A Time-domain Multi-measurement Group Operational Modal Identification Method, Device and Terminal

Abstract

The present invention belongs to the technical field of structural health monitoring, and discloses a time-domain multi-measurement group operational modal identification method, device and terminal. The time-domain signals of a large civil structure to be monitored are measured in a multi-measurement group manner, the collected time-domain signals are analyzed, and a time series prediction recurrence formula is constructed; the integration and fusion of multi-measurement group information and the construction of a joint likelihood function are carried out, and a time-domain non-deterministic modal analysis system is constructed based on the multi-measurement group joint likelihood function and the modal parameter joint prior distribution; time-domain modal non-deterministic judgment and hyperparameter joint inference are carried out to obtain the time-domain modal parameter joint probability distribution, and the prediction and reconstruction of the time-domain free response are carried out. The present invention can naturally realize the effective fusion of any multi-group measurement data in Bayesian time-domain modal analysis, and fundamentally solves the difficulty of unifying the directions of local mode shape vectors of each measurement group during the assembly process.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring, and particularly relates to a time-domain multi-measurement set operation modal identification method, device and terminal. Background Technique

[0002] Modal parameters, namely natural vibration frequency, damping ratio, and modal shape, belong to the inherent dynamic characteristic parameters of a structure and are key parameters for research such as vibration-based structural health monitoring, structural damage identification, finite element model updating, and vibration prediction and control. For large-scale civil engineering structures such as super high-rise buildings, long-span bridges, and large dams, modal parameters are also an important basis for studying and evaluating their seismic resistance, wind resistance, and ability to resist other dynamic loads. Modal identification is the process of reasonably analyzing the dynamic response signals obtained from experimental measurements to extract modal parameters. According to whether external excitation signals are used, modal analysis can be divided into classical methods based on both excitation and response signals and modern methods that only use response signals. For large-scale civil engineering structures, it is more practical to identify modal parameters only using the dynamic response signals under ambient excitation, which has received extensive attention from scholars at home and abroad. At present, some effective deterministic modal analysis methods have been proposed. However, in practical applications, due to factors such as measurement noise, environmental factor interference, and incomplete measurement information, the modal identification results inevitably have non-determinacy, which may have a significant impact on the final results through gradual transmission and accumulation. However, currently, the vast majority of relevant research work and engineering applications can only consider the modal parameter identification results themselves and are difficult to quantify the non-determinacy of the modal analysis results. Modal analysis essentially belongs to a parameter identification problem and can be effectively carried out within the framework of Bayesian theory, which means regarding the modal parameter identification problem as a Bayesian inference problem, inferring the posterior distribution from the prior information of modal parameters, so as to synchronously quantify the modal parameter identification results and their non-determinacy degree, which is crucial for the scientificity and reliability of related research and applications based on modal parameters.

[0003] In recent years, research on exploring and quantitatively interpreting the uncertainty law of modal parameters based on Bayesian theory has gradually attracted attention (such as DOI: 10.1002 / 9780470824566, 10.1007 / 978-981-10-4118-1). Among them, frequency-domain modal parameter identification based on Bayesian inference has received great attention (such as DOI: 10.1016 / j.ymssp.2011.07.007, 10.1016 / j.ymssp.2014.07.027, 10.1016 / j.ymssp.2020.106663, 10.6052 / j.issn.1000-4750.2012.07.0560, 10.3969 / j.issn.1671-2439.2015.06.006, 10.6052 / j.issn.1000-4750.2018.11.0604; CN109254321B, CN108052958B). Such methods usually rely on the fast Fourier transform of the original time-domain signal for modal identification and uncertainty assessment. However, there are still the following problems with such Bayesian frequency-domain modal analysis methods: First, such methods usually require manual specification of the analysis frequency band range for each order of mode, and the bandwidth will have a certain impact on the uncertainty quantification of the modal parameter identification results. Second, such methods need to adopt different theoretical formulas to deal with sparse modes and dense modes respectively, and the discrimination of modal density and sparsity problems itself also requires certain manual experience, increasing the difficulty of practical application. Third, this type of method separates the identification and uncertainty quantification of spectral variables such as frequency and damping ratio from the modal shape. Although it can effectively reduce the dimension of the modal parameter vector to be identified, the uncertainty of the natural frequency and damping ratio is independent of that of the modal shape, affecting the uncertainty quantification of the overall modal parameters. Fourth, such methods usually rely on maximum likelihood estimation without prior assumptions, which affects the reliability and robustness of the modal parameter inference process and its results.

