Electromagnetic eddy current defect imaging method based on sparse representation of tightly-supported radial basis function

Abstract

The invention discloses an electromagnetic eddy current defect imaging method based on tight-supported radial basis function sparse representation, which comprises the following steps: acquiring eddy current response signals of different excitation combinations, and realizing three-dimensional reconstruction of defects by adopting a tight-supported radial basis function sparse representation algorithm; setting the position of a sparse representation primary function, and carrying out sparse representation on the conductivity distribution through a tightly-supported radial primary function; inputting the eddy current response signal into a tightly-supported radial basis function sparse representation algorithm to obtain a defect reconstruction objective function of tightly-supported radial basis function sparse representation; the fitting coefficient vector is iteratively solved according to the measured value through the SART algorithm, the objective function is solved, and whether defect reconstruction is converged or not is judged according to whether the deviation of two reconstruction results before and after the iteration process is smaller than a threshold value or not; a final defect reconstruction result is output by conducting multiple times of iteration updating on the coefficient of the tightly-supported radial basis function, and defect information is obtained. According to the method, the distribution information of the near-surface defects of the metal component can be obtained only in a computational imaging mode without the help of a mechanical scanning device.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic eddy current nondestructive testing and imaging, and in particular to an electromagnetic eddy current defect imaging method based on sparse representation of compactly supported radial basis functions. Background Art

[0002] Electromagnetic eddy current nondestructive testing (NDT) technology, based on the principle of electromagnetic induction, identifies defects or assesses material properties by detecting changes in eddy currents in conductive materials. When a detection coil carrying an alternating current is placed near a conductive material, the alternating magnetic field generated by the coil induces eddy currents on the material's surface. The distribution, intensity, and flow pattern of eddy currents are affected by the material's electrical conductivity, magnetic permeability, geometry, and defects. Cracks, corrosion, or changes in conductivity in the material alter the path and intensity of the eddy currents, generating a variable secondary magnetic field. This magnetic field acts inversely on the detection coil, causing its impedance to change. By measuring the amplitude and phase changes in the coil's impedance, it is possible to determine whether the material contains defects or performance anomalies. Flaw imaging visually displays the defect's shape, location, and size through two-dimensional or three-dimensional images, providing a more intuitive representation of the defect type. This avoids the subjectivity and uncertainty inherent in traditional detection methods and improves detection accuracy. Summary of the Invention

[0003] The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

[0004] This paper proposes an electromagnetic eddy current defect imaging method based on sparse representation using compactly supported radial basis functions. This method uses an array of eddy current sensors to collect eddy current excitation and detection data from the area to be reconstructed, obtaining response signals under different excitation and reception modes. This method then employs a sparse representation reconstruction algorithm based on compactly supported radial basis functions to achieve high-precision reconstruction of the defect's three-dimensional morphology. This technical solution simultaneously achieves 3D visualization of damage defects and quantitative assessment of their defect information, providing theoretical and technical support for the health monitoring of metal structures.

[0005] Another object of the present invention is to propose an electromagnetic eddy current defect imaging system based on sparse representation of compactly supported radial basis functions.

[0006] To achieve the above objectives, the present invention proposes, on one hand, an electromagnetic eddy current defect imaging method based on sparse representation of compactly supported radial basis functions, comprising:

[0007] Design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on the successive excitation and successive reception mode;

[0008] Setting the position of the sparse representation basis function and sparsely representing the conductivity distribution through the compactly supported radial basis function coefficients at different positions; and inputting the eddy current response signal into the compactly supported radial basis function sparse representation algorithm to obtain the defect reconstruction objective function of the compactly supported radial basis function sparse representation;

[0009] Based on the defect reconstruction objective function, the SART algorithm is used to iteratively solve the fitting coefficient vector according to the measurement value, and the defect reconstruction result is updated using an iterative method;

[0010] Comparing the deviation of the defect reconstruction results before and after the iteration to see whether it is less than a preset threshold, so as to determine whether the defect reconstruction has converged based on the comparison result;

[0011] Defect information is obtained based on the final defect reconstruction result; wherein the defect information includes the location, size and quantity information of the defect.

