A method, apparatus, and storage medium for identifying structural modal parameters

Abstract

The application provides a method, device and storage medium for identifying structural modal parameters. The method comprises: obtaining dynamic response information of a structure in a running state through a channel; performing Fourier transform on the dynamic response information to determine a power spectrum of the structure; determining a natural frequency of each modal of the structure based on the power spectrum; determining a filter frequency band of an i-th modal signal based on the natural frequency of the i-th modal; determining a first matrix; determining a second matrix based on the first matrix; performing singular value decomposition on the second matrix to determine a singular vector corresponding to a maximum singular value; and determining a modal parameter of the structure based on the singular vector, the modal parameter being a modal shape of the structure. The application has the advantages of high efficiency and high precision in identifying modal parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of modal parameter determination, and in particular to a method for identifying modal parameters of a structure, an electronic device and a computer readable storage medium. BACKGROUND

[0002] Modal parameters are important parameters for wind-resistant and earthquake-resistant design of large civil engineering structures, and the modal parameters include modal frequencies, modal damping ratios and modal shapes. Identifying modal parameters of a structure in a working state means that modal parameters are calculated from environmental vibration signals of the structure. Traditional working modal parameter identification methods have been widely used in the field of structural modal analysis. However, due to various unavoidable uncertainty factors in dynamic tests and modal analysis processes, the identified results often deviate from the true values, which makes it particularly important to quantitatively evaluate the uncertainty of the identified results. In recent years, the Bayesian modal parameter identification method has made significant progress. This method not only provides optimal estimates of modal parameters, but also quantitatively evaluates the uncertainty of the identified results. However, when the method is applied to large civil engineering structures such as large bridges or high-rise buildings with multiple measurement channels, the dimension of the existing Bayesian method increases exponentially in the optimization solving stage, and the computational efficiency is significantly reduced. On the other hand, the existing Bayesian method also has problems such as insufficient accuracy in damping identification. Therefore, it is of great theoretical and practical significance to develop a more efficient modal parameter identification method. SUMMARY

[0003] The technical problem solved by the present application is to overcome the shortcomings of the prior art and provide a method for identifying modal parameters of a structure, an electronic device and a computer readable storage medium, to at least solve the problems of low efficiency and / or low accuracy in identifying modal parameters in the related art.

[0004] To solve the above technical problems, the technical solution provided by the present application is:

[0005] The present application provides a method for identifying modal parameters of a structure (corresponding to a Bayesian space-time decomposition method), which comprises: acquiring dynamic response information of a structure in a running state through a measurement channel, wherein the dynamic response information includes acceleration response information or speed response information or displacement response information; performing Fourier transform on the dynamic response information to determine the power spectrum of the structure; based on the power spectrum, determining the natural frequency of each order modal of the structure ; wherein i is a modal index, k is an index of a physical frequency point, i and k are positive integers greater than 0; determining a filter frequency band of the i-th modal signal based on a natural frequency of the i-th modal; determining a first matrix, the first matrix containing information of the i-th modal signal of each of the measurement channels filtered by the filter frequency band; determining a second matrix based on the first matrix, the second matrix being an autocorrelation matrix of the first matrix; performing singular value decomposition on the second matrix to determine a singular vector corresponding to a maximum singular value; determining a modal parameter of the structure based on the singular vector, the modal parameter being a modal shape of the structure.

[0006] In some embodiments, the method further comprises: determining a standard deviation corresponding to the modal shape based on the modal shape; determining modal response information based on the modal shape and the first matrix; performing Fourier transform on the modal response information to determine an autocorrelation power spectrum of the modal response; determining an objective function to be optimized containing the autocorrelation power spectrum; determining a modal frequency and a modal damping ratio based on the objective function; determining a variance corresponding to the modal frequency and the modal damping ratio respectively based on the modal frequency and the modal damping ratio.

[0007] In some embodiments, the formula for determining the power spectrum of the structure comprises:

[0008] wherein, represents the dynamic response information , represents dividing the signal into M segments, r represents an index of the number of segments, and the subscript is an index of the th physical frequency point , wherein , represents frequency resolution, represents vector transposition, represents complex vector conjugate transposition, represents the power spectrum amplitude corresponding to the signal at the frequency point ;

[0009] The formula for determining the second matrix comprises: , is a matrix of signals in each of the measurement channels.

