A cantilever beam damage identification method based on multi-scale reconstruction of attractor multifractal spectrum

Abstract

The present invention provides a cantilever beam damage identification method based on a multi-fractal spectrum of a multi-scale reconstruction attractor, comprising: collecting the original acceleration signal of the cantilever beam through a dynamic force measurement system, performing stationary wavelet decomposition on the pre-processed acceleration signal to obtain a multi-scale sub-signal; selecting a multi-scale sub-signal that can characterize the main vibration characteristics of the cantilever beam for phase space reconstruction and normalization processing to obtain a normalized multi-scale reconstruction attractor; constructing a multi-fractal spectrum of the multi-scale reconstruction attractor, and establishing a damage index based on the singularity index of the multi-fractal spectrum; identifying and locating cantilever beam damage based on the relative numerical size of the damage index. This method can quantify the structural damage characteristics of the multi-scale phase space domain from the perspective of multi-fractals, breaking through the problems of low recognition accuracy, weak damage sensitivity, and insufficient noise resistance in the cantilever beam damage characterization method in the prior art, and providing a simple, fast, and accurate cantilever beam damage identification method.

Description

Technical Field

[0001] The invention relates to the technical field of structural damage diagnosis, and in particular to a cantilever beam damage identification method based on a multi-scale reconstructed attractor multifractal spectrum. Background Art

[0002] During service, beam structures are subjected to long-term effects of complex environmental loads and gradual aging of internal materials, which will inevitably lead to structural damage. The evolution and accumulation of early damage will reduce the structural bearing capacity and threaten its operational safety. In severe cases, it may even lead to overall failure and damage of the structure. Structural dynamic nondestructive testing is an important technology for timely detection of structural damage and plays an irreplaceable role in ensuring the safe operation of structures. However, traditional dynamic nondestructive testing methods are based on linear theory and cannot extract nonlinear features that are more sensitive to damage. In particular, curvature modes used for damage location require differential operations on the modal vibration shapes, which greatly reduces the noise resistance of the resulting damage indicators.

[0003] The damage detection method based on reconstructed attractors is a new structural nondestructive testing method that has emerged with the rapid development of chaos theory. It is currently being gradually applied to structural damage identification in the fields of machinery and civil engineering. The basic principle is that the presence of damage will lead to changes in the dynamic behavior of the structural attractor, and then the damage is identified by comparing the topological morphology differences of the response attractor in the non-destructive and damaged states. On the one hand, the existing methods use the structural dynamic response to directly reconstruct the phase space to obtain the reconstructed attractor, without effectively separating the damage information from the interference noise before reconstruction, which will cause a decrease in the accuracy of loss identification; on the other hand, the existing methods focus more on the topological morphology differences of the reconstructed attractor, but pay less attention to the nonlinear operation laws of complex systems.

[0004] To this end, the present invention proposes a cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum. Summary of the invention

[0005] To solve the above problems, the present invention separates the damage information part and the noise part in the vibration signal through multi-scale analysis, quantitatively describes the influence of damage on the nonlinear motion law of the structure through multi-fractal analysis, and then establishes a damage index based on the multi-fractal characteristics of the multi-scale reconstruction attractor to judge the health state of the beam structure and locate the structural damage. Compared with the existing methods, the multi-fractal spectrum method of the multi-scale reconstruction attractor established by the present invention breaks through the problems of low recognition accuracy, weak damage sensitivity, and insufficient noise resistance in the cantilever beam damage characterization method in the prior art, and provides a simple, fast and accurate cantilever beam damage identification method.

[0006] The present invention provides the following technical solutions.

[0007] A cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum includes the following steps:

[0008] The original acceleration signal of the cantilever beam is collected by the dynamic force measurement system, and the original acceleration signal is preprocessed by smoothing and filtering to obtain a preprocessed acceleration signal;

[0009] Perform stationary wavelet decomposition on the acceleration signal to obtain multi-scale sub-signals with the same data length;

[0010] Multi-scale sub-signals representing the vibration characteristics of the cantilever beam are selected for phase space reconstruction and normalization processing to obtain a multi-scale reconstructed attractor.

