Structural damping ratio identification method and device considering frequency spectrum leakage error compensation

Abstract

The invention discloses a structural damping ratio identification method and device considering frequency spectrum leakage error compensation. The method comprises the following steps: firstly, obtaining a cut-off free attenuation signal under impact vibration, and carrying out Fourier transform on an autocorrelation function and a cross-correlation function of the signal to obtain a response power spectral density matrix influenced by a spectrum leakage error; singular value decomposition is carried out on the response power spectrum density function through a frequency domain decomposition method to obtain a damping ratio and an inherent frequency, a spectrum leakage error is calculated through the calculated inherent frequency and the damping ratio, and the error obtained through calculation is substituted into an output power spectrum. And the inherent frequency and the damping ratio are identified by using the power spectrum after the frequency spectrum leakage error is compensated, and the above process is iterated for multiple times, so that the frequency spectrum leakage error in damping ratio identification can be compensated. When the free attenuation data is used for identifying the damping ratio, spectrum leakage errors caused by data truncation can be made up, the signal-to-noise ratio of the data can be improved, the influence of noise can be reduced, and the identification precision of the damping ratio is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering structure detection data analysis, and relates to a method and device for identifying a structural damping ratio under an impact test. Background Art

[0002] Engineering structure inspection is an important means of regularly maintaining structures and ensuring their safety. Modal parameters reflect the dynamic characteristics of structures and can often be used to analyze the safe in-service status of bridges. Therefore, accurately identifying modal parameters is very important for bridge health inspection.

[0003] As one of the most important modal parameters, damping reflects a structure's ability to dissipate vibration energy. Its identification is crucial for evaluating a structure's dynamic characteristics. In practical engineering, damping not only helps reduce the amplitude of structural resonance, preventing damage caused by dynamic response reaching ultimate stress, but also helps the structure quickly recover to a stable state when subjected to dynamic forces.

[0004] There are many common damping identification methods in engineering. In 2010, Han Jianping et al. proposed a new modal parameter identification method based on natural excitation technology to identify the modal frequency and modal damping ratio of the structure; in 2020, Wan Xi et al. proposed a damping ratio identification method for civil engineering structures based on improved empirical wavelet transform under environmental excitation; in 2016, Wang proposed a frequency domain spatial decomposition method, which uses mode shape orthogonality to construct an expression for the enhanced output power spectrum and uses it to identify the natural frequency and damping ratio; in 2023, Qu et al. proposed an iterative frequency domain decomposition method to solve the problem of inaccurate damping ratio identification caused by time-frequency transformation of the frequency domain decomposition method under environmental excitation. Impact vibration testing is a common means of damping ratio identification. Damping ratio analysis is performed through the free decay data of the structure. Truncating the data at the end of the decay period can improve the signal-to-noise ratio of the free decay data and reduce the impact of environmental noise on damping ratio identification, but it also introduces spectrum leakage errors. Summary of the Invention

[0005] The present invention aims to provide a method and device for compensating for spectrum leakage errors in damping ratio identification, thereby solving the problem of inaccurate damping ratio identification due to data truncation during shock and vibration testing using structural free attenuation data to identify the damping ratio.

[0006] The technical solution of the present invention:

[0007] A structural damping ratio identification method considering compensation for spectrum leakage error has the following steps:

[0008] (1) Structural response analysis and initial modal parameter identification

[0009] The displacement response of the structure is obtained and its correlation function is obtained by using the displacement response. The correlation function is Fourier transformed to obtain the power spectrum density function, and then the power spectrum density function matrix of the displacement response is obtained; the diagonal of the power spectrum density function matrix of the displacement response is the self-power spectrum density function of each degree of freedom, and the non-diagonal is the cross-spectrum density function between different degrees of freedom; the power spectrum density function matrix of the displacement response is subjected to singular value decomposition, the maximum singular value s and its corresponding unitary matrix u are retained, and then the curve of the maximum singular value s with respect to the frequency ω is drawn. The frequencies corresponding to the different peak points of the curve are the natural frequencies of each mode of the structure, that is, ω1~ω m , the unit matrix u1~u corresponding to the peak point m The vibration mode of the structure Let the initial solution order be n=1;

[0010] (2) Calculation of the output power spectrum of the structural single-order modal contribution

[0011] Use the structure's mode shapes And the power spectrum density function matrix G of the displacement response of the structure yy (ω) Output power spectrum of the single-order modal contribution of the constructed structure And draw the curve, let the initial iteration number k = 1;