[0010] In some embodiments, the method further comprises:

[0011] filtering the measurement channels based on the filter frequency band to obtain i-th modal signals of the plurality of measurement channels;

[0012] wherein the filter frequency band is .

[0013] In some embodiments, performing singular value decomposition on the second matrix to determine the singular vector corresponding to the maximum singular value includes:

[0014] Performing singular value decomposition on the second matrix yields a third and a fourth matrix, where the third matrix is ​​a unitary matrix and the fourth matrix is ​​a diagonal matrix; the unitary matrix is... The diagonal matrix is: ,in, The maximum singular value of the i-th mode. for The corresponding singular vectors, To measure the number of channels, For diagonal matrix, divide Other singular values, To and The corresponding feature vectors;

[0015] The singular vector corresponding to the maximum singular value is determined based on the third matrix and the fourth matrix.

[0016] In some embodiments, the method further includes:

[0017] The fifth matrix is ​​determined based on the third matrix and the fourth matrix, and the fifth matrix is ​​the covariance matrix.

[0018] The formula for determining the fifth matrix is: ;

[0019] in, , and It is obtained based on the singular value decomposition of the second matrix. In response to the total number of points, the The maximum singular value of the first-order mode. To measure the number of channels; For the maximum singular value, for The corresponding singular vectors, To measure the number of channels, To remove Other singular values, To and The corresponding feature vectors;

[0020] The standard deviation is determined based on the diagonal elements of the fifth matrix.

[0021] In some embodiments, the formula for determining the modal response information includes: , It is a singular vector. is a signal matrix, t is a signal acquisition time;

[0022] The formula for determining the autocorrelation power spectrum includes: , represents dividing the signal into M segments, subscript is the index of the th physical frequency point , is a power spectrum;

[0023] The objective function is:

[0024] wherein, , represents , , and a set of , , , and target values to be solved; is the power spectral density of the excitation force; is the power spectral density of the noise; is the frequency to be identified; is the damping to be identified.

[0025] In some embodiments, the method further includes:

[0026] determining a sixth matrix based on the objective function, the sixth matrix being a Hessian matrix;

[0027] The determination of the variances of the modal frequencies and the modal dampings corresponding to the modal frequencies and the modal dampings respectively based on the modal frequencies and the modal dampings includes:

[0028] determining the variances of the modal frequencies and the modal dampings based on the diagonal elements of the inverse matrix of the sixth matrix.

[0029] The present application provides a device for identifying structural modal parameters, comprising:

[0030] an acquisition module configured to acquire dynamic response information of a structure in a running state through a measurement channel, the dynamic response information including acceleration response information or speed response information or displacement response information;

[0031] a determination module configured to perform Fourier transform on the dynamic response information to determine a power spectrum of the structure, and determine a natural frequency of each modal of the structure based on the power spectrum ; wherein i is a modal index, k is an index of a physical frequency point, i and k are positive integers greater than 0; determining a filter frequency band of the i-th modal signal based on a natural frequency of the i-th modal; determining a first matrix, the first matrix comprising information of the i-th modal signal filtered by the filter frequency band of each of the measurement channels; determining a second matrix based on the first matrix, the second matrix being an autocorrelation matrix of the first matrix; performing singular value decomposition on the second matrix to determine a singular vector corresponding to a maximum singular value; and determining a modal parameter of the structure based on the singular vector, the modal parameter being a modal shape of the structure.

[0032] The application further provides an electronic device, comprising a memory for storing a computer program, and a processor for executing the computer program to implement the steps of any of the above methods for identifying modal parameters of a structure.

[0033] The application further provides a computer-readable storage medium having a computer program stored therein, wherein the computer program, when executed by a processor, implements the steps of any of the above methods for identifying modal parameters of a structure.

[0034] Compared with the prior art, the application has the following advantages:

[0035] Since the Fourier transform can be performed on the dynamic response information obtained from the measurement channels to determine the power spectrum of the structure, the analysis of the dynamic response information in the frequency domain can be achieved. ; determining a filter frequency band of the i-th modal signal based on a natural frequency of the i-th modal; determining a first matrix, the first matrix comprising information of the i-th modal signal filtered by the filter frequency band of each of the measurement channels. In this way, after filtering, the noise of the signal has been greatly reduced, which can improve the accuracy of the modal parameters and reduce the uncertainty. A second matrix is determined based on the first matrix, the second matrix being an autocorrelation matrix of the first matrix; singular value decomposition is performed on the second matrix to determine a singular vector corresponding to a maximum singular value; and a modal parameter of the structure is determined based on the singular vector, the modal parameter being a modal shape of the structure. In this way, by singular value decomposition, the determination dimension of the modal parameters is reduced, thereby improving the efficiency of determining the modal parameters. Compared with the related art, the method for identifying modal parameters of a structure can solve the technical problems of inaccurate and low-efficiency identification of modal parameters of a structure, and can achieve the technical effects of higher accuracy of identifying modal parameters of a structure and higher efficiency of identifying modal parameters of a structure. BRIEF DESCRIPTION OF DRAWINGS