[0012] The electromagnetic eddy current defect imaging method based on compactly supported radial basis function sparse representation according to the embodiment of the present invention may also have the following additional technical features:

[0013] In one embodiment of the present invention, a planar array eddy current sensor is designed, and eddy current response signals of different excitation combinations are obtained based on a successive excitation and successive reception mode, including:

[0014] Design a 4×4 planar array eddy current sensor and calculate the tomographic sensitivity matrix based on the finite element numerical model;

[0015] The sensitivity matrix is weighted to compensate for the insensitive area of the sensitive field;

[0016] The 4×4 coils are numbered, the first numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; the second numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; and so on, a successive excitation-successive reception mode is used to finally obtain full coverage eddy current information.

[0017] In one embodiment of the present invention, the eddy current response signal is input into a compactly supported radial basis function sparse characterization algorithm to obtain a defect reconstruction objective function of the compactly supported radial basis function sparse characterization, including:

[0018] The electromagnetic parameter distribution in eddy current tomography is defined as σ, the induced voltage of the array eddy current sensor is U, the sensitivity matrix is S, and the inverse problem of the imaging process is expressed as:

[0019]

[0020] Q radial basis functions are evenly arranged in the area to be reconstructed. The function value of the basis function at the point (x, y) is:

[0021]

[0022] Where R is the compact support radius, β is the compact support parameter; when the point (x, y) and the basis function center (x i ,y j ) exceeds the compact support radius R, the basis function value is 0;

[0023] The grid point (x j ,y j ) is represented by a linear combination of Q radial basis functions:

[0024]

[0025] Where, φ q (x i ,y j ) represents the qth grid point as the primitive center point (x i ,y j ) radial basis function value at α q is the radial basis function coefficient with the qth grid point as the center of the primitive, q is the total number of radial basis function center points involved in the fitting, satisfying q≤n, and is expressed in matrix form as:

[0026] Wα q =U

[0027] Where, the value of the M×Q matrix W is determined by the radial basis function type and the sensitivity matrix, and the Q×1 column vector α q is the radial basis function coefficient, and the M×1 column vector U is the detected eddy current data, i.e., the measurement value;

[0028] Inverse problem of imaging process:

[0029]

[0030] In one embodiment of the present invention, the SART algorithm is used to iteratively solve the fitting coefficient vector according to the measurement value, and the defect reconstruction result is updated using an iterative method, including:

[0031] The SART algorithm is used to solve the basis function coefficient vector, and the iterative formula is expressed as:

[0032]

[0033] The iterative calculation results are corrected by combining the median filtering algorithm, namely:

[0034]

[0035] Where, and are the basis function coefficient vectors for the kth iteration and the k+1th iteration, respectively, and λ is the relaxation factor; Yes Perform median filtering, that is, the value of each grid point is equal to the median value of the surrounding neighborhood grid points, and the weight factor τ is used to adjust the weight of the correction value;

[0036] According to the coefficient of iteration The conductivity distribution reconstruction results are obtained to achieve defect imaging.

[0037] In one embodiment of the present invention, when If it is less than 0.01, the iteration ends; otherwise, the compactly supported radial basis function continues to be updated.

[0038] To achieve the above-mentioned object, the present invention further proposes an electromagnetic eddy current defect imaging system based on sparse representation of compactly supported radial basis functions, comprising:

[0039] The eddy current sensor building module is used to design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on a successive excitation and successive reception mode;

[0040] An objective function construction module is used to set the position of the sparse representation basis function and perform sparse representation of the conductivity distribution through the coefficients of the compactly supported radial basis function at different positions; and input the eddy current response signal into the compactly supported radial basis function sparse representation algorithm to obtain the defect reconstruction objective function of the compactly supported radial basis function sparse representation;

[0041] The defect reconstruction result update module is used to iteratively solve the fitting coefficient vector according to the measurement value based on the defect reconstruction objective function through the SART algorithm, and update the defect reconstruction result using an iterative method;

[0042] The defect reconstruction result comparison module is used to compare whether the deviation of the defect reconstruction results before and after the iteration is less than a preset threshold, so as to determine whether the defect reconstruction has converged according to the comparison result;

[0043] The defect reconstruction result output module is used to obtain defect information based on the final defect reconstruction result; wherein the defect information includes the location, size and quantity information of the defect.