[0011] According to the multi-scale reconstruction attractor, a multi-fractal spectrum is formed; and according to the singularity index of the multi-fractal spectrum, a damage index is established;

[0012] The damaged cantilever beam is identified based on the relative numerical values ​​of the damage indicators.

[0013] Preferably, when the acceleration signal is subjected to stationary wavelet decomposition, the wavelet basis function used is rbio2.4 and the number of wavelet decomposition layers is 3.

[0014] Preferably, the selecting of multi-scale sub-signals characterizing the main vibration characteristics of the cantilever beam for phase space reconstruction and normalization processing comprises the following steps:

[0015] The stationary wavelet transform approximate coefficients containing the main frequency range of structural vibration are used as multi-scale sub-signals to characterize the main vibration characteristics of the structure, and after boundary truncation processing, they are recorded as multi-scale sub-signals s;

[0016] The phase space is reconstructed for the truncated multi-scale sub-signal s to obtain a multi-scale reconstructed attractor;

[0017] The multi-scale reconstructed attractor is normalized so that the value range of each phase space dimension is [0,1].

[0018] Preferably, in the boundary truncation processing of the multi-scale sub-signal, the boundary truncation lengths on the left and right sides of the multi-scale sub-signal are both 1% of the total length of the sub-signal.

[0019] Preferably, the phase space reconstruction of the multi-scale sub-signal s comprises the following steps:

[0020] The coordinates of the phase point in the reconstructed attractor Y are calculated as follows:

[0021] y k =(s k ,s k +τ,…,s k +(m-1)τ)

[0022] In the formula, y k represents the kth phase point in the reconstructed attractor Y, s k represents the kth signal amplitude of the multi-scale sub-signal after truncation, m and τ are the embedding dimension and delay time of the embedding parameters;

[0023] Calculate the covariance matrix C of the reconstructed attractor Y:

[0024] C=Y T Y

[0025] Perform eigenvalue decomposition on the covariance matrix C:

[0026] C=ΦΛΦ -1

[0027] Where Φ is a square matrix whose columns are eigenvectors, and Λ is a diagonal matrix whose main diagonal elements are eigenvalues;

[0028] Projecting the reconstructed attractor Y along its first principal direction yields:

[0029] Z=YΦ

[0030] Z is the multi-scale reconstructed attractor obtained by phase space reconstruction.

[0031] Preferably, the embedding parameters of the phase space reconstruction are m=2 and τ=1.

[0032] Preferably, the construction of the multifractal spectrum comprises the following steps:

[0033] Count the total number of phase points of the multi-scale reconstructed attractor Z, denoted as M;

[0034] Preset weight factor sequence qV and grid size sequence sV;

[0035] For each grid size sV m , split the multi-scale reconstruction attractor Z into G m ×G m The number of phase points in each grid is counted and recorded as g m,ij , where sV m represents the mth element of sV, G m Indicates the grid size is sV m The number of grids when

[0036] Calculate the percentage of phase points at each grid point to the total number of phase points:

[0037] p m，ij =g m，ij / M×100%

[0038] Calculate intermediate variables:

[0039]

[0040]

[0041] Mf mt =∑ i ∑ j [μ mt，ij ·log 10 (p mt，ij )]

[0042] Mf mt =∑ i ∑ j [μ mt，ij ·log 10 (μ mt，ij )]

[0043] Msc=-log 10 (sV)

[0044] In the formula, q t represents the tth element of qV;

[0045] By Ma mt , Mf mt The linear regression coefficients of Msc are used to determine the singularity index variable matrix α q 、f q ;

[0046] Plot the multi-scale reconstructed attractor multifractal spectrum represented by f~α.

