A method and device for identifying structural modal parameters based on random subspace algorithm

Abstract

The present invention belongs to the field of structural vibration modal testing, and relates to a structural modal parameter identification method and device based on a random subspace algorithm. First, in a working state monitoring system of the structure, a vibration signal of the structure is collected by an acceleration sensor arranged. After the vibration signal of the structure is collected, the vibration signal is preprocessed to remove noise interference. By adjusting the number of rows and columns of a Toeplitz matrix formed by the vibration signal and combining the relationship between the vibration signal and the modal energy, the loss of the real mode can be reduced. Then, the modal parameters of the structure are identified by the relationship between the system matrix and the modal parameters. The modal parameter results are obtained by a random subspace method, and the recognition accuracy of the modal parameters is improved. Finally, the identified structural modal parameters are compared and analyzed with the modal characteristic parameters inherent in the structure to judge whether the structure is damaged. The present invention can well approach the real value of the structural parameter and has accurate safety assessment capability.

Description

Technical Field

[0001] The invention belongs to the field of structural vibration modal testing, and relates to a structural modal parameter identification method and device based on a random subspace algorithm. Background Art

[0002] With the continuous development of industrial technology, some large structures play an increasingly important role in production and life, and their structures are becoming more and more complex. People are paying more and more attention to their safety and durability. How to quickly identify the location and degree of structural damage has become a difficult problem that some experts and scholars urgently need to solve. In actual use, it is very important to predict the damage of the structure in a timely manner. More importantly, once some important parts of the structure are damaged, the degree of damage develops rapidly. If it is not discovered in time, it will soon lead to the destruction of the entire structure, and the consequences are disastrous.

[0003] In order to solve the problem of safe use of the entire structure, especially large and complex structures, the identification of the degree of structural damage has become the focus of domestic and foreign scholars. In particular, the analysis of the structure using the vibration response of the structure and the system dynamic characteristic parameters has become a hot topic of research at home and abroad in recent decades. The basic idea is that structural damage will cause changes in physical parameters (mass, stiffness, etc.) in the structure, and the modal parameters (modal frequency, modal vibration shape, modal damping, etc.) of the structure will change accordingly. According to this change, the location and degree of structural damage can be determined. According to different technical levels, the damage determination and quality assessment of engineering structures can be divided into the following four levels: ① predict whether the structure is damaged; ② determine the damage location; ③ determine the degree of damage; ④ estimate the life of the structure after damage. The characteristic indicators that can be used to identify the degree of structural damage based on vibration data are: the natural frequency of the structure, the displacement modal vibration shape of the structure, the curvature modal vibration shape of the structure, the strain mode of the structure, the displacement (velocity, acceleration) frequency response function of the structure, and the modal strain energy of the structure.

[0004] Modal parameter identification of structures is the focus of research in the field of structural health monitoring. Modal analysis plays a very important role in the health monitoring of large structures. Important modal parameters in large structures include natural frequency, damping ratio and modal vibration mode. Therefore, the important task of modal parameter identification is to identify the frequency and vibration mode of the structure. The random subspace method is a linear system identification method developed in recent years. This method does not require artificial excitation and directly extracts the modal parameters of the structure from the response output signal of the environmental excitation. These modal parameters will be used as input for structural health monitoring, assessment of damaged structures and structural control.

[0005] However, as one of the modal parameter identification methods, the random subspace method has been widely used in the modal parameter identification of actual engineering structures, but it still has problems such as difficulty in determining the system order, missing modes, subjectivity in real mode screening, and inaccuracy in the extraction of real modal parameters. Therefore, there is an urgent need for a detection method that can accurately determine the order of the system model to obtain the real mode of the structure, and then obtain real and reliable frequency modal parameters, damping ratio modal parameters and high-precision vibration type modal parameters. The modal parameters obtained by the random subspace method are compared with the inherent modal parameters of the structure to determine whether the structure is damaged, and then further determine the location and extent of the damage. Summary of the invention

[0006] In order to solve the deficiencies of the above-mentioned prior art, the present invention proposes a structural modal parameter identification method based on a random subspace algorithm, in order to accurately determine the order of the system model to obtain the true mode of the structure, and obtain true and reliable frequency modal parameters, damping ratio modal parameters and high-precision vibration type modal parameters.