[0004] In contrast, time-domain modal analysis methods based on Bayesian inference have received less attention (such as DOI: 10.1016 / S0266-8920(01)00004-2, 10.1002 / eqe.135), but theoretically, they can avoid most of the above problems existing in Bayesian frequency-domain modal analysis methods. Such time-domain methods usually stack the modal frequencies, damping ratios, and modal shape vectors of each order to be identified, and then carry out identification based on the stacked vector of the composed modal parameters. The main advantages are that all modal parameters can be identified at one time, and the operation is directly based on the original time-domain data, effectively avoiding the truncation and leakage errors that may be caused when using Fourier transform to analyze and process time-domain signals in the above frequency-domain methods, and having certain advantages in damping and dense modal identification. However, in practical applications, such Bayesian time-domain modal analysis methods still have the following difficulties and deficiencies: (1) When dealing with the operational modal analysis problem of large civil engineering structures with a large number of degrees of freedom to be observed, the computational amount of high-dimensional modal parameter stacked vector identification and non-deterministic evaluation of such methods will be quite considerable; (2) Due to the significant difference in the order of magnitude between the natural vibration frequencies, damping ratios, and modal shapes in the modal parameter stacked vector, and the lack of effective constraints on high-dimensional modal shape vectors, it is extremely difficult for the high-dimensional modal parameter vector stacking to converge or even impossible to converge at all; (3) The full coverage of a large number of measurement points of degrees of freedom to be measured in large civil engineering structures usually needs to be achieved in batches in the form of multiple measurement groups, and currently, there is no effective solution for the effective fusion of multi-measurement group data in such time-domain modal analysis methods; (4) Such time-domain identification methods currently are also based on maximum likelihood estimation without prior assumptions, which will affect the reliability of the modal analysis process and its non-deterministic evaluation; (5) Such time-domain identification methods can only identify modal parameters and cannot realize the dynamic response prediction and reconstruction based on modal parameters.

[0005] Through the above analysis, the main problems and defects existing in the existing time-domain technologies are as follows:

[0006] (1) The existing technology lacks effective constraints on high-dimensional modal shape vectors, resulting in the non-convergence of the high-dimensional modal parameter vector identification process;

[0007] (2) The existing technology lacks effective fusion measures for multi-measurement group data; the existing technology cannot adaptively consider the influence of prior distribution on the modal identification results;

[0008] (3) The existing technology cannot realize the free response signal reconstruction on the observed degrees of freedom. Summary of the Invention

[0009] Aiming at the problems existing in the existing technology, the present invention provides a time-domain multi-measurement group operational modal identification method, device, and terminal.

[0010] The present invention is implemented as follows. A time-domain multi-measurement group operational modal identification method, the method comprising:

[0011] Adopt a multi-measurement group method to measure the environmental excitation signals of the large civil structure to be monitored, analyze the collected time-domain signals, and construct a time series prediction recurrence formula;

[0012] Perform the integration and fusion of multi-measurement group information and the construction of a joint likelihood function, and construct a time-domain non-deterministic modal analysis system based on the multi-measurement group joint likelihood function and the modal parameter joint prior distribution;

[0013] Perform time-domain modal non-deterministic judgment and hyperparameter joint inference to obtain the joint probability distribution of time-domain modal parameters, and further carry out the prediction and reconstruction of time-domain free response.

[0014] Further, the time-domain multi-measurement group operational modal identification method includes the following steps:

[0015] Step 1, perform multi-measurement group time-domain signal acquisition under environmental excitation for the large civil structure object to be monitored, and analyze and process the collected signals;

[0016] Step 2, combine the measured time-domain free response data of each measurement group based on the dynamic response stacking vectors at different times, and effectively fuse all the combined measurement data to form a complete measurement data integration corresponding to all degrees of freedom to be measured;

[0017] Step 3, construct the prediction probability distribution expression of the dynamic response vector stacking and the joint likelihood function of the complete modal parameter vector stacking under all degrees of freedom to be measured based on the time series recurrence relationship of the response vector stacking;

[0018] Step 4, impose a standard orthogonality constraint on the high-dimensional modal shape matrix as the prior distribution of the modal shape; at the same time, assume that the modal circular frequency and modal damping ratio are respectively multivariate normal distributions, and construct the joint prior distribution of the modal parameter vector stacking including undetermined hyperparameters;

[0019] Step 5, construct the conditional probability distribution update expression of the complete modal parameter vector stacking, and establish a Bayesian time-domain multi-measurement group non-deterministic operational modal analysis system; further perform time-domain identification of the complete modal parameter vector stacking in the operating state;

[0020] Step 6, simultaneously obtain the joint non-deterministic degree quantification of the modal frequency, damping ratio, and modal shape vector stacking based on the approximate covariance matrix of the maximum a posteriori estimation;

[0021] Step 7: Based on the maximum a posteriori estimation of the stacked complete modal parameter vectors obtained under the condition of integrated fusion of multi-measurement group response data, construct a time-domain free response prediction model based on the time-domain recurrence relation expression for all degrees of freedom to be measured, and reconstruct the free vibration response decay signal within the time history.

