time-invariant vibration response signal, carrying out the recognition of the underdetermined modal of the monocular camera; reconstructing the time-invariant vibration response signal into a compressed sensing model, training the time-invariant vibration response signal to obtain an ESTD dictionary, performing modal recognition on the time-invariant vibration response signal according to the ESTD dictionary and the compressed sensing model, and when the vibration response signal is the time-invariant vibration response signal, performing modal recognition on the time-invariant vibration response signal. The time-varying vibration response signals are divided into a limited number of time-invariant vibration response signals by using a sliding window, a strong sparse ESTD dictionary is obtained in combination with the thought of transfer learning, and then modal recognition of the time-varying vibration response signals is obtained. According to the method, underdetermined modal recognition under a time-invariant structure and a time-varying structure can be solved, and the recognition speed and precision of underdetermined modal recognition parameters are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of modal parameter recognition, and in particular relates to an underdetermined modal recognition method and device based on a monocular camera. Background Art

[0002] In actual engineering applications, due to the cost and the difficulty of installing instruments to measure response signals, traditional structural parameter measurement methods (such as mass, stiffness, damping, etc.) become difficult to implement, and sensors can only be arranged at limited key locations for dynamic response measurement. This leads to incomplete structural response measurement information, which cannot meet the requirements of overdetermination and positive determination, and is not conducive to structural dynamics working modal analysis. The advantages of using a monocular camera to measure vibration signals include high cost-effectiveness, easy setup and use, avoiding complex calibration and object matching between multiple cameras, and providing displacement measurement with obvious field of view advantages compared to traditional physical sensors. Therefore, it is of great importance and urgent significance to study the problem of underdetermined working modal analysis of time-varying structures based on monocular cameras.

[0003] For time-varying structures, the working modal analysis methods can be divided into two categories: time domain methods and time-frequency domain methods. The existing patent document CN104698837B "A method, device and application for identifying working modal parameters of time-varying structures" has achieved good results on the modal parameters of time-varying structures by combining sliding windows with limited memory principal component analysis; the patent document CN116776708B "Time-varying working modal parameter adaptive identification method, device, equipment and medium" combines sliding windows with blind source separation and popular 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] On the underdetermination problem, the existing patent document CN112507606B "Underdetermined working modal parameter identification method and detection method based on RBF network" identifies modal parameters under the condition of time-invariant structure, but does not consider the modal parameter identification under time-varying structure. Summary of the invention

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

[0006] The present invention is achieved through the following technical solutions:

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

[0008] Step S1, arranging a limited number of characteristic targets in the linear vibration system, using a monocular camera to collect multiple images including all characteristic targets, respectively determining characteristic points in each image, and obtaining a vibration response signal according to the characteristic points in the images at two adjacent moments, and when the vibration response signal is a time-invariant vibration response signal, entering step S21, and when the vibration response signal is a time-varying vibration response signal, entering step S31;

[0009] Step S21, performing short-time Fourier transform on the time-invariant vibration response signal, and obtaining the modal vibration matrix by using single source point detection estimation, and then proceeding to step S22;

[0010] Step S22, based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model by using underdetermined blind source separation, and then proceeding to step S23;

[0011] Step S23, training the time-invariant vibration response signal based on the K-SVD dictionary learning method to obtain an ESTD dictionary, obtaining the modal response through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and obtaining the natural frequency and loss damping ratio of each order modal vibration mode based on the modal response, so as to realize modal recognition of the time-invariant vibration response signal;

[0012] Step S31, using a sliding window with a set window length to divide the time-varying vibration response signal into a finite number of time-invariant vibration response signals, performing short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and using single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstructing the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation, and entering step S32;

[0013] Step S32, performing K-SVD dictionary-based learning training on the time-invariant vibration response signal in the current sliding window to obtain a corresponding strong sparse ESTD dictionary, the learning training sample is the modal recognition result corresponding to the time-invariant vibration response signal in the previous sliding window, and the initialization dictionary for learning training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window;

[0014] Step S33, according to the strong sparse ESTD dictionary and the compressed sensing model corresponding to the time-invariant vibration response signal of the current sliding window, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained by a sparse reconstruction algorithm, and the instantaneous natural frequency and the instantaneous damping ratio of each order modal vibration type 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;

[0015] Step S34, repeating steps S32 to S33 until the modal recognition results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

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

[0017] Step S11, arranging a number of characteristic targets in the linear vibration system, and using a monocular camera to collect a plurality of images including all the characteristic targets;

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

[0019] Step S13, obtaining the Euclidean distance between feature point pairs in the images at two adjacent moments by using the FLANN feature point matching algorithm, and retaining the feature point pairs corresponding to the Euclidean distances less than the set distance threshold;

[0020] Step S14, respectively calculate the angle between the direction vector formed by each feature point pair and the average direction vector, and retain the feature point pairs corresponding to the angles less than the set 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, Represents the direction vector formed by the i'th pair of feature points;

[0021] Step S15, respectively calculating the distances between the feature point pairs retained in step S14, and finding the average value of all distances as the pixel displacement of the two adjacent images, combining the timestamp information of the two adjacent images, and obtaining the displacement signal corresponding to the current feature target;

[0022] Step S16, repeating steps S11 to S15 to obtain the displacement signal corresponding to each characteristic target to form a vibration response signal.

