Defect echo sparse representation method based on shear wave characteristics and dictionary shrinkage

Abstract

The invention provides a defect echo sparse representation method based on shear wave characteristics and dictionary shrinkage, and the method comprises the following steps: constructing a dictionary based on frequency characteristics and attenuation characteristics of horizontal shear guided waves, the frequency characteristics being represented by wave number characteristics, and the attenuation characteristics being a weak damping system; carrying out clustering shrinkage on dictionary atoms by adopting a clustering shrinkage algorithm based on K-Means; and constructing a convex optimization model based on a basis pursuit denoising problem, solving an L1 norm regularization problem through a sparse coefficient vector solution algorithm, and approximately obtaining a comprehensive understanding of a sparse vector. According to the method, denoising of the non-shear wave signals and feature extraction of the shear wave signals are achieved through sparse representation of the signals, the method is particularly suitable for sparse decomposition of defect signals generated during shear wave defect detection, the signals obtained after sparse representation can assist in defect positioning, and the method has wide application prospects in some other signal processing scenes.

Description

Technical Field

[0001] The present invention relates to the technical fields of signal processing and nondestructive testing, and particularly relates to a sparse representation method for defect echo based on shear wave characteristics and dictionary shrinkage Background Art

[0002] In engineering backgrounds such as bridge engineering, building construction, and oil and gas transportation, welds, as the key nodes for connecting materials, are the core elements to ensure engineering quality. Fatigue loads such as external alternating pressure and mechanical vibration, as well as sudden external force impacts, etc., can easily cause stress concentration at the welds, thereby triggering weld cracking. Therefore, regular inspection of welds is crucial. However, since the areas with welds in in-use buildings, bridges, pipelines, etc. are often in harsh and enclosed environments, it is a major challenge for maintenance personnel to detect whether cracks have occurred at the welds. In traditional ultrasonic testing methods, the thickness change of the propagation medium has a great influence on the signal, and the signal will be distorted at the intersection of the weld and the steel medium. In contrast, the SH0-mode horizontal shear guided wave can effectively solve this problem. Therefore, the defect location technology based on horizontal shear guided waves has become an important tool for weld nondestructive testing. This technology mainly studies two types of problems, namely the excitation method of horizontal shear guided waves and the denoising algorithm for defect echo signals. Due to the complexity of the detection environment and the special structural characteristics of the detection object, the received guided wave signals often contain clutter and environmental noise, which brings problems to the extraction of defect echoes. Therefore, there is an urgent need for a method that can effectively solve this problem Summary of the Invention

[0003] The purpose of the present invention is to solve the deficiencies existing in the prior art. The present invention proposes a sparse representation method for defect echo based on shear wave characteristics and dictionary shrinkage. The present invention can process and analyze the signals generated when detecting defects using horizontal shear guided waves and achieve defect location. The dictionary based on the fusion of the wave number characteristics and weak damping attenuation characteristics of horizontal shear guided waves can use the characteristics of horizontal shear guided waves as the standard during signal extraction, and uniformly treat noise and clutter of other components as noise; the clustering shrinkage algorithm is used to delete redundant atoms in the dictionary, which can reduce the computational amount during atom matching and improve the algorithm operation efficiency while maintaining the sparsity of the dictionary; the split augmented Lagrangian shrinkage algorithm has good convergence and can further improve the algorithm operation efficiency

[0004] To achieve the above purpose, the present invention provides a sparse representation method for defect echo based on shear wave characteristics and dictionary shrinkage, including the following steps:

[0005] Construct a dictionary based on the frequency characteristics and attenuation characteristics of horizontal shear guided waves, where the frequency characteristics are represented by wave number characteristics, and the attenuation characteristics are a weakly damped system

[0006] Next, a clustering and shrinking algorithm based on K-Means is used to cluster and shrink the dictionary atoms, reducing the data volume while maintaining the sparsity of the dictionary.

[0007] Finally, a convex optimization model based on the basis pursuit denoising problem is constructed, and the L1-norm regularization problem is solved through a sparse coefficient vector solving algorithm, and a reasonable solution of the sparse vector can be approximately obtained. Specifically, the split augmented Lagrangian shrinkage algorithm is introduced to solve the sparse coefficient.