[0022] Furthermore, the multi-measurement group time-domain signal acquisition for the large-scale civil structure object to be monitored and the analysis and processing of the acquired signals include:

[0023] According to the structure and geometric dimensions of the large-scale civil structure object to be monitored, determine the measurement group division and reference measurement degree of freedom configuration scheme in the modal test, and then sequentially collect the dynamic response signals under ambient excitation in batches according to the measuring point configuration of each measurement group;

[0024] For the measured response data of each measurement group, use a reasonably constructed band-pass filter to extract the time-domain response signals within the concerned frequency band, and then obtain the free response decay signals of all channels under each measurement group through the natural excitation method; meanwhile, preliminarily locate multiple order frequency peaks within the concerned frequency band through the modal indicator function.

[0025] Furthermore, the combination of the measured time-domain free response data of each measurement group based on the dynamic response stacked vectors at different times and the effective fusion of all the combined measurement data include:

[0026] First, the combination of the measured time-domain free response data of each measurement group based on the dynamic response stacked vectors at different times is carried out using the following formula:

[0027]

[0028]

[0029]

[0030] Secondly, the effective fusion of all the combined measurement data is carried out using the following formula:

[0031]

[0032] Furthermore, the time series recurrence relation of the response vector stacking is as follows:

[0033]

[0034] The predicted probability distribution form of the dynamic response vector stacking is as follows:

[0035]

[0036] Among them, represents the covariance matrix of a multivariate normal distribution, and α represents an undetermined hyperparameter;

[0037] The joint likelihood function of the stacked complete modal parameter vectors under all degrees of freedom to be measured is as follows:

[0038]

[0039] where θ represents the stacked modal parameter vectors under the complete degrees of freedom to be measured,

[0040] The joint prior distribution of the stacked modal parameter vectors of the undetermined hyperparameters is as follows:

[0041]

[0042] where θ represents the modal parameter vector; I R represents the R-order unit vector;

[0043] The update expression of the conditional probability distribution of the stacked complete modal parameter vectors is as follows:

[0044]

[0045] Further, the following standard orthogonality constraints are imposed on the high-dimensional modal shape matrix:

[0046]

[0047] where β, γ, and δ all represent undetermined hyperparameters, and ||·|| represents the 2-norm of the vector.

[0048] Further, the time-domain identification of the stacked complete modal parameter vectors in the operating state includes:

[0049] Use the following formula for the time-domain identification of the stacked complete modal parameter vectors in the operating state;

[0050]

[0051] where the squared error to are given respectively as follows:

[0052]

[0053]

[0054]

[0055]

[0056] The residual vector is as follows:

[0057]

[0058] Among them, and i R respectively represent MO [l] and the R-dimensional all-ones vector,

[0059] Furthermore, the construction of the time-domain free response prediction model based on the time-domain recurrence relation expression on all degrees of freedom to be measured includes:

[0060] Construct a time-domain free response prediction model based on the time-domain recurrence relation expression on all degrees of freedom to be measured by using the following formula:

[0061]

[0062] Another object of the present invention is to provide a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the steps of the time-domain multi-measurement set operational modal identification method.

[0063] Another object of the present invention is to provide a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the processor executes the steps of the time-domain multi-measurement set operational modal identification method.

[0064] Combined with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by the present invention are:

[0065] First, the present invention can naturally achieve the measurement set fusion of Bayesian time-domain modal analysis. The present invention can naturally achieve the seamless integration and fusion of any number of sets of measurement information in the time domain. This measurement set data fusion strategy abandons the traditional method that relies on the assembly of local modal vibration modes of each measurement set, and fundamentally solves the difficulty in unifying the directions of local vibration mode vectors of each measurement set during the assembly process. Moreover, this difficulty becomes more prominent as the number of measurement sets increases. This strategy is crucial for improving the efficiency of multi-measurement set time-domain modal analysis of large-scale civil engineering structures.

[0066] The present invention can efficiently achieve the stable solution of high-dimensional modal parameter vector stacking. The present invention effectively ensures the rapid convergence of high-dimensional modal parameter vector stacking by designing modal parameter prior distribution, especially implementing standard orthogonalization constraints on modal vibration vectors of each order, and further uses nonlinear least squares and hyperparameter joint inference strategies based on sparse finite differences to effectively improve the recognition efficiency and noise robustness in high-dimensional modal parameter space, while also effectively weakening the influence of the order of magnitude differences of various modal parameters on the stability of time domain recognition.