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

[0024] Step S211: The time-invariant vibration response signal is expressed in modal coordinates as in, represents the displacement signal corresponding to the i-th characteristic target, n is the number of characteristic targets set, is the mode shape matrix, is the mth mode shape, m is the order of the mode shape, is the modal response matrix, is the modal response vector, [] T Represents matrix transpose;

[0025] Step S212: Apply short-time Fourier transform to the modal coordinate representation to obtain a time-invariant vibration response signal in the time-frequency domain: Among them, G X (t,f) and G Q (t,f) are the results of short-time Fourier transform of X(t) and Q(t) respectively;

[0026] Step S213: According to the formula Calculate the frequency energy of the time-invariant vibration response signal in the time-frequency domain, where represents the frequency energy corresponding to the displacement signal corresponding to the i-th characteristic target, represents the frequency energy of the j-th mode shape, φ ij represents the j-th mode shape corresponding to the i-th characteristic target;

[0027] Step S214: When the frequency f is within the frequency interval [f j -Δ,f j +Δ], we get The single source point detection method is used to calculate the slope of the highest energy point at each frequency to obtain the modal vibration matrix Φ, where Δ represents the set frequency threshold, f j Represents the frequency value corresponding to the jth frequency interval.

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

[0029] Step S221, underdetermined blind source separation of the time-invariant vibration response signal X(t) is expressed as X(t)=AS(t), wherein A is a mixing matrix, each column of which corresponds to each order mode shape in the mode shape matrix Φ, and S(t) represents the recovered source signal in the time domain;

[0030] Step S222: The reconstructed compressed sensing model is expressed as in, is the observation vector, Λ is the sparse matrix of the mixing matrix A under the sparse domain constraint condition, is the sparse representation of the source signal in the sparse domain.

[0031] Furthermore, in step S31, the time-invariant vibration response signal in the j'th sliding window is expressed in modal coordinates as Where L is the length of the sliding window, j' is the number of the sliding window, and τ is the middle time of the sliding window. represents the mode shape matrix of the time-invariant vibration response signal in the j'th sliding window, Represents 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 order of modal vibration mode. When the natural frequency of each order of modal vibration mode corresponding to the time-invariant vibration response signal in the previous sliding window window differs from the natural frequency of each order of modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window window by 1, the current sliding window window is taken as the first sliding window window and re-enters step S32.

[0033] Furthermore, in step S33, the single degree of freedom technology is used to extract the instantaneous natural frequency and loss damping ratio from the instantaneous modal response.

[0034] The present 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: used to arrange a limited number of characteristic targets in the linear vibration system, use a monocular camera to collect multiple images including all characteristic targets, determine the characteristic points in each image respectively, and obtain a vibration response signal according to the characteristic points in the images at two adjacent moments, and determine whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal;

[0037] Time-invariant vibration response signal recognition module: used to perform short-time Fourier transform on the time-invariant vibration response signal, and use single source point detection to estimate the modal vibration matrix; based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after using underdetermined blind source separation; based on the K-SVD dictionary learning method, the time-invariant vibration response signal is trained to obtain an ESTD dictionary, and the modal response is obtained through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and the natural frequency and loss damping ratio of each order modal vibration mode are obtained based on the modal response, so as to realize the modal recognition of the time-invariant vibration response signal;

[0038] Time-varying vibration response signal recognition module: used to divide 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, perform short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and use single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstruct the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation; perform K-SVD dictionary-based learning and training on the time-invariant vibration response signal in the current sliding window to obtain the corresponding strongly sparse ESTD dictionary, and the learning and training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window. The initialization dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window; based on the strong sparse ESTD dictionary and compressed sensing model corresponding to the time-invariant vibration response signal in the current sliding window, 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 modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window are obtained based on the instantaneous modal response, and the modal recognition result corresponding to the time-invariant vibration response signal in the current sliding window is obtained; and the process is repeated until the modal recognition 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. The present invention first uses a monocular camera to collect an image of a characteristic target, and obtains a vibration response signal based on the collected image. When the vibration response signal is a time-invariant vibration response signal, the time-invariant vibration response signal is subjected to short-time Fourier transform, and a modal vibration shape matrix is ​​obtained by using single source point detection estimation; based on the modal vibration shape matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after using underdetermined blind source separation; based on the K-SVD dictionary learning method, the time-invariant vibration response signal is trained to obtain an ESTD dictionary, and the modal response is obtained by a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and the natural frequency and loss damping ratio of each order modal vibration shape are obtained according to the modal response, so as to realize the time-invariant vibration response. Modal recognition of the signal; when the vibration response signal is a time-varying vibration response signal, the time-varying vibration response signal is divided into a finite number of time-invariant vibration response signals through a sliding window, and then the instantaneous modal model and compressed sensing model of the time-invariant vibration response signal in each sliding window are respectively obtained by the same method as the time-invariant vibration response signal. Next, the idea of ​​transfer learning is used to perform K-SVD dictionary-based learning training on the time-invariant vibration response signal in the sliding window to obtain the corresponding strong sparse ESTD dictionary. Finally, the modal recognition results corresponding to the time-invariant vibration response signal in each sliding window are obtained according to the strong sparse ESTD dictionary and the compressed sensing model, and then the modal recognition results of the time-varying vibration response signal are obtained. In this process, the feature target is collected by means of a monocular camera, and the vibration response signal is obtained according to the collected image, which can avoid the defects of incomplete structural response measurement information, failure to meet the requirements of overdetermination and positive determination, and inconvenience for structural dynamics working modal analysis in the prior art using sensors for measurement, and is cost-effective, convenient to arrange, and has obvious field of view advantages. Combining the sliding window and transfer learning methods, the time-invariant underdetermined working modal analysis method is extended and applied to the time-varying underdetermined working modal analysis method, thereby solving the underdetermined modal recognition under time-invariant and time-varying structures. For time-varying vibration response signals, when performing learning and training based on the K-SVD dictionary to obtain the corresponding strong sparse ESTD dictionary, the learning and training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window, and the initialization dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window. This can reduce the training time of dictionary learning, thereby effectively improving the recognition speed. When estimating the modal vibration shape, due to the low frequency amplitude of the ambient noise, the frequency energy of the noise is usually located at low coordinates (generally near 0), so the modal vibration shape estimated by the slope of the highest point of the frequency energy is less affected by Gaussian white noise and has better robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention is further described in detail below with reference to the accompanying drawings.