[0007] The technical solution adopted by the present invention to solve the technical problem is: a structural modal parameter identification method based on a random subspace algorithm, comprising the following steps:

[0008] Step 1: Collect acceleration response data of i measuring points on the structure {y r |r=1,2,...,i};where y r Represents the acceleration response data of the rth measuring point;

[0009] Step 2: Preprocess the collected acceleration response data, calculate the covariance of each column of measured data after preprocessing, and construct a covariance matrix; use singular value decomposition to perform singular value decomposition on the covariance matrix to obtain the corresponding singular value matrix, and calculate the singular value matrix by principal component analysis method to obtain the approximate model order k of the structure;

[0010] Step 3: Use the acceleration response data obtained in step 1 to establish the Hankel matrix, which contains all the response signals of the structure; divide the Hankel matrix into blocks of “past y p ” and “future f ” Two parts, each with the same number of block rows;

[0011] Step 4: Through the Hankel matrix constructed in step 3, we can know from the discrete random state space equation that the output covariance can be defined as: In actual testing, only j data can be obtained. Assuming that the output data has various states, then:

[0012]

[0013]

[0014] In Equation (1): v k , w k are different zero-mean Gaussian white noises respectively; x k+1 represents the state vector at the (k + 1)-th moment.

[0015] Step 5: The covariance sequences calculated in Step 4 are used to form a Toeplitz matrix. The main function of forming the Toeplitz matrix is to reduce the data volume while maintaining the original information of the structural measured response signal, thereby improving the calculation efficiency.

[0016] Step 6: The stable poles are obtained by using the eigenvalue method for the Toeplitz matrix respectively, and the power spectrum curve diagram is obtained by using the weighted overlapping averaging method. Then, it is compared whether the number of stable axes formed by the stable poles is equal to the number of peaks in the power spectrum curve diagram obtained by the weighted overlapping averaging method; furthermore, it is judged whether there is mode missing. If there is mode missing, the linear phase filtering technology is used. It will shift the time of the frequency components according to the fact that the signal energy is proportional to the frequency, ensuring that the delays of the frequency components passing through the filter are consistent, making the phases of different mode components in each classification group synchronous, so as to ensure that the signal is not distorted, and then the mode identification analysis is carried out on the mode components in each classification group.

[0017] Step 7: By analyzing the relationship between the number of rows of the Toeplitz matrix and the system state matrix, it can be concluded that the Toeplitz matrices composed of different numbers of rows not only affect the calculation speed of the system, but also have an inestimable impact on the identification accuracy of the modal parameters; therefore, according to the model approximation order k and the total length l of the response data obtained in Step 2, the number of rows i of the Toeplitz matrix needs to satisfy k < i < l. Determining the appropriate system order under such a condition helps to improve the identification accuracy of the algorithm and can reduce the introduction of false modes and the missing of true modes at the same time.

[0018] Step 8: It can be deduced from the definition of the state space equation that the observable matrix O and the controllable matrix M, and the system is observable and controllable; calculate the Toeplitz matrices corresponding to different i values and perform singular value decomposition on them; then calculate the system state matrix A and the output matrix C.

[0019] Step 9: Perform eigenvalue decomposition on the system state matrix A, and then obtain the frequency, damping and vibration mode modal parameters of the model.

[0020] Step 10: Draw a stability diagram from the poles obtained by performing eigenvalue decomposition on the system matrix A, and mark them in the stability diagram with different symbols and colors to satisfy different relationships among frequency, damping and vibration mode.