[0067] The present invention can directly realize the prediction and reconstruction of the time-domain dynamic response signal. Based on the Bayesian time-domain modal analysis framework of the present invention and the corresponding maximum a posteriori estimation of modal parameters, a prediction framework of the time-domain dynamic response signal can be directly constructed, effectively realizing the reconstruction of the time history of the free response attenuation signal on the complete measurement degree of freedom, and the quality of the reconstructed response signal provides a key quantitative basis for real-time diagnosis and evaluation of the degree of change of the dynamic characteristics of the monitored structure relative to the initial state, which is of great significance for monitoring and tracking the evolution of performance degradation of large structures during long-term service.

[0068] Second, the present invention can naturally realize the effective fusion of any multiple groups of measurement data in Bayesian time-domain modal analysis, abandoning the traditional practice of relying on the identification and assembly of local modal vibration modes of the measurement group, and fundamentally solving the difficulty of unifying the directions of local vibration mode vectors of each measurement group during the assembly process; at the same time, the present invention ensures the effective convergence of high-dimensional modal vibration mode vector stacking through standard orthogonalization prior constraints, and combines the nonlinear least squares of sparse finite differences with hyperparameter joint inference to achieve efficient identification and non-deterministic quantification of high-dimensional modal parameter vector stacking; in addition, the present invention can also directly carry out time-domain dynamic response signal prediction, effectively realize the reconstruction of the time history of free response attenuation signals on complete measurement degrees of freedom, and provide a key reference for real-time diagnosis of changes in structural dynamic characteristics during long-term monitoring of the health status of large civil engineering structures.

[0069] Third, the present invention can naturally realize the seamless integration of any multiple groups of time domain measurement information of large-scale engineering structures, and effectively solve the problem of efficient and stable convergence of high-dimensional modal parameter vectors. At the same time, it can also directly reconstruct the time history of free response signals in all measurement degrees of freedom, and is expected to realize online diagnosis and quantitative evaluation of the degree of change of structural dynamic characteristics, and reveal in real time the performance evolution process of the monitored large-scale civil engineering structure during its long service life. It will help solve the traditional problem of real-time tracking of performance degradation of large-scale structures during long-term operation. At the same time, it is of great significance to develop an efficient real-time monitoring and evaluation system for the service status of large structures, ensure the safe and healthy service of large structures, and effectively protect the safety of national property and the lives and property of the people.

[0070] Fourth, due to the great limitations of testing costs and testing channels, the overall dynamic testing of large civil engineering structures usually needs to be decomposed into several measurement groups. Currently, traditional methods for dealing with multi-measurement group problems rely on the assembly of local modal vibration modes of each measurement group, resulting in difficulties in unifying the directions of local vibration mode vectors of each measurement group. Moreover, this difficulty becomes more prominent as the number of measurement groups increases. It is a technical problem that people have always been eager to solve but have never succeeded in solving. The measurement group data fusion strategy of the present invention can naturally achieve seamless integration of any number of groups of measurement information in the time domain, fundamentally solving the problem of unifying the directions of local vibration mode vectors of each measurement group during the assembly process, which is crucial for improving the efficiency of multi-measurement group time-domain operational modal analysis of large civil engineering structures.

[0071] The number of overall measurement degrees of freedom of large civil engineering structures is huge, generating high-dimensional or even ultra-high-dimensional stacked vectors of modal parameters. Traditional methods lack effective constraints on high-dimensional modal vibration mode vectors and cannot consider the significant differences in the orders of magnitude of various parameters in the stacked modal vectors, resulting in extremely difficult convergence in the process of identifying high-dimensional modal parameter vectors. The present invention effectively solves the problems of efficient convergence and noise robustness of high-dimensional modal parameter vectors by imposing a standard orthonormalization constraint on the modal vibration mode vectors and implementing a joint inference strategy for hyperparameters based on sparse finite difference nonlinear least squares. At the same time, it also effectively overcomes the influence of the differences in the orders of magnitude of modal parameters on the stability of time-domain identification.