[0008] Among them, for the excitation guided wave signal, a horizontally polarized shear wave of a single mode is excited on the surface to be measured using an electromagnetic ultrasonic excitation device with good directivity, and the excitation signal is H(t).

[0009] Signal acquisition and preprocessing

[0010] A piezoelectric ceramic sensor is used to collect the guided wave signal to obtain the original signal set.

[0011] The original signal is preliminarily denoised, and the part of the signal with a large frequency difference from the excitation signal is filtered out, and a suitable signal segment is extracted to obtain the preprocessed signal h(t).

[0012] Construct a dictionary D based on the excitation signal and the shear wave characteristics:

[0013] Fuse the shear wave number characteristics and the weak damping attenuation characteristics to construct dictionary atoms based on the excitation signal;

[0014] According to the actual situation, select a suitable interval for the attenuation coefficient S.

[0015] Cluster and shrink the dictionary atoms: Use a clustering and shrinking algorithm based on K-Means.

[0016] Convert the feature extraction problem into a convex optimization problem: Construct a convex optimization model based on basis pursuit denoising.

[0017] Solve for the sparse coefficient vector: By splitting variables, convert the convex optimization model from an unconstrained optimization form to a constrained optimization form;

[0018] Use the augmented Lagrangian algorithm to solve the constrained optimization model, and approximately solve the optimal solution of the sparse coefficient vector through the convergence of the iterative process;

[0019] Iterative process:

[0020]

[0021] Where s is the sparse coefficient, v is the splitting variable, λ is the Lagrange multiplier, μ is the penalty factor, l is the number of iterations, r is the auxiliary variable in the iterative process of the sparse coefficient s and the splitting variable v, y is the input signal, and D is the over-complete dictionary.

[0022] Signal reconstruction: Obtain the reconstructed signal through the constructed dictionary and the optimal solution of the obtained sparse coefficient vector.

[0023] Result output:

[0024] Extract the time points where the wave peaks of the incident signal, defect echo, and end echo are located, and obtain the distance between the electromagnetic ultrasonic excitation device and the center point of the sensor, and the distance between the electromagnetic ultrasonic excitation device and the propagation boundary.

[0025] From the above data, the distance between the electromagnetic ultrasonic excitation device and the defect can be estimated by calculating the following formula:

[0026]

[0027] Where is the estimated distance between the electromagnetic ultrasonic exciter and the defect, x1 is the distance between the electromagnetic ultrasonic exciter and the sensor, x3 is the distance between the electromagnetic ultrasonic exciter and the propagation boundary, T1 is the time when the incident wave peak is located, T2 is the time when the defect echo wave peak is located, and T3 is the time when the end echo wave peak arrives.

[0028] The definition of the propagation boundary is: the end point of the unidirectional propagation path of the directional horizontal shear wave excited by the electromagnetic excitation device on the specimen to be tested, specifically the boundary of the structure of the specimen to be tested on the directional shear wave propagation path. The structure boundary on the non-shear wave propagation path does not belong to the propagation boundary here. The shear wave should rebound and be attenuated at the propagation boundary and will not propagate into another medium.

[0029] According to one aspect of the present invention, the present invention is applied to defect location based on horizontal shear guided waves.

[0030] The defect location process is as follows: First, use an electromagnetic ultrasonic excitation device to excite horizontally polarized shear waves that propagate circumferentially on the surface to be measured; then place sensors on the propagation path of the horizontally polarized shear waves to receive incident waves, defect echoes, and boundary echoes; next, perform preliminary filtering on the received signals to filter out waveforms with frequencies significantly different from the excitation signal frequency; then construct an over-complete dictionary based on the wavenumber characteristics and weakly damped attenuation characteristics of the horizontally polarized shear waves; then use the clustering and shrinking algorithm based on K-Means to cluster and shrink the dictionary atoms, and delete some redundant dictionary atoms while maintaining the sparsity of the dictionary to reduce the computational amount; next, construct a convex optimization model for basis pursuit denoising and use the split augmented Lagrangian shrinkage algorithm to solve it to reconstruct the signal after feature extraction; finally, in the processed signal diagram, extract the time at which the wave peaks of the incident wave, defect echo, and boundary echo are located, and obtain the distances between the electromagnetic ultrasonic excitation device and the sensor and the propagation boundary, and realize the location of the defect by calculating the distance between the electromagnetic ultrasonic excitation device and the defect.

