Method for improving weak modal recognition precision in random subspace method modal recognition

Abstract

The invention discloses a method for improving weak modal recognition precision in random subspace method modal recognition. The method comprises the following steps: performing noise reduction on a signal through symplectic geometry mode decomposition, constructing a track matrix for a noisy signal, solving a characteristic value and a corresponding initial single component by utilizing symplectic geometry similarity transformation, eliminating a noise component by introducing a singular entropy increment first-order sensitivity index, and further superposing the reserved initial single component signals to obtain a reconstructed signal; and finally, identifying modal parameters of the structure by adopting a random subspace method according to the reconstructed signal. According to the method, the noise influence among all modes can be effectively eliminated, the mode parameter identification performance of the random subspace method under the low signal-to-noise ratio is ensured, and particularly, the identification precision of a weak mode can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing and structural modal parameter identification and analysis, and specifically relates to a method for improving the accuracy of structural weak mode identification under low signal-to-noise ratio. Background Art

[0002] Modal identification plays an important role in civil engineering, machinery, aerospace and other fields. It provides indispensable data support for monitoring work such as structural model modification, damage identification and safety assessment. However, when collecting signals, they are often inevitably affected by external noise, resulting in reduced modal identification accuracy and weak modal information being submerged by noise, resulting in modal omissions. Therefore, eliminating noise in the signal is an effective way to ensure the accuracy of modal identification results.

[0003] However, the existing signal denoising methods still have certain defects, which makes them difficult to apply in modal identification. For example, in wavelet analysis denoising, the wavelet basis function and decomposition parameters are difficult to determine; the noise of singular value decomposition is distributed at various orders, resulting in incomplete denoising; the decomposition ability of empirical mode decomposition is poor under noise interference; the decomposition effect of variational mode decomposition is highly dependent on two parameters: the penalty factor and the number of decomposition layers, and it is difficult to optimize these two parameters.

[0004] Especially in strong noise environments, existing signal denoising methods have problems such as insufficient decomposition capabilities, which makes it difficult to identify weak modes or unreliable identification results when identifying modal parameters.

[0005] The present invention proposes a method for solving the problem that the modal recognition result of a structure is unreliable when the structure is in a low signal-to-noise ratio background under environmental excitation. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for improving the accuracy of identifying weak modes by the random subspace method, so as to solve the problem that weak modes are difficult to identify in the existing modal identification. In order to achieve the above invention purpose, the technical solution adopted by the present invention is:

[0007] A method for improving the accuracy of weak mode recognition in random subspace method mode recognition comprises the following steps:

[0008] Step 1: For a response signal x = [x1, x2, x3, …, xn] of length n, construct a trajectory matrix X, where the dimension of X is determined by the following formula: m = n-(d-1)τ, τ is the time delay, generally τ = 1, d is the embedding dimension, and d = 1.8 × (fs / f0), f0 is the lowest frequency of the system, and fs is the sampling frequency of the signal;

[0009] Step 2: Use the trajectory matrix X to establish the covariance matrix A = X^TX, and construct the Hamiltonian matrix M, and obtain the eigenvalues ​​of A and their corresponding eigenvectors through symplectic geometric similarity transformation;

[0010] Step 3: Use the singular entropy increment first-order sensitivity index to sort and truncate the eigenvalues ​​to eliminate the noise component. The specific calculation formula is: Ei = f(λi, ΔEi) (where λi is the i-th order eigenvalue, ΔEi is the i-th order singular entropy increment, and Ei is the i-th order sensitivity). The components exceeding the set threshold are regarded as noise and eliminated, and the retained components are regarded as effective components.

[0011] Step 4: Reconstruct the retained effective components by superposition to obtain the noise reduction signal;

[0012] Step 5: Use the random subspace method to process the denoised signal and identify and obtain the modal parameters of the structure.

[0013] Optionally, the calculation formula for the embedded dimension d in step one is d=1.8×(fs / f0), where f0 represents the lowest frequency of the system and fs represents the sampling frequency of the signal.