[0072] Traditional methods can usually only identify modal parameters and cannot achieve the prediction of time-domain dynamic responses based on modal parameters, resulting in the inability to diagnose the structural health state in real time. The present invention directly constructs a prediction framework for time-domain dynamic response signals based on the modal identification results, effectively realizing the reconstruction of the time history of free response signals at the observed degrees of freedom, which provides a key quantitative basis for the degree of variation of the structural dynamic characteristics relative to the initial state, and effectively solves the traditional problem of real-time monitoring and tracking of the performance evolution process of large structures during long-term service. Description of the Drawings

[0073] Figure 1 is the schematic diagram of the principle of the time-domain multi-measurement group operational modal identification method provided by the embodiment of the present invention;

[0074] Figure 2 is the flowchart of the time-domain multi-measurement group operational modal identification method provided by the embodiment of the present invention;

[0075] Figure 3 is the schematic diagram of the four-measurement group division scheme of the modal test of a 12-story frame structure provided by the embodiment of the present invention;

[0076] Figure 4 is the modal indicator function diagram after the fusion of four groups of measurement information provided by the embodiment of the present invention;

[0077] Figure 5 It is a non-deterministic identification result diagram of modal frequencies of all orders in the case of four measurement groups provided by an embodiment of the present invention;

[0078] Figure 6 It is a non-deterministic identification result diagram of damping ratios of all orders in the case of four measurement groups provided by an embodiment of the present invention;

[0079] Figure 7 It is a non-deterministic identification result diagram of modal shapes of all orders in the case of four measurement groups provided by an embodiment of the present invention;

[0080] Figure 8 It is a free response reconstruction result diagram of complete measurement points in the case of four measurement groups provided by an embodiment of the present invention. Detailed implementation manners

[0081] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0082] As Figure 1 shown is the schematic diagram of the method of the present invention, and as Figure 2 shown is the flow chart of the method of the present invention; the time-domain multi-measurement group operational modal identification method provided by the embodiment of the present invention includes the following steps:

[0083] S101. Perform multi-measurement group time-domain signal acquisition on the large civil structure object to be monitored under ambient excitation, and analyze and process the acquired signals;

[0084] S102. Combine the measured time-domain free response data of each measurement group based on the dynamic response stacking vectors at different times, and effectively fuse all the combined measurement data to form a complete measurement data integration corresponding to all degrees of freedom to be measured;

[0085] S103. Construct the prediction probability distribution expression of the dynamic response vector stacking and the joint likelihood function of the complete modal parameter vector stacking under all degrees of freedom to be measured based on the time series recurrence relationship of the response vector stacking;

[0086] S104. Apply the standard orthogonality constraint to the high-dimensional modal shape matrix as the prior distribution of the modal shape; at the same time, assume that the modal circular frequency and the modal damping ratio are respectively multivariate normal distributions, and construct the joint prior distribution of the modal parameter vector stacking including undetermined hyperparameters;

[0087] S105. Construct an updated expression for the conditional probability distribution of the stacked complete modal parameter vector, and establish a Bayesian time-domain multi-measurement-group non-deterministic operational modal analysis system; further perform time-domain identification of the stacked complete modal parameter vector under the operating state.

[0088] S106. Quantify the joint non-determinacy of the modal frequency, damping ratio, and the stacked modal shape vector based on the approximate covariance matrix of the maximum a posteriori estimation.

[0089] S107. Based on the maximum a posteriori estimation of the stacked complete modal parameter vector obtained under the condition of integrated fusion of multi-measurement-group response data, construct a time-domain free response prediction model based on the time-domain recurrence relation expression for all degrees of freedom to be measured, and reconstruct the decaying signal of the free vibration response within the time history.

[0090] The time-domain multi-measurement-group operational modal identification method provided by the embodiments of the present invention specifically includes:

[0091] The free vibration response of the i-th observed degree of freedom of the structure to be monitored at time t is expressed by the modal superposition method as follows:

[0092]

[0093] Where, represents the i-th element of the j-th modal shape vector, O represents the number of all degrees of freedom to be observed, and R represents the measured modal order. ω j and ξ j represent the undamped natural circular frequency and modal damping ratio of the j-th order respectively, represents the corresponding damped natural circular frequency. A j and B j are undetermined coefficients related to the j-th order mode and dependent on the initial conditions.

[0094] Divide all degrees of freedom to be measured of the object structure into L measurement groups. Using formula (1), the present invention can obtain the response vector of the observed degrees of freedom corresponding to the l-th measurement group at t = nΔt The expression is:

[0095]

[0096] Where, O [l] represents the number of observed degrees of freedom under the l-th measurement group, represents the modal parameter vector corresponding to the l-th measurement group, represents the modal shape matrix corresponding to the measurement degrees of freedom of this measurement group, which is obtained by matrix extracted from the complete measurement degree of freedom shape matrix Operator This means stacking matrices into vectors along their columns. and They represent the vectors composed of the circular frequencies and damping ratios of each order of modal. represents a matrix related to time t=nΔt and containing only the modal circular frequency and damping ratio information. represents the undetermined coefficient A associated with the first measurement group j With B j , j=1,2,…,R,the vector formed by.