[0031] According to one aspect of the present invention, there is provided a storage medium in which instructions are stored, and when a computer reads the instructions, the computer is caused to execute the method for sparse representation of defect echoes based on shear wave characteristics and dictionary shrinkage described in any one of the above.

[0032] According to another aspect of the present invention, there is provided an electronic device including a processor and the above storage medium, and the processor executes the instructions in the storage medium.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] By constructing an over-complete dictionary based on the wavenumber characteristics and weakly damped attenuation characteristics of horizontally polarized shear waves, the present invention can realize the feature extraction of horizontally polarized shear waves. The wavenumber characteristics map the wavelength characteristics of horizontally polarized shear waves, and the weakly damped attenuation characteristics map the energy attenuation of horizontally polarized shear waves during propagation. The weakly damped attenuation satisfies the exponential attenuation characteristics and is similar to the actual natural attenuation. Therefore, compared with the dictionaries constructed by traditional similar waveforms (such as the dictionary constructed by Morlet wavelets), the extraction of the wavenumber characteristics and amplitude characteristics of horizontally polarized shear waves is more accurate, and it is not easy to extract noise or other clutter together.

[0035] Before the atom matching stage, the present invention adds a step of clustering and shrinking the dictionary atoms. Since the dictionary considers extremely small distance intervals during construction, the data processing of the dictionary is also an important factor affecting the algorithm operation efficiency. By adopting the clustering and shrinking method based on K-Means, the dictionary atoms are pre-pruned, and while ensuring the sparsity of the dictionary, the dictionary data volume is reduced, which is beneficial to improving the algorithm operation efficiency.

[0036] The defect location method of the present invention is based on horizontal shear guided waves and is applicable to the detection and location of defects in special curved surface structures. By preliminarily filtering the original signal, part of the clutter interference can be reduced, and the accuracy of feature extraction can be improved. Description of the Drawings

[0037] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Apparently, the described embodiments are some but not all of the embodiments of the present invention.

[0038] Unless otherwise defined, the technical terms or scientific terms used herein shall have the ordinary meanings as understood by those of ordinary skill in the art to which the present invention pertains.

[0039] Figure 1 It is a flowchart of the method for a preferred embodiment of the present invention;

[0040] Figure 2 It is a flowchart of dictionary construction for a preferred embodiment of the present invention;

[0041] Figure 3 It is a flowchart of dictionary atom clustering shrinkage for a preferred embodiment of the present invention;

[0042] Figure 4 It is a drawing of dictionary atoms with imaginary parts in a preferred embodiment of the present invention;

[0043] Figure 5 It is a drawing of some dictionary atoms without imaginary parts in a preferred embodiment of the present invention;

[0044] Figure 6 It is a schematic diagram of the signal processing result obtained by the pipeline defect detection experiment system in a preferred embodiment of the present invention, where (a) is the original signal, (b) is the sparse coefficient diagram of the reconstructed signal, and (c) is the waveform diagram of the reconstructed signal. Detailed Embodiments

[0045] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Embodiment 1:

[0047] As Figure 1-6 shown, the embodiment of the present invention discloses a defect echo sparse representation method based on shear wave characteristics and dictionary shrinkage, including the following steps:

[0048] It includes signal acquisition and preprocessing, dictionary construction, dictionary atom clustering shrinkage, convex optimization model solution, and defect location, as Figure 1As shown in the figure, it specifically includes the following steps:

[0049] 1. Signal acquisition and preprocessing is to perform preliminary noise reduction on the acquired original signal, filtering out part of the signals with frequencies significantly different from the excitation signal. Specifically, a band-pass filter is used to filter the original signal. The low-frequency parameter of the band-pass filter is set to be 50 kHz lower than the excitation frequency, and the high-frequency parameter is set to be 50 kHz higher than the excitation frequency.

