Time-frequency analysis method for pipeline weld crack electromagnetic acoustic emission aliasing signal

By performing TQWT decomposition and penalty function inducing group sparse processing on electromagnetic acoustic emission signals, combined with the waveguide dispersion curve, the problem of signal interference and modal recognition in electromagnetic acoustic emission signals detection is solved, and the accuracy of signal separation and modal recognition is improved.

CN120277401APending Publication Date: 2025-07-08NANTONG UNIV
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Patent Information

Application Number
CN202510355015.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-25
Publication Date
2025-07-08

AI Technical Summary

Technical Problem

In the prior art, electromagnetic acoustic emission signal detection has electromagnetic interference, weak signal and low signal-to-noise ratio, which leads to difficulty in extracting effective signals and difficult modal identification.

Method used

The time-frequency analysis method of electromagnetic acoustic aliased signals of pipeline weld cracks is adopted, and the signal is decomposed by TQWT, and the penalty function is used to induce group sparse construction cost function, and modal identification is performed by combining the MM algorithm and the guided dispersion curve to separate the signal-to-noise ratio.

Benefits of technology

The aliasing wave packets in the electromagnetic acoustic transmitting signal are effectively separated, which improves the signal-to-noise ratio of the signal, reduces the modal aliasing phenomenon, and improves the accuracy of modal recognition.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention belongs to the technical field of nondestructive testing, and particularly relates to a time-frequency analysis method for electromagnetic acoustic emission aliasing signals of pipeline weld cracks, which comprises the following steps: decomposing electromagnetic acoustic emission signals based on adjustable Q-factor wavelet transform (TQWT) to obtain a plurality of sub-band wavelet coefficients; a penalty function is used for inducing group sparsity of the electromagnetic acoustic emission signals to construct a cost function, the cost function is minimized, and an MM algorithm is introduced for solving; performing TQWT inverse transformation on the wavelet coefficient after group sparse solution to obtain a reconstructed electromagnetic acoustic emission signal; discrete wavelet transform is carried out on the reconstructed signal to extract time-frequency characteristics, and modal recognition is carried out in combination with a pipeline guided wave conversion frequency dispersion curve. According to the method, aliasing wave packets in the original electromagnetic acoustic emission signals can be separated, and the signal-to-noise ratio of the signals is improved, so that the modal aliasing phenomenon is reduced, the modal recognition accuracy is improved, and the method has a wide application prospect.
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Description

Technical Field

[0001] The invention belongs to the technical field of nondestructive testing, and in particular relates to a time-frequency analysis method for electromagnetic and acoustic emission aliasing signals of pipeline weld cracks. Background Art

[0002] Welds are key parts of pipeline structures, and their quality directly affects the service performance of pipelines. However, under complex environmental conditions, welds are susceptible to fatigue loads and impacts, leading to stress concentration and cracking, which poses a major safety hazard. Among pipeline weld damages, circumferential cracks are particularly common. The expansion of circumferential cracks will not only seriously weaken the structural integrity of the pipeline and greatly shorten the service life of the pipeline, but may also cause environmental pollution and safety risks.

[0003] As an advanced nondestructive testing technology, electromagnetic acoustic emission can induce inherent acoustic emission responses from metal cracks through electromagnetic coupling compared with traditional acoustic emission testing technology. It has the advantages of controllable detection process and sensitivity to tiny defects. It has unique advantages in the detection of circumferential cracks in pipeline welds. According to the guided wave theory, modal identification of electromagnetic acoustic emission signals can be used for further defect location and quantification. However, electromagnetic acoustic emission signals contain both guided wave components and acoustic emission components, and the signal structure is complex. At the same time, electromagnetic interference often exists in actual detection, and electromagnetic acoustic emission signals are generally weak, and the signal-to-noise ratio is low, which brings challenges to the extraction of effective signals. In addition, the multi-mode effect and dispersion effect of guided waves further increase the difficulty of modal identification of signals. Summary of the invention

[0004] The present invention solves the technical problems in the prior art that electromagnetic interference often exists in actual electromagnetic signal detection, and the electromagnetic acoustic emission signal is generally weak, the signal-to-noise ratio is low, and effective signal extraction is difficult; the present invention proposes a time-frequency analysis method for electromagnetic acoustic emission aliasing signals of pipeline weld cracks, which can separate the aliased wave packets in the original electromagnetic acoustic emission signal, improve the signal-to-noise ratio of the signal, thereby reducing the modal aliasing phenomenon and improving the accuracy of modal recognition.