[0097] The present invention sets the first measurement group from t = nΔt to n M Free response vector at time Δt to By stacking, and combining with formula (2), we can obtain the mapping relationship between the vector stack and the coefficient vector to be determined, that is:

[0098]

[0099] Among them, n M =n+M-1.

[0100] Similarly, we can establish t = (n + s) Δt to (n M +s)Δt time dynamic response vector stacking expression:

[0101]

[0102] Among them, the time point offset s≥1, and at the same time, n s =n+s,

[0103] The present invention constructs a recursive relationship for predicting the dynamic response vector stack at (n+s)Δt by combining formulas (3) and (4), that is,

[0104]

[0105] Among them, the time state transfer matrix Given by:

[0106]

[0107]

[0108] According to the time series recursive relationship given by formula (5), the present invention further assumes that the dynamic response vector stack at time t = (n + s) Δt is It obeys the following multivariate normal distribution form:

[0109]

[0110] Among them, represents the covariance matrix of the multivariate normal distribution, and α is a to-be-determined hyperparameter.

[0111] The present invention first combines the measured time-domain free response data of a single measurement group in the form, and then further effectively fuses all L groups of combined measurement data to form a complete measurement data set corresponding to all degrees of freedom to be measured, that is:

[0112]

[0113] Among them, represents the MO [l] ×MO [l] dimensional identity matrix.

[0114] Based on the effective fusion of multi-measurement group measured data, the present invention constructs a stacked modal parameter vector under the complete degrees of freedom to be measured, and the form of the joint likelihood function is as follows:

[0115]

[0116] The prior distribution of the modal parameter vector θ is jointly composed of various modal parameter distributions, and it is expressed as:

[0117]

[0118] Among them, the modal circular frequency and the modal damping ratio are respectively assumed to be multivariate normal distributions with ω0 and ξ0 as the means and β -1 I R and γ -1 I R as the covariance, and I R represents the R-order unit vector. The prior distribution represents the standard orthogonality constraint imposed by the present invention on the high-dimensional modal vibration mode vector matrix, that is

[0119]

[0120] Among them, β, γ, and δ are all to-be-determined hyperparameters, and ||·|| represents the 2-norm of the vector.

[0121] On the premise of given multi-measurement group data fusion , combining formulas (10) and (11), the posterior probability distribution of the modal parameter vector θ is expressed according to Bayesian theory as:

[0122]

[0123] Under the condition of given specific values of each hyperparameter, the present invention obtains the conditional maximum a posteriori estimation of the modal parameter vector by maximizing the logarithmic form of the conditional posterior probability distribution in formula (13). And it is further expressed in the form of nonlinear least squares, that is

[0124]

[0125] where the squared error to are given respectively as follows:

[0126]

[0127] Meanwhile, the specific form of the residual vector is given as follows:

[0128]

[0129] where and i R respectively represent MO [l] and the R-dimensional all-ones vector, It should be noted that in practical applications, ω0 can be obtained based on the frequency-domain analysis of the original time-domain signal, and ξ0 is usually taken as 0, indicating that the modal damping information is unknown.

[0130] The present invention first obtains the conditional maximum a posteriori estimation of the modal parameter vector through formula (16) and then sequentially obtains the conditional estimations of each undetermined hyperparameter based on the expansion formula of the evidence logarithm in formula (13). The specific expression forms are as follows:

[0131]

[0132] where represents the derivative operator, which is efficiently implemented through sparse finite differences. The hyperparameter estimated values in formula (17) are used to further update the maximum a posteriori estimation of the stacked modal parameter vector in formula (14), and this is repeated until the convergent maximum a posteriori estimation of the modal parameter is obtained and the corresponding covariance matrix

[0133] Furthermore, the present invention utilizes the obtained maximum a posteriori estimation value of the modal parameter under the condition of multi-measurement group fusion Based on the time-domain recurrence relation expression in formula (5), a time-domain free vibration response prediction and reconstruction model is constructed on all degrees of freedom of the measured quantity to realize the real-time reconstruction of the free response, that is:

[0134]

