A method and device for identifying structural modal parameters with known excitation and response

Abstract

The present invention belongs to the technical field of engineering structure detection data analysis, and proposes a method and device for identifying structural modal parameters with known excitation and response. The excitation signal of the structure and the response signal of the structure are obtained, and the autocorrelation function of the signal is Fourier transformed to obtain the power spectrum matrix of the excitation and the power spectrum matrix of the response. The power spectrum matrix of the response is subjected to singular value decomposition by the frequency domain decomposition method, and the unitary matrix and frequency corresponding to the maximum singular value peak are obtained. The transpose and unitary matrix of the obtained unitary matrix are multiplied on the left and right sides of the response power spectrum matrix and the excitation power spectrum matrix to obtain an enhanced response power spectrum and an enhanced excitation power spectrum. The ratio of the two is a single-peak function, and the corresponding unitary matrix and frequency are the vibration mode and natural frequency of the structure. The present invention solves the problem of modal parameter identification caused by false modal interference caused by excitation in the current method for identifying modal parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering structure detection data analysis, and in particular to a method and device for identifying structural modal parameters with known excitation and response. Background Art

[0002] Engineering structure inspection is an important means to regularly maintain structures and ensure structural safety. Modal parameters reflect the dynamic characteristics of structures and can be used to evaluate structural performance. Therefore, it is crucial to use structural inspection data to identify structural modal parameters.

[0003] The modal parameters of a structure, including natural frequency and mode shapes, are determined by the vibration characteristics of the structure itself. In practical engineering, these modal parameters are often used to reflect inherent characteristics such as structural stiffness and to analyze whether the structure is in a safe state. Therefore, accurately identifying modal parameters is extremely important in engineering inspections.

[0004] There are many methods for identifying modal parameters in engineering. Wang Tong proposed FSDD in 2006, using least squares estimation to fit the enhanced output power spectrum function to obtain more accurate modal parameters; Brincker, R. proposed FDD in 2000, which uses singular value decomposition of the output power spectrum of the structure to obtain the vibration mode and natural frequency. The method is simple to use and accurate; Yang applied the blind source separation algorithm to contactless modal parameter identification in 2014, and solved the problem of spectrum aliasing caused by low sampling frequency. In 2020, Haszal proposed an improved FDD method that uses maximum likelihood estimation to update the output power spectrum. This method also has good recognition accuracy under noisy conditions. Identifying the modal parameters of the structure only by the output response can have a high recognition accuracy when it is white noise, but when the excitation is non-stationary, the identification will be interfered by the false modes caused by the excitation. Summary of the Invention

[0005] The present invention is based on solving the problem of modal parameter identification of false modal interference caused by excitation, and provides a method and device for identifying structural modal parameters with known excitation and response.

[0006] The technical solution of the present invention is as follows: The present invention derives a method for identifying structural modal parameters with known excitation and response, first obtaining the excitation signal and the response signal of the structure, performing Fourier transform on the autocorrelation function of the signal to obtain the power spectrum matrix of the excitation and the power spectrum matrix of the response. The power spectrum matrix of the response is subjected to singular value decomposition by the frequency domain decomposition method (FDD), and the unitary matrix and frequency corresponding to the peak of the maximum singular value curve are obtained. The transpose and unitary matrix of the obtained unitary matrix are multiplied on the left and right sides of the response power spectrum matrix and the excitation power spectrum matrix to obtain an enhanced response power spectrum function matrix and an enhanced excitation power spectrum function matrix. If the ratio of the two is a single-peak function, the corresponding unitary matrix and frequency are the vibration mode and natural frequency of the structure.

[0007] A method for identifying structural modal parameters with known excitation and response, the steps are as follows:

[0008] (1) Obtain the response signal of the structure y = [y1(t),y2(t),y3(t)…y n (t)] and the excitation signal x=[x1(t),x2(t),x3(t)…x n (t)], and obtain the cross-correlation function of the response signal and the cross-correlation function of the excitation signal and Perform Fourier transform on the cross-correlation function to obtain the power spectrum function, and then obtain the corresponding power spectrum function matrix The power spectrum function matrix of the sum excitation The diagonal of the power spectrum function matrix is the auto-power spectrum density function of each degree of freedom, and the off-diagonal is the cross-spectrum density function between different degrees of freedom;

[0009] (2) Perform singular value decomposition on the power spectrum function matrix of the response, retain the maximum singular value s and its corresponding unitary matrix u, then draw the curve of the maximum singular value s with respect to the frequency ω, and pick up the unitary matrices u1~u corresponding to all peak points of the maximum singular value curve m and frequencies ω1~ω m ; Let the initial solution order be p=1;

[0010] (3) Using the unitary matrix u p , p∈[1,m], to construct the enhanced response power spectrum function matrix u p T G yy (ω)u p And the enhanced excitation power spectrum function matrix u p T G xx (ω)u p ;

[0011] (4) Use the enhanced response power spectrum function matrix and the enhanced excitation power spectrum function matrix to construct the function When the function is a single peak function, the corresponding unitary matrix u p and the frequency ω is the true mode shape of the structure and the natural frequency When the function is not a single peak function, the corresponding unitary matrix u p And the frequency ω is false modal information and is discarded;

[0012] (5) Let p = p + 1, repeat (3) to (4) until p = m, and obtain the modal parameters of each order of the structure.