[0014] Optionally, the first-order sensitivity Ei of the singular entropy increment in step 3 is used to determine the truncation order to ensure the retention of effective components and the elimination of noise components.

[0015] Optionally, through the noise reduction processing of step three and step four, the accuracy of the random subspace method in weak mode recognition can be effectively improved, which is particularly suitable for low signal-to-noise ratio environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flow chart of a method for improving the accuracy of weak mode recognition in random subspace method mode recognition according to the present invention;

[0017] Figure 2 is a graph of singular entropy increment and first-order sensitivity;

[0018] Figure 3 It is the time domain diagram of noisy signal and noise-reduced signal;

[0019] Figure 4 The spectrum diagram of the denoising process, (a) is the spectrum diagram of the symplectic geometric mode decomposition (SGMD), (b) is the spectrum diagram of the empirical mode decomposition (EMD), (c) is the spectrum diagram of the variational mode decomposition (VMD), (d) is the spectrum diagram of the singular value decomposition (SVD);

[0020] Figure 5 The noisy signal and the denoised signal obtained by the method of the present invention are further identified using the random subspace method. (a) and (b) are the first two-order frequencies, vibration modes and MAC values ​​of the structure identified under the noisy signal, and (c) and (d) are the first two-order frequencies, vibration modes and MAC values ​​of the structure identified under the denoised signal by the present invention. DETAILED DESCRIPTION

[0021] The following will be combined with the embodiments of the present invention Figure 1-Figure 5 , the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0022] The present invention provides a method for improving the accuracy of identifying weak modes by a random subspace method, by introducing symplectic geometric mode decomposition for noise reduction, using the reconstructed trajectory matrix to perform symplectic geometric similarity transformation, obtaining the corresponding eigenvalues ​​and corresponding eigencomponents, determining the truncation order by singular entropy increment and first-order sensitivity, superimposing and reconstructing the components before truncation as effective components, realizing signal noise reduction, and finally using the random subspace method to identify the natural frequency, vibration mode and damping ratio of the structure. The invention relates to the field of dynamic signal processing, and in particular to the measurement of structural dynamic characteristics.

[0023] The complete technical solution of the present invention is as follows:

[0024] refer to Figure 1 , a method for improving the accuracy of weak mode recognition in random subspace method modal recognition, comprising the following steps:

[0025] Step 1: For the response signal x = [x1, x2, x3, ..., xn], n is the data length. Construct a trajectory matrix X:

[0026]

[0027] In the formula, m = n-(d-1)τ; τ represents the time delay, which is generally taken as τ = 1; d represents the embedding dimension, d = 1.8×(fs / f0), f0 represents the lowest frequency of the system, and fs represents the sampling frequency of the signal.

[0028] Step 2: Using the trajectory matrix X, we can establish the covariance matrix A = XTX, and further construct the Hamiltonian matrix M:

[0029]

[0030] At the same time, the eigenvalues ​​and corresponding eigenvectors of A are obtained through symplectic geometric similarity transformation.

[0031] Step 3: The noise reduction signal is obtained by screening the effective components and reconstructing them. The singular entropy increment first-order sensitivity is used for sorting and truncation, and the components exceeding the threshold are removed as noise. The calculation formula of the singular entropy increment first-order sensitivity is as follows:

[0032]

[0033] E i =E i =ΔE i+1 -ΔE i

[0034] Where λi represents the i-th order eigenvalue, ΔEi is the i-th order singular entropy increment, and Ei is the i-th order sensitivity.

[0035] Step 4: Use the random subspace method to process the denoised signal and obtain the modal parameters of the structure; refer to Figure 2 In step 2, the first-order sensitivity becomes flat around the 130th order.

[0036] Although the existing denoising methods can improve the accuracy of random subspace modal identification, they suffer from modal loss and insufficient denoising capabilities in the context of low signal-to-noise ratio, as well as computational efficiency issues. Although symplectic geometry has strong modal decomposition capabilities, it has problems such as endpoint effects and modal aliasing, which results in certain defects in its reconstruction denoising.