[0005] The present invention adopts the following technical solutions:

[0006] A time-frequency analysis method for electromagnetic and acoustic emission aliasing signals of pipeline weld cracks comprises the following steps:

[0007] Step S1, collecting electromagnetic acoustic emission signals of circumferential cracks in pipeline welds;

[0008] Step S2, decomposing the electromagnetic acoustic emission signal based on TQWT to obtain multiple sub-band wavelet coefficients;

[0009] Step S3: Use a penalty function to induce group sparsity of the electromagnetic acoustic emission signal to construct a cost function, minimize the cost function, and introduce the MM algorithm for solution;

[0010] Step S4: Perform the inverse TQWT on the wavelet coefficients after group sparse solution to obtain the reconstructed electromagnetic acoustic emission signal;

[0011] Step S5: Perform discrete wavelet transform on the reconstructed signal to extract time-frequency features, and combine with the converted dispersion curve of the pipeline guided wave for mode identification.

[0012] Further, the specific content of step S2 is as follows: TQWT is a multi-channel filter. The frequency-domain representation of the electromagnetic acoustic emission signal is obtained by using the unit discrete Fourier transform, and through a series of high-pass and low-pass filters, the output of the low-scale filter is continuously decomposed by two-channel iteration. Among them, the quality factor Q and the redundancy r can change the oscillation and attenuation characteristics of TQWT. The quality factor Q can be expressed as:

[0013]

[0014] where f c is the center frequency of the signal, and BW represents the bandwidth of the signal.

[0015] Further, Q, r, α, and β satisfy the following relationship:

[0016]

[0017] where α is the low-pass scale transformation coefficient, β is the high-pass scale transformation coefficient, and Q and r directly determine the parameters of the filter bank.

[0018] Further, in TQWT, J is the decomposition level, and there is a theoretical upper limit value J max , and the calculation formula is:

[0019]

[0020] where N is the length of the signal, is the floor operator.

[0021] Further, the specific content of step S3 is as follows: The electromagnetic acoustic emission signal has group sparsity, while the noise signal does not have group sparsity. Therefore, groups with larger pulse amplitudes in the signal can be regarded as a whole, and pulses are not allowed to appear in other groups. In this way, the wave packets are separated, the influence of noise is reduced, and the signal-to-noise ratio of the electromagnetic acoustic emission signal is improved. The cost function constructed by using a penalty function to induce group sparsity is:

[0022]

[0023] where v iare the wavelet coefficients of the TQWT subbands, are the wavelet coefficients after group-sparse solution, λ is the regularization parameter, and γ is the penalty function that induces group sparsity, is the group with K points starting from index j of the i-th subband.

[0024] Furthermore, the cost function can be transformed into a minimization problem:

[0025]

[0026] The MM algorithm is an iterative method for solving complex optimization problems by constructing a surrogate function. In group-sparse processing, by alternately updating the weight coefficients and optimization variables, it not only maintains the convergence of the objective function but also avoids the numerical instability problem inherent in non-convex optimization. By optimizing the above formula using a non-convex penalty function and then transforming the non-convex optimization problem into a convex optimization problem, the MM algorithm can be used to solve it.

[0027] Furthermore, the specific content of step S5 is as follows: Wavelet transform can be used to analyze the guided-wave dispersion characteristics of electromagnetic acoustic emission signals in the time-frequency domain. The discrete wavelet transform has the advantages of small computational complexity and fast analysis speed. The continuous wavelet transform of the reconstructed signal y(t) can be defined as:

[0028]

[0029] where ψ * (t) is the wavelet mother function, a is the scale parameter, and b is the translation parameter,

[0030] Furthermore, for the collected discrete signal, a = 2 -p , b = 2 -p k, where p, k ∈ Z, and the corresponding wavelet basis function is:

[0031] ψ p,k (t) = 2 p / 2 ψ(2 p t - k)

[0032] Therefore, the discrete wavelet transform of the reconstructed signal y(t) is:

[0033]

[0034] Furthermore, the propagation of guided waves in the pipeline satisfies the Navier equation of motion:

[0035]

[0036] where μ and λ are the lame constants, ρ is the pipeline density, and u is the displacement, is the Hamiltonian operator, is the Laplacian operator. After solving the above equation according to the theory of elastic dynamics, the dispersion curve of pipeline guided waves can be plotted.