[0042] Figure 1 It is a flow chart of modal identification of time-varying vibration response signals provided by the present invention.

[0043] Figure 2 It is a detailed flow chart of the modal identification of the time-varying vibration response signal provided by the present invention.

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

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

[0046] Figure 5 The present invention provides a flow chart of the time-varying underdetermined operating modal analysis method.

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

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

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

[0050] Fig. 9 It is a schematic diagram of the values ​​of the theoretical natural frequency provided by the present invention at various time points.

[0051] Fig.10 It is a schematic diagram of the modal vibration shapes of various orders at different time points provided by the present invention. DETAILED DESCRIPTION

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

[0053] Step S1, arranging a limited number of characteristic targets in the linear vibration system, using a monocular camera to collect multiple images including all characteristic targets, respectively determining characteristic points in each image, and obtaining a vibration response signal according to the characteristic points in the images at two adjacent moments, and when the vibration response signal is a time-invariant vibration response signal, entering step S21, and when the vibration response signal is a time-varying vibration response signal, entering step S31;

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

[0055] Step S11, arranging a number of characteristic targets in the linear vibration system, and using a monocular camera to collect multiple images including all characteristic targets. In this embodiment, the linear vibration system is a bridge, and the characteristic targets are attached to the bridge. The monocular camera collects 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 by using the Shi_Tomasi corner point detection algorithm;

[0057] The expression of Shi_Tomasi corner detection algorithm is R=min(λ 1 ,λ 2 ), λ 1 and λ 2 Calculate the eigenvalue of the autocorrelation matrix for each pixel. If R exceeds the set threshold, the point is identified as a corner point, which is a feature point.

[0058] Step S13, obtaining the Euclidean distance between feature point pairs in the images at two adjacent moments by using the FLANN feature point matching algorithm, and retaining the feature point pairs corresponding to the Euclidean distances less than the set distance threshold;

[0059] According to the formula Calculate the Euclidean distance between the feature points of one image and the nearest K feature points of the feature points of another image in two adjacent moments, d 1i represents the i-th feature point of one of the images, d 2j Represents the jth feature point of another image;

[0060] Step S14, respectively calculate the angle between the direction vector formed by each feature point pair and the average direction vector, and retain the feature point pairs corresponding to the angles less than the set 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, Represents the direction vector formed by the i'th pair of feature points;

[0061] Step S15, respectively calculating the distances between the feature point pairs retained in step S14, and finding the average value of all distances as the pixel displacement of the two adjacent images, combining the timestamp information of the two adjacent images, and obtaining the displacement signal corresponding to the current feature target;

[0062] Step S16, repeating steps S11 to S15 to obtain the displacement signal corresponding to each characteristic target to form a vibration response signal.

[0063] Step S21, performing short-time Fourier transform on the time-invariant vibration response signal, and obtaining the modal vibration matrix by using single source point detection estimation, and then proceeding to step S22;

[0064] The specific steps include:

[0065] Step S211: The time-invariant vibration response signal is decomposed in modal coordinates as in, represents the displacement signal corresponding to the i-th characteristic target, n is the number of characteristic targets set, n is less than the number of degrees of freedom, t represents time, T represents the sampling duration, R n×T represents a matrix of dimension n×T in the range of real numbers, is the mode shape matrix, is the mth mode shape vector, the order of the mth mode shape, is the modal response matrix obtained by decomposing X(t), is the modal response vector, [] T Represents matrix transpose;

[0066] The meaning of underdetermination is to use n observations to infer m modal response signals. The natural frequencies of modal response signals of different orders are not equal to each other. After decoupling, the corresponding modal vibration shapes are orthogonal to each other, and the modal responses are independent of each other, that is, Φ satisfies Q(t) satisfies Among them, n <m<n dof , n dof is the number of degrees of freedom.

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

[0068]

[0069] Among them, G X (t,f) and G Q (t,f) are the results of short-time Fourier transform of X(t) and Q(t), respectively, f represents the frequency, represents the result of short-time Fourier transform corresponding to the vibration response signal measured by the i-th target;

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

[0071] Step S214: When the frequency f is within the interval [f j -Δ,f j +Δ], we get The single source point detection method is used to calculate the slope of the highest energy point at each frequency to obtain the modal vibration matrix Φ, where Δ represents the set frequency threshold, f j Represents the frequency value corresponding to the jth frequency interval.