[0012] (3) Identification of structural damping ratio

[0013] The damping ratio of the structure is calculated using the half-power bandwidth method, and the output power spectrum G of the single-order mode contribution of the structure is converted to yy n (ω) Two frequency points corresponding to half the peak height of the curve f n 1,k ,f n 2,k Substitute into the damping ratio calculation formula of the structure Calculate the damping ratio ξ of the nth mode of the structure n The k-th iteration value of ;

[0014] (4) Calculation of structural spectrum leakage error

[0015] The acquisition time t of the structural response m , calculate the damping ratio ξ of the structure n k The kth iteration value of and the identified natural frequency ω n Calculate the spectral leakage error of the structure and substitute these parameters into the formula of the spectral leakage error function of the structure In the equation, the spectrum leakage error function corresponding to the k-th iteration of the n-th mode of the structure is calculated, where j is the imaginary unit and ω is the frequency variable;

[0016] (5) Compensation of spectrum leakage error in structural damping ratio identification

[0017] Considering the damping ratio of the structure, the output power spectrum G of the single-order mode contribution is required. yy n (ω) is calculated. In order to calculate the damping ratio without the interference of spectrum leakage error, the spectrum leakage error function E of the structure is n k (ω) is substituted into the leakage error compensation calculation formula of the output power spectrum Calculate the output power spectrum G after compensating for the leakage error yy n,k (ω), and plot G yy n,k (ω) curve, and the two frequency points f corresponding to half the peak height n 1,k+1 ,f n 2,k+1 Substitute it into the damping ratio calculation formula of the half-power band frame method again Calculate the damping ratio ξ of the nth mode n The k+1th iteration value of

[0018] (6) Let k = k + 1, repeat (5) to (6) until The spectrum leakage error can be compensated and the nth-order damping ratio can be obtained;

[0019] (7) Let n = n + 1, and repeat (3) to (7) until n = m, that is, the damping ratio of all modes of the structure is obtained.

[0020] A structural damping ratio identification device for compensating for spectrum leakage error, comprising:

[0021] An acquisition module is used to obtain measured response data of the structure;

[0022] A memory device for storing measured data and a data processing program;

[0023] The processor is used to execute a data processing program in the memory. When the data processing program is executed, the processor will be used to read the measured response data of the structure, where the response data is collected and stored over a period of time; use the data processing program to analyze the measured response data to obtain modal information and obtain the damping ratios of each order of the structure.

[0024] The beneficial effects of the present invention are as follows: when using free decay data to identify the damping ratio, the spectrum leakage error caused by data truncation can be compensated, which not only improves the signal-to-noise ratio of the data and reduces the influence of noise, but also improves the identification accuracy of the damping ratio. DETAILED DESCRIPTION

[0025] The following further illustrates the implementation of the present invention in combination with the technical solution.

[0026] Take a 3-DOF structure as an example. Assume that the mass of each DOF is 1kg, 1.5kg, and 2kg respectively. Its stiffness matrix and damping matrix are as follows:

[0027]

[0028] The excitation is in the form of an impulse function, and the response signal is the displacement of each degree of freedom of the structure.

[0029] (1) Obtain the displacement response of the structure y = [y1(t),y2(t),y3(t)…y m (t)], and the displacement response is used to obtain its correlation function Perform Fourier transform on the correlation function to obtain the power spectrum density function, and then obtain the power spectrum density function matrix 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;

[0030] (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, and then draw the curve of the maximum singular value s with respect to the frequency ω. The frequencies corresponding to the different peak points of the curve are the natural frequencies of each mode of the structure, that is, ω1~ω m , the unit matrix u1~u corresponding to the peak point m Vibration mode Let the initial solution order be n=1.

[0031] From this the natural frequency can be obtained:

[0032] ω=[15.138728.284339.6336]

[0033] Vibration shape:

[0034]

[0035] (3) Use vibration mode to construct the output power spectrum of single-order modal contribution And draw the curve, let the initial number of iterations k = 1.

[0036] (4) G yy n (ω) Two frequency points corresponding to half the peak height of the curve f n 1,k ,f n 2,k Substitute into the formula Obtain the damping ratio ξ of the nth order mode n The k-th iteration value of .

[0037] (5) The acquisition time t of the structural response m , calculate the damping ratio ξ of the structure n k The kth iteration value of and the identified natural frequency ω n Calculate the spectral leakage error of the structure and substitute these parameters into the calculation formula of the spectral leakage error function of the structure The spectrum leakage error corresponding to the k-th iteration of the n-th mode of the structure is calculated.