[0135] To verify the correctness of the technical solution of the present invention, consider Figure 3 the 12-story planar shear-type frame shown. A horizontal sensor can be arranged on each floor of this planar frame structure to sense the horizontal movement of each floor slab. For this frame structure, considering the insufficient number of test hardware channels available in practical applications, all 12 degrees of freedom to be measured are decomposed into 4 measurement groups, and the measurement channel Ch.12 of the top floor slab of the frame is selected as the common reference channel. Among them, the first 3 measurement groups each contain 4 measurement channels, and the last measurement group contains 3 measurement channels. The mass and inter-story stiffness of each floor slab of this frame model are taken as 5 kg and 1000 N / m respectively, and it is assumed that the damping ratio of each mode is 3%. A Gaussian white noise excitation with a frequency of 50 Hz is applied simultaneously in the horizontal direction of each floor slab to stimulate the horizontal movement mode of this frame structure. At the same time, a 10% root-mean-square noise signal is added to the acceleration response of each measurement channel to simulate the noise interference objectively existing in the actual measurement signal. It should be noted that in the time-domain operational modal analysis process of the present invention, it is assumed that the input white noise excitation is not measurable, that is, only the output response signal is used for modal parameter identification. Considering identifying all 12 modal parameters of this shear-type frame structure, therefore, the overall dimension of the modal frequency, modal damping ratio, and modal shape vector stack to be identified is: (2 + 12) × 12 = 168. In addition, the present invention uses the natural excitation technique with the measurement point Ch.12 on the top floor of the frame as the reference channel to obtain the free vibration responses of all channels, and it is specifically realized based on the cross-correlation function analysis of time-domain signals.

[0136] Figure 4 represents the modal indicator function after the measurement information fusion of the four measurement groups, where the vertical thick solid line and the thin dashed line respectively represent the maximum a posteriori estimate of the modal frequency and the corresponding initial estimate value. It can be clearly seen from the figure that although some of the initial frequency estimates deviate significantly from the true values, the optimal values of the modal frequencies identified by the present invention under multi-measurement group fusion and noise background are quite consistent with the spectral peaks of the singular values of the modal indicator function, indicating the reliability of the frequency identification results. In addition, it can also be found from the figure that for the last few high-order modes, due to the influence of modal damping and the excitation frequency band range, the spectral peaks are quite unclear and it is difficult or even impossible to determine by visual observation. The identification of these high-order weak modes causes considerable difficulties in the practical application of traditional modal identification methods because traditional methods usually rely on accurate resonance peak extraction to further identify the modal damping ratio and modal shape.

[0137] Figures 5 to 6The maximum a posteriori estimates of the modal frequencies and damping ratios identified by the present invention under the condition of four measurement sets of noise data and the corresponding coefficient of variation (COV) are given. It can be clearly seen from the figure that the identified values of the modal frequencies are almost exactly the same as the true values. For the damping ratio, the identified optimal estimate also quite agrees with the pre-assumed true value, which fully demonstrates the accuracy of the modal parameter identification of the present invention. In addition, from the comparison of the identification results of the COV values of the modal frequencies and damping ratios, there is a difference in order of magnitude between the uncertainty degrees of the damping ratio and the modal frequency, which indicates that the identification result of the modal damping ratio is more uncertain than the modal frequency. This clearly interprets from the perspective of probability theory the established fact that the identification accuracy of the damping ratio in practical applications is far less than that of the modal frequency. This also fully reflects the advantage of the present invention in the identification of the modal damping ratio and its non-deterministic parameters under the conditions of multi-measurement sets and noise in the time domain.

[0138] Figure 7 Shows the maximum a posteriori estimates of the modal shapes of each order given by the present invention in the case of four measurement sets and the corresponding coefficient of variation. Among them, for the convenience of comparison, the amplitudes of the modal shapes of each order are normalized, and the COV values are displayed in the form of their absolute values. It can be clearly seen from the figure that the modal shapes of all orders quite agree with the corresponding true values, which fully demonstrates the accuracy of the modal shape identification of the present invention under the information fusion of multi-measurement sets and the noise environment. In addition, the degree of non-determinacy of the modal shape identification is clearly quantified by the COV value. The result shows that the non-determinacy of the modal shape is one order of magnitude higher than that of the modal frequency, indicating that the modal shape has relatively greater non-determinacy and less accuracy in practical applications. Further, Figure 8 Represents the free response signal directly reconstructed by the present invention based on the modal analysis result under the conditions of multi-measurement sets and measurement noise, and is compared with the true response. It is clearly shown in the figure that the reconstructed and predicted response results quite agree, which also corroborates the reliability and accuracy of the proposed modal analysis and dynamic response reconstruction method from another perspective.

[0139] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated designed hardware. Those of ordinary skill in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code is provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and their modules of the present invention can be implemented by hardware circuits of programmable hardware devices such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above hardware circuits and software such as firmware.