[0072] Specifically, when the frequency of each modal response is greater than 2Δ, the following formula can be obtained:

[0073]

[0074] When the vibration response signal has only a few frequency bands dominating in a short period of time, that is, only in the frequency interval f∈[f j -Δ,f j +Δ], So we get the formula This formula is the same as the linear expression, so the frequency-energy ratio of each modal response is consistent, so the modal vibration shape Φ can be estimated by calculating the slope of the highest energy point at each frequency through the single-source point detection (SSP) technology, that is, finding the frequency peak corresponding to the highest energy point.

[0075] Step S22, based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model by using underdetermined blind source separation, and then proceeding to step S23;

[0076] The specific steps include:

[0077] Step S221, Underdetermined Blind Source Separation (UBSS) of the time-invariant vibration response signal X(t) is expressed as Right now Among them, A∈R n×m is the mixing matrix, which is estimated by the whitened signal using the ica algorithm, represents the i-th column vector in the mixing matrix A, each column of A corresponds to each order mode shape in the mode shape matrix Φ, S(t)∈R m×T represents the recovered source signal in the time domain, and substitutes the estimated A 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 expressed as Right now in, is the observation vector, that is, the transpose of X(t), Λ is the sparse matrix of the mixing matrix A under the sparse domain constraint, that is, Λ is the diagonal matrix of A, is the sparse representation of the source signal in the sparse domain, that is, the transpose of S(t).

[0079] Step S23, training the time-invariant vibration response signal based on the K-SVD dictionary learning method to obtain an ESTD dictionary, obtaining the modal response through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and extracting the natural frequency and loss damping ratio of each order mode shape from the modal response using the single degree of freedom technology to achieve modal recognition of the time-invariant vibration response signal;

[0080] The K-SVD (K-Singular Value Decomposition) algorithm aims to find an overcomplete dictionary ESTD (Estimated Source-Trained Dictionary) and a sparse matrix X through an iterative process, so that Y ≈ DX, where Y is the input signal matrix, D is the ESTD dictionary matrix, and X is the sparse coefficient matrix. The goal of the algorithm is to minimize the error between Y and DX while maintaining the sparsity of X.

[0081] Step S31, using a sliding window with a set window length to divide the time-varying vibration response signal into a finite number of time-invariant vibration response signals, performing short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and using single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstructing the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation, and entering step S32;

[0082] Specifically, the time-invariant vibration response signal in the j'th sliding window is expressed in modal coordinates as: Wherein, L represents the sliding window length, j' represents the sliding window number, j'=1,2,…,L',…,T-L',+1, L' is the duration of the time segment contained in each sliding window, τ is the middle moment of the sliding window, which is used as the instantaneous modal parameter of the time-varying vibration response signal. represents the mode shape matrix of the time-invariant vibration response signal in the j'th sliding window, Represents the modal response matrix of the time-invariant vibration response signal within the j'th sliding window.

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

[0084] Step S32: Figure 5 As shown in the figure, the time-invariant vibration response signal in the current sliding window is trained based on the K-SVD dictionary to obtain the corresponding strong sparse ESTD dictionary. In the process of K-SVD training the ESTD dictionary, transfer learning is introduced. Due to the "short-term time-invariant" assumption of the sliding window, the modal parameters of the current sliding window are similar to the modal parameters of the next sliding window. Therefore, Figure 3 As shown in , during the migration process, the training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window, and unsupervised dictionary learning is achieved during the movement of each sliding window, as shown in Figure 4 As shown, the initialization dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window;

[0085] Among them, when the time-invariant vibration response signal in the first sliding window is subjected to the learning training based on the K-SVD dictionary, the training process is the same as the training process of the aforementioned time-invariant vibration response signal (i.e., described in step S23). 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 of modal vibration mode. When the natural frequency of each order of modal vibration mode corresponding to the time-invariant vibration response signal in the previous sliding window window differs from the natural frequency of each order of modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window window by 1, the current sliding window window is taken as the first sliding window window and re-enters step S32 to prevent the accumulation of errors caused by transfer learning.

[0086] Step S33, according to the strong sparse ESTD dictionary and the compressed sensing model corresponding to the time-invariant vibration response signal of the current sliding window, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained by a sparse reconstruction algorithm, and the instantaneous natural frequency and the instantaneous damping ratio of each order modal vibration type 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;

[0087] Specifically, the single degree of freedom technique is used to extract the instantaneous natural frequency and loss damping ratio from the transient modal response.

[0088] Step S34, repeating steps S32 to S33 until the modal recognition results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

[0089] An underdetermined modal recognition device based on a monocular camera comprises:

[0090] Signal determination module: used to arrange a limited number of characteristic targets in the linear vibration system, collect multiple images including all characteristic targets using a monocular camera, determine the characteristic points in each image respectively, obtain a vibration response signal according to the characteristic points in the images at two adjacent moments, and determine whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal;

[0091] Time-invariant vibration response signal recognition module: used to perform short-time Fourier transform on the time-invariant vibration response signal, and use single source point detection to estimate the modal vibration matrix; based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after using underdetermined blind source separation; based on the K-SVD dictionary learning method, the time-invariant vibration response signal is trained to obtain an ESTD dictionary, and the modal response is obtained through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and the natural frequency and loss damping ratio of each order modal vibration mode are obtained based on the modal response, so as to realize the modal recognition of the time-invariant vibration response signal;