[0037] Therefore, in order to obtain a reliable denoised signal, the present invention uses the first-order sensitivity of the singular entropy increment to determine the effective components after the symplectic geometric similarity transformation, and directly superimposes and reconstructs the denoised signal without considering the influence of endpoint effects and modal aliasing on signal decomposition.

[0038] This method solves the problem that traditional SGMD needs to consider modal aliasing and relies on iteratively increasing the embedding dimension of the trajectory matrix, which causes the amount of calculation to gradually increase. At the same time, compared with other signal processing methods, it will not lose weak modal information, thereby improving the integrity of the denoised signal and the reliability of modal recognition.

[0039] refer to Figure 3 ,Comparing the noisy signal and the SGMD noise reduction signal, it can be seen that the ,purpose of noise reduction is achieved in the present invention.

[0040] refer to Figure 4 By observing the signal under 5dB noise background and the spectrum diagram of each signal processing technology, it can be analyzed that the SGMD method can effectively remove the noise between weak modal information; EMD has poor anti-noise interference ability; although VMD has excellent noise reduction performance, it is highly dependent on the two parameters of penalty factor and decomposition layer number. The optimization algorithm and other methods have low calculation efficiency for its optimization, and the final noise reduction signal still has the problem of weak modal information loss; the noise reduction under SVD is not thorough enough, and its noise information is evenly distributed at each order.

[0041] refer to Figure 5 , the first two modal identification results of the structure under the noisy signal and the noise reduction signal of the present invention are given. The vibration shape identified by the noise reduction signal obtained by the present invention is very close to the theoretical value, while the vibration shape error obtained by direct identification of the noisy signal is very large.

[0042] The present invention does not simply introduce the first-order sensitivity of the singular entropy increment to determine the truncation order to obtain the effective component and superimpose and reconstruct to obtain the noise reduction signal, but combines the signal processing technology with the random subspace method modal recognition technology to improve the accuracy of modal recognition by eliminating the noise influence between modes, and has a subsequent program to verify whether the obtained data is reliable and whether it can be used for subsequent research.

[0043] The above description is only a preferred example of the present invention and is not intended to limit the present invention. Without departing from the design spirit of the present invention, various deformations, modifications, and substitutions made to the technical solution of the present invention by ordinary technicians in this field should fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for improving the accuracy of weak mode recognition in random subspace method modal recognition, characterized in that The following steps are involved: Step 1: For a response signal x = [x1, x2, x3, …, xn] of length n, construct a trajectory matrix X, where the dimension of X is determined by the following formula: m = n-(d-1)τ, τ is the time delay, generally τ = 1, d is the embedding dimension, and d = 1.8 × (fs / f0), f0 is the lowest frequency of the system, and fs is the sampling frequency of the signal; Step 2: Use the trajectory matrix X to establish the covariance matrix A = X^TX, and construct the Hamiltonian matrix M, and obtain the eigenvalues ​​of A and their corresponding eigenvectors through symplectic geometric similarity transformation; Step 3: Use the singular entropy increment first-order sensitivity index to sort and truncate the eigenvalues ​​to eliminate the noise component. The specific calculation formula is: Ei = f(λi, ΔEi) (where λi is the i-th order eigenvalue, ΔEi is the i-th order singular entropy increment, and Ei is the i-th order sensitivity). The components exceeding the set threshold are regarded as noise and eliminated, and the retained components are regarded as effective components. Step 4: Reconstruct the retained effective components by superposition to obtain the noise reduction signal; Step 5: Use the random subspace method to process the denoised signal and identify and obtain the modal parameters of the structure.

2. The method according to claim 1, characterized in that The calculation formula of the embedding dimension d in step 1 is d=1.8×(fs / f0), where f0 represents the lowest frequency of the system and fs represents the sampling frequency of the signal.

3. The method according to claim 1, characterized in that The first-order sensitivity Ei of the singular entropy increment in step 3 is used to determine the truncation order to ensure the retention of effective components and the elimination of noise components.

4. The method according to claim 1, characterized in that Through the noise reduction processing in steps three and four, the accuracy of the random subspace method in weak mode recognition can be effectively improved, which is particularly suitable for low signal-to-noise ratio environments.

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