[0036] The application will be described in more detail below based on the embodiments and with reference to the drawings. In which:

[0037] Figure 1 is a flowchart of a method for identifying structural modal parameters provided by the application;

[0038] Figure 2 is a flowchart of a method for determining singular vectors provided by the application;

[0039] Figure 3 is a flowchart of a method for identifying structural modal parameters provided by the application;

[0040] Figure 4 is a flowchart of a method for determining parameters provided by the application;

[0041] Figure 5 is a flowchart of a method for identifying structural modal parameters provided by the application;

[0042] Figure 6 is a flowchart of a method for determining parameters provided by the application;

[0043] Figure 7 is a schematic diagram of an acceleration response process provided by the application;

[0044] Figure 8 is a schematic diagram of a frequency band distribution provided by the application;

[0045] Figure 9 is a schematic diagram of a MAC value provided by the application;

[0046] Figure 10 is a schematic diagram of a device for identifying structural modal parameters provided by the application. DETAILED DESCRIPTION

[0047] The application will be described in more detail below based on the embodiments and with reference to the drawings. In which:

[0048] In order to better understand the embodiments of the present disclosure, first, some application examples are described:

[0049] In some embodiments, modal parameters including frequency, damping and mode shape (also referred to as modal frequency, modal damping ratio and modal mode shape, not limited in the present disclosure) are important parameters for wind resistance and earthquake resistance design of large civil engineering structures, and identification of modal parameters of a structure in a working state refers to inverse calculation of modal parameters from environmental vibration signals of the structure. Although relevant working state modal parameter identification methods perform well in identifying natural frequency and modal mode shape, their effectiveness in damping ratio identification is still limited. Moreover, factors such as measurement noise, environmental changes and model errors will cause certain uncertainty in modal parameter identification. Bayesian theorem provides a powerful framework for modal parameter identification and uncertainty quantification, and provides a probabilistic alternative to traditional deterministic methods. The advantage of the Bayesian modal identification method is that it can provide effective uncertainty quantification for optimal estimation, which not only enhances the robustness of the identification method, but also provides a more scientific basis for state assessment and engineering decision-making.

[0050] In some embodiments, for structures with a large number of measurement channels (such as large bridges or high-rise buildings), the efficiency of the relevant Bayesian modal identification method is still relatively low, and the accuracy of damping identification in the traditional Bayesian modal identification method needs to be further improved.

[0051] Embodiments of the present application provide a method for identifying modal parameters of a structure, which is described in detail in combination with an execution process of identifying modal parameters of a structure.

[0052] Please refer to Figure 1 Embodiments of the present application provide a method for identifying modal parameters of a structure, which comprises:

[0053] Step 101: Obtain dynamic response information of the structure in a working state through a measurement channel.

[0054] In some embodiments, the dynamic response information comprises acceleration response information or speed response information or displacement response information.

[0055] In some embodiments, the dynamic response information of the target structure in the working state can be obtained through a plurality of measurement channels. Exemplarily, the number of measurement channels of each set of dynamic response information is , and the total number of responses is .

[0056] In some embodiments, the structure can be a large bridge or a high-rise building, but is not limited thereto.

[0057] In some embodiments, the dynamic response information can be real-time information obtained at different time periods and / or different positions of the target structure.

[0058] Step 102, performing Fourier transform on the dynamic response information to determine the power spectrum of the structure.

[0059] In some embodiments, the Fourier transform can be performed on the obtained dynamic response information in step 102.

[0060] In some embodiments, the power spectrum density matrix of the target structure can be determined as:

[0061] wherein, represents the Fourier transform of the , represents dividing the signal into M segments, r represents the index of the number of segments, and the subscript is the index of the th physical frequency point , wherein , represents the frequency resolution, represents vector transposition, represents complex vector conjugate transposition, represents the power spectrum amplitude corresponding to the signal at the frequency point .