[0092] Time-varying vibration response signal recognition module: used to divide 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, perform short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and use single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstruct the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation; perform K-SVD dictionary-based learning and training on the time-invariant vibration response signal in the current sliding window to obtain the corresponding strongly sparse ESTD dictionary, and the learning and training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window. The initialization dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window; based on the strong sparse ESTD dictionary and compressed sensing model corresponding to the time-invariant vibration response signal in the current sliding window, 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 modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window are obtained based on the instantaneous modal response, and the modal recognition result corresponding to the time-invariant vibration response signal in the current sliding window is obtained; and the process is repeated until the modal recognition results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

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

[0094] In order to verify the correctness and effectiveness of the present invention, a five-degree-of-freedom mass-spring-damper model is established in Matlab / Simulink, wherein the mechanical control equation of the five-degree-of-freedom mass-spring-damper system is expressed as:

[0095]

[0096] The mass matrix is ​​set to M = diag([1 2 2 2 3]), and the stiffness coefficients are set to k 1 =0, k 12 =800, k 24 =800, k 34 =2400, k 45 =3200, that is, the stiffness matrix is ​​set to: The damping matrix is ​​set to C = 0.5M + 0.0004K, the sampling frequency is set to 100 Hz, and the initial velocity and displacement are set to x = [0; 0; 0; 0; 1] m and

[0097]

[0098] In terms of parameter settings, the overlap interval of 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 of sparse dictionary learning is set to L = 250, overlap P = 249, and the number of block sequences of hierarchical coupling K = 4. The number of iterations of K-SVD dictionary learning is 10.

[0099] In terms of evaluation methods and indicators, since the underdetermined working modal parameter identification method is mainly divided into modal vibration shape estimation and modal response reconstruction stages, and the current existing methods have different research focuses, the present invention compares the modal vibration shape estimation method and the modal response reconstruction method with the existing research methods respectively.

[0100] 1) Use the Modal Assurance Criterion (MAC) method to evaluate the identification accuracy of the modal vibration shape:

[0101] in, represents the theoretical i-th mode shape, Indicates the i-th order mode shape to be identified. The closer the MAC value is to 1, the higher the identification accuracy is.

[0102] 2) Define the correlation coefficient to evaluate the accuracy of the reconstructed modal coordinate response:

[0103]

[0104] in, represents the theoretical j-th modal coordinate response, represents the reconstructed j-th modal coordinate response, ρ j The closer it is to 1, the higher the recognition accuracy.

[0105] 3) The natural frequency and damping ratio are compared with the theoretical values ​​to evaluate their identification accuracy.

[0106] The identification results of the underdetermined case without measurement noise are as follows:

[0107] In the underdetermined case, the vibration response signals of channels 2 and 5 are used as input to compare the modal parameter identification effects of different methods. First, in order to determine the influence of sparsity on the reconstruction accuracy of modal response in the underdetermined case, Figure 6 The figure shows the variation of the correlation coefficient (average of the fifth order) of the reconstructed modal response of the present invention (FEESTD) with sparsity.

[0108] In order to verify the modal vibration shape identification effect of the FEESTD method under underdetermined conditions, 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), SCA-DBSCAN are compared respectively. M (Based on the improved density space clustering component analysis algorithm) and other methods to identify the modal vibration shapes. Table 1 shows the comparison of the MAC values ​​of the modal vibration shapes identified by different methods.

[0109] Table 1

[0110]

[0111] In order to verify the modal response recognition effect of the FEESTD method under underdetermined conditions, the modal response recognition effects of methods such as DCTCS (DCT discrete cosine transform combined with CS compressed sensing), ESTD, MTD (The Mixture-Trained Dictionary, mixed training dictionary), SCA (independent component analysis method), SOBI (second-order blind recognition algorithm), NUBSS (Novel UBSS, new underdetermined blind source separation), and ADCS (Adaptive Dictionary Compression Sensing) are compared. From the recognition results in Table 1, it can be seen that SCA-DBSCAN MThe clustering effect is better, so SCA uses DBSCAN M Clustering algorithm, the sparsity of FEESTD is set to 30. Tables 2 to 4 show the modal response correlation coefficients reconstructed by different methods and the identified natural frequencies and damping ratios. Table 5 shows the time overhead of different methods.

[0112] Table 2 Comparison of modal response correlation coefficients reconstructed by different methods when n=2

[0113]

[0114] Table 3 Comparison of natural frequencies identified by different methods with theoretical values ​​when n=2

[0115]

[0116] Table 4 Comparison of damping ratios identified by different methods with theoretical values ​​when n=2

[0117]

[0118] Table 5 Time cost of different methods when n=2

[0119]

[0120] Identification results of underdetermined cases with added measurement noise:

[0121] In order to test the noise resistance of different methods, Gaussian white noise with different signal-to-noise ratios is added to the response signal under underdetermined conditions. SCA-FCM, SCA-Kmeans, and SCA-DBSCAN are compared respectively. M The MAC values ​​of the modal vibration shapes identified by and FEESTD are shown in Table 6. The correlation coefficients of the modal responses reconstructed by SCA (clustering algorithm using DBSCANM), DCTCS, NUBSS, ADCS and FEESTD methods are compared, as shown in Table 7.

[0122] Table 6 Comparison of MAC values ​​of identified modal vibration shapes under different noise conditions

[0123]

[0124] Table 7 Comparison of correlation coefficients of reconstructed modal responses under different noise conditions

[0125]

[0126]

[0127] It can be seen from the recognition results in Tables 1 to 4 that, in the underdetermined case, the SOBI method can only identify the modal parameters of the modes equal to the number of sensors, the DCTCS, ESTD, and MTD methods have poor modal parameter recognition effects, and FEESTD can identify high-order modes higher than the number of sensors, and has higher recognition accuracy than clustering-based methods such as SCA and ADCS.