[0037] Furthermore, the coordinate axes of the discrete wavelet transform diagram of the electromagnetic acoustic emission signal are frequency - time (f - t), and the coordinate axes of the pipeline guided wave dispersion curve are frequency - group velocity (f - c g ). In order to superimpose the two diagrams, it is necessary to convert the coordinate axes of the pipeline guided wave dispersion curve by means of the distance l from the sensor to the circumferential crack of the pipeline:

[0038]

[0039] where c g is the group velocity of the pipeline guided wave.

[0040] Thus, the coordinate axes of the converted dispersion curve of the pipeline guided wave can be obtained as frequency - time (f - t), and then the converted dispersion curve can be superimposed with the discrete wavelet transform diagram of the electromagnetic acoustic emission signal, so as to realize the modal identification of the electromagnetic acoustic emission signal.

[0041] The present invention has the following advantages compared with the prior art:

[0042] The present invention reconstructs the electromagnetic acoustic emission signal based on the GS - TQWT model, separates the signal wave packets, and improves the signal - to - noise ratio. Then, it combines the converted dispersion curve of the pipeline guided wave and the discrete wavelet transform diagram to perform modal identification on the signal. Through experimental research on the electromagnetic acoustic emission of circumferential cracks in pipeline welds, the effectiveness and superiority of this method are verified. The method proposed by the present invention can effectively reduce the modal aliasing phenomenon and improve the accuracy of modal identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is the flow chart of the time - frequency analysis method for the aliasing mode of the electromagnetic acoustic emission signal of circumferential cracks in pipeline welds;

[0044] Figure 2 is the experimental system diagram for the detection of the electromagnetic acoustic emission signal of circumferential cracks in pipeline welds;

[0045] Figure 3 is the collected electromagnetic acoustic emission signal, where (a) is the original electromagnetic acoustic emission signal and (b) is the reconstructed electromagnetic acoustic emission signal;

[0046] Figure 4 is the pipeline guided wave dispersion curve, where (a) is the phase velocity and (b) is the group velocity;

[0047] Figure 5The first three wave packets in the collected electromagnetic acoustic emission signals and the modal identification results, where (a) are the first three wave packets of the original electromagnetic acoustic emission signal, (b) are the first three wave packets of the reconstructed electromagnetic acoustic emission signal, (c) is the superimposed diagram of the discrete wavelet transform of the first three wave packets of the original electromagnetic acoustic emission signal and the pipeline guided wave conversion dispersion curve, and (d) is the superimposed diagram of the discrete wavelet transform of the first three wave packets of the reconstructed electromagnetic acoustic emission signal and the pipeline guided wave conversion dispersion curve. Specific implementation manner

[0048] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0049] Example 1:

[0050] As Figure 1 shown, a time-frequency analysis method for electromagnetic acoustic emission aliasing signals of pipeline weld cracks includes the following steps:

[0051] Step S1, collect electromagnetic acoustic emission signals of circumferential cracks in the pipeline weld;

[0052] Step S2, based on the GS-TQWT model, decompose the electromagnetic acoustic emission signal by TQWT to obtain multiple sub-band wavelet coefficients;

[0053] Step S3, use a penalty function to induce group sparsity of the electromagnetic acoustic emission signal to construct a cost function, minimize the cost function and introduce the MM algorithm to solve it;

[0054] Step S4, perform inverse TQWT on the wavelet coefficients after group sparsity solution to obtain the reconstructed electromagnetic acoustic emission signal;

[0055] Step S5, perform discrete wavelet transform on the reconstructed signal to extract time-frequency features, and combine the pipeline guided wave conversion dispersion curve for modal identification.

[0056] Specifically, step S1 includes: As Figure 2 shown, after setting up the experimental system, set the sampling frequency of the data acquisition device to 2 MHz, and select a five-cycle sine wave signal modulated by a Hann window with a center frequency of 250 kHz as the excitation signal. After applying the excitation signal to the excitation device, electromagnetic acoustic emission signals gradually start to be generated at the tip of the circumferential crack.

[0057] As Figure 3As shown in (a), approximately 800 sampled data points collected after injecting the excitation signal were selected as the original electromagnetic acoustic emission signal, with a time length of approximately 400 μs. It can be seen that the original electromagnetic acoustic emission signal contains multiple large-amplitude wave packets, including guided wave signals, acoustic emission signals, and noise signals, and there are overlapping and sticking phenomena between different wave packets. Figure 3 Parts a, b, and c in (a) are the parts where the wave packet sticking is the most serious, which greatly increases the difficulty of modal identification.