[0044] The electromagnetic eddy current defect imaging method and system based on sparse representation of compactly supported radial basis functions (CBFs) in the embodiments of the present invention first designs a planar array eddy current sensor to obtain eddy current field distribution information on a metal flat plate. Subsequently, a series of compactly supported RBFs are set for the region to be reconstructed. Leveraging their advantages in data fitting, these functions are used to fit the conductivity distribution within the imaging region. The coefficient vectors are then iteratively solved for the eddy current data using the classical iterative method SART. The coefficient vectors are then combined with the RBF matrix to calculate the conductivity distribution of the region to be reconstructed, effectively achieving three-dimensional defect distribution imaging.

[0045] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0047] Figure 1 is a flow chart of an electromagnetic eddy current defect imaging method based on sparse representation of compactly supported radial basis functions according to an embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of a planar array eddy current sensor according to an embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of a compactly supported Gaussian radial basis function according to an embodiment of the present invention;

[0050] Figure 4 is a three-dimensional imaging result diagram of a defect according to an embodiment of the present invention;

[0051] Figure 5 3 is a structural diagram of an electromagnetic eddy current defect imaging system based on sparse representation of compactly supported radial basis functions according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0054] The following describes an electromagnetic eddy current defect imaging method and system based on compactly supported radial basis function sparse representation according to an embodiment of the present invention with reference to the accompanying drawings.

[0055] Figure 1 FIG. 1 is a flow chart of an electromagnetic eddy current defect imaging method based on sparse representation of compactly supported radial basis functions according to an embodiment of the present invention. Figure 1 Shown, including:

[0056] S1, design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on the successive excitation and successive reception mode.

[0057] Specifically, such as Figure 2 As shown in the figure, a 4×4 planar array eddy current sensor is designed. According to the finite element numerical model, the eddy current tomography sensitivity matrix S is calculated. Subsequently, the sensitivity matrix is weighted to compensate for the insensitive area of the sensitive field. The 4×4 planar coil array is numbered to excite coil 1 and measure the received signals of coils 2-16; coil 2 is excited and the received signals of coils 3-16 are measured. And so on, a successive excitation-successive reception mode is adopted to finally achieve full coverage of eddy current information acquisition.

[0058] S2, setting the position of the sparse characterization basis function, and sparsely characterizing the conductivity distribution through the compactly supported radial basis function coefficients at different positions; and inputting the eddy current response signal into the compactly supported radial basis function sparse characterization algorithm to obtain the defect reconstruction objective function of the compactly supported radial basis function sparse characterization.

[0059] Specifically, the position of the sparse representation basis function (x i ,y i ), through the compactly supported radial basis function coefficients [α1 * ,α2 * ,…,α n * ] sparsely characterize the conductivity distribution. Figure 3 , which is a schematic diagram of a compactly supported Gaussian radial basis function according to an embodiment of the present invention.

[0060] Specifically, the steps include:

[0061] Step S2.1: The area of the metal copper plate to be imaged is 30 mm × 30 mm. The electromagnetic parameter distribution in eddy current tomography is defined as σ, the induced voltage of the array eddy current sensor is U, and the sensitivity matrix is S. The inverse problem of the imaging process can be expressed as:

[0062]

[0063] Step S2.2: Determine the positions of the compactly supported Gaussian radial basis functions (x i ,y i ), the arrangement of the basis functions is in the form of 5×5, and the function value of the Gaussian compactly supported basis function q at the point (x, y) is:

[0064]

[0065] Where R is the compact support radius, which is set to 2, and β is the compact support hyperparameter, which is set to 3. i ,y j ) between r=||(x,y)-(x i ,y i )|| exceeds the compact support radius R, the basis function value is 0.