[0128] It can be seen from the recognition results in Tables 6 and 7 that, in the case of noise, the accuracy of the modal vibration shapes and reconstructed modal responses estimated by various methods will decrease with the increase of noise, but the accuracy of FEESTD recognition is higher, indicating that the modal vibration shape estimation and modal response reconstruction of the FEESTD method have better robustness.

[0129] In order to verify the correctness and effectiveness of the linear time-varying underdetermined operating modal analysis method based on FEESTD, a three-degree-of-freedom spring oscillator with a linear time-varying structure is used, in which the mass matrix varies with time.

[0130] like Figure 7 The three-degree-of-freedom spring oscillator system shown in the figure is composed of three blocks, three springs and three dampers in series, where the initial displacement and velocity of the three blocks are 0, and the damping ratio of the three dampers is c 1 =c 2 =c 3 =0.01Ns / m, stiffness is k 1 =k 2 =k 3 =1000N / m, mass m 2 and m 3 The mass is 1kg, and the block m 1 The quality of changes with time is as follows:

[0131]

[0132] For the three-degree-of-freedom spring oscillator experiment, MATLAB / Newmark-β was used to simulate and obtain the response signal. The sampling frequency of the signal was 40 Hz and the sampling time was T = 2000 s. The Gaussian white noise excitation applied to the object m_1 and the simulated response signal are shown in Figure 8 shown.

[0133] The theoretical natural frequency modal vibration shape is obtained by simulating the undamped finite element method. The values ​​of the natural frequency at each time point are as follows: Fig. 9 As shown, the modal vibration shapes of t = 56.425s, t = 695.75s, t = 1335.075s, and t = 1974.4s are selected respectively, and the modal vibration shape diagram is drawn as shown in Fig.10 shown.

[0134] Parameter settings: To simulate the underdetermined condition, the response signals collected from the 1st and 3rd channels are used as input. The window length of the sliding window 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 of SCA uses the L1 norm minimization method.

[0135] The modal confidence criterion MAC is used to evaluate the recognition accuracy of the modal vibration mode in each window, and the number of windows with MAC less than 0.8 is counted. The natural frequency identified in each window is compared with the theoretical value, and the number of windows with the difference between the natural frequency recognition value and the theoretical value greater than 1 is counted to evaluate the recognition accuracy of the natural frequency.

[0136] The results of time-varying underdetermined transient modal parameter identification without measurement noise are as follows:

[0137] (1) Instantaneous mode shape identification effect

[0138] In order to verify the modal vibration mode recognition effect of the proposed method MWTL-FEESTD (FEESTD with sliding window transfer learning) in the case of underdetermined time-varying structures, MW-SOBI (sliding window second-order blind 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 are compared respectively. M (Sliding Window SCA based on improved DBSCAN clustering) and other methods. In order to more intuitively show the effect of the MAC value of the modal vibration type identified by different comparison methods, as shown in Table 8, the time points of the modal vibration type MAC < 0.8 identified by different comparison methods are counted.

[0139] Table 8 Number of time points at which MAC values ​​of modal vibration shapes are not identified by different methods

[0140]

[0141]

[0142] (2) Instantaneous natural frequency identification effect

[0143] In order to verify the proposed method MWTL-FEESTD in the case of time-varying structural underdetermined natural frequency identification effect and the time cost before and after adding transfer learning, MW-SOBI and MW-SCA (clustering algorithm using DBSCAN) are compared. M ), MW-FEESTD (sliding window frequency energy and ESTD dictionary method without adding transfer learning) and other methods. As shown in Table 9, the number of moments when the natural frequencies are not identified by different methods is counted. As shown in Table 10, the time overhead of different methods in the entire time-varying period is compared.

[0144] Table 9 Number of time points where natural frequencies are not identified by different methods

[0145]

[0146] Table 10 Time cost of different methods

[0147]

[0148] In order to verify the effect of adding transfer learning in the training sample construction and the adaptive dictionary initialization process, the recognition effect and time cost of the natural frequency before and after adding transfer learning are compared. The comparison results are shown in Table 11.

[0149] Table 11 Recognition accuracy and time cost before and after adding transfer learning

[0150]

[0151]

[0152] In actual engineering, signals are often interfered by external noise, so the robustness of the working modal parameter analysis algorithm is of great significance. In order to test the noise resistance of different methods, Gaussian white noise with a signal-to-noise ratio of 15dB is added to the response signal under the condition of time-varying underdetermination. In this embodiment, the results of time-varying underdetermination transient modal parameter identification under measurement noise are as follows:

[0153] (1) Instantaneous mode shape identification effect

[0154] In order to verify the modal vibration shape identification effect of MWTL-FEESTD under noise conditions, the MW-SOBI, MW-SCA-FCM, MW-SCA-Kmeans, and MW-SCA-DBSCAN are statistically analyzed as shown in Table 12. M The number of time points at which MAC<0.8 of the modal vibration shape identified by the above methods.