[0062] Step 103, determining the natural frequency of each modal of the structure based on the power spectrum .

[0063] In some embodiments, i is the modal index, k is the index of the physical frequency point, and i and k are positive integers greater than 0.

[0064] In some embodiments, the peak point of each modal is obtained by using the peak picking method. Assuming that the peak point of the i th modal corresponds to the horizontal coordinate (frequency) of , and the corresponding vertical coordinate is .

[0065] Step 104, determining the filter band of the i th modal signal based on the natural frequency of the i th modal.

[0066] In some embodiments, the signal in the measurement channel associated with the peak point of the i th modal is filtered to determine the i th modal signal.

[0067] In some embodiments, the filter band can be selected , and all filtered channel signals can be stored in a matrix .

[0068] Step 105, determining a first matrix.​

[0069] In some embodiments, the first matrix comprises information of the i-th order modal signal of each measurement channel after being filtered by the filter frequency band.

[0070] In some embodiments, each measurement channel is filtered based on the filter frequency band to obtain an i-th order modal signal of the plurality of measurement channels.

[0071] At step 106, a second matrix is determined based on the first matrix.

[0072] In some embodiments, the second matrix is an autocorrelation matrix of the first matrix.

[0073] For example, the second matrix is an autocorrelation matrix :

[0074]

[0075] At step 107, singular value decomposition is performed on the second matrix to determine a singular vector corresponding to a maximum singular value.

[0076] Thus, since the Fourier transform can be performed on the dynamic response information obtained from the measurement channels to determine the power spectrum of the structure, the analysis of the dynamic response information in the frequency domain can be achieved. Based on the power spectrum, the natural frequency of each order modal of the structure is determined; based on the natural frequency of the i-th order modal, the filter frequency band of the i-th order modal signal is determined; the first matrix is determined, which comprises information of the i-th order modal signal of each measurement channel after being filtered by the filter frequency band. Thus, after filtering, the noise of the signal has been greatly reduced, which can improve the accuracy of the modal parameters and reduce the uncertainty. The second matrix is determined based on the first matrix, which is an autocorrelation matrix of the first matrix; singular value decomposition is performed on the second matrix to determine a singular vector corresponding to a maximum singular value; and the modal parameters of the structure are determined based on the singular vector, which are the modal shapes of the structure. Thus, by singular value decomposition, the determination dimension of the modal parameters is reduced, thereby improving the efficiency of determining the modal parameters. Compared with the way of identifying the modal parameters of the structure in the related art which is easily affected by the environment and low in efficiency, the method of identifying the modal parameters of the structure in the present application can solve the technical problems of inaccurate and low-efficiency identification of the modal parameters of the structure, and can achieve the technical effects of higher accuracy of identifying the modal parameters of the structure and higher efficiency of identifying the modal parameters of the structure.

[0077] In some embodiments, referring to Figure 2 , step 107 comprises:

[0078] Step 201: performing singular value decomposition on the second matrix to obtain a third matrix and a fourth matrix, the third matrix being a unitary matrix, and the fourth matrix being a diagonal matrix;

[0079] Step 202: determining a singular vector corresponding to a maximum singular value based on the third matrix and the fourth matrix.

[0080] For example, singular value decomposition of using the SVD function in MATLAB can obtain a unitary matrix (corresponding to the third matrix) and a diagonal matrix, which is (corresponding to the fourth matrix). Extract the singular vector corresponding to the maximum singular value . .

[0081] In some embodiments, referring to Figure 3 , the method further comprises:

[0082] Step 301: determining a modal parameter of the structure based on the singular vector.

[0083] In some embodiments, the modal parameter is a modal shape of the structure.

[0084] In some embodiments, the singular vector obtained in step 202 is the modal shape.

[0085] Step 302: determining a standard deviation of the modal shape based on the modal shape.

[0086] In some embodiments, referring to Figure 4 , the method further comprises:

[0087] Step 401: determining a modal shape;

[0088] Step 402: determining a standard deviation corresponding to the modal shape.

[0089] In some embodiments, the modal parameter is a modal shape; determining a fifth matrix based on the third matrix and the fourth matrix, the fifth matrix being a covariance matrix; determining a standard deviation based on diagonal elements in the fifth matrix; and calculating a standard deviation corresponding to the modal shape based on the standard deviation.

