Laser ultrasonic Lamb wave signal noise reduction method for metal aluminum sheet defect detection

Abstract

The invention discloses a laser ultrasonic Lamb wave signal noise reduction method for metal aluminum sheet defect detection. Comprising the following steps: collecting a Lamb wave signal to be measured, carrying out decomposition processing on the Lamb wave signal by adopting complete adaptive noise ensemble empirical mode decomposition (CEEMDAN), and solving the modal aliasing problem of a multi-order intrinsic mode (I MF) component by utilizing a Pearson coefficient method to obtain an I MF component without modal aliasing; calculating a permutation entropy value of each order of component, setting a threshold value, screening effective signal components, and performing primary reconstruction; performing stationary wavelet (SWT) decomposition processing on the primary reconstruction signal to obtain a low-frequency approximation coefficient and a high-frequency detail coefficient; constraining the high-frequency detail coefficient through an L2 regularization method; and carrying out secondary reconstruction on the reserved approximation coefficient and the detail coefficient after L2 constraint to obtain a Lamb wave signal after final noise reduction. The signal quality of the Lamb wave signal is improved, and the accuracy of defect detection of the metal aluminum sheet is improved.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing and signal processing technology, and in particular to a laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum sheets. Background Technology

[0002] Aluminum, as an important industrial material, is widely used in aerospace, automotive, construction and other fields. The surface quality of aluminum sheets directly affects their mechanical properties and service life. Surface defects such as scratches and dents can easily lead to stress concentration, thus requiring efficient non-destructive testing technology for quality control.

[0003] Laser ultrasonic testing, as an emerging non-contact inspection method, uses pulsed lasers to excite ultrasonic waves and optical sensors to receive the signals, thereby detecting defects in materials. For thin sheet materials, Lamb waves are an ideal inspection tool due to their sensitivity to minute defects. However, in practical applications, laser ultrasonic Lamb wave signals face severe noise interference problems: the thermoelastic effect and plasma oscillations generated during laser excitation introduce high-frequency random noise, and environmental vibrations and electromagnetic interference further degrade signal quality. Simultaneously, the inherent multimode and dispersion characteristics of Lamb waves make effective features easily submerged by noise.

[0004] Traditional denoising methods such as Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD) have significant limitations when processing such signals. EMD introduces mode aliasing, and while EEMD mitigates this problem by adding noise, it suffers from low computational efficiency and large reconstruction errors. Existing methods struggle to effectively preserve the defect features of Lamb wave signals while denoising, especially in cases like thin aluminum sheets where the signal is easily interfered with due to its small thickness.

[0005] Therefore, there is an urgent need to develop a dedicated noise reduction method for laser ultrasonic Lamb wave signals of thin aluminum sheets, which can improve the signal-to-noise ratio while maintaining the integrity of the signal in the time domain, and provide reliable technical support for high-quality non-destructive testing of aluminum materials. Summary of the Invention

[0006] To address at least one of the aforementioned technical problems, this invention proposes a laser ultrasonic Lamb wave signal noise reduction method for defect detection in thin aluminum sheets.

[0007] The first aspect of this invention provides a laser-ultrasonic Lamb wave signal noise reduction method for defect detection in thin aluminum sheets, comprising:

[0008] Two points, A and B, are set on the surface of the aluminum sheet. Point A is the laser excitation position, and point B is the position for detecting the Lamb wave signal. The Lamb wave signal of the aluminum sheet is obtained by detecting it through a laser device.

[0009] The detected Lamb wave signal was decomposed using CEEMDAN to obtain several IMF components that meet the decomposition termination condition.

[0010] Extract the IMF components of each order from the decomposition, perform time modeling on the IMF components, calculate the permutation entropy value of each order of time modeling, filter the effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and reconstruct the effective IMF components once.

[0011] The reconstructed signal is decomposed using SWT to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients.

[0012] The L2 regularization method is used to constrain the high-frequency noise detail coefficients. The low-frequency approximation coefficients obtained by decomposition are reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal.

[0013] In this scheme, two points A and B are set on the surface of the aluminum sheet. Point A is the laser excitation position, and point B is the Lamb wave signal detection position. The Lamb wave signal of the aluminum sheet is obtained by detecting it using a laser device. Specifically:

[0014] A laser ultrasonic testing system was set up, the aluminum plate sample was fixed on the system platform, the pulse laser of the testing system was started, and then the Sagnac interferometer was adjusted to perform laser detection on the position of the aluminum plate with defects to be detected.

[0015] Lamb wave signals of thin aluminum sheets were acquired using the LabVIEW data platform.