[0047] Preferably, the preset weight factor sequence qV and the grid size sequence sV are respectively: qV=-2:0.2:2, sV=2:1:8.

[0048] Preferably, the damage index is calculated as follows:

[0049]

[0050]

[0051] in:

[0052] Δα r =α max -α q =0

[0053] Δα l =α q＝0 -α min

[0054] Δf r =f max -fmin，r

[0055] Δf l =f max -f min，l

[0056] In the formula, α max , α min , α q＝0 、f max 、f min，r 、f min，l They correspond to the α and f values ​​at the endpoints and vertices in the f~α multifractal spectrum respectively.

[0057] Preferably, the identifying and locating cantilever beam damage according to the relative numerical values ​​of the damage indicators comprises the following steps:

[0058]

[0059] Among them, MFID represents the relative value of the multifractal spectrum singularity damage index, λ and κ represent the damage characteristic vector composed of damage index λ and κ respectively. denote the mean of the damage characteristic vectors λ and κ, σ λ , σ κ They represent the standard deviation of the damage feature vectors λ and κ respectively.

[0060] Beneficial effects of the present invention:

[0061] The present invention provides a cantilever beam damage identification method based on multi-scale singular attractor multifractal spectrum, which separates the damage information part and the noise part in the vibration signal through multi-scale analysis, quantitatively describes the influence of the damage on the nonlinear motion law of the structure through multi-fractal analysis, and then establishes a damage index based on the multi-fractal characteristics of the multi-scale reconstruction attractor to judge the health state of the beam structure and locate the structural damage. Compared with the existing methods, the multi-scale reconstruction attractor multifractal spectrum method established by the present invention breaks through the problems of low recognition accuracy, weak damage sensitivity, and insufficient noise resistance in the cantilever beam damage characterization method in the prior art, and provides a simple, fast and accurate cantilever beam damage identification method. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0063] Figure 2 are the cantilever beam acceleration response signals x and a before and after smoothing in the embodiment of the present invention;

[0064] Figure 3 A time domain diagram of a stationary wavelet transformed multi-scale sub-signal s according to an embodiment of the present invention;

[0065] Figure 4 A schematic diagram of a multi-scale reconstruction attractor Z according to an embodiment of the present invention;

[0066] Figure 5 The multifractal spectrum characterized by f~α at different measuring points of the cantilever beam of the embodiment of the present invention;

[0067] Figure 6 A schematic diagram of multifractal spectrum singularity parameter variables used in calculating damage indicators in an embodiment of the present invention;

[0068] Figure 7 This is the cantilever beam damage identification result based on the multi-scale reconstruction attractor multifractal spectrum according to an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0070] Example 1

[0071] The present invention provides a cantilever beam damage identification method based on a multi-scale reconstruction attractor multifractal spectrum. Figure 1-7 As shown:

[0072] S1: The acceleration signal of the cantilever beam is collected by the dynamic force measurement system, which is recorded as x = {x i}, i = 1, 2,…, N, N is the data length.

[0073] S2: Perform smoothing filtering preprocessing on the original acceleration signal to obtain the preprocessed acceleration signal, denoted as a = {a i}, the MATLAB function command corresponding to smoothing filter preprocessing is “smooth”.

[0074] S3: Perform stationary wavelet decomposition on the preprocessed acceleration signal a to obtain multi-scale sub-signals with the same data length. The MATLAB function command corresponding to the stationary wavelet decomposition is "swt", the wavelet basis function is "rbio2.4", and the wavelet decomposition layer number is 3.

[0075] S4: Select multi-scale sub-signals that can characterize the main vibration characteristics of the cantilever beam for phase space reconstruction and normalization processing to obtain a normalized multi-scale reconstructed attractor, specifically including:

[0076] S4.1: The stationary wavelet transform approximate coefficients containing the main frequency range of structural vibration are used as the multi-scale sub-signal characterizing the main vibration characteristics of the structure. After boundary truncation processing, it is recorded as the multi-scale sub-signal s; the boundary truncation lengths on both sides of the multi-scale sub-signal are 1% of the total length of the sub-signal.