[0090] For example, the covariance matrix of the modal shape can be obtained by the following formula:

[0091]

[0092] wherein, , , may be obtained from the foregoing examples, in response to the total number of points, for measuring the number of channels.

[0093] Step 303, determining modal response information based on the modal shape and the first matrix.

[0094] Step 304, performing Fourier transform on the modal response information to determine the autocorrelation power spectrum of the modal response.

[0095] Step 305, determining a target function to be optimized containing the autocorrelation power spectrum.

[0096] Step 306, determining the modal frequency and modal damping ratio based on the target function.

[0097] In some embodiments, referring to Figure 5 , the foregoing method comprises:

[0098] Step 501, determining modal response information associated with the peak point of the i-th order modal based on the first matrix and the singular vector.

[0099] For example, the modal response information The acquisition formula can be:

[0100]

[0101] Step 502, performing Fourier transform on the modal response information to determine the autocorrelation power spectrum density matrix of the modal response.

[0102] For example, The autocorrelation power spectrum density vector .

[0103]

[0104] wherein each operation identifier is consistent with the definition of the foregoing operation identifier.

[0105] Step 503, determining a target function to be optimized containing the autocorrelation power spectrum density matrix.

[0106] For example, the target function can be:

[0107]

[0108] wherein , represents , , and the set of , , , and is a target value to be solved. is a power spectral density of the exciting force; is a power spectral density of the noise; is a frequency to be identified; is a damping to be identified.

[0109] Step 504, determining the modal parameters based on the objective function, the modal parameters including the frequency and the damping.

[0110] The frequency can be referred to as a modal frequency, and the damping can be referred to as a modal damping ratio.

[0111] Step 307, determining the variance corresponding to the modal frequency and the modal damping ratio respectively based on the modal frequency and the modal damping ratio.

[0112] In this way, while identifying the modal shape, the modal damping ratio and the modal frequency, the standard deviation or variance of the identification result is calculated synchronously as the best estimate, and the uncertainty of the identification result is quantified. Compared with the related art, the method for identifying the structural modal parameters can solve the technical problems of inaccurate identification of the structural modal parameters, low efficiency and large uncertainty, and can achieve the technical effects of higher accuracy of the identification of the structural modal parameters, higher efficiency of the identification of the structural modal parameters and reduced uncertainty.

[0113] In some embodiments, referring to Figure 6 , the method further includes:

[0114] Step 601, determining a sixth matrix based on the objective function, the sixth matrix being a Hessian matrix;

[0115] Step 602, determining the variance of the modal frequency and the modal damping ratio based on the diagonal elements of the inverse matrix of the sixth matrix.

[0116] For example, the Hessian matrix at , , and is solved , and the inverse of the matrix is obtained , The diagonal elements of the matrix are the variances of , , and .

[0117] For a more complete and comprehensive understanding of the above embodiments, the following is described by an exemplary embodiment:

[0118] The present application proposes a new framework of time-frequency domain operational modal analysis based on Bayesian inference, called Bayesian modal spatio-temporal decomposition method (BMSD). The core idea of the method is to reduce the dimension of the optimization problem by using a two-stage decomposition framework, effectively reducing the number of parameters in the optimization stage, improving the overall operational efficiency, improving the accuracy of the Bayesian method through modal decomposition and spatio-temporal decomposition, and reducing the uncertainty of damping identification, thereby improving the efficiency and accuracy of practical engineering applications.

[0119] It should be noted that the core logic of Bayesian modal parameter identification is to convert all the modal parameters to be identified: frequency, damping, and mode shape into an optimization problem for solving. For example, a large-span bridge has 10 measurement accelerometers installed. Assuming we want to identify the parameters of the first-order mode of the bridge, then it includes the first-order frequency, damping, and mode shape (10 channels) a total of 12 parameters. Assuming that the modal parameters of the first four orders are to be identified, then 48 parameters need to be solved in the optimization solution. The method of the present disclosure is to decompose in two layers, the first layer is to separate each order of modal identification by means of filter, corresponding to the following step S4. The second layer is to identify the mode shape first (without optimization solution) and then identify the frequency and damping (by optimization solution) for the separated modal parameters, which corresponds to steps S5 and S6. In this way, the number of parameters for each optimization solution is reduced from 48 to 8 (divided into four times, each time 2). The dimension of the optimization solution problem is greatly reduced. The higher the dimension of the optimization solution problem, the lower the accuracy of the solution, and the lower the computational efficiency, which is the advantage of the method.