[0016] In this scheme, the CEEMDAN is used to decompose the detected Lamb wave signal to obtain several IMF components that satisfy the decomposition termination condition, specifically as follows:

[0017] S1, Gaussian white noise is added to the acquired Lamb wave signal Y(t), L n (t) represents Gaussian white noise added n times, and follows a distribution N(0,1):

[0018] Y n (t)=Y(t)+θ0L n (t), n=1,2,…,N

[0019] Among them, Y n (t) represents the nth signal after adding white noise; θ0 is the standard deviation of the noise; n is the number of times noise was added;

[0020] S2, input the Y(t) with added white noise into EMD for decomposition to obtain the first-order component IMF1 of CEEMDAN:

[0021]

[0022] Calculate the first residual component r1:

[0023] r1=Y(t)-IMF1

[0024] S3, Obtaining the k-th modal component E based on EMD decomposition. k (·), Gaussian white noise is added to the residual components to generate a new sequence r1(n)=r1+θ1E1[L n (t)]; Then, EMD decomposition is performed on the signal r1(n) to decompose the second-order intrinsic mode component IMF2. The residual component after removing the second-order intrinsic mode component is r2:

[0025]

[0026] Where θ1 is the added white noise signal.

[0027] S4, repeat step S3 to obtain the k-th eigenmode component IMF. K and the k-th residual component r k :

[0028]

[0029] r k =r k-1 -IMF k

[0030] Repeat steps S1-S4 until the residual component r is reached. k If there are fewer than two extreme points, stop the signal decomposition. When the signal decomposition stops, the k-th order eigenmode component and one residual component are obtained. The signal Y(t) is represented as:

[0031]

[0032] Where Y(t) is the acquired Lamb wave signal, These are the eigenmode components of the decomposition, r k For the residual components.

[0033] In this scheme, the decomposition processing of the detected Lamb wave signal using CEEMDAN also includes:

[0034] During the decomposition of CEEMDAN, mode aliasing is monitored by calculating the spectral correlation coefficient between adjacent IMF components. The spectral correlation coefficient is obtained by calculating the Pearson correlation coefficient of the power spectral density function of adjacent IMF components.

[0035] When the spectral correlation coefficient is higher than the preset aliasing determination threshold, modal aliasing is determined to exist between the adjacent IMF components;

[0036] Based on the center frequency of the IMF component with modal aliasing, the frequency band energy distribution of the added Gaussian white noise is adjusted. The next round of CEEMDAN decomposition is performed based on the Gaussian white noise with the frequency band energy distribution. The aliased modes are gradually separated through the iterative process until the spectral correlation coefficient is lower than the aliasing determination threshold. Finally, the set of IMF components with suppressed modal aliasing is output.

[0037] In this scheme, adjusting the frequency band energy distribution of the added Gaussian white noise based on the center frequency of the IMF component where modal aliasing is determined specifically involves:

[0038] Extract the adjacent IMF components that are determined to have mode aliasing, calculate their respective center frequencies, and determine the frequency band range of their overlap.

[0039] Based on the overlapping frequency band range, a bandpass filter with a preset passband is generated. The bandpass filter is used to filter standard Gaussian white noise to generate auxiliary noise with frequency band energy concentrated in the aliasing frequency band.

[0040] The auxiliary noise is superimposed with a portion of Gaussian white noise with energy below a preset value and frequency band above a preset value to synthesize a new target auxiliary noise. The energy decomposition of the new target auxiliary noise is specifically enhanced in the aliasing frequency band, while it is weakened in other frequency bands. The new target auxiliary noise is used for CEEMDAN decomposition in subsequent iterations to obtain the aliasing-suppressed IMF component, and the aliased IMF components are updated.

[0041] In this scheme, the extraction and decomposition of each order of IMF components, the time modeling of the IMF components, the calculation of the permutation entropy value of each order of time-modeled components, the screening of effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and the reconstruction of the effective IMF components are specifically as follows:

[0042] For each order of IMF component obtained from the decomposition, each order IMF component is regarded as a time series of length N, X = {x(a), a = 1, 2, 3, ..., N}, where the length of the IMF component is consistent with the length of the Lamb wave. The phase space of X is reconstructed to obtain the following reconstructed matrix:

[0043]

[0044] Where h is the embedding dimension, λ is the time delay, and b is the number of reconstructed components;

[0045] Rearranging the row vectors of H in ascending order yields a new sequence:

[0046] T(l)={j1,j2,…,j h}, l=1,2,…,l(l≤h!)

[0047] Where {j1,j2,…,j h} represents the new sequence after recombination. There are l ≤ h! different combinations of symbol sequences. By counting the frequency of each permutation in the reconstructed sequence, the probability sequence [d1, d2, ..., dn] can be obtained. l ], thus we can obtain

[0048] The permutation entropy of a time series is defined as follows, and normalization is performed:

[0049]

[0050] Among them, H p P is the permutation entropy value; P is the normalized entropy value.

[0051] A normalized entropy threshold is set, and effective IMF components and noisy IMF components are filtered according to the normalized entropy threshold. The effective IMF components are superimposed with the corresponding residual components to form the first reconstructed Lamb wave signal Z(t), which is expressed as:

[0052] Z(t)=∑ 有效MF IMF k +r k .