[0077] S4.2: Perform phase space reconstruction on the truncated multi-scale sub-signal s to obtain a multi-scale reconstructed attractor.

[0078] S4.2.1: Calculate the coordinates of the phase point in the reconstructed attractor Y as follows:

[0079] y k =(s k ,s k +τ,…,s k +(m-1)τ) (1)

[0080] In the formula, y k represents the kth phase point in the reconstructed attractor Y, s k represents the kth signal amplitude of the multi-scale sub-signal after truncation processing, m and τ are the embedding dimension and delay time of the embedding parameters; the embedding parameters of phase space reconstruction are m=2 and τ=1.

[0081] S4.2.2: Calculate the covariance matrix C of the reconstructed attractor Y:

[0082] C=Y T Y (2)

[0083] S4.2.3: Perform eigenvalue decomposition on the covariance matrix C:

[0084] C=ΦΛΦ -1 (3)

[0085] Where Φ is a square matrix whose columns are eigenvectors, and Λ is a diagonal matrix whose main diagonal elements are eigenvalues.

[0086] S4.2.4: Project the reconstructed attractor Y along its first principal direction to obtain:

[0087] Z=YΦ (4)

[0088] Z is the multi-scale reconstructed attractor obtained by phase space reconstruction.

[0089] S4.3: Normalize the multi-scale reconstructed attractor so that the value range of each phase space dimension is [0,1].

[0090] S5: Construct a multi-fractal spectrum of multi-scale reconstruction attractors and establish a damage index based on the singularity index of the multi-fractal spectrum. Specifically include:

[0091] S5.1: Count the total number of phase points of the multi-scale reconstructed attractor Z, denoted as M.

[0092] S5.2: Preset the weight factor sequence qV and the grid size sequence sV; the preset weight factor sequence qV and the grid size sequence sV are respectively: qV = -2:0.2:2, sV = 2:1:8.

[0093] S5.3: For each grid size sV m , split the multi-scale reconstruction attractor Z into G m ×G m The number of phase points in each grid is counted and recorded as g m,ij , where sV m represents the mth element of sV, G m Indicates the grid size is sV m The number of grids at .

[0094] S5.4: Calculate the percentage of phase points at each grid point to the total number of phase points:

[0095] p m,ij =g m,ij / M×100% (5)

[0096] S5.5: Calculate intermediate variables:

[0097]

[0098]

[0099] Ma mt =∑ i ∑ j [μ mt，ij ·log 10 (p m，ij )] (8)

[0100] Mf mt =∑ i ∑ j [μ mt，ij ·log 10 (μ mt，ij )] (9)

[0101] Msc=-log 10 (sV) (10)

[0102] In the formula, q t Represents the tth element of qV.

[0103] S5.6: Through Ma mt , Mf mtThe linear regression coefficients of Msc are used to determine the singularity index variable matrix α q 、f q .

[0104] S5.7: Draw the multi-scale reconstructed attractor multifractal spectrum represented by f~α.

[0105] S5.8: Establish damage index based on multifractal spectrum singularity index:

[0106]

[0107]

[0108] in:

[0109] Δα r =α max -α q＝0

[0110] Δα l =α q＝0 -α min

[0111] Δf r =f max -f min，r

[0112] Δf l =f max -f min，l

[0113] In the formula, α max , α min , α q＝0 、f max 、f min，r 、f min，l They correspond to the α and f values ​​at the endpoints and vertices in the f~α multifractal spectrum respectively.

[0114] S6: Identify and locate cantilever beam damage based on the relative numerical values ​​of damage indicators. Specifically include:

[0115]

[0116] Among them, MFID represents the relative value of the multi-fractal spectrum singularity damage index, M and κ represent the damage characteristic vector composed of damage index λ and κ respectively. denote the mean of the damage characteristic vectors λ and κ, σ λ , σ κ They represent the standard deviation of the damage feature vectors λ and κ respectively.