[0050] 2. Dictionary construction is to construct an over-complete dictionary that fuses the wavenumber characteristics of horizontal shear waves and weak damping attenuation characteristics. As Figure 2 shown, the specific steps are as follows:

[0051] 2.1) First, the construction of dictionary atoms is based on the excitation signal. Therefore, d i = H(t)

[0052] 2.2) Then, by fusing the wavenumber characteristics of shear waves, we can obtain d i = ∫H(ω)e -jN(ω)x e jωt dω

[0053] 2.3) Finally, fusing the weak damping attenuation characteristics, the specific steps are as follows:

[0054] 2.3.1) From the weak damping system, the envelope equation of the weak damping attenuation curve is y = Ae -Sωt

[0055] 2.3.2) From this, the weak damping attenuation ratio can be obtained as: This equation can also be expressed as

[0056]

[0057] 2.3.3) In the weak damping system, S 2 << 1. Therefore, the weak damping attenuation coefficient is: where M is the number of cycles between two peaks. The weak damping attenuation coefficient is based on the initial position and continuously increases with the increase of the propagation distance.

[0058] 2.4) Finally, the dictionary atom expression that fuses the wavenumber characteristics of shear waves and weak damping attenuation characteristics is: h(t) = ∫H(ω)e -jS(ω)x e jωt e -Swt dω

[0059] In the formula, the interval of the attenuation coefficient S should be between 1.2 ≥ S > 0. To better show the natural attenuation characteristics of the constructed dictionary, the interval of the attenuation coefficient S is taken as 0.6 ≥ S > 0. With the amplitude as the abscissa and the imaginary part as the ordinate, Figure 4Dictionary waveform diagram. The imaginary part is ignored, and the dictionary waveform diagrams at 4 different distances are taken as Figure 5 shown. There is a multiple relationship of 10 between the 4 different distances, so the exponential decay characteristic of weak damping decay can be reflected. The constructed dictionary representation is as follows:

[0060] 2.5) D = [d1 d2 d3 d4 … d n

[0061] 3. The dictionary atom clustering and shrinking adopts the K-Means clustering and shrinking method, as Figure 3 shown. The specific steps are as follows:

[0062] 3.1) Step 1: Use the dictionary atom D = [d1 d2 d3 d4 … d n as the input of the K-Means clustering method, and select k data from the input dictionary atoms as the initial clustering centers (k1 k2 k3 … k3).

[0063] 3.2) Step 2: Calculate the distance between each sample of the input data D and the k data used as the initial clustering centers using the Euclidean distance. Each sample is classified into the nearest clustering center to form the initial K categories

[0064] 3.3) Step 3: Update the clustering centers of each category. The new clustering center is the average value of all samples in each initial category

[0065] 3.4) Step 4: Set the maximum distance parameter to limit the Euclidean distance between each clustering center and the maximum sample. Eliminate the samples that do not meet the maximum distance in each category to further shrink the atoms.

[0066] 3.5) Step 5: Use the squared error criterion function as the objective function and calculate it as follows:

[0067]

[0068] In the formula, N i is the atom set of the i-th category, and k i is the clustering center of the i-th category. E is the sum of the Euclidean squared distances between all data samples and their respective clustering centers. Repeat Step 2, Step 3, and Step 4 until E converges, then the clustering process is completed.

[0069] 4. Solve the convex optimization model. The specific steps are as follows:

[0070] 4.1) Step 1: Construct the convex optimization model based on basis pursuit denoising as

[0071]

[0072] ​4.2) Step 2: Transform the unconstrained form into the constrained form by splitting the variable s :

[0073]

[0074] 4.3) Step 3: Use the augmented Lagrangian method to solve the constrained optimization model, and approximately solve the optimal solution of the sparse coefficient vector through the convergence of the iterative process. The iterative equation set can be obtained as follows:

[0075]

[0076] r l+1 = r l -(s l+1 - v l+1 )

[0077] 4.4) Step 4: Considering computability, c l+1 in the iterative equation set can be obtained from (D T D + μI) -1 [D T y + μ(v l + r l ). Here, I is the identity matrix with the same dimension as the dictionary D; v l+1 can be obtained by using the soft threshold operator . When the set iterative conditions are met, the optimal coefficient representation coefficient s can be obtained.