[0066] Step S2.3: The grid point (x j ,y j ) is represented by a linear combination of 25 radial basis functions:

[0067]

[0068] Where, φ q (x i ,y j ) represents the qth grid point as the primitive center point (x i ,y j ) radial basis function value at α q is the radial basis function coefficient with the qth grid point as the center of the primitive, q is the total number of radial basis function center points involved in the fitting, satisfying q≤n, and is expressed in matrix form as:

[0069] Wα q =U

[0070] Where, the value of the M×Q matrix W is determined by the radial basis function type and the sensitivity matrix, and the Q×1 column vector α q is the radial basis function coefficient, and the M×1 column vector U is the detected eddy current data, that is, the measurement value.

[0071] The inverse problem of the imaging process can be expressed and further obtained:

[0072]

[0073] S3, based on the defect reconstruction objective function, uses the SART algorithm to iteratively solve the fitting coefficient vector according to the measurement value, and uses the iterative method to update the defect reconstruction result.

[0074] In one embodiment of the present invention, the SART algorithm, which has obvious advantages in reconstruction speed and anti-interference performance, is used to solve the radial basis function fitting coefficient vector in the defect reconstruction objective function. The iterative formula is expressed as follows:

[0075]

[0076] Then, a median filtering algorithm is used to correct the iterative calculation results, namely

[0077]

[0078] Where, and are the basis function coefficient vectors for the kth iteration and the k+1th iteration, respectively, and λ is the relaxation factor, which is set to 0.1. Yes Perform median filtering, that is, the value of each grid point is equal to the median value of the grid points around it, and the weight factor τ is used to adjust the weight of the correction value and is set to 0.3. The conductivity distribution reconstruction results can be obtained, thereby realizing the imaging of defects.

[0079] S4, comparing whether the deviation of the defect reconstruction results before and after the iteration is less than a preset threshold, so as to determine whether the defect reconstruction has converged according to the comparison result.

[0080] Specifically, step S3 is repeatedly performed, and whether the defect reconstruction has converged is determined based on whether the deviation between the two defect reconstruction results before and after the iteration is less than a threshold;

[0081] Specifically, when If it is less than 0.01, the iteration ends; otherwise, continue to execute step S3 to update the compactly supported radial basis function.

[0082] S5, obtaining defect information based on the final defect reconstruction result; wherein the defect information includes the location, size and quantity information of the defect.

[0083] The iteration coefficient Substituting the sparse representation expression, the conductivity distribution result of the reconstructed area is obtained, and then the defect location, size and quantity information are accurately evaluated and quantified through the difference in conductivity imaging results. The defect reconstruction result is as follows: Figure 4 shown.

[0084] In the embodiment of the present invention, four different defect distributions on the surface of the metal copper plate are specifically including a central single defect, a non-central single defect, two defects, and three defects. The eddy current detection device is used to obtain the response signals of different defects. Then, the defect distribution is reconstructed by using the proposed electromagnetic eddy current defect imaging method based on compactly supported Gaussian radial basis function. The results are as follows: Figure 4 shown.

[0085] According to the method for measuring the inner diameter and conductivity of a metal pipe based on multi-frequency eddy current characteristics according to an embodiment of the present invention, the full range of eddy current signals can be measured according to the eddy current array's successive excitation and successive reception to achieve metal component defect imaging. A planar flat array eddy current sensor is built, and the sensitivity matrix is calculated through a finite element numerical model. The eddy current response signal is input into a sparse representation reconstruction algorithm model based on a level set of compactly supported radial basis functions to obtain a defect sparse representation reconstruction objective function based on compactly supported radial basis functions. The objective function is solved through SART iteration, and the compactly supported radial basis function coefficient parameters are continuously iteratively updated to achieve defect imaging. The defect distribution reconstructed by the imaging method proposed in the present invention is consistent with the experimental results, and can achieve accurate positioning and evaluation of the defect position of metal components without the need for a mechanical scanning device, and has broad application prospects.