[0038] (6) E n k (ω) is substituted into the formula Draw G yy n,k (ω) curve, and the two frequency points f corresponding to half the peak height n 1,k+1 ,f n 2,k+1 Substitute into the formula Obtain the damping ratio ξ of the nth order mode n The k+1th iteration value of .

[0039] (7) Let k = k + 1, repeat (4) to (6) until That is, the nth-order damping ratio is obtained.

[0040] (8) Let n = n + 1, and repeat (3) to (7) until n = m, thus obtaining all the damping ratios of the structure.

[0041] Damping ratio of each order of structure:

[0042] ξ=[0.00170.00190.0024]

[0043] The analysis results show that the present invention can effectively compensate for the spectrum leakage error introduced by data truncation, reduce the influence of noise and improve the recognition accuracy of the damping ratio.

Claims

1. A structural damping ratio identification method for compensating for spectrum leakage error, characterized in that: Here are the steps: (1) Structural response analysis and initial modal parameter identification The displacement response of the structure is obtained and its correlation function is obtained by using the displacement response. The correlation function is Fourier transformed to obtain the power spectrum density function, and then the power spectrum density function matrix of the displacement response is obtained; the diagonal of the power spectrum density function matrix of the displacement response is the self-power spectrum density function of each degree of freedom, and the non-diagonal is the cross-spectrum density function between different degrees of freedom; the power spectrum density function matrix of the displacement response is subjected to singular value decomposition, the maximum singular value s and its corresponding unitary matrix u are retained, and then the curve of the maximum singular value s with respect to the frequency ω is drawn. The frequencies corresponding to the different peak points of the curve are the natural frequencies of each mode of the structure, that is, ω1~ω m , the unit matrix u1~u corresponding to the peak point m The vibration mode of the structure Let the initial solution order be n=1; (2) Calculation of the output power spectrum of the structural single-order modal contribution Use the structure's mode shapes And the power spectrum density function matrix G of the displacement response of the structure yy (ω) Output power spectrum of the single-order modal contribution of the constructed structure And draw the curve, let the initial iteration number k = 1; (3) Identification of structural damping ratio The damping ratio of the structure is calculated using the half-power bandwidth method, and the output power spectrum G of the single-order mode contribution of the structure is converted to yy n (ω) Two frequency points corresponding to half the peak height of the curve f n 1,k ,f n 2,k Substitute into the damping ratio calculation formula of the structure Calculate the damping ratio ξ of the structure's nth mode n The k-th iteration value of ; (4) Calculation of structural spectrum leakage error The acquisition time t of the structural response m , calculate the damping ratio ξ of the structure n k The kth iteration value of and the identified natural frequency ω n Calculate the spectral leakage error of the structure and substitute these parameters into the formula of the spectral leakage error function of the structure In the equation, the spectrum leakage error function corresponding to the k-th iteration of the n-th mode of the structure is calculated, where j is the imaginary unit and ω is the frequency variable; (5) Compensation of spectrum leakage error in structural damping ratio identification Considering the damping ratio of the structure, the output power spectrum G of the single-order mode contribution is required. yy n (ω) is calculated. In order to calculate the damping ratio without the interference of spectrum leakage error, the spectrum leakage error function E of the structure is n k (ω) is substituted into the leakage error compensation calculation formula of the output power spectrum Calculate the output power spectrum G after compensating for the leakage error yy n,k (ω), and plot G yy n,k (ω) curve, and the two frequency points f corresponding to half the peak height n 1,k+1 ,f n 2,k+1 Substitute it into the damping ratio calculation formula of the half-power band frame method again Calculate the damping ratio ξ of the nth mode n The k+1th iteration value of (6) Let k = k + 1, repeat (5) to (6) until The spectrum leakage error can be compensated and the nth-order damping ratio can be obtained; (7) Let n = n + 1, and repeat (3) to (7) until n = m, that is, the damping ratio of all modes of the structure is obtained.

2. A structural damping ratio identification device for compensating for spectrum leakage error, characterized in that: The device for identifying the structural damping ratio under impact vibration testing includes: An acquisition module is used to obtain measured response data of the structure; A memory device for storing measured data and a data processing program; The processor is used to execute a data processing program in the memory. When the data processing program is executed, the processor will be used to read the measured response data of the structure, where the response data is collected and stored over a period of time; use the data processing program to analyze the measured response data to obtain modal information and obtain the damping ratios of each order of the structure.

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