[0155] Table 12 Number of time points of MAC values ​​of unidentified mode shapes by different methods

[0156]

[0157] (2) Instantaneous natural frequency identification effect

[0158] In order to verify the natural frequency recognition effect of MWTL-FEESTD under noise conditions, the MW-SOBI and MW-SCA (clustering algorithm is DBSCAN) are statistically analyzed as shown in Table 13. M ), MW-FEESTD and other methods fail to identify the number of moments of natural frequency.

[0159] Table 13 Number of time points where natural frequencies are not identified by different methods under noise conditions

[0160]

[0161] From the identification results in Tables 8 and 9, it can be seen that when the input is the response signal of only two channels, MW-SOBI can only identify the second-order modal parameters. This method can only solve the problem of modal parameter identification of time-varying structures under positive and overdetermined conditions. Both MWTL-FEESTD and MW-SCA methods based on different clustering algorithms can well identify the third-order modal parameters, but the MWTL-FEESTD method has better identification effect than the MW-SCA method based on different clustering algorithms.

[0162] From the time overhead of different methods in Table 10, it can be seen that the MWTL-FEESTD method with transfer learning has a smaller time overhead than the MW-FEESTD method without transfer learning, and is similar to the time overhead of the MW-SCA method. From the results in Table 11, it can be seen that adding transfer learning in the process of training sample construction can improve the recognition accuracy of modal parameters and improve the recognition speed of the method. Adding transfer learning in the process of ESTD dictionary initialization can effectively improve the recognition speed of the method.

[0163] From the recognition results in Tables 12 and 13, it can be seen that the modal vibration modes and natural frequencies identified by methods such as MW-SCA and MW-SOBI are affected by noise and have more unidentified time points, while the MWTL-FEESTD method has fewer unidentified time points than other methods, indicating that this method misses fewer modes and has better anti-noise performance.

[0164] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0165] When estimating the modal vibration shape, the present invention estimates the modal vibration shape by the slope of the highest point of the frequency energy, which is less affected by Gaussian white noise and has better robustness performance, because the frequency amplitude of the ambient noise is low and the frequency energy of the noise is usually located at low coordinates (generally near 0).

[0166] The present invention adopts a dictionary learning method based on transfer learning to quickly converge to a specified error, thereby reducing the training time of dictionary learning, reducing the time complexity of the method, and effectively improving the recognition speed of modal parameters.

[0167] The above description is only a preferred embodiment of the present invention, and therefore cannot be used to limit the scope of implementation of the present invention. That is, equivalent changes and modifications made according to the scope of the patent application of the present invention and the contents of the specification should still fall within the scope covered by the patent of the present invention.

Claims

1. An underdetermined modality recognition method based on a monocular camera, characterized in that: The steps include: Step S1, arranging a limited number of characteristic targets in the linear vibration system, using a monocular camera to collect multiple images including all characteristic targets, respectively determining characteristic points in each image, and obtaining a vibration response signal according to the characteristic points in the images at two adjacent moments, and when the vibration response signal is a time-invariant vibration response signal, entering step S21, and when the vibration response signal is a time-varying vibration response signal, entering step S31; Step S21, performing short-time Fourier transform on the time-invariant vibration response signal, and obtaining the modal vibration matrix by using single source point detection estimation, and then proceeding to step S22; Step S22, based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model by using underdetermined blind source separation, and then proceeding to step S23; Step S23, training the time-invariant vibration response signal based on the K-SVD dictionary learning method to obtain an ESTD dictionary, obtaining the modal response through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and obtaining the natural frequency and loss damping ratio of each order modal vibration mode based on the modal response, so as to realize modal recognition of the time-invariant vibration response signal; Step S31, using a sliding window with a set window length to divide the time-varying vibration response signal into a finite number of time-invariant vibration response signals, performing short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and using single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstructing the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation, and entering step S32; Step S32, performing K-SVD dictionary-based learning training on the time-invariant vibration response signal in the current sliding window to obtain a corresponding strong sparse ESTD dictionary, the learning training sample is the modal recognition result corresponding to the time-invariant vibration response signal in the previous sliding window, and the initialization dictionary for learning training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window; Step S33, according to the strong sparse ESTD dictionary and the compressed sensing model corresponding to the time-invariant vibration response signal of the current sliding window, the instantaneous modal response corresponding to the time-invariant vibration response signal in the current sliding window is obtained by a sparse reconstruction algorithm, and the instantaneous natural frequency and the instantaneous damping ratio of each order modal vibration type 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; Step S34, repeating steps S32 to S33 until the modal recognition results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

2. The underdetermined modality recognition method based on a monocular camera according to claim 1, characterized in that: In step S1, obtaining the vibration response signal specifically includes the following steps: Step S11, arranging a number of characteristic targets in the linear vibration system, and using a monocular camera to collect a plurality of images including all the characteristic targets; Step S12: for the current feature target, determine the feature points corresponding to the current feature target in each image by using the Shi_Tomasi corner point detection algorithm; Step S13, obtaining the Euclidean distance between feature point pairs in the images at two adjacent moments by using the FLANN feature point matching algorithm, and retaining the feature point pairs corresponding to the Euclidean distances less than the set distance threshold; Step S14, respectively calculate the angle between the direction vector formed by each feature point pair and the average direction vector, and retain the feature point pairs corresponding to the angles less than the set 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, Represents the direction vector formed by the i'th pair of feature points; Step S15, respectively calculating the distances between the feature point pairs retained in step S14, and finding the average value of all distances as the pixel displacement of the two adjacent images, combining the timestamp information of the two adjacent images, and obtaining the displacement signal corresponding to the current feature target; Step S16, repeating steps S11 to S15 to obtain the displacement signal corresponding to each characteristic target to form a vibration response signal.