[0021] Step 11: The stability diagram drawn with the model order as the ordinate and the frequency as the abscissa can clearly reflect the distribution of the real poles and false poles of the structure under different model orders; in order to obtain the overall modal characteristic parameters and local modal characteristic parameters of the structure, the data characteristics in the stability diagram are analyzed to obtain the modal parameters corresponding to different model orders, and then the relevant information of the structure is extracted;

[0022] Step 12: Redraw the stability diagram based on the actual working conditions to obtain modal parameters that are closer to the natural modes of the structure;

[0023] Step 13: Since noise interference is inevitably introduced into the measured data, noise poles will be generated in the calculation process; this will introduce false modes into the stability diagram, which will greatly interfere with the extraction of the final modal parameters of the system; the multiple groups of modal parameters obtained by identification are represented by different subsets, each of which contains frequency, damping ratio and modal vibration shape; define the distance formula of the modal parameters between each subset, set the threshold limit of the distance formula, and judge each subset to eliminate the pseudo mode;

[0024] Step 14: After eliminating the false modes caused by calculation poles and noise, the graph theory clustering method is used to cluster the structural modal results based on the distance defined by the structural frequency and the modal confidence criterion index, and the number of clusters and the clustering threshold are set to automatically identify the true modal parameters of the structure.

[0025] Preferably, the preprocessing in step 2 includes: constructing a trend term using a polynomial function, eliminating the trend term from the vibration signal, and smoothing the signal from which the trend term has been removed by using a smoothing average method.

[0026] Preferably, the preprocessing in step 2 includes: performing pole-symmetric modal decomposition on the collected acceleration response signal to obtain decomposed intrinsic modal components and residual components, separating the obtained components using a blind source separation method, and performing frequency domain conversion on the separated signal to obtain a noise component for noise reduction processing.

[0027] Preferably, the modal parameter automatic identification method in step 13 uses modal parameters to reasonably set the clustering threshold and the number of clustering elements according to the similarity between stable points; this method comprehensively utilizes modal parameters such as frequency, damping ratio, and modal confidence criterion, and does not perform a simple linear weighted summation of these modal parameters, but uses modal parameters to reasonably set the clustering threshold and the number of clustering elements according to the similarity between stable points, effectively giving play to the local similarity characteristics of modal parameters to perform better clustering analysis to extract modal information.

[0028] The present invention also proposes a structural modal parameter automatic identification device, comprising:

[0029] The data acquisition module is used to collect the vibration response acceleration signal of the structure. The vibration response acceleration signal is the acceleration response data generated when the structure is stimulated by a hammer. Due to the different excitation forces applied to the structure, it is necessary to combine the material properties of the actual engineering structure and the results of numerical analysis to reasonably set the sampling frequency and sampling time and evaluate the rationality of the selection of the acceleration sensor measurement points.

[0030] Data preprocessing module, due to the influence of factors such as environmental noise, it is necessary to eliminate the trend term and reduce noise of the collected acceleration vibration response data; use polynomial function to construct the trend term, eliminate the trend term of the vibration signal, and perform smoothing, using the smoothing average method; perform pole symmetric modal decomposition on the collected acceleration response signal to obtain the inherent modal component and residual component, use the blind source separation algorithm to separate the obtained inherent modal component and residual component, perform frequency domain conversion on the separated signal to obtain the noise component for noise reduction;

[0031] The initial parameter and modal identification module includes: a system order setting unit, a parameter identification unit and a modal screening unit; wherein, the system order setting unit needs to have a pre-estimation of the order of the structure in the process of modal parameter identification of the structure. If the order is set too large, it is easy to introduce false modes, which is not conducive to the subsequent extraction of modal parameters. If the order is set too small, it is easy to cause the loss of real modes, and the extracted modal information cannot accurately reflect the physical information of the structure. At this time, the acceleration response data generated by the excitation force applied to the structure is used to perform principal component analysis and combine the length of the acceleration response data, as well as the relationship between the modal energy components of different order modes and their corresponding stable poles to set the value range of the system order; the parameter identification unit uses the random subspace method to extract the natural frequency, damping ratio and vibration type modal parameters under different system orders from the collected acceleration response data of the structure; the modal screening unit sets reasonable frequency, damping and modal confidence criterion threshold limits in combination with the actual engineering experience of the structure to obtain the initial modal parameters after eliminating some unstable poles;