[0053] In this scheme, the SWT decomposition process is performed on the reconstructed signal to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients, specifically as follows:

[0054] The reconstructed signal Z(t) is decomposed by stationary wavelet transform. The stationary wavelet transform decomposition is performed by inserting zeros between the high-pass filter L(t) and the low-pass filter H(t). The signal length is extended according to the zero-insertion operation so that the length of the low-frequency approximation coefficients and the high-frequency noise detail coefficients after each decomposition is consistent with the length of Z(t).

[0055] The mathematical expression for SWT decomposition is as follows, where the low-frequency approximation coefficient Ac is the output of the low-pass filter H(t), and the high-frequency noise detail coefficients Dc are the output of the high-pass filter L(t). The expression for the first-level decomposition is:

[0056] A c1 =Z(t)*H(t),D c1 =Z(t)*L(t)

[0057] Subsequent layer decomposition is achieved through iterative zero-placing operations. The decomposition expression for the (j+1)th layer is:

[0058]

[0059] Where Dc represents the noise-dominated high-frequency component in the Lamb wave signal, Ac represents the signal-dominated low-frequency component, and * represents the convolution operation.

[0060] In this scheme, the L2 regularization method is used to constrain the high-frequency noise detail coefficients. The low-frequency approximation coefficients obtained from the decomposition are then reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal. Specifically:

[0061] The initial loss function for the high-frequency noise detail coefficients Dc is defined as J(w; x, Y), where w is the weighting coefficient, x is the input signal Dc, and Y is the desired clean signal feature template for the output, which is obtained by labeling historical data.

[0062] Add the L2 regularization term to the loss function to form a new objective function J. i :

[0063]

[0064] Where λ is a hyperparameter of regularization strength, It is a difference matrix. The square of the L2 norm;

[0065] By minimizing the objective function J i The high-frequency detail coefficients Dc′ after constraint are obtained by solving. Ac and Dc′ are reconstructed by stationary wavelet inverse transform, and its expression is: Q(t)=ISWT(Ac,Dc′), where Q(t) is the final denoised Lamb wave signal.

[0066] This invention discloses a laser-ultrasonic Lamb wave signal denoising method for defect detection in thin aluminum sheets. The method includes the following steps: acquiring the Lamb wave signal to be tested; decomposing the Lamb wave signal using fully adaptive ensemble empirical mode decomposition (CEEMDAN) to obtain multi-order intrinsic mode (IMF) components that satisfy the decomposition termination condition; calculating the permutation entropy value of each component and setting a threshold to filter valid signal components for primary reconstruction; performing stationary wavelet (SWT) decomposition on the primary reconstructed signal to obtain low-frequency approximation coefficients and high-frequency detail coefficients; constraining the high-frequency detail coefficients using L2 regularization; and performing a secondary reconstruction using the retained approximation coefficients and the L2-constrained detail coefficients to obtain the final denoised Lamb wave signal. This method improves the signal quality of the Lamb wave signal and enhances the accuracy of defect detection in thin aluminum sheets. Attached Figure Description

[0067] Figure 1 This invention illustrates a laser-ultrasound method for defect detection in thin aluminum sheets.

[0068] Flowchart of Lamb wave signal noise reduction method;

[0069] Figure 2 The acquired Lamb wave signal;

[0070] Figure 3 Lamb wave signal with Gaussian white noise added;

[0071] Figure 4 The 16th-order IMF components decomposed by the CEEMDAN algorithm;

[0072] Figure 5 The normalized permutation entropy value of each IMF;

[0073] Figure 6 These are the detail coefficients and approximation coefficients of the SWT decomposition in the examples;

[0074] Figure 7 These are the detail coefficients of the L2 regularization constraint in the embodiment;

[0075] Figure 8 The image shows the noise reduction effect of the Lamb wave signal;

[0076] Figure 9 The image shows the noise reduction effect of the EMD algorithm.

[0077] Figure 10 The image shows the noise reduction effect of the EEMD algorithm.

[0078] Figure 11 The image shows the noise reduction effect of the wavelet thresholding algorithm. Detailed Implementation

[0079] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0080] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0081] Figure 1 The flowchart of a laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum sheets according to the present invention is shown.

[0082] like Figure 1 As shown, the first aspect of the present invention provides a laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum sheets, comprising:

[0083] Two points, A and B, are set on the surface of the aluminum sheet. Point A is the laser excitation position, and point B is the position for detecting the Lamb wave signal. The Lamb wave signal of the aluminum sheet is obtained by detecting it through a laser device.

[0084] The detected Lamb wave signal was decomposed using CEEMDAN to obtain several IMF components that meet the decomposition termination condition.

[0085] Extract the IMF components of each order from the decomposition, perform time modeling on the IMF components, calculate the permutation entropy value of each order of time modeling, filter the effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and reconstruct the effective IMF components once.

[0086] The reconstructed signal is decomposed using SWT to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients.

[0087] The L2 regularization method is used to constrain the high-frequency noise detail coefficients. The low-frequency approximation coefficients obtained by decomposition are reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal.