[0086] In order to implement the above embodiment, Figure 5 As shown, this embodiment also provides an electromagnetic eddy current defect imaging system 10 based on compactly supported radial basis function sparse representation, including:

[0087] The eddy current sensor building module 100 is used to design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on a successive excitation and successive reception mode;

[0088] The objective function construction module 200 is used to set the position of the sparse representation basis function and perform sparse representation of the conductivity distribution through the compactly supported radial basis function coefficients at different positions; and input the eddy current response signal into the compactly supported radial basis function sparse representation algorithm to obtain the defect reconstruction objective function of the compactly supported radial basis function sparse representation;

[0089] The defect reconstruction result updating module 300 is used to iteratively solve the fitting coefficient vector according to the measurement value through the SART algorithm based on the defect reconstruction objective function, and update the defect reconstruction result using an iterative method;

[0090] The defect reconstruction result comparison module 400 is used to compare whether the deviation of the defect reconstruction results before and after the iteration is less than a preset threshold, so as to determine whether the defect reconstruction has converged based on the comparison result;

[0091] The defect reconstruction result output module 500 is used to obtain defect information based on the final defect reconstruction result; wherein the defect information includes the position, size and quantity information of the defect.

[0092] Furthermore, the eddy current sensor building block 100 is further configured to:

[0093] Design a 4×4 planar array eddy current sensor and calculate the tomographic sensitivity matrix based on the finite element numerical model;

[0094] The sensitivity matrix is weighted to compensate for the insensitive area of the sensitive field;

[0095] The 4×4 coils are numbered, the first numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; the second numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; and so on, a successive excitation-successive reception mode is used to finally obtain full coverage eddy current information.

[0096] Furthermore, the objective function construction module 200 is further configured to:

[0097] The electromagnetic parameter distribution in eddy current tomography is defined as σ, the induced voltage of the array eddy current sensor is U, the sensitivity matrix is S, and the inverse problem of the imaging process is expressed as:

[0098]

[0099] Q radial basis functions are evenly arranged in the area to be reconstructed. The function value of the basis function at the point (x, y) is:

[0100]

[0101] Where R is the compact support radius, β is the compact support parameter; when the point (x, y) and the basis function center (x i ,y j ) exceeds the compact support radius R, the basis function value is 0;

[0102] The grid point (x j ,y j ) is represented by a linear combination of Q radial basis functions:

[0103]

[0104] Where, φ q (x i ,y j ) represents the qth grid point as the primitive center point (x i ,y j ) radial basis function value at α q is the radial basis function coefficient with the qth grid point as the center of the primitive, q is the total number of radial basis function center points involved in the fitting, satisfying q≤n, and is expressed in matrix form as:

[0105] Wα q =U

[0106] Where, the value of the M×Q matrix W is determined by the radial basis function type and the sensitivity matrix, and the Q×1 column vector α qis the radial basis function coefficient, and the M×1 column vector U is the detected eddy current data, i.e., the measurement value;

[0107] Inverse problem of imaging process:

[0108]

[0109] Furthermore, the defect reconstruction result updating module 300 is further configured to:

[0110] The SART algorithm is used to solve the basis function coefficient vector, and the iterative formula is expressed as:

[0111]

[0112] The iterative calculation results are corrected by combining the median filtering algorithm, namely:

[0113]

[0114] Where, and are the basis function coefficient vectors for the kth iteration and the k+1th iteration, respectively, and λ is the relaxation factor; Yes Perform median filtering, that is, the value of each grid point is equal to the median value of the surrounding neighborhood grid points, and the weight factor τ is used to adjust the weight of the correction value;

[0115] According to the coefficient of iteration The conductivity distribution reconstruction results are obtained to achieve defect imaging.

[0116] Further, when If it is less than 0.01, the iteration ends; otherwise, the compactly supported radial basis function continues to be updated.