[0032] False mode elimination module: because the collected acceleration response data usually contains noise, false modes of numerical models, etc., the existence of these false modes will interfere with the extraction of true modal parameters; the distance formula is constructed using the frequency and modal confidence criterion modal parameters of the structure and a reasonable threshold limit is set to eliminate the false modes contained in the initial mode;

[0033] The real mode combination module analyzes the modal data in combination with the stability diagram after removing the false modes, obtains the state space model of the structure under different system orders, identifies the modal parameters of each model, plots all the modal parameters obtained on the stability diagram to determine the modal parameters of the structure, and combines the same modal parameters under different model orders;

[0034] The module for automatic picking of true modal parameters uses the characteristics of sample data as the index of the class, makes full use of the modal information of each stable point to construct a clustering tree, splits the clustering tree to fit the curve, automatically sets the clustering threshold limit and the number of clustering elements, and then clusters the data with similar characteristics better, thereby realizing the automatic picking of true modal parameters.

[0035] The beneficial effects of the present invention are:

[0036] The present invention processes the acceleration response data of the measuring point, determines the optimal number of rows of the Toeplitz matrix by combining the estimated system model order with the total length of the acceleration response data, and uses the random subspace method to identify the modal parameters of the modified Toeplitz matrix, thereby obtaining high-precision frequency modal parameters and damping ratio modal parameters. This improves the modal parameter identification accuracy of the random subspace method. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is an overall flow chart of a structural modal parameter identification method based on a random subspace algorithm;

[0038] Figure 2 is the displacement response diagram of measuring point 2;

[0039] Figure 3 is the second-order vibration mode diagram;

[0040] Figure 4 Determine the system model order flow chart for the present invention;

[0041] Figure 5 It is a flow chart of pole marking of the present invention;

[0042] Figure 6 Eliminate false modal flow charts for the present invention;

[0043] Figure 7 This is a flow chart of modal parameter picking of the present invention;

[0044] Figure 8 It is a schematic diagram of a device for automatic identification of structural modal parameters in the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the relevant technologies in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] refer to Figures 1 to 8 , a structural modal parameter identification method based on random subspace algorithm, arranging acceleration sensors on a certain structure and measuring the vibration acceleration response signal of the corresponding measuring point;

[0047] During the data collection process, it may be affected by changes in environmental conditions (such as temperature and humidity), and may contain a small number of abnormal test values, which will lead to trend items in the collected discrete data;

[0048] The trend term is constructed by using polynomial function, the trend term is eliminated from the vibration signal, and the signal with the trend term eliminated is smoothed by using the smoothing average method;

[0049] The noise interference cannot be avoided in the acceleration response signal collected under the environmental excitation condition, so the collected acceleration response signal is subjected to noise reduction processing;

[0050] The acquired acceleration response data is used to construct a Hankel matrix;

[0051] Perform singular value decomposition on the constructed Hankel matrix;

[0052] The inverse process of singular value decomposition is used to obtain the reconstruction matrix, and the corresponding elements of the reconstruction matrix are weighted and averaged to obtain the response signal after noise reduction;

[0053] Perform principal component analysis on the singular value matrix after singular value decomposition of the Hankel matrix to obtain the possible order of the structural model;

[0054] The Hankel matrix contains all the response signals of a structure. The Hankel matrix is ​​divided into blocks of “past y p " and "future f ” Two parts, each with the same number of block rows;

[0055] According to the discrete-time random state space model:

[0056]

[0057] In formula (1): v k , w k are different zero-mean Gaussian white noises; x k+1 represents the state vector at the k+1th moment;

[0058] Determine the output covariance matrix R of the system model i and the covariance matrix G of the next state and output

[0059]

[0060]

[0061] In formula (2): j is the j data obtained in the actual test;

[0062] The random subspace algorithm makes full use of the observable matrix and controllable matrix of the structure. i , control matrix M i