[0120] It should be noted that the modal decomposition corresponds to the filter modal decomposition in the following step S4. The spatio-temporal decomposition corresponds to steps S5 and S6. Here, the damping identification uncertainty is reduced because after decomposition, the parameters for each optimization solution are frequency and damping, and the low-dimensional optimization problem identification result is relatively accurate and has small uncertainty. On the other hand, the signals used for optimization solution (modal response in the following step S8) are filtered and obtained by steps S5-S6, in which the noise has been greatly reduced, which helps to improve the accuracy of damping identification and reduce uncertainty.

[0121] The method comprises:

[0122] Step S1, collecting the structural dynamic response of the structure (corresponding to the target structure) in the running state (which can be acceleration, speed or displacement, corresponding to dynamic response information). The number of measurement channels for each set of dynamic response is The total number of response points is .

[0123] Step S2: Perform Fourier transform on all channels respectively, and then use formula (1) to calculate the power spectral density matrix of the structure.

[0124] (1)

[0125] in, Indicates the Fourier transform, This represents dividing the signal into M segments, where r represents the index of the number of segments. It is the first physical frequency points The index, where , Indicates frequency resolution. This represents the transpose of a vector. This represents the conjugate transpose of a complex vector. Represents the signal at a frequency point The corresponding power spectral amplitude at that location.

[0126] Step S3: Using the peak picking method, obtain the x and y coordinates of the peak points of each mode. Assume the... The x-axis (frequency) corresponding to the peak point of the first mode is: The corresponding ordinate is .

[0127] Step S4: Use filtering techniques to extract the i-th order mode signal, and select the filtering frequency band as [missing information]. Store all filtered channel signals as a single... matrix middle.

[0128] Step S5: Solve for the autocorrelation matrix using the following formula. :

[0129] (2)

[0130] Step S6, use the SVD function in MATLAB to... Singular value decomposition yields a unitary matrix. and diagonal array Extracting the maximum singular value. The corresponding singular vector This serves as the result of modal mode identification.

[0131] Step S7, the covariance matrix of the mode shape can be calculated by equation (3). The standard deviation (SD) of each element in the covariance matrix can be obtained from the covariance matrix. extracted from the diagonal elements of

[0132] (3)

[0133] wherein , , are obtained from step S6.

[0134] Step S8, the modal response of the i-th order is calculated by using formula (4) :

[0135] (4)

[0136] Step S9, Fourier transform is performed on , and the self-power spectral density vector of is calculated by using formula (5) .

[0137] (5)

[0138] wherein each operator symbol has the same meaning as in formula (1).

[0139] Step S10, the objective function to be optimized and solved is constructed, as shown in the following formula:

[0140] (6)

[0141] wherein , represent the set of , , and , , , , and are the objective values to be solved. is the power spectral density of the exciting force; is the power spectral density of the noise; is the frequency to be identified; is the damping to be identified;

[0142] Step S11, the initial values of , , and are selected, the fmincon function in MATLAB is used for optimization and solving, and the solved , , and optimal value , , and .

[0143] Step S12, solving At , , and Hessian matrix , and the inverse of the matrix is obtained , The diagonal elements of the matrix are the variances of , , and .

[0144] In the above example, in terms of processing efficiency, since the response is first filtered and decomposed into two layers of decomposition strategy, the optimization solution of the objective function only contains 4 parameters, and the modal identification result can be obtained directly from the singular vector, which greatly reduces the number of parameters in the traditional Bayesian modal parameter identification method. The problem of inverse of ill-conditioned matrix in the process of quantifying uncertainty is avoided.

[0145] In the above example, in terms of processing accuracy, the single-mode response after two decompositions is used for damping identification, which maximally reduces the influence of noise on damping identification, improves the calculation accuracy of modal damping ratio, and reduces the uncertainty of damping identification.