3. The underdetermined modality recognition method based on a monocular camera according to claim 2, characterized in that: The step S21 comprises the following steps: Step S211: The time-invariant vibration response signal is expressed in modal coordinates as in, represents the displacement signal corresponding to the i-th characteristic target, n is the number of characteristic targets set, is the mode shape matrix, is the mth mode shape, m is the order of the mode shape, is the modal response matrix, is the modal response vector, [] T Represents matrix transpose; Step S212: Apply short-time Fourier transform to the modal coordinate representation to obtain a time-invariant vibration response signal in the time-frequency domain: Among them, G X (t,f) and G Q (t,f) are the results of short-time Fourier transform of X(t) and Q(t) respectively; Step S213: According to the formula Calculate the frequency energy of the time-invariant vibration response signal in the time-frequency domain, where represents the frequency energy corresponding to the displacement signal corresponding to the i-th characteristic target, represents the frequency energy of the j-th mode shape, φ ij represents the j-th mode shape corresponding to the i-th characteristic target; Step S214: When the frequency f is within the frequency interval [f j -Δ,f j +Δ], we get The single source point detection method is used to calculate the slope of the highest energy point at each frequency to obtain the modal vibration matrix Φ, where Δ represents the set frequency threshold, f j Represents the frequency value corresponding to the jth frequency interval.

4. The underdetermined modality recognition method based on a monocular camera according to claim 3, characterized in that: The step S22 comprises the following steps: Step S221, underdetermined blind source separation of the time-invariant vibration response signal X(t) is expressed as X(t)=AS(t), wherein A is a mixing matrix, each column of which corresponds to each order mode shape in the mode shape matrix Φ, and S(t) represents the recovered source signal in the time domain; Step S222: The reconstructed compressed sensing model is expressed as in, is the observation vector, Λ is the sparse matrix of the mixing matrix A under the sparse domain constraint condition, is the sparse representation of the source signal in the sparse domain.

5. The underdetermined modality recognition method based on a monocular camera according to claim 4, characterized in that: In step S31, the time-invariant vibration response signal in the j'th sliding window is expressed in modal coordinates as: Where L is the length of the sliding window, j' is the number of the sliding window, and τ is the middle time of the sliding window. represents the mode shape matrix of the time-invariant vibration response signal in the j'th sliding window, Represents the modal response matrix of the time-invariant vibration response signal within the j'th sliding window.

6. The underdetermined modality recognition method based on a monocular camera according to claim 5, characterized in that: 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 order modal vibration mode. When the natural frequency of each order modal vibration mode corresponding to the time-invariant vibration response signal in the previous sliding window window differs from the natural frequency of each order modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window window by 1, the current sliding window window is taken as the first sliding window window and re-enters step S32.

7. The underdetermined modality recognition method based on a monocular camera according to claim 6, characterized in that: In step S33, the single degree of freedom technique is used to extract the instantaneous natural frequency and the loss damping ratio from the instantaneous modal response.

8. An underdetermined modal recognition device based on a monocular camera, characterized in that: include: Signal determination module: used to arrange a limited number of characteristic targets in the linear vibration system, use a monocular camera to collect multiple images including all characteristic targets, determine the characteristic points in each image respectively, and obtain a vibration response signal according to the characteristic points in the images at two adjacent moments, and determine whether the vibration response signal is a time-invariant vibration response signal or a time-varying vibration response signal; Time-invariant vibration response signal recognition module: used to perform short-time Fourier transform on the time-invariant vibration response signal, and use single source point detection to estimate the modal vibration matrix; based on the modal vibration matrix, the time-invariant vibration response signal is reconstructed into a compressed sensing model after using underdetermined blind source separation; based on the K-SVD dictionary learning method, the time-invariant vibration response signal is trained to obtain an ESTD dictionary, and the modal response is obtained through a sparse reconstruction algorithm based on the ESTD dictionary and the compressed sensing model, and the natural frequency and loss damping ratio of each order modal vibration mode are obtained based on the modal response, so as to realize the modal recognition of the time-invariant vibration response signal; Time-varying vibration response signal recognition module: used to divide 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, perform short-time Fourier transform on the time-invariant vibration response signal in each sliding window, and use single source point detection to estimate the instantaneous modal vibration shape corresponding to each time-invariant vibration response signal, and reconstruct the time-invariant vibration response signal in each sliding window into a compressed sensing model after using underdetermined blind source separation; perform K-SVD dictionary-based learning and training on the time-invariant vibration response signal in the current sliding window to obtain the corresponding strongly sparse ESTD dictionary, and the learning and training samples are the modal recognition results corresponding to the time-invariant vibration response signal in the previous sliding window. The initialization dictionary for learning and training is the strong sparse ESTD dictionary corresponding to the time-invariant vibration response signal in the previous sliding window; based on the strong sparse ESTD dictionary and compressed sensing model corresponding to the time-invariant vibration response signal in the current sliding window, 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 modal vibration mode corresponding to the time-invariant vibration response signal in the current sliding window are obtained based on the instantaneous modal response, and the modal recognition result corresponding to the time-invariant vibration response signal in the current sliding window is obtained; and the process is repeated until the modal recognition results corresponding to the time-invariant vibration response signals in all sliding windows are obtained.

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