[0063] The conversion of the Hankel matrix into the Toeplitz matrix can reduce the dimension of the data while maintaining the original information of the signal, thereby improving the calculation efficiency and quickly obtaining the modal parameters of the system;

[0064] The calculated output covariance sequence forms a block Toeplitz matrix T 1|i , if we assume that the data is ergodic and j→∞, we get;

[0065]

[0066] Toeplitz is an i×i square matrix, where i is a manually selected parameter. When i takes different values, the condition number of the Toeplitz matrix will also change, resulting in different effects of the perturbation of the output data on the solution of the system matrix. When the Toeplitz matrix condition number is smaller, the perturbation of the response data will have a smaller perturbation on the system matrix, resulting in a smaller error in the modal parameters solved according to the system matrix;

[0067] In the process of data processing, such as singular value decomposition, the low-energy characteristic components in the response signal will be suppressed. Although such an operation is conducive to eliminating noise, it may weaken some useful low signal-to-noise ratio components and make them indistinguishable from noise. This leads to the possibility of modal missing in the recognition result. Considering the different energy distributions between different modal components in the response signal, the data in each modal component group are solved by the eigenvalue method to obtain stable poles, and the power spectrum curve obtained by the weighted overlapping average method is used to compare whether the number of stable poles is consistent with the number of peaks in the power spectrum curve. If not, the linear phase filtering technology is applied, which will time-shift the frequency components according to the signal energy being proportional to the frequency, ensuring the consistency of the delay of each frequency component passing through the filter, so that the phases of different modal components in each classification group are synchronized, which can reduce or even avoid the inhibitory effect of the data operation on the low-order modal energy characteristics, thereby obtaining the full modal information of the structure.

[0068] Combined with the above-mentioned approximate determination of the order of a certain structural model, the control of modal missingness and the total length of the response data, the number of rows of the Toeplitz matrix is ​​determined, so that the modal parameters obtained by the solution are closer to the real parameters of a certain structure;

[0069] Perform singular value decomposition on the Toeplitz matrix;

[0070]

[0071] In formula (5), U1, V1 are unitary matrices consisting of left and right singular vectors corresponding to non-zero singular values, S1 is a diagonal matrix of singular values ​​with descending order, U2, V2 are unitary matrices consisting of left and right singular vectors corresponding to zero singular values;

[0072] By decomposing the Toeplitz matrix, we can further derive the expression of the observation matrix and the control matrix;

[0073]

[0074] According to the time-delay signal of the output covariance matrix, the expression of the Toeplitz matrix can be obtained;

[0075] T 2|i+1 =O i AM i (7)

[0076] From the relationship between formula (5) and formula (7), we can know that

[0077] T 1|i A=T 2|i+1 (8)

[0078] For a matrix p, ||p|| m (m=1 or 2, etc.) is called the condition number of the matrix p.

[0079] From the properties of the solution of the linear equation system px=q, we know that if the condition number of the matrix p is large, a small change in q can cause a large change in the solution x, and the numerical stability is poor. If the condition number of the matrix p is small, a small change in q will also cause a small change in x, and the numerical stability is good. Therefore, the smaller the condition number, the smaller the error of the calculation result and the higher the accuracy of the calculation result.

[0080] It can be seen that the condition number of the Toeplitz matrix affects the stability and accuracy of the system solution, so it is feasible to control the number of its rows and columns;

[0081] Construct the correlation matrix based on the definition of the output covariance matrix:

[0082]

[0083]

[0084]

[0085] From formula (5), we can know that formula (11) is the covariance matrix composed of noise signals;

[0086] The variance of the known noise can be assumed to be τ 2 , then the covariance matrix of all noise signals is

[0087] D2=τ 2 E i (12)

[0088] In formula (12), E i is the i-th order identity matrix;

[0089] From equations (11) and (12), we can get

[0090] S2=iτ 2 E i-n (13)

[0091] Combining the above formulas (7) to (11), we can get

[0092]

[0093] Through the observation matrix, control matrix and Toeplitz matrix, the state matrix and output matrix of the system can be obtained;