[0146] In some embodiments, the method of the above disclosed embodiments is experimentally verified, and the specific conditions are as follows:

[0147] In some embodiments, a ten-story shear frame model is designed to verify the effectiveness of the method according to the characteristics of low-frequency dense modes of large civil engineering structures. The specific parameter settings are: the mass of each layer m = 1 x 10 4 kg, the interlayer stiffness k = 2.5 x 10 5 N / m, to ensure that the natural frequency of the structure is less than 2Hz; the damping ratio is set to 0.5%. It is assumed that each layer is excited by an independent Gaussian white noise with a power spectral density of 10 m²s⁻³; the acceleration response of each layer is recorded at a sampling frequency of 100Hz, and the total duration is 1000 seconds. Each measurement channel is superimposed with a Gaussian white noise with a root mean square (RMS) amplitude of 1μg as measurement noise. Please refer to Figure 7 , which shows the acceleration response time history of the ten measurement channels, please refer to Figure 8 , which gives the power spectral density of the first channel and the frequency band distribution used for modal identification.

[0148] In some embodiments, the modal shape is extracted by the method of the embodiments of the present disclosure first, and Table 1 summarizes the identified modal shape and its coefficient of variation (c.o.v.), Figure 9 The visualization result of the modal shape is given. The coefficient of variation of each modal shape generally remains in the range of 0.01% to 0.1%, indicating that the identification result has a low uncertainty and a high reliability. Such a low level of uncertainty shows that the BMSD method can provide robust and repeatable modal shape estimation. To verify the accuracy of the identification result, Figure 9 The modal assurance criterion (MAC) value between the identified modal shape and the theoretical modal shape is also given. As shown in the figure, all the MAC values are close to 1.0, indicating that the identified modal shape has a high consistency and excellent correlation with the theoretical modal shape.

[0149]

[0150] In some embodiments, the modal frequency and damping ratio are identified based on the modal coordinates by the method of the embodiments of the present disclosure, and Table 2 lists the identified natural frequency, damping ratio, and its corresponding coefficient of variation (c.o.v.) and percentage error. The identification error of the natural frequency is less than 0.5%, and the coefficient of variation is also less than 0.5%; while the identification error of the damping ratio ranges from 5% to 20%, and the coefficient of variation of part of the modes (Xth and Yth) is relatively large, and the coefficient of variation of the remaining damping ratios is less than 10%, indicating that the damping ratio identification result has a relatively high uncertainty. This finding is consistent with the conclusions of existing research.

[0151]

[0152] Through the description of the above embodiments, those skilled in the art can clearly understand that the method according to the above embodiments can be realized by means of software and the necessary general hardware platform, of course, it can also be realized by hardware, but in many cases the former is a better embodiment.

[0153] Please refer to Figure 10 The embodiments of the present disclosure also provide a device for identifying structural modal parameters, comprising:

[0154] The acquisition module 101 is configured to acquire dynamic response information of the structure in the running state through a measurement channel, and the dynamic response information includes acceleration response information or speed response information or displacement response information.

[0155] The determination module 102 is configured to perform Fourier transform on the dynamic response information to determine the power spectrum of the structure, and determine the natural frequency of each modal of the structure based on the power spectrum. ; wherein i is a modal index, k is an index of a physical frequency point, i and k are positive integers greater than 0; determining a filter frequency band of the i th modal signal based on a natural frequency of the i th modal; determining a first matrix, the first matrix comprising information of the i th modal signal filtered by the filter frequency band of each of the measurement channels; determining a second matrix based on the first matrix, the second matrix being an autocorrelation matrix of the first matrix; performing singular value decomposition on the second matrix to determine a singular vector corresponding to a maximum singular value; and determining a modal parameter of the structure based on the singular vector, the modal parameter being a modal shape of the structure.

[0156] The features of the embodiments of the device for identifying modal parameters of a structure can be understood in conjunction with the related descriptions of the embodiments of the method for identifying modal parameters of a structure, which will not be repeated here.

[0157] Embodiments of the present application also provide an electronic device, comprising a memory and a processor, the memory storing a computer program, and the processor being configured to execute the computer program to perform the steps in any of the above method embodiments for identifying modal parameters of a structure.

[0158] Embodiments of the present application also provide a computer readable storage medium storing a computer program, wherein the computer program is configured to perform the steps in any of the above method embodiments for identifying modal parameters of a structure when executed.

[0159] In an example embodiment, the above computer readable storage medium can include, but is not limited to, a U disk, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and various media that can store computer programs.

[0160] Embodiments of the present application also provide a computer program product comprising a computer program, the computer program being executed by a processor to perform the steps in any of the above method embodiments for identifying modal parameters of a structure.

[0161] Embodiments of the present application also provide another computer program product comprising a non-volatile computer readable storage medium storing a computer program, the computer program being executed by a processor to perform the steps in any of the above method embodiments for identifying modal parameters of a structure.