[0058] Specifically, step S2 includes: TQWT is a multi-channel filter. The frequency-domain representation of the electromagnetic acoustic emission signal is obtained by using the unit discrete Fourier transform and is continuously decomposed through a series of high-pass and low-pass filters by two-channel iterative decomposition of the output of the low-scale filter. Among them, the quality factor Q and the redundancy r can change the oscillation and attenuation characteristics of TQWT. The quality factor Q can be expressed as:

[0059]

[0060] In the formula, f c is the center frequency of the signal, and BW represents the bandwidth of the signal.

[0061] Specifically, Q, r, α, and β satisfy the following relationship:

[0062]

[0063] In the formula, α is the low-pass scale transformation coefficient, β is the high-pass scale transformation coefficient, and Q and r directly determine the parameters of the filter bank.

[0064] Specifically, in TQWT, J is the decomposition layer number, and there is a theoretical upper limit value J max , and the calculation formula is:

[0065]

[0066] In the formula, N is the length of the signal, is the floor operator.

[0067] Specifically, step S3 includes: The electromagnetic acoustic emission signal has group sparsity, while the noise signal does not have group sparsity. Therefore, groups with larger pulse amplitudes in the signal can be regarded as a whole, and pulses are not allowed to appear in other groups, thereby separating the wave packets, reducing the influence of noise, and improving the signal-to-noise ratio of the electromagnetic acoustic emission signal. The cost function induced by the penalty function to construct group sparsity is:

[0068]

[0069] In the formula, v i is the wavelet coefficient of the TQWT sub-band, The wavelet coefficients after group sparse solution, λ is the regularization parameter, and γ is the penalty function that induces group sparsity. is a group with K points starting from index j of the i-th subband.

[0070] Specifically, the cost function can be transformed into a minimization problem:

[0071]

[0072] Specifically, the MM algorithm is an iterative method for solving complex optimization problems by constructing a surrogate function. In group sparse processing, by alternately updating the weight coefficients and optimization variables, it not only maintains the convergence of the objective function but also avoids the numerical instability problem inherent in non-convex optimization. By optimizing the above formula using a non-convex penalty function and then transforming the non-convex optimization problem into a convex optimization problem, the MM algorithm can be used for solution.

[0073] Specifically, step S4 includes: performing an inverse TQWT on the wavelet coefficients after group sparse solution to obtain the reconstructed electromagnetic acoustic emission signal. As shown in Figure 3 (b), the three places a, b, and c with severe wave packet adhesion in the original electromagnetic acoustic emission signal correspond to a', b', and c' in the reconstructed electromagnetic acoustic emission signal. There is an obvious separation phenomenon in the wave packets at a', b', and c'. These wave packets contain potential electromagnetic acoustic emission mode signals, and after separation, it is helpful for further modal identification.

[0074] Specifically, considering that the distance between the sensor and the circumferential crack is only 55 mm, in order to avoid echo interference, the first three wave packets in the signal are selected for modal identification. As shown in Figure 5 (a) and Figure 5 (b), in order to ensure the accuracy of the reconstruction of the first three wave packets, the data of the first 200 sampling points in the original electromagnetic acoustic emission signal are intercepted again for reconstruction, and the time length is about 100 μs.

[0075] Specifically, Figure 5 (b) The reconstructed signal contains three wave packets. The first wave packet appears around 14.5 μs to 35 μs, the second wave packet appears around 41.5 μs to 59.5 μs, and the third wave packet appears around 62 μs to 86.5 μs. It can be clearly seen that there is no overlapping part between the three wave packets, and the interference caused by noise is reduced.