[0094] Perform eigenvalue decomposition on the state matrix of the system to obtain the modal parameters of the structure;

[0095] It can be found that in the eigenvalue matrix, the more the number of main diagonal elements is, the more complex the signal is. Therefore, the elements in the eigenvalue matrix can be used to reflect the amount of information contained in the signal;

[0096] By analyzing the information contained in the eigenvalue matrix of the corresponding order when the order changes within the set threshold range, it is possible to obtain the true modal parameters close to the structure. Therefore, it is feasible to identify the true order of the system through this method;

[0097] In order to better observe the modal characteristics of the structure, the poles obtained for each model order are used to draw a stability diagram with frequency as the abscissa and order as the ordinate;

[0098] These poles are classified according to stability based on the steady-state judgment conditions and marked with different icons and colors;

[0099] The process and conditions for steady-state judgment are as follows: Assume that the i-th order model obtains a certain extreme point λ i and the pole λ obtained by the i+1th order model i+1 , according to the corresponding poles, the modal parameters of frequency and damping ratio are calculated to see whether they meet the following conditions, and are displayed in the stability diagram with different icons and colors;

[0100]

[0101]

[0102] In formula (15), f and f′ are the modal frequency parameters obtained by the i-order model and the i+1-order model, respectively, and Δf is the threshold;

[0103] In formula (16), ξ, ξ′ are the modal damping parameters obtained by the i-order model and the i+1-order model, respectively, and Δξ is the threshold;

[0104] It is difficult to apply overall excitation to large structures when using dynamics to diagnose structures. Generally, only local excitation can be achieved to obtain local vibration responses of the structure. Moreover, local vibration of the structure can more accurately reflect the local characteristics of the structure than overall vibration.

[0105] The low-order modes mainly reflect the overall dynamic characteristics of the structure, while the high-order local modes reflect the local dynamic characteristics of the structure. The effective combination of the two can make full use of the measured information and help improve the calculation efficiency of the model. On the basis of satisfying the overall and local dynamic characteristics of the structure, the model can be appropriately condensed to reduce the scale of solution calculation and improve optimization efficiency;

[0106] Analyze the data points in the steady-state diagram and reconstruct the steady-state diagram to obtain modal parameters that better meet actual needs;

[0107] As a time-domain identification method, the random subspace algorithm cannot directly estimate the model order. In order to ensure the acquisition of all modal information, the model order is often assumed to be large, which inevitably introduces a large number of calculation poles.

[0108] These calculation poles and the noise poles caused by the measurement noise will greatly interfere with the picking of the final modal parameters;

[0109] The covariance-driven random subspace algorithm is used to identify the modal parameters of N groups of structural signals, and N groups of identification results are obtained. Each group of results includes the corresponding frequency value, damping ratio and vibration mode coefficient.

[0110] Establish N groups of subsets, start from the first group of subsets, calculate the distances between adjacent subsets in sequence, and form a distance matrix;

[0111] According to whether the above distance formula is satisfied, the corresponding mode type is judged to eliminate the pseudo mode;

[0112] The method of graph clustering is used to pick up the parameters of the modes after removing the false modes;

[0113] The graph clustering method maps the stable graph after removing the false modes to an undirected graph, maps the stable points in the stable graph to the vertices in the undirected graph, and the edges in the undirected graph describe the connection between the stable points. The weight of each edge in the undirected graph is defined according to the modal similarity between the stable points. A minimum spanning tree is constructed on the undirected graph, a threshold is defined, and the edges with weights greater than the threshold are removed from the constructed minimum spanning tree, and the minimum spanning tree of the merged new category is calculated. Each minimum spanning tree makes full use of the modal information of the stable points as a clustering tree, splits the clustering tree for curve fitting, and automatically sets the clustering threshold limit and the number of clustering elements, so that data with similar characteristics can be better clustered. At the same time, the distance formula is defined according to the frequency and modal vibration shape similarity to set the corresponding threshold, and the stable points after the above clustering are clustered again. At this time, the stable points in the stable graph have been divided into different classes according to the similarity between them. According to the number of elements in the set class, it is judged whether the class is a real modal class, so as to realize the automatic picking of the real modal parameters.