[0013] A structural modal parameter identification device with known excitation and response includes: an acquisition module for acquiring measured excitation signal data and response signal data of a bridge;

[0014] A memory device for storing measured excitation signal data, response signal data and a data processing program;

[0015] A processor is configured to execute a data processing program stored in the memory. When the data processing program is executed, the processor is configured to:

[0016] The measured excitation signal data and response signal data of the bridge are read. The excitation signal data and response signal data are collected and stored at the same time. A data processing program is used to analyze the measured excitation signal data and response signal data to obtain modal information and discard false modes to obtain the true modal parameters of the structure.

[0017] Beneficial effects of the present invention: The method proposed in the present invention can eliminate false modes caused by non-stationary excitation when obtaining structural response and excitation signals. Unlike experimental modes, it does not require a fixed excitation form, and only requires obtaining the excitation signal to complete the identification of modal parameters, and has good anti-noise ability. DETAILED DESCRIPTION

[0018] The following further illustrates the implementation of the present invention in combination with the technical solution.

[0019] Taking a 3-DOF structure as an example, assuming that the mass of each degree of freedom is 10 kg, its stiffness matrix and damping matrix are as follows:

[0020]

[0021]

[0022] The form of excitation is non-stationary excitation, and the response signal is the displacement of each degree of freedom of the structure.

[0023] (1) Obtain the response signal of the structure y = [y1(t),y2(t),y3(t)…y n (t)] and the excitation signal x=[x1(t),x2(t),x3(t)…x n (t)], and obtain the cross-correlation function and Perform Fourier transform on the correlation function to obtain the power spectrum function, and then obtain the corresponding power spectrum function matrix And the power spectrum function matrix of the excitation The diagonal line is the auto-power spectral density function of each degree of freedom, and the off-diagonal line is the cross-spectral density function between different degrees of freedom;

[0024] (2) Perform singular value decomposition on the power spectrum function of the response, retain the maximum singular value s and its corresponding unitary matrix u, then draw the curve of the maximum singular value s with respect to the frequency ω, and pick up the unitary matrices u1~u corresponding to all peak points of the maximum singular value curve m and frequencies ω1~ω m ; Let the initial solution order be p=1;

[0025] The unitary matrix u1~u corresponding to the peak value obtained m :

[0026]

[0027] The frequency corresponding to the peak value obtained is:

[0028] ω=[4.9974 11.7326 19.4264 44.7611]

[0029] (3) Use the obtained unitary matrix u p To construct the enhanced response power spectrum function matrix u p T G yy (ω)u p And the enhanced excitation power spectrum function matrix u p T G xx (ω)u p ;

[0030] (4) Use the enhanced response power spectrum function matrix and the enhanced excitation power spectrum function matrix to construct the function If the function is a single peak function, the corresponding identity matrix u p and frequency ω p The vibration mode of the structure and the natural frequency

[0031] (5) Let p = p + 1, repeat (3) to (4) until p = m, and the modal parameters of each order of the structure can be obtained;

[0032] Finally, the vibration modes of each order of the structure are:

[0033]

[0034] Natural frequencies of each order of the structure:

[0035]

Claims

1. A method for identifying structural modal parameters with known excitation and response, characterized in that: Here are the steps: (1) Obtain the response signal of the structure y = [y1(t),y2(t),y3(t)…y n (t)] and the excitation signal x=[x1(t),x2(t),x3(t)…x n (t)], and obtain the cross-correlation function of the response signal and the cross-correlation function of the excitation signal and Perform Fourier transform on the cross-correlation function to obtain the power spectrum function, and then obtain the corresponding power spectrum function matrix The power spectrum function matrix of the sum excitation The diagonal of the power spectrum function matrix is the auto-power spectrum density function of each degree of freedom, and the off-diagonal is the cross-spectrum density function between different degrees of freedom; (2) Perform singular value decomposition on the power spectrum function matrix of the response, retain the maximum singular value s and its corresponding unitary matrix u, then draw the curve of the maximum singular value s with respect to the frequency ω, and pick up the unitary matrices u1~u corresponding to all peak points of the maximum singular value curve m and frequencies ω1~ω m ; Let the initial solution order be p=1; (3) Using the unitary matrix u p , p∈[1,m], to construct the enhanced response power spectrum function matrix u p T G yy (ω)u p And the enhanced excitation power spectrum function matrix u p T G xx (ω)u p ; (4) Use the enhanced response power spectrum function matrix and the enhanced excitation power spectrum function matrix to construct the function When the function is a single peak function, the corresponding unitary matrix u p and the frequency ω is the true mode shape of the structure and the natural frequency When the function is not a single peak function, the corresponding unitary matrix u p And the frequency ω is false modal information and is discarded; (5) Let p = p + 1, repeat (3) to (4) until p = m, and obtain the modal parameters of each order of the structure.

2. A device for identifying structural modal parameters with known excitation and response, characterized in that: Implementing the structural modal parameter identification method with known excitation and response as claimed in claim 1; The structural modal parameter identification device with known excitation and response includes: an acquisition module for acquiring measured excitation signal data and response signal data of a bridge; A memory device for storing measured excitation signal data, response signal data and a data processing program; A processor is configured to execute a data processing program stored in the memory. When the data processing program is executed, the processor is configured to: The measured excitation signal data and response signal data of the bridge are read. The excitation signal data and response signal data are collected and stored at the same time. A data processing program is used to analyze the measured excitation signal data and response signal data to obtain modal information and discard false modes to obtain the true modal parameters of the structure.

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