[0117] According to the embodiment of the present invention, the metal pipe inner diameter and conductivity measurement system based on multi-frequency eddy current characteristics can realize the imaging of metal component defects by measuring the full range of eddy current signals according to the successive excitation and successive reception of the eddy current array. A planar flat array eddy current sensor is built, and the sensitivity matrix is calculated through the finite element numerical model. The eddy current response signal is input into the sparse representation reconstruction algorithm model based on the level set of the compactly supported radial basis function to obtain the defect sparse representation reconstruction objective function based on the compactly supported radial basis function. The objective function is solved through SART iteration, and the coefficient parameters of the compactly supported radial basis function are continuously iteratively updated to achieve defect imaging. The defect distribution reconstructed by the imaging method proposed in the present invention is consistent with the experimental results, and can realize the accurate positioning and evaluation of the defect position of the metal component without the need for a mechanical scanning device, and has broad application prospects.

[0118] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0119] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

Claims

1. A method for electromagnetic eddy current defect imaging based on sparse representation of compactly supported radial basis functions, characterized in that: include: Design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on the successive excitation and successive reception mode; Set the position of the sparse representation basis function and perform sparse representation of the conductivity distribution through the coefficients of the compactly supported radial basis function at different positions; and inputting the eddy current response signal into a compactly supported radial basis function sparse representation algorithm to obtain a defect reconstruction objective function of the compactly supported radial basis function sparse representation; Based on the defect reconstruction objective function, the SART algorithm is used to iteratively solve the fitting coefficient vector according to the measurement value, and the defect reconstruction result is updated using an iterative method; Comparing the deviation of the defect reconstruction results before and after the iteration to see whether it is less than a preset threshold, so as to determine whether the defect reconstruction has converged based on the comparison result; Defect information is obtained based on the final defect reconstruction result; wherein the defect information includes the location, size and quantity information of the defect.

2. The method according to claim 1, characterized in that Design a planar array eddy current sensor and obtain eddy current response signals for different excitation combinations based on a successive excitation and successive reception mode, including: Design a 4×4 planar array eddy current sensor and calculate the tomographic sensitivity matrix based on the finite element numerical model; The sensitivity matrix is weighted to compensate for the insensitive area of the sensitive field; The 4×4 coils are numbered, the first numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; the second numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; and so on, a successive excitation-successive reception mode is used to finally obtain full coverage eddy current information.

3. The method according to claim 2, characterized in that The eddy current response signal is input into the compactly supported radial basis function sparse representation algorithm to obtain the defect reconstruction objective function of the compactly supported radial basis function sparse representation, including: The electromagnetic parameter distribution in eddy current tomography is defined as σ, the induced voltage of the array eddy current sensor is U, the sensitivity matrix is S, and the inverse problem of the imaging process is expressed as: Q radial basis functions are evenly arranged in the area to be reconstructed. The function value of the basis function at the point (x, y) is: Where R is the compact support radius, β is the compact support parameter; when the point (x, y) and the basis function center (x i ,y j ) exceeds the compact support radius R, the basis function value is 0; The grid point (x j ,y j ) is represented by a linear combination of Q radial basis functions: Where, φ q (x i ,y j ) represents the qth grid point as the primitive center point (x i ,y j ) radial basis function value at α q is the radial basis function coefficient with the qth grid point as the center of the primitive, q is the total number of radial basis function center points involved in the fitting, satisfying q≤n, and is expressed in matrix form as: Wα q =U Where, the value of the M×Q matrix W is determined by the radial basis function type and the sensitivity matrix, and the Q×1 column vector α q is the radial basis function coefficient, and the M×1 column vector U is the detected eddy current data, i.e., the measurement value; Inverse problem of imaging process:

4. The method according to claim 3, characterized in that The SART algorithm is used to iteratively solve the fitting coefficient vector based on the measured values, and the defect reconstruction results are updated using an iterative method, including: The SART algorithm is used to solve the basis function coefficient vector, and the iterative formula is expressed as: The iterative calculation results are corrected by combining the median filtering algorithm, namely: Where, and are the basis function coefficient vectors for the kth iteration and the k+1th iteration, respectively, and λ is the relaxation factor; Yes Perform median filtering, that is, the value of each grid point is equal to the median value of the surrounding neighborhood grid points, and the weight factor τ is used to adjust the weight of the correction value; According to the coefficient of iteration The conductivity distribution reconstruction results are obtained to achieve defect imaging.