[0078] 5. Defect location can be obtained from the time where the wave peaks of the incident wave, defect echo, and boundary echo are located, and the relationship between the propagation boundary and the distance between the excitation source, and between the sensor and the excitation source. The specific formula is as follows:

[0079] 5.1)

[0080] To verify the effectiveness of the proposed method, experiments are carried out on the experimental platform shown in Figure 6 . Figure 6 The half - pipe specimen used in Figure 6(a) shows the original signal obtained. Due to the curved structure characteristics of the pipeline, the electromagnetic ultrasonic excitation device does not fully conform to the pipeline shape. Since the magnetic field generated by the magnet is not completely perpendicular to the pipeline surface, some clutter of other modes is generated. The experimental parameter settings are as follows: the reference distance is 300 mm, the dictionary atom distance step is set to 0.15e-3, the sampling frequency is 2Mhz, and the time length is 500 μs. Therefore, the dictionary dimension is 1000x2000. In the clustering and shrinking of dictionary atoms, the initial clustering centers are 1200 randomly selected atoms. After shrinking, while maintaining the sparsity of the dictionary atoms, the number is reduced. To meet the matrix requirements for the algorithm operation, the dimension of the shrunk dictionary is trimmed to 1000x1200 to meet the calculation requirements. μ = 4, l = 25, λ = 7, where μ and l are the optimal values obtained after testing multiple groups of parameters, and λ is positively correlated with the noise variance. The calculation formula is λ = max|D T y|, after being processed by the present invention, the obtained sparse coefficients are as Figure 6 (b) shown, and the reconstructed signal is as Figure 6 (c) shown. The peak times of the incident wave, defect echo, and boundary echo are 0.0000845 s, 0.000152 s, and 0.0002835 s respectively. After calculation, the defect position is 86 mm, the actual is 85 mm, and the error is 1.18%.

[0081] In summary, a method for sparse representation of defect echoes based on shear wave characteristics and dictionary shrinking of the present invention includes: preliminarily filtering the received signal to filter out waveforms with a large frequency difference from the excitation signal; constructing an over-complete dictionary based on the horizontal shear wave wavenumber characteristics and weak damping attenuation characteristics; using a clustering and shrinking algorithm based on K-Means to cluster and shrink the dictionary atoms, and deleting some redundant dictionary atoms to reduce the calculation amount while maintaining the sparsity of the dictionary; constructing a convex optimization model for basis pursuit denoising, and using a split augmented Lagrangian shrinking algorithm to solve the sparse coefficients; finally realizing the sparse representation of the signal, so as to extract the shear wave signal from the cluttered signal and realize the precise positioning of pipeline weld defects.

[0082] Example 2:

[0083] The computer-readable storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the steps in the method for sparse representation of defect echoes based on shear wave characteristics and dictionary shrinking in Example 1.

[0084] The computer-readable storage medium of this embodiment may be an internal storage unit of the terminal, such as the hard disk or memory of the terminal; the computer-readable storage medium of this embodiment may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash card, etc. equipped on the terminal; further, the computer-readable storage medium may also include both the internal storage unit and the external storage device of the terminal.

[0085] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal, and the computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0086] Embodiment 3:

[0087] The computer device of this embodiment includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps of the defect echo sparse representation method based on shear wave characteristics and dictionary shrinkage in Embodiment 1.

[0088] In this embodiment, the processor may be a central processing unit, or may also be other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.; the memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0089] Those skilled in the art should understand that the content disclosed in the embodiment can be provided as a method, a system, or a computer program product. Therefore, this solution can be implemented in the form of a hardware embodiment, a software embodiment, or a form combining software and hardware embodiments. Moreover, this solution can be implemented in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0090] This solution is described with reference to the flowcharts and / or block diagrams of the method and computer program product according to the embodiments of this solution. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions; these computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate for implementation in the processFigure 1 one process or multiple processes and / or blocks Figure 1 a device for the functions specified in one block or multiple blocks.

[0091] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured article including an instruction device, and the instruction device implements the processes Figure 1 one process or multiple processes and / or blocks Figure 1 the functions specified in one block or multiple blocks.

[0092] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide for implementing the processes Figure 1 one process or multiple processes and / or blocks Figure 1 the steps of the functions specified in one block or multiple blocks.