[0114] Automatically classify stable points with similar frequencies and vibration modes in the stability diagram, define the distance between modes of frequency index, and define the distance between vibration modes based on confidence criteria;

[0115]

[0116] d ij2 =1-MAC i，j (18)

[0117] Based on the distance matrix, the distance between each stable point is taken as a sample, and then one third of the relevant modal distance is taken as d ij1 The threshold value of

[0118] Combined with actual engineering experience, MAC can be selected i，j is 0.1, and then d ij2 The threshold value of

[0119] When the above formulas (17) and (18) are satisfied, the corresponding stable points are classified into one category, and the number of elements is counted to complete the automatic identification of modal parameters;

[0120] In combination with the content of the present invention, the vibration response data obtained by long-term health monitoring of a bridge structure is analyzed and processed, and the modal parameters are identified by using the improved random subspace identification method proposed by the present invention, thereby obtaining the frequency modal parameters. As shown in Table 1, compared with the frequency modal parameters obtained by the traditional random subspace identification method, the method of the present invention improves the recognition accuracy of the modal parameters and has greatly improved the accuracy.

[0121] Table 1

[0122]

[0123] In summary, the present invention provides a method and device for identifying structural modal parameters based on a random subspace algorithm. The present invention determines the optimal number of rows of the Toeplitz matrix by processing the acceleration response data of the measuring points and combining the estimated system model order with the total length of the acceleration response data. The random subspace method is used to identify the modal parameters of the modified Toeplitz matrix, and high-precision frequency modal parameters and damping ratio modal parameters are obtained, thereby improving the modal parameter identification accuracy of the random subspace method. Therefore, the present invention has broad application prospects.

[0124] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for identifying structural modal parameters based on random subspace algorithm, characterized in that: The following steps are involved: Step 1: Collect acceleration response data of i measuring points on the structure {y r |r=1,2,...,i};where y r Represents the acceleration response data of the rth measuring point; Step 2: Preprocess the collected acceleration response data, calculate the covariance of each column of measured data after preprocessing, and construct a covariance matrix. Use the singular value decomposition method to perform singular value decomposition on the covariance matrix to obtain a singular value matrix. Use the principal component analysis method to calculate the singular value matrix to obtain the approximate model order k of the structure; Step 3: Use the acceleration response data obtained in step 1 to establish the Hankel matrix, which contains all the response signals of the structure; divide the Hankel matrix into blocks of "past y p " and "future f ” Two parts, each with the same number of block rows; Step 4: Using the Hankel matrix constructed in step 3, the output covariance is defined as: In the test, j data are obtained, and the output data is assumed to have various states of experience. Then the discrete state space equation and output covariance formula are as follows: In formula (1): v k , w k are different zero-mean Gaussian white noises; x k+1 represents the state vector at the k+1th moment; Step 5: The covariance sequence calculated in step 4 is used to form a Toeplitz matrix. The Toeplitz matrix is ​​used to reduce the amount of data while maintaining the original information of the measured response signal of the structure, thereby improving the calculation efficiency. Step 6: Use the eigenvalue method to solve the Toeplitz matrix to obtain the stable poles, use the weighted overlapping average method to obtain the power spectrum curve, and compare whether the number of stable axes formed by the stable poles is equal to the number of peaks in the power spectrum curve of the weighted overlapping average method; then determine whether there is a mode loss. If there is a mode loss, use the linear phase filtering technology, which will time-shift the frequency component according to the signal energy being proportional to the frequency, ensuring that the delay of each frequency component passing through the filter is consistent, so that the phases of different modal components in each classification group are synchronized, thereby ensuring that the signal is not distorted, and then perform modal identification analysis on the modal components in each classification group; Step 7: By analyzing the relationship between the number of rows of the Toeplitz matrix and the system state matrix, the Toeplitz matrix composed of different numbers of rows is obtained. Based on the model approximation order k obtained in step 2 and the total length of the response data l, the number of rows i of the Toeplitz matrix must satisfy k<i<l; Step 8: Calculate the Toeplitz matrix corresponding to different i values, perform singular value decomposition on it, and then calculate the state matrix A and output matrix C of the system; Step 9: Perform eigenvalue decomposition on the state matrix A of the system, and obtain the frequency, damping and vibration mode parameters according to the relationship between the eigenvalue and the controllable matrix and the observable matrix; Step 10: Draw a stability diagram based on the poles obtained by eigenvalue decomposition of the system matrix A, and mark them in the stability diagram with different symbols and colors according to different calculation formulas that satisfy the frequency, damping, and vibration mode and the set threshold limits; Step 11: Analyze the data characteristics in the stability diagram, obtain the corresponding modal parameters under different model orders, extract the relevant information of the structure according to the relationship between the vertical and horizontal coordinates of the stability axis in the stability diagram, and obtain the overall modal characteristic parameters and local modal characteristic parameters of the structure; Step 12: Adjust the threshold of the modal parameters according to the actual working conditions, redraw the stability diagram, and obtain modal parameters that are closer to the natural modes of the structure; Step 13: The multiple groups of modal parameters obtained by identification are represented by different subsets, and the distance formula of the modal parameters between the subsets is defined, and the distance threshold is set. Each subset is judged to eliminate the pseudo-mode, so as to ensure that the real modal information of the structure can be obtained; Step 14: Use graph theory clustering as a modal parameter automatic identification method, and establish a minimum spanning tree for the stability diagram after eliminating false modes caused by calculation poles and noise poles. According to the defined frequency and modal confidence distance formula, take the distance between each stable pole as a sample, and comprehensively use the modal parameters such as frequency, damping ratio, and modal confidence criterion. Set the number of clusters and the cluster threshold limit to complete the automatic picking of modal parameters.