[0162] While the present application has been described with reference to the preferred embodiments, it is to be understood that various modifications can change the scope of the present application to which they are not intended to deviate. In particular, the technical features mentioned in the various embodiments can be combined in any manner, provided that there is no structural conflict. The present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method of identifying structural modal parameters, characterized by, The method comprises: obtaining dynamic response information of the structure in the running state by measuring the channel acquisition structure, the dynamic response information comprising acceleration response information or speed response information or displacement response information; performing Fourier transform on the dynamic response information to determine the power spectrum of the structure; determining a natural frequency of each mode of the structure based on the power spectrum ; wherein, is a mode index, is an index of a physical frequency point, and is a positive integer greater than 0. based on the natural frequency of the first order mode, determine a filter band for the first order mode signal; determining a first matrix comprising information of each of the measurement channels filtered by the filter bands of the order modal signals; determining a second matrix based on the first matrix, the second matrix being an autocorrelation matrix of the first matrix; performing singular value decomposition on the second matrix to determine a singular vector corresponding to the maximum singular value; determining the modal parameters of the structure based on the singular vector, the modal parameters being the modal shapes of the structure; determining the standard deviation corresponding to the modal shape based on the modal shape; determining modal response information based on the modal shape and the first matrix; a formula for determining the modal response information comprises: , is a singular vector, is a signal matrix, the is a signal acquisition time; Performing a Fourier transform on the modal response information determines an autocorrelation power spectrum of the modal response; determining the autocorrelation power spectrum includes: , represents dividing the signal into segments, subscript is the index of the physical frequency point , wherein, is the power spectrum; determining a target function to be optimized comprising the autocorrelation power spectrum; the target function being: wherein representing , , and a set, , , , and a target value to be solved; is the power spectral density of the excitation force; is the power spectral density of the noise; is the frequency to be identified; is the damping to be identified; determining the modal frequency and the modal damping ratio based on the objective function; determining the variances corresponding to the modal frequency and the modal damping ratio respectively based on the modal frequency and the modal damping ratio.

2. The method of claim 1, wherein, The formula for determining the power spectrum of the structure comprises: wherein, denotes the power response information of a Fourier transform, denotes a division of the signal into segments, denotes an index of the number of segments, the index is the index of the physical frequency point , wherein , denotes the frequency resolution, denotes the vector transpose, denotes the complex vector conjugate transpose, denotes the power spectral amplitude corresponding to the signal at the frequency point ; The formula for determining the second matrix comprises: , is a matrix of signals in each of the measurement channels.

3. The method of claim 1, wherein, The method further comprises: filtering the measurement channels based on the filter band to obtain the i-th order modal signal of the plurality of measurement channels; The filter frequency band is .

4. The method of claim 1, wherein, The step of performing singular value decomposition on the second matrix to determine a singular vector corresponding to the maximum singular value comprises: performing singular value decomposition on the second matrix to obtain a third matrix and a fourth matrix, the third matrix being a unitary matrix, and the fourth matrix being a diagonal matrix; the unitary matrix is , and the diagonal matrix is , wherein is the maximum singular value of the mth order mode, is the corresponding singular vector, is the number of measurement channels, is the singular value in the diagonal matrix except , is the singular value in the diagonal matrix except , is the corresponding eigenvector. determining the singular vector corresponding to the maximum singular value based on the third matrix and the fourth matrix.

5. The method of claim 4, wherein, The method further comprises: determining a fifth matrix based on the third matrix and the fourth matrix, the fifth matrix being a covariance matrix; wherein a formula for determining the fifth matrix is: wherein, , and are obtained based on singular value decomposition of the second matrix, is a total number of responses, the is a maximum singular value of the first order modal. determining the standard deviation based on the diagonal elements in the fifth matrix.

6. The method of claim 1, wherein, The method further comprises: determining a sixth matrix based on the objective function, the sixth matrix being a Hessian matrix; The step of determining the variances corresponding to the modal frequency and the modal damping ratio respectively based on the modal frequency and the modal damping ratio comprises: determining the variances of the modal frequency and the modal damping ratio based on the diagonal elements of the inverse matrix of the sixth matrix.

7. An electronic device, comprising: It comprises: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the method for identifying the modal parameters of the structure according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, wherein the computer program is executed by the processor to implement the steps of the method for identifying the modal parameters of the structure according to any one of claims 1 to 6.

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