[0093] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. Among them, the storage medium can be a magnetic disk, an optical disc, a read-only memory (ROM), or a random access memory (RAM), etc.

[0094] The examples described in the present invention are only descriptions of the preferred embodiments of the present invention, and do not limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various deformations and improvements made by those skilled in the art to the technical solutions of the present invention should all fall within the protection scope of the present invention.

Claims

1. A sparse representation method for defect echoes based on shear wave characteristics and dictionary shrinkage, characterized in that, It includes the following steps: Construct a dictionary based on the frequency characteristics and attenuation characteristics of horizontal shear waves, where the frequency characteristics are represented by wavenumber characteristics, and the attenuation characteristic is a weakly damped system; Adopt a clustering and shrinking algorithm based on K-Means to cluster and shrink the dictionary atoms; Construct a convex optimization model based on the basis pursuit denoising problem, solve the L1-norm regularization problem through a sparse coefficient vector solving algorithm, and approximately obtain a reasonable solution of the sparse vector.

2. The method according to claim 1, characterized in that, The step of constructing the dictionary based on the frequency characteristics and attenuation characteristics of horizontal shear waves includes: Set an exciting guided wave signal, and use an electromagnetic ultrasonic exciting device with good directivity to excite a single-mode horizontal shear wave on the surface to be measured, and the exciting signal is H(t); Signal acquisition and preprocessing, using piezoelectric ceramic sensors to collect guided wave signals and obtaining a set of original signals Perform preliminary noise reduction processing on the original signal, filter out part of the signals with frequencies greatly different from the exciting signal, and extract an appropriate signal segment to obtain the preprocessed signal h(t).

3. The method according to claim 2, wherein The step of constructing the dictionary based on the frequency characteristics and attenuation characteristics of horizontal shear waves also includes: constructing a dictionary D based on the exciting signal and shear wave characteristics, fusing the shear wave wavenumber characteristics and weakly damped attenuation characteristics to construct dictionary atoms based on the exciting signal; according to the actual situation, select an appropriate interval of the attenuation coefficient S.

4. The method according to claim 3, characterized in that, Convert the feature extraction problem into a convex optimization problem: construct a convex optimization model based on basis pursuit denoising.

5. The method according to claim 1, characterized in that Sparse coefficient vector solving: By splitting variables, convert the convex optimization model from an unconstrained optimization form to a constrained optimization form; Use the augmented Lagrangian algorithm to solve the constrained optimization model, and approximately solve the optimal solution of the sparse coefficient vector through the convergence of the iterative process; Iterative process: r l+1 = r l -(s l+1 - v l+1 ) In the formula, s is the sparse coefficient, v is the split variable, λ is the Lagrange multiplier, μ is the penalty factor, l is the number of iterations, r is the auxiliary variable in the iterative process of the sparse coefficient s and the split variable v, y is the input signal, and D is the over-complete dictionary.

6. The method according to claim 5, characterized in that The specific steps of signal reconstruction are as follows: obtain the reconstructed signal through the constructed dictionary and the optimal solution of the obtained sparse coefficient vector 7. The method according to claim 6, wherein Among them, the specific steps of result output are: Extract the time points where the peaks of the incident signal, defect echo, and end echo are located, and obtain the distance between the electromagnetic ultrasonic exciting device and the center point of the sensor, and the distance between the electromagnetic ultrasonic exciting device and the propagation boundary.

8. The method according to claim 1, wherein The formula for calculating the distance that can estimate the distance between the electromagnetic ultrasonic exciting device and the defect is: Wherein, is the estimated distance between the electromagnetic ultrasonic actuator and the defect, x1 is the distance between the electromagnetic ultrasonic actuator and the sensor, x3 is the distance between the electromagnetic ultrasonic actuator and the propagation boundary, T1 is the time when the peak of the incident wave arrives, T2 is the time when the peak of the defect echo arrives, and T3 is the time when the peak of the end echo arrives.

9. The method according to claim 1, wherein Apply it to defect location based on horizontal shear waves.

10. A storage medium, characterized in that, The storage medium stores instructions, and when the computer reads the instructions, it causes the computer to execute the defect echo sparse representation method based on shear wave characteristics and dictionary shrinkage as described in any one of claims 1-8.

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