[0088] It should be noted that by setting laser excitation points and signal detection points on the surface of the aluminum sheet and acquiring Lamb wave signals, non-contact, high-sensitivity ultrasonic signal acquisition is achieved. Complete ensemble empirical mode decomposition is used to adaptively decompose the original Lamb wave signal into eigenmode components at different time scales, effectively alleviating mode aliasing and improving decomposition accuracy, thus separating different frequency characteristic components in the signal. By constructing a time series model and calculating the complexity of each mode component based on permutation entropy, effective components containing structural damage information are accurately identified, while noise-dominated invalid components are eliminated, thereby achieving one-time reconstruction enhancement. The signal principal components and propagation path information are analyzed. Then, the signal length is kept constant by utilizing the stationary wavelet transform to perform multi-scale decomposition on the first reconstructed signal, extracting physically meaningful low-frequency approximation coefficients and detail coefficients containing high-frequency noise, thereby achieving fine separation in the time and frequency domains. Finally, L2 regularization constraints are applied to the high-frequency noise detail coefficients to suppress their non-smooth energy, enabling the reconstruction stage to better preserve the continuity and structure of the Lamb wave propagation characteristics. This results in a final secondary reconstructed signal with better signal-to-noise ratio and waveform fidelity, thereby improving the availability and detection accuracy of the Lamb wave signal in the defect detection process of thin aluminum sheets.

[0089] According to an embodiment of the present invention, two points A and B are set on the surface of the aluminum sheet, where point A is the laser excitation position and point B is the Lamb wave signal detection position. The Lamb wave signal of the aluminum sheet is obtained by detecting it using a laser device. Specifically:

[0090] A laser ultrasonic testing system was set up, the aluminum plate sample was fixed on the system platform, the pulse laser of the testing system was started, and then the Sagnac interferometer was adjusted to perform laser detection on the position of the aluminum plate with defects to be detected.

[0091] Lamb wave signals of thin aluminum sheets were acquired using the LabVIEW data platform.

[0092] According to an embodiment of the present invention, the step of using CEEMDAN to decompose the detected Lamb wave signal to obtain several IMF components that satisfy the decomposition termination condition is specifically as follows:

[0093] S1, Gaussian white noise is added to the acquired Lamb wave signal Y(t), L n (t) represents Gaussian white noise added n times, and follows a distribution N(0,1):

[0094] Y n (t)=Y(t)+θ0L n (t), n=1,2,…,N

[0095] Among them, Y n (t) represents the nth signal after adding white noise; θ0 is the standard deviation of the noise; n is the number of times noise was added;

[0096] S2, input the Y(t) with added white noise into EMD for decomposition to obtain the first-order component IMF1 of CEEMDAN:

[0097]

[0098] Calculate the first residual component r1:

[0099] r1=Y(t)-IMF1

[0100] S3, Obtaining the k-th modal component E based on EMD decomposition. k (·), Gaussian white noise is added to the residual components to generate a new sequence r1(n)=r1+θ1E1[L n (t)]; Then, EMD decomposition is performed on the signal r1(n) to decompose the second-order intrinsic mode component IMF2. The residual component after removing the second-order intrinsic mode component is r2:

[0101]

[0102] Where θ1 is the added white noise signal.

[0103] S4, repeat step S3 to obtain the k-th eigenmode component IMF. K and the k-th residual component r k :

[0104]

[0105] r k =r k-1 -IMF k

[0106] Repeat steps S1-S4 until the residual component r is reached. k If there are fewer than two extreme points, stop the signal decomposition. When the signal decomposition stops, the k-th order eigenmode component and one residual component are obtained. The signal Y(t) is represented as:

[0107]

[0108] Where Y(t) is the acquired Lamb wave signal, These are the eigenmode components of the decomposition, r k For the residual components.

[0109] It should be noted that the time series of the acquired Lamb wave signal to be measured is denoted as Y(t), and its waveform is shown in [reference needed]. Figure 2 Import the Lamb wave signal, set the algorithm parameters, and add 15dB Gaussian white noise. The waveform is shown below. Figure 3 The amplitude is 0.02 of the signal standard deviation, the set number is set to 500, and the maximum number of iterations is set to 1000. Signal decomposition yields 16th-order IMF components ranging from high to low frequencies. The decomposition is shown in [reference needed]. Figure 4 The EMD is decomposed into empirical mode decomposition.

[0110] According to an embodiment of the present invention, the decomposition processing of the detected Lamb wave signal using CEEMDAN further includes:

[0111] During the decomposition of CEEMDAN, mode aliasing is monitored by calculating the spectral correlation coefficient between adjacent IMF components. The spectral correlation coefficient is obtained by calculating the Pearson correlation coefficient of the power spectral density function of adjacent IMF components.

[0112] When the spectral correlation coefficient is higher than the preset aliasing determination threshold, modal aliasing is determined to exist between the adjacent IMF components;

[0113] Based on the center frequency of the IMF component with modal aliasing, the frequency band energy distribution of the added Gaussian white noise is adjusted. The next round of CEEMDAN decomposition is performed based on the Gaussian white noise with the frequency band energy distribution. The aliased modes are gradually separated through the iterative process until the spectral correlation coefficient is lower than the aliasing determination threshold. Finally, the set of IMF components with suppressed modal aliasing is output.