[0117] In this embodiment,

[0118] In order to verify the effectiveness of the cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum of the present invention, a physical model experiment was carried out and the acceleration response of the cantilever beam was extracted for analysis.

[0119] The overall process of the method of the present invention is shown in Figure 1 In this embodiment, the geometric dimensions of the beam structure are length×height×width=0.38×0.01×0.02m 3 ; Physical parameters: elastic modulus is 1.93×10 11 Pa, Poisson's ratio is 0.29, and the material density is 7750kg / m 3 ; The boundary conditions are one end fixed and the other end free; the simple harmonic load is 10mm away from the fixed end; the damage position is 72mm away from the fixed end; 11 acceleration sensors are arranged along the length of the cantilever beam, the sampling frequency is 12800Hz, and the analysis frequency is 5000Hz. The collected acceleration signal is recorded as x, such as Figure 2 The discrete points are shown in Figure 2.

[0120] The original acceleration signal x is smoothed and filtered, and the smoothed acceleration signal a is obtained through the MATLAB function "smooth", as shown in Figure 2 As shown by the solid line in the middle. The wavelet basis function is selected as "rbio2.4" and the wavelet decomposition layer number is 3. The smoothed acceleration signal a is subjected to stationary wavelet decomposition. The corresponding MATLAB command function is "swt" to obtain a multi-scale sub-signal without downsampling. The stationary wavelet transform approximate coefficients containing the main frequency range of structural vibration are selected as the multi-scale sub-signal representing the main vibration characteristics of the structure. After the boundary truncation processing is performed, it is recorded as s, as shown in Figure 3 As shown. Taking the embedding parameters as m = 2, τ = 1, the phase space reconstruction of the truncated multi-scale sub-signal s is performed according to formulas (1) to (4), and the multi-scale reconstruction attractor Z is obtained, as shown in Figure 4 The preset weight factor sequence qV and grid size sequence sV are qV = -2:0.2:2 and sV = 2:1:8 respectively. The intermediate variables of the multifractal spectrum are calculated according to formulas (5) to (10), and the multifractal spectrum of the multiscale reconstructed attractor represented by f~α at different measuring points is obtained, as shown in Figure 5 As shown. According to (11) to (13), the multifractal spectrum damage index MFID at each measuring point is calculated. The intermediate variables of the singularity parameters used are as follows: Figure 6 As shown, the calculation result of MFID is as follows Figure 7As shown, it can be seen that the MFID value at measuring point 3 is the largest, indicating that damage may occur at measuring point 3, which is consistent with the actual damage location. Therefore, the multi-scale reconstruction attractor multi-fractal spectrum method established in the present invention can effectively identify and locate cantilever beam damage, breaking through the problems of low recognition accuracy, weak damage sensitivity, and insufficient noise resistance in the cantilever beam damage characterization method in the prior art, and providing a simple, fast, and accurate cantilever beam damage identification method.

[0121] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum, characterized in that: The following steps are involved: The original acceleration signal of the cantilever beam is collected by the dynamic force measurement system, and the original acceleration signal is preprocessed by smoothing and filtering to obtain a preprocessed acceleration signal; Perform stationary wavelet decomposition on the acceleration signal to obtain multi-scale sub-signals with the same data length; Multi-scale sub-signals representing the vibration characteristics of the cantilever beam are selected for phase space reconstruction and normalization processing to obtain a multi-scale reconstructed attractor. According to the multi-scale reconstruction attractor, a multi-fractal spectrum is formed; and according to the singularity index of the multi-fractal spectrum, a damage index is established; According to the relative numerical values ​​of the damage indicators, the damaged cantilever beam is identified; The construction of the multifractal spectrum comprises the following steps: Count the total number of phase points of the multi-scale reconstructed attractor Z, denoted as M; Preset weight factor sequence qV and grid size sequence sV; For each grid size sV m , split the multi-scale reconstruction attractor Z into G m ×G m The number of phase points in each grid is counted and recorded as g m,ij , where sV m represents the mth element of sV, G m Indicates the grid size is sV m The number of grids when Calculate the percentage of phase points at each grid point to the total number of phase points: p m,ij =g m,ij / M×100% Calculate intermediate variables: He has mt =∑ i ∑ j [μ mt,ij ·log 10 (p m,ij )] Mf mt =∑ i ∑ j [m mt,ij ·log 10 (m mt,ij )] Msc=-log 10 (sV) In the formula, q t represents the tth element of qV; By Ma mt , Mf mt The linear regression coefficients of Msc are used to determine the singularity index variable matrix α q 、f q ; Plot the multi-scale reconstructed attractor multifractal spectrum represented by f~α.

2. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 1 is characterized in that: When the acceleration signal is subjected to stationary wavelet decomposition, the wavelet basis function is rbio2.4 and the wavelet decomposition layer number is 3.

3. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 1 is characterized in that: The method of selecting a multi-scale sub-signal characterizing the vibration characteristics of the cantilever beam for phase space reconstruction and normalization processing comprises the following steps: The stationary wavelet transform approximate coefficients containing the main frequency range of structural vibration are used as multi-scale sub-signals to characterize the main vibration characteristics of the structure, and after boundary truncation processing, they are recorded as multi-scale sub-signals s; The phase space is reconstructed for the truncated multi-scale sub-signal s to obtain a multi-scale reconstructed attractor; The multi-scale reconstructed attractor is normalized so that the value range of each phase space dimension is [0,1].

4. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 3 is characterized in that: In the boundary truncation processing of the multi-scale sub-signal, the boundary truncation lengths on the left and right sides of the multi-scale sub-signal are both 1% of the total length of the sub-signal.

5. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 3 is characterized in that: The phase space reconstruction of the multi-scale sub-signal s comprises the following steps: The coordinates of the phase point in the reconstructed attractor Y are calculated as follows: y k =(s k ,s k +t,…,s k +(m-1)τ) In the formula, y k represents the kth phase point in the reconstructed attractor Y, s k represents the kth signal amplitude of the multi-scale sub-signal after truncation, m and τ are the embedding dimension and delay time of the embedding parameters; Calculate the covariance matrix C of the reconstructed attractor Y: C=Y T AND Perform eigenvalue decomposition on the covariance matrix C: C=FLF -1 Where Φ is a square matrix whose columns are eigenvectors, and Λ is a diagonal matrix whose main diagonal elements are eigenvalues; Projecting the reconstructed attractor Y along its first principal direction yields: Z=YΦ Z is the multi-scale reconstructed attractor obtained by phase space reconstruction.

6. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 5 is characterized in that: The embedding parameters of the phase space reconstruction are m=2 and τ=1.

7. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 1 is characterized in that: The preset weight factor sequence qV and the grid size sequence sV are respectively: qV=-2:0.2:2, sV=2:1:

8.

8. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 1 is characterized in that: The damage index is calculated as follows: in: Da r =a max -a q＝0 Da l =a q＝0 -a min Δf r =f max -f min,r Δf l =f max -f min,l In the formula, α max , α min , α q＝0 、f max 、f min,r 、f min,l They correspond to the α and f values ​​at the endpoints and vertices in the f~α multifractal spectrum respectively.

9. The cantilever beam damage identification method based on multi-scale reconstruction attractor multifractal spectrum according to claim 1 is characterized in that: The method of identifying and locating cantilever beam damage according to the relative numerical values ​​of the damage indicators comprises the following steps: Among them, MFID represents the relative value of the multifractal spectrum singularity damage index, λ and κ represent the damage characteristic vector composed of damage index λ and κ respectively. denote the mean of the damage characteristic vectors λ and κ, σ λ , σ κ They represent the standard deviation of the damage feature vectors λ and κ respectively.

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