[0140] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A time-domain multi-measurement group operational modal identification method, characterized in that Including: Step 1: Collect multi - measurement - group time - domain signals of a large civil - structure object to be monitored under ambient excitation, and analyze and process the collected signals; Step 2: Combine the measured time - domain free - response data of each measurement group based on the dynamic - response stacked vectors at different times, and effectively fuse all the combined measurement data to form a complete measurement - data integration corresponding to all degrees of freedom to be measured; Step 3: Construct the predictive probability - distribution expression of the dynamic - response vector stack and the joint likelihood function of the complete modal - parameter vector stack under all degrees of freedom to be measured based on the time - series recurrence relationship of the response - vector stack; Step 4: Impose an orthonormalization constraint on the high - dimensional modal - shape matrix as the prior distribution of the modal - shape; meanwhile, assume that the modal circular frequency and the modal damping ratio are respectively multivariate normal distributions, and construct the joint prior distribution of the modal - parameter vector stack containing undetermined hyperparameters; Step 5: Construct the conditional - probability - distribution update expression of the complete modal - parameter vector stack, and establish the system of Bayesian time - domain multi - measurement - group non - deterministic operational modal analysis; And perform the time - domain identification of the complete modal - parameter vector stack in the operating state; Step 6: Obtain the joint non - deterministic quantification of the modal frequency, damping ratio, and modal - shape vector stack based on the approximate covariance matrix of the maximum a posteriori estimation; Step 7: Based on the maximum a posteriori estimation of the complete modal - parameter vector stack obtained under the condition of multi - measurement - group response - data integration and fusion, construct a time - domain free - response prediction model based on the time - series recurrence - relationship expression for all degrees of freedom to be measured, and reconstruct the free - vibration response decay signal within the time history; Constructing a time - domain free - response prediction model based on the time - series recurrence - relationship expression for all degrees of freedom to be measured includes: Using the following formula to construct a time - domain free - response prediction model based on the time - series recurrence - relationship expression for all degrees of freedom to be measured:

2. The time-domain multi-measurement group operational modal identification method according to claim 1, characterized in that The collection of multi - measurement - group time - domain signals of a large civil - structure object to be monitored under ambient excitation, and the analysis and processing of the collected signals include: According to the structure and geometric dimensions of the large civil - structure object to be monitored, determine the measurement - group division and the reference - measurement - degree - of - freedom configuration scheme in the modal test, and then collect the dynamic - response signals under ambient excitation batch - by - batch according to the measuring - point configuration of each measurement group; For the measured response data of each measurement group, use a reasonably constructed band - pass filter to extract the time - domain response signals within the concerned frequency band, and then obtain the free - response decay signals of all channels under each measurement group through the natural - excitation method; meanwhile, preliminarily locate multiple order - frequency peaks within the concerned frequency band through the modal - indicator function.

3. The time-domain multi-measurement group operational modal identification method according to claim 1, wherein The combination of the measured time - domain free - response data of each measurement group based on the dynamic - response stacked vectors at different times, and the effective fusion of all the combined measurement data include: First, use the following formula to combine the measured time - domain free - response data of each measurement group based on the dynamic - response stacked vectors at different times: Second, use the following formula to effectively fuse all the combined measurement data:

4. The time-domain multi-measurement group operational modal identification method according to claim 1, characterized in that, The time series recurrence relation of the stacked response vectors is as follows: The expression form of the predicted probability distribution of the stacked dynamic response vectors is as follows: Among them, represents the covariance matrix of the multivariate normal distribution, and α represents the hyperparameter to be determined; The joint likelihood function of the stacked complete modal parameter vectors under all degrees of freedom to be measured is as follows: where, θ represents the stacking of modal parameter vectors under the complete degrees of freedom to be measured, The joint prior distribution of the stacked modal parameter vectors of the undetermined hyperparameters is as follows: where θ represents the modal parameter vector; I R represents the R-order unit vector; The update expression of the conditional probability distribution of the stacked complete modal parameter vectors is as follows:

5. The time-domain multi-measurement group operational modal identification method according to claim 1, wherein The following standard orthogonality constraints are imposed on the high-dimensional modal shape matrix: Where β, γ, and δ all represent undetermined hyperparameters, and ||·|| represents the 2-norm of the vector.

6. The time-domain multi-measurement-group operational modal identification method according to claim 1, characterized in that The time-domain identification of the stacked complete modal parameter vectors in the operating state includes: The time-domain identification of the stacked complete modal parameter vectors in the operating state is performed using the following formula; Among them, the squared error to are given as follows respectively: Residual vector is as follows: Among them, and i R respectively represent MO [l] and the R-dimensional all-1 vector, 7. A computer device, characterized in that, The computer device includes a memory and a processor. When the computer program stored in the memory is executed by the processor, the processor executes the steps of the time-domain multi-measurement group operating modal identification method according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program. When the computer program is executed by a processor, the processor executes the steps of the time-domain multi-measurement group operating modal identification method according to any one of claims 1-6.

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