[0114] According to an embodiment of the present invention, adjusting the frequency band energy distribution of the added Gaussian white noise based on the center frequency of the IMF component where modal aliasing is determined specifically involves:

[0115] Extract the adjacent IMF components that are determined to have mode aliasing, calculate their respective center frequencies, and determine the frequency band range of their overlap.

[0116] Based on the overlapping frequency band range, a bandpass filter with a preset passband is generated. The bandpass filter is used to filter standard Gaussian white noise to generate auxiliary noise with frequency band energy concentrated in the aliasing frequency band.

[0117] The auxiliary noise is superimposed with a portion of Gaussian white noise with energy below a preset value and frequency band above a preset value to synthesize a new target auxiliary noise. The energy decomposition of the new target auxiliary noise is specifically enhanced in the aliasing frequency band, while it is weakened in other frequency bands.

[0118] The new target auxiliary noise is used for CEEMDAN decomposition in subsequent iterations to obtain aliasing-suppressed IMF components, and the aliased IMF components are updated.

[0119] It should be noted that in the laser ultrasonic Lamb wave signal processing of thin aluminum sheets, the reason for proposing to introduce the spectral correlation monitoring of adjacent intrinsic mode components and adaptively adjust the frequency band energy distribution of auxiliary noise in the iterative process of complete set empirical mode decomposition is based on the technical problem that empirical mode decomposition methods are prone to mode aliasing when facing non-stationary, nonlinear signals or similar frequency components. Mode aliasing can cause a single mode to contain multiple frequency components at the same time or the same frequency component to be dispersed in multiple modes, thereby weakening the physical meaning of each intrinsic mode component, reducing the accuracy of subsequent feature extraction, and affecting the reliability of defect localization and identification. By calculating the power spectral density function of adjacent IMF components and quantifying their spectral correlation using the Pearson correlation coefficient, it is possible to determine in real time whether there is significant spectral overlap and mode aliasing. When the correlation exceeds a preset judgment threshold, aliasing is considered to exist and an adaptive intervention process is initiated. This process first extracts the center frequencies of adjacent modes identified as aliased and determines their overlapping frequency bands. Then, based on the overlapping frequency band, a bandpass filter is designed to perform spectral weighting on standard Gaussian white noise to generate auxiliary noise with energy concentrated in the aliasing frequency band. This directionally enhanced auxiliary noise is then superimposed with low-energy broad-spectrum noise that retains information from other frequency bands to form a new target noise source for the next round of decomposition. The aforementioned iterative mechanism, by directionally enhancing and suppressing frequency band energy during the noise introduction stage, enables subsequent CEEMDAN decomposition to specifically separate originally overlapping frequency band components. This suppresses spectral coupling between modes, improves the frequency band purity and modal independence of each order IMF, and enhances the stability and repeatability of the decomposition. Consequently, it provides clearer time-frequency structure information for effective component selection based on permutation entropy and subsequent wavelet domain denoising, ultimately improving the signal-to-noise ratio of Lamb wave signals in defect detection tasks. The application of the new target auxiliary noise to subsequent CEEMDAN decomposition in the iterative process allows the added noise to more effectively excite and separate mutually entangled signal components within the aliasing frequency band. This results in clearer decoupling of IMF components with different characteristics after overall averaging, achieving targeted suppression of modal aliasing.

[0120] According to an embodiment of the present invention, the extraction and decomposition of each order of IMF components, the time modeling of the IMF components, the calculation of the permutation entropy value of each order of time-modeled components, the selection of effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and the reconstruction of the effective IMF components are specifically as follows:

[0121] For each order of IMF component obtained from the decomposition, each order IMF component is regarded as a time series of length N, X = {x(a), a = 1, 2, 3, ..., N}, where the length of the IMF component is consistent with the length of the Lamb wave. The phase space of X is reconstructed to obtain the following reconstructed matrix:

[0122]

[0123] Where h is the embedding dimension, λ is the time delay, and b is the number of reconstructed components;

[0124] Rearranging the row vectors of H in ascending order yields a new sequence:

[0125] T(l)={j1,j2,…,j h}, l=1,2,…,l(l≤h!)

[0126] Where {j1,j2,…,j h} represents the new sequence after recombination. There are l ≤ h! different combinations of symbol sequences. By counting the frequency of each permutation in the reconstructed sequence, the probability sequence [d1, d2, ..., dn] can be obtained. l ], thus we can obtain

[0127] The permutation entropy of a time series is defined as follows, and normalization is performed:

[0128]

[0129] Among them, H p P is the permutation entropy value; P is the normalized entropy value.

[0130] A normalized entropy threshold is set, and effective IMF components and noisy IMF components are filtered according to the normalized entropy threshold. The effective IMF components are superimposed with the corresponding residual components to form the first reconstructed Lamb wave signal Z(t), which is expressed as:

[0131] Z(t)=∑ 有效MF IMF k +r k .