5. The method according to claim 4, characterized in that when If it is less than 0.01, the iteration ends; otherwise, the compactly supported radial basis function continues to be updated.

6. An electromagnetic eddy current defect imaging system based on sparse representation of compactly supported radial basis functions, characterized in that: include: The eddy current sensor building module is used to design a planar array eddy current sensor and obtain eddy current response signals of different excitation combinations based on a successive excitation and successive reception mode; The objective function construction module is used to set the position of the sparse representation basis function and perform sparse representation of the conductivity distribution through the coefficients of the compactly supported radial basis functions at different positions; and inputting the eddy current response signal into a compactly supported radial basis function sparse representation algorithm to obtain a defect reconstruction objective function of the compactly supported radial basis function sparse representation; The defect reconstruction result update module is used to iteratively solve the fitting coefficient vector according to the measurement value based on the defect reconstruction objective function through the SART algorithm, and update the defect reconstruction result using an iterative method; The defect reconstruction result comparison module is used to compare whether the deviation of the defect reconstruction results before and after the iteration is less than a preset threshold, so as to determine whether the defect reconstruction has converged according to the comparison result; The defect reconstruction result output module is used to obtain defect information based on the final defect reconstruction result; wherein the defect information includes the location, size and quantity information of the defect.

7. The system according to claim 6, characterized in that Eddy current sensor building blocks, also used for: Design a 4×4 planar array eddy current sensor and calculate the tomographic sensitivity matrix based on the finite element numerical model; The sensitivity matrix is weighted to compensate for the insensitive area of the sensitive field; The 4×4 coils are numbered, the first numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; the second numbered coil is excited, and the receiving signals of the coils with the remaining coil numbers are measured; and so on, a successive excitation-successive reception mode is used to finally obtain full coverage eddy current information.

8. The system according to claim 7, characterized in that Objective function building blocks, also used for: The electromagnetic parameter distribution in eddy current tomography is defined as σ, the induced voltage of the array eddy current sensor is U, the sensitivity matrix is S, and the inverse problem of the imaging process is expressed as: Q radial basis functions are evenly arranged in the area to be reconstructed. The function value of the basis function at the point (x, y) is: Where R is the compact support radius, β is the compact support parameter; when the point (x, y) and the basis function center (x i ,y j ) exceeds the compact support radius R, the basis function value is 0; The grid point (x j ,y j ) is represented by a linear combination of Q radial basis functions: Where, φ q (x i ,y j ) represents the qth grid point as the primitive center point (x i ,y j ) radial basis function value at α q is the radial basis function coefficient with the qth grid point as the center of the primitive, q is the total number of radial basis function center points involved in the fitting, satisfying q≤n, and is expressed in matrix form as: Wα q =U Where, the value of the M×Q matrix W is determined by the radial basis function type and the sensitivity matrix, and the Q×1 column vector α q is the radial basis function coefficient, and the M×1 column vector U is the detected eddy current data, i.e., the measurement value; Inverse problem of imaging process:

9. The system according to claim 8, characterized in that The defect reconstruction result update module is also used to: The SART algorithm is used to solve the basis function coefficient vector, and the iterative formula is expressed as: The iterative calculation results are corrected by combining the median filtering algorithm, namely: Where, and are the basis function coefficient vectors for the kth iteration and the k+1th iteration, respectively, and λ is the relaxation factor; Yes Perform median filtering, that is, the value of each grid point is equal to the median value of the surrounding neighborhood grid points, and the weight factor τ is used to adjust the weight of the correction value; According to the coefficient of iteration The conductivity distribution reconstruction results are obtained to achieve defect imaging.

10. The system according to claim 9, characterized in that when If it is less than 0.01, the iteration ends; otherwise, the compactly supported radial basis function continues to be updated.

Images