2. The method for identifying structural modal parameters based on random subspace algorithm according to claim 1, characterized in that: The preprocessing in step 2 includes: constructing a trend term using a polynomial function, eliminating the trend term of the vibration signal, and performing smoothing processing using a smoothing average method.

3. The structural modal parameter identification method based on random subspace algorithm according to claim 1 is characterized in that: The preprocessing in step 2 includes: performing pole symmetric modal decomposition on the collected acceleration response signal to obtain inherent modal components and residual components, separating the obtained components using a blind source separation method, and performing frequency domain conversion on the separated signal to obtain a noise component for noise reduction processing.

4. The method for identifying structural modal parameters based on random subspace algorithm according to claim 1, characterized in that: In the step 13, the automatic modal parameter identification method uses modal parameters to reasonably set the clustering threshold and the number of clustering elements according to the similarity between stable points.

5. A structural modal parameter identification device based on random subspace algorithm, characterized in that: The structural modal parameter identification method according to any one of claims 1 to 4 comprises: A data acquisition module is used to acquire a vibration response acceleration signal of the structure, wherein the vibration response acceleration signal is a vibration signal generated when an external load excites the structure; A data preprocessing module is used to eliminate trend items and reduce noise on the collected acceleration vibration response data; Initial parameter and mode identification module, including: system order setting unit, parameter identification unit and mode screening unit; The false mode elimination module is used to construct a distance formula using the frequency and vibration mode parameters of the structure and set a reasonable threshold limit to eliminate the false modes contained in the initial mode; The real mode combination module is used to obtain the state space model of the structure under different system orders based on the modal parameters after eliminating the false modes, combined with the stability diagram theory, and perform modal parameter identification on each model. All the modal parameters obtained are plotted on the stability diagram to determine the modal parameters of the structure, and the same modal parameters under different model orders are combined; The module for automatic picking of true modal parameters is used to take the characteristics of sample data as the index of the class, make full use of the modal information of each stable point to construct a clustering tree, split the clustering tree to fit the curve, automatically set the clustering threshold limit and the number of clustering elements, and then better cluster the data with similar characteristics, so as to realize the automatic picking of true modal parameters.

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