[0132] It should be noted that the entropy values ​​of each order IMF component are calculated using the permutation entropy algorithm and then normalized. A threshold of 0.6 is set to distinguish between effective feature components and noise components. Components with entropy values ​​above the threshold are removed, while components with entropy values ​​below the threshold are reconstructed into Z(t). The threshold setting is detailed in [link to relevant documentation]. Figure 5 Normalized entropy can reflect the randomness of a signal to a certain extent and can serve as a reference standard for distinguishing useful signals from noisy signals. A higher P value indicates stronger randomness, a more chaotic signal, and a relatively higher noise component. Conversely, a lower P value indicates a more regular signal and richer useful information. Reconstructing the phase space of X aims to transform the one-dimensional signal into a multi-dimensional phase space, facilitating entropy calculation.

[0133] Normalized permutation entropy values ​​of IMF components of each order:

[0134]

[0135]

[0136] According to an embodiment of the present invention, the step of performing SWT decomposition on the reconstructed signal to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients is specifically as follows:

[0137] The reconstructed signal Z(t) is decomposed by stationary wavelet transform. The stationary wavelet transform decomposition is performed by inserting zeros between the high-pass filter L(t) and the low-pass filter H(t). The signal length is extended according to the zero-insertion operation so that the length of the low-frequency approximation coefficients and the high-frequency noise detail coefficients after each decomposition is consistent with the length of Z(t).

[0138] The mathematical expression for SWT decomposition is as follows, where the low-frequency approximation coefficient Ac is the output of the low-pass filter H(t), and the high-frequency noise detail coefficients Dc are the output of the high-pass filter L(t). The expression for the first-level decomposition is:

[0139] A c1 =Z(t)*H(t),D c1 =Z(t)*L(t)

[0140] Subsequent layer decomposition is achieved through iterative zero-placing operations. The decomposition expression for the (j+1)th layer is:

[0141]

[0142] Where Dc represents the noise-dominated high-frequency component in the Lamb wave signal, Ac represents the signal-dominated low-frequency component, and * represents the convolution operation.

[0143] It should be noted that by introducing Stationary Wavelet Transform (SWT), the reconstructed signal Z(t) is decomposed using SWT. The wavelet basis function is selected as dB4, and the decomposition level is set to 5. The SWT decomposition yields the approximation coefficients Ac of the low-frequency component and the detail coefficients Dc of the high-frequency component. The decomposition is shown in [reference needed]. Figure 6 The process ensures that the lengths of the low-frequency approximation coefficients and high-frequency noise detail coefficients after each decomposition layer are consistent with the length of Z(t), thereby avoiding signal shift and Gibbs phenomenon caused by downsampling in Discrete Wavelet Transform (DWT).

[0144] According to an embodiment of the present invention, the L2 regularization method is used to constrain the high-frequency noise detail coefficients, and the low-frequency approximation coefficients obtained by decomposition are reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal, specifically as follows:

[0145] The initial loss function for the high-frequency noise detail coefficients Dc is defined as J(w; x, Y), where w is the weighting coefficient, x is the input signal Dc, and Y is the desired clean signal feature template for the output, which is obtained by labeling historical data.

[0146] Add the L2 regularization term to the loss function to form a new objective function J. i :

[0147]

[0148] Where λ is a hyperparameter of regularization strength, It is a difference matrix. The square of the L2 norm;

[0149] By minimizing the objective function J i The high-frequency detail coefficients Dc′ after constraint are obtained by solving. Ac and Dc′ are reconstructed by inverse stationary wavelet transform (ISWT), and its expression is: Q(t)=ISWT(Ac,Dc′), where Q(t) is the final denoised Lamb wave signal.

[0150] It should be noted that by using the L2 regularization method to constrain the high-frequency detail coefficients, the constrained high-frequency detail coefficients enable Dc′ to preserve the high-frequency characteristics of the signal while suppressing abnormal fluctuations caused by noise.

[0151] The constraint parameter λ = 100 is set, and its constraint waveform is shown below. Figure 7 The retained fifth-level approximation coefficients are reconstructed using the fifth-level detail coefficients under L2 regularization constraints to obtain the denoised signal Q(t), the waveform of which is shown in [Figure showing...]. Figure 8 The signal-to-noise ratio of the denoised signal is calculated to be 30.39 dB.

[0152] To demonstrate the effectiveness of the method, the EMD algorithm, EEMD algorithm, and wavelet thresholding algorithm were used to denoise the signal Y(t). The denoised waveform is shown below. Figure 9 , Figure 10 , Figure 11 After calculation, the signal-to-noise ratios of the signal Y(t) after denoising using the EMD algorithm, EEMD algorithm, and wavelet thresholding algorithm are 26.32dB, 25.14dB, and 25.62dB, respectively.