[0076] Specifically, step S5 includes: Wavelet transform can be used to analyze the guided wave dispersion characteristics of electromagnetic acoustic emission signals in the time-frequency domain. The discrete wavelet transform has the advantages of small computational complexity and fast analysis speed. The continuous wavelet transform of the reconstructed signal y(t) can be defined as:

[0077]

[0078] where ψ * (t) is the mother wavelet function, a is the scale parameter, b is the translation parameter,

[0079] Specifically, for the discrete signal collected, a = 2 -p , b = 2 -p k, where p, k ∈ Z, and the corresponding wavelet basis function is:

[0080] ψ p,k (t) = 2 p / 2 ψ(2 p t - k)

[0081] Therefore, the discrete wavelet transform of the reconstructed signal y(t) is:

[0082]

[0083] Specifically, the propagation of guided waves in the pipeline satisfies the Navier equation of motion:

[0084]

[0085] where μ and λ are the lame constants, ρ is the pipeline density, u is the displacement, is the Hamiltonian operator, is the Laplace operator. After solving the above equation according to the theory of elastic dynamics, the dispersion curve of pipeline guided waves can be plotted, as Figure 4 shown.

[0086] Specifically, the coordinate axes of the discrete wavelet transform diagram of the electromagnetic acoustic emission signal are frequency - time (f - t), and the coordinate axes of the pipeline guided wave dispersion curve are frequency - group velocity (f - c g ). In order to superimpose the two diagrams, it is necessary to convert the coordinate axes of the pipeline guided wave dispersion curve by means of the distance l from the sensor to the circumferential crack of the pipeline:

[0087]

[0088] where c g is the group velocity of the pipeline guided wave.

[0089] Thus, the coordinate axes of the converted dispersion curve of the pipeline guided wave can be obtained as frequency - time (f - t), and then the converted dispersion curve can be superimposed with the discrete wavelet transform diagram of the electromagnetic acoustic emission signal, so as to realize the modal recognition of the electromagnetic acoustic emission signal.

[0090] Example 2:

[0091] Since the electromagnetic acoustic emission signal cannot be generated immediately upon excitation in the experiment, based on the above embodiments, the conversion dispersion curve in this embodiment also needs to be modified along the time axis. The excitation signal in this embodiment contains 40 sampling points, and the time length is approximately 20 μs. Therefore, half of the excitation signal time, that is, 10 μs, is selected, and the conversion dispersion curve is translated 10 μs to the right along the time axis.

[0092] Specifically, as Figure 5 (c) shows, the discrete wavelet transform diagram of the first three wave packets of the original electromagnetic acoustic emission signal contains three peak positions, and there is an obvious adhesion phenomenon between the second and the third peak positions. As Figure 5 (d) shows, the discrete wavelet transform diagram of the first three wave packets of the reconstructed electromagnetic acoustic emission signal also contains three peak positions, but there is almost no adhesion between the three peak positions, and the first peak is relatively enhanced. Among them, the first peak position appears around 16.4 μs to 36.3 μs, the second peak position appears around 40.3 μs to 58.7 μs, and the third peak position appears around 62.7 μs to 80.1 μs, corresponding to Figure 5 the three wave packets of the signal in (b), and these three wave packets contain multiple modes.

[0093] Specifically, the potential multimodal components contained in the wave packet can be determined by observing the overlapping situation between the conversion dispersion curve of the pipe guided wave and the peak positions of the discrete wavelet transform diagram. Considering that the polarization direction of the sensor is perpendicular to the bonding surface, only the modes containing the radial displacement component can be detected by the sensor. Therefore, in this embodiment, only the longitudinal and bending modes are considered, and the torsional mode containing only the circumferential displacement is not considered. At the same time, since the L(0,2) mode mainly contains the axial displacement component, and in this embodiment, both the sensor and the crack are in the circumferential direction, the L(0,2) mode is not within the scope of consideration either.

[0094] Specifically, as Figure 5 (b) and Figure 5 (d) show, the first wave packet in the signal, that is, around 14.5 μs to 35 μs, contains the F(1,2) and F(1,3) modes. Since the conversion dispersion curves of the L(0,1) and F(1,1) modes pass through the second and third peak positions of the discrete wavelet transform diagram successively, it can be seen that there is a certain order in the excitation of the L(0,1) and F(1,1) modes. The second wave packet, that is, around 41.5 μs to 59.5 μs, and the third wave packet, that is, around 62 μs to 82 μs, respectively contain the L(0,1) or F(1,1) modes.