[0153] from Figure 8 , Figure 9 It can be seen that the EMD and EEMD noise reduction methods have a relatively weak effect on noise removal; the noise amplitude reduction is not significant, and the processed signal waveform still contains a considerable amount of noise. Figure 10 It can be seen that the noise signal amplitude after wavelet threshold denoising is small, but the peak and trough values ​​of the signal are not effectively preserved, and the signal has obvious distortion. Figure 8 The method employed in this invention overcomes these shortcomings, accurately preserves effective features, ensures that key waveforms are smoother and more continuous, achieves the highest signal-to-noise ratio after noise reduction, and has the best noise reduction effect.

[0154] This invention discloses a laser-ultrasonic Lamb wave signal denoising method for defect detection in thin aluminum sheets. The method includes the following steps: acquiring the Lamb wave signal to be tested; decomposing the Lamb wave signal using fully adaptive ensemble empirical mode decomposition (CEEMDAN) to obtain multi-order intrinsic mode (IMF) components that satisfy the decomposition termination condition; calculating the permutation entropy value of each component and setting a threshold to filter valid signal components for primary reconstruction; performing stationary wavelet (SWT) decomposition on the primary reconstructed signal to obtain low-frequency approximation coefficients and high-frequency detail coefficients; constraining the high-frequency detail coefficients using L2 regularization; and performing a secondary reconstruction using the retained approximation coefficients and the L2-constrained detail coefficients to obtain the final denoised Lamb wave signal. This method improves the signal quality of the Lamb wave signal and enhances the accuracy of defect detection in thin aluminum sheets.

[0155] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0156] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0157] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0158] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0159] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0160] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A laser-ultrasonic Lamb wave signal noise reduction method for defect detection in thin aluminum sheets, characterized in that, Includes the following steps: Two points, A and B, are set on the surface of the aluminum sheet. Point A is the laser excitation position, and point B is the position for detecting the Lamb wave signal. The Lamb wave signal of the aluminum sheet is obtained by detecting it through a laser device. The detected Lamb wave signal was decomposed using CEEMDAN to obtain several IMF components that meet the decomposition termination condition. Extract the IMF components of each order from the decomposition, perform time modeling on the IMF components, calculate the permutation entropy value of each order of time modeling, filter the effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and reconstruct the effective IMF components once. The reconstructed signal is decomposed using SWT to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients. The L2 regularization method is used to constrain the high-frequency noise detail coefficients. The low-frequency approximation coefficients obtained by decomposition are reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal.

2. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 1, characterized in that, The process involves setting two points, A and B, on the surface of the aluminum sheet. Point A is the laser excitation position, and point B is the Lamb wave signal detection position. The Lamb wave signal of the aluminum sheet is obtained by detecting it using a laser device. Specifically: A laser ultrasonic testing system was set up, the aluminum plate sample was fixed on the system platform, the pulse laser of the testing system was started, and then the Sagnac interferometer was adjusted to perform laser detection on the position of the aluminum plate with defects to be detected. Lamb wave signals of thin aluminum sheets were acquired using the LabVIEW data platform.

3. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 1, characterized in that, The detected Lamb wave signal is decomposed using CEEMDAN to obtain several IMF components that satisfy the decomposition termination condition, specifically: S1, Gaussian white noise is added to the acquired Lamb wave signal Y(t), L n (t) represents Gaussian white noise added n times, and follows a distribution N(0,1): Y n (t)=Y(t)+θ0L n (t),n=1,2,…,N Among them, Y n (t) represents the nth signal after adding white noise; θ0 is the standard deviation of the noise; n is the number of times noise was added; S2, input the Y(t) with added white noise into EMD for decomposition to obtain the first-order component IMF1 of CEEMDAN: Calculate the first residual component r1: r1=Y(t)-IMF1 S3, Obtaining the k-th modal component E based on EMD decomposition. k (·), Gaussian white noise is added to the residual components to generate a new sequence r1(n)=r1+θ1E1[L n (t)]; Then, EMD decomposition is performed on the signal r1(n) to decompose the second-order intrinsic mode component IMF2. The residual component after removing the second-order intrinsic mode component is r2: r2=r1-IMF2 Where θ1 is the added white noise signal. S4, repeat step S3 to obtain the k-th eigenmode component IMF. K and the k-th residual component r k : r k =r k-1 -IMF k Repeat steps S1-S4 until the residual component r is reached. k If there are fewer than two extreme points, stop the signal decomposition. When the signal decomposition stops, the k-th order eigenmode component and one residual component are obtained. The signal Y(t) is represented as: Where Y(t) is the acquired Lamb wave signal, These are the eigenmode components of the decomposition, r k For the residual components.

4. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 3, characterized in that, The decomposition processing of the detected Lamb wave signal using CEEMDAN also includes: During the decomposition of CEEMDAN, mode aliasing is monitored by calculating the spectral correlation coefficient between adjacent IMF components. The spectral correlation coefficient is obtained by calculating the Pearson correlation coefficient of the power spectral density function of adjacent IMF components. When the spectral correlation coefficient is higher than the preset aliasing determination threshold, modal aliasing is determined to exist between the adjacent IMF components; Based on the center frequency of the IMF component with modal aliasing, the frequency band energy distribution of the added Gaussian white noise is adjusted. The next round of CEEMDAN decomposition is performed based on the Gaussian white noise with the frequency band energy distribution. The aliased modes are gradually separated through the iterative process until the spectral correlation coefficient is lower than the aliasing determination threshold. Finally, the set of IMF components with suppressed modal aliasing is output.

5. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 4, characterized in that, The step of adjusting the frequency band energy distribution of the added Gaussian white noise based on the center frequency of the IMF component where modal mixing is determined to exist is specifically as follows: Extract the adjacent IMF components that are determined to have mode aliasing, calculate their respective center frequencies, and determine the frequency band range of their overlap. Based on the overlapping frequency band range, a bandpass filter with a preset range of passband is generated. The standard Gaussian white noise is filtered using the bandpass filter to generate auxiliary noise with frequency band energy concentrated in the aliasing frequency band. The auxiliary noise is superimposed with a portion of Gaussian white noise with energy below a preset value and frequency band above a preset value to synthesize a new target auxiliary noise. The energy decomposition of the new target auxiliary noise is specifically enhanced in the aliasing frequency band, while it is weakened in other frequency bands. The new target auxiliary noise is used for CEEMDAN decomposition in subsequent iterations to obtain the aliasing-suppressed IMF component, and the aliased IMF components are updated.

6. The laser-ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 1, characterized in that, The process involves extracting and decomposing IMF components of each order, performing time modeling on the IMF components, calculating the permutation entropy value of each time-modeled component, filtering the effective IMF components and noisy IMF components of the Lamb wave signal based on the permutation entropy value, and performing a reconstruction on the effective IMF components. Specifically: For each order of IMF component obtained from the decomposition, each order IMF component is regarded as a time series of length N, X = {x(a), a = 1, 2, 3, ..., N}, where the length of the IMF component is consistent with the length of the Lamb wave. The phase space of X is reconstructed to obtain the following reconstructed matrix: b=n-(h-1)λ Where h is the embedding dimension, λ is the time delay, and b is the number of reconstructed components; Rearranging the row vectors of H in ascending order yields a new sequence: T(l)={j1,j2,…,j h },l=1,2,…,l(l≤h!) Where {j1,j2,…,j h } represents the new sequence after recombination. There are l ≤ h! different combinations of symbol sequences. By counting the frequency of each permutation in the reconstructed sequence, the probability sequence [d1, d2, ..., dn] can be obtained. l ], thus we can obtain The permutation entropy of a time series is defined as follows, and normalization is performed: Among them, H p P is the permutation entropy value; P is the normalized entropy value. A normalized entropy threshold is set, and effective IMF components and noisy IMF components are filtered according to the normalized entropy threshold. The effective IMF components are superimposed with the corresponding residual components to form the first reconstructed Lamb wave signal Z(t), which is expressed as: Z(t)=∑ 有效IMF IMF k +r k 。 7. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 1, characterized in that, The SWT decomposition process is performed on the reconstructed signal to obtain several low-frequency approximation coefficients and high-frequency noise detail coefficients, specifically: The reconstructed signal Z(t) is decomposed by stationary wavelet transform. The stationary wavelet transform decomposition is performed by inserting zeros between the high-pass filter L(t) and the low-pass filter H(t). The signal length is extended according to the zero-insertion operation so that the length of the low-frequency approximation coefficients and the high-frequency noise detail coefficients after each decomposition is consistent with the length of Z(t). The mathematical expression for SWT decomposition is as follows, where the low-frequency approximation coefficient Ac is the output of the low-pass filter H(t), and the high-frequency noise detail coefficients Dc are the output of the high-pass filter L(t). The expression for the first-level decomposition is: A c1 =Z(t)*H(t),D c1 =Z(t)*L(t) Subsequent layer decomposition is achieved through iterative zero-placing operations. The decomposition expression for the (j+1)th layer is: Where Dc represents the noise-dominated high-frequency component in the Lamb wave signal, Ac represents the signal-dominated low-frequency component, and * represents the convolution operation.

8. The laser ultrasonic Lamb wave signal noise reduction method for defect detection of thin aluminum plates according to claim 1, characterized in that, The L2 regularization method is used to constrain the high-frequency noise detail coefficients. The low-frequency approximation coefficients obtained from the decomposition are then reconstructed with the L2-constrained high-frequency noise detail coefficients to obtain the final denoised Lamb wave signal. Specifically: The initial loss function for the high-frequency noise detail coefficients Dc is defined as J(w; x, Y), where w is the weighting coefficient, x is the input signal Dc, and Y is the desired clean signal feature template, which is obtained by labeling historical data. Add the L2 regularization term to the loss function to form a new objective function J. i : Where λ is a hyperparameter of regularization strength, It is a difference matrix. The square of the L2 norm; By minimizing the objective function J i The high-frequency detail coefficients Dc′ after constraint are obtained by solving. Ac and Dc′ are reconstructed by stationary wavelet inverse transform, and its expression is: Q(t)=ISWT(Ac,Dc′), where Q(t) is the final denoised Lamb wave signal.

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