[0095] In summary, the time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of pipeline weld cracks proposed by the present invention includes: based on the GS-TQWT model, decomposing the electromagnetic acoustic emission signal by TQWT to obtain multiple sub-band wavelet coefficients; using a penalty function to induce the group sparsity of the electromagnetic acoustic emission signal to construct a cost function and transforming it into a minimization problem, and then solving it by introducing the MM algorithm; performing the inverse TQWT on the wavelet coefficients after group sparsity solution to obtain the reconstructed electromagnetic acoustic emission signal; performing discrete wavelet transform on the reconstructed signal to extract time-frequency features, and combining with the pipeline guided wave conversion dispersion curve for mode identification. The results show that this method can separate the aliased wave packets in the original electromagnetic acoustic emission signal, improve the signal-to-noise ratio of the signal, thereby reducing the mode aliasing phenomenon and improving the accuracy of mode identification, and has broad application prospects.

[0096] Only some exemplary embodiments of the present invention have been described above by way of illustration. Without doubt, for those of ordinary skill in the art, various different ways can be used to modify the described embodiments without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A time-frequency analysis method for electromagnetic acoustic emission aliasing signals of pipeline weld cracks, characterized in that It includes the following steps: S1: Collect the electromagnetic acoustic emission signals of the circumferential cracks of the pipeline welds; S2: Decompose the electromagnetic acoustic emission signals based on TQWT to obtain multiple sub-band wavelet coefficients; S3: Use the penalty function to induce the group sparsity of the electromagnetic acoustic emission signals to construct a cost function, minimize the cost function and introduce the MM algorithm to solve it; S4: Perform the inverse TQWT on the wavelet coefficients after the group sparsity solution to obtain the reconstructed electromagnetic acoustic emission signals; S5: Perform the discrete wavelet transform on the reconstructed signals to extract the time-frequency features, and combine with the dispersion curves of the pipeline guided waves for mode identification.

2. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 1, characterized in that The specific content of step S2 is as follows: TQWT is a multi-channel filter. Among them, the quality factor Q and the redundancy r change the oscillation and attenuation characteristics of TQWT; The quality factor Q is expressed as: where f c is the center frequency of the signal, and BW represents the bandwidth of the signal.

3. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 2, characterized in that, Q, r, α, β satisfy the following relationship: In the formula, α is the low-pass scale transformation coefficient, and β is the high-pass scale transformation coefficient.

4. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 3, characterized in that In the TQWT, J is the decomposition level, and there is a theoretical upper limit value J max , and the calculation formula is: where N is the length of the signal, is the floor operator.

5. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 1, wherein The specific content of step S3 is as follows: According to the group sparsity of the electromagnetic acoustic emission signals, the cost function constructed by using the penalty function to induce group sparsity is: where \(v\) i is the wavelet coefficient of the TQWT subband, is the wavelet coefficient after group sparse solution, \(\lambda\) is the regularization parameter, and \(\gamma\) is the penalty function for inducing group sparsity, is the group with \(K\) points starting from index \(j\) of the \(i\)-th subband.

6. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 5, wherein Convert the cost function into a minimization problem: By using a non-convex penalty function to optimize the above formula, and then transforming the non-convex optimization problem into a convex optimization problem, the MM algorithm is used to solve it 7. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 1, wherein The specific content of step S5 is as follows: The continuous wavelet transform of the reconstructed signal y(t) is defined as: where ψ * (t) is the mother wavelet function, a is the scale parameter, and b is the translation parameter, 8. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 7, wherein For the discrete signals collected, a = 2 -p , b = 2 -p k, where p, k ∈ Z, and the corresponding wavelet basis function is: ψ p,k (t) = 2 p / 2 ψ(2 p t - k) Therefore, the discrete wavelet transform of the reconstructed signal y(t) is:

9. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 8, wherein The propagation of guided waves in the pipeline satisfies the Navier equation of motion: where μ and λ are the Lame constants, ρ is the density of the pipe, u is the displacement, is the Hamiltonian operator, is the Laplacian operator. After solving the above equation according to the theory of elastodynamics, the dispersion curve of the pipe guided wave is plotted.

10. The time-frequency analysis method for the electromagnetic acoustic emission aliasing signal of the pipeline weld crack according to claim 9, characterized in that, In order to superimpose the discrete wavelet transform diagram of the electromagnetic acoustic emission signals with the dispersion curves of the pipeline guided waves, it is necessary to convert the coordinate axes of the pipeline guided wave dispersion curves by means of the distance l from the sensor to the circumferential crack of the pipeline: where c g is the group velocity of the guided wave in the pipeline; After obtaining the converted dispersion curves of the pipeline guided waves, superimpose them with the discrete wavelet transform diagram to realize the mode identification of the electromagnetic acoustic emission signals.