A method for detecting defects in a carbon fiber cable

Abstract

This invention relates to a defect detection method for carbon fiber cables, comprising the following steps: S1. Constructing a simulation model of the carbon fiber composite cable and obtaining a sensitivity matrix; S2. Setting up a detection probe; S3. The detection probe acquires the detection voltage of the carbon fiber cable under test; S4. Calculating the initial grayscale value set of all pixels on the cross-section detected by the detection probe at the location of the carbon fiber cable under test based on the detection voltage, sensitivity matrix, and defect-free voltage; S5. Calculating the initial residual based on the results output from S1-S4, and updating the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable under test using the Krylov subspace algorithm; S6. Updating the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable under test based on the last iteration update and creating an image. When a defect is found in the image, the location detected by the detection probe is the location of the defect. This invention reconstructs the cross-sectional image using the Krylov subspace algorithm, making the cross-section of the carbon fiber cable clearer.

Description

Technical Field

[0001] This invention relates to a defect detection method, specifically a defect detection method for carbon fiber cables. Background Technology

[0002] Carbon fiber reinforced polymers are becoming increasingly important in many fields due to their excellent properties, such as corrosion resistance, fatigue resistance, and tensile strength. Carbon fiber composites are widely used in wind power, aerospace, and energy sectors. Furthermore, carbon fiber composite cables can serve as tensile structures for long-span load-bearing components. However, during the manufacturing and use of carbon fiber cables, debonding and chain breakage defects often occur due to in-service static loads, natural loads, and cyclic loads. Once defects appear within the carbon fiber, they can easily jeopardize the structural integrity of the cable, even leading to catastrophic failures such as cable breakage. Therefore, periodic non-destructive testing of defects in carbon fiber cables is imperative. This is essential to ensuring the safe and efficient operation of these cables in long-span structures.

[0003] Electromagnetic tomography (EMT) is a non-destructive testing technique based on the principle of electromagnetic induction. It reconstructs the defect distribution of conductive or magnetic materials within an object by utilizing voltage data and sensitivity obtained from electromagnetic coils surrounding the object. It offers advantages such as non-contact operation and fast imaging speed, and can be used for dynamic monitoring and static detection of defects on and near material surfaces. It has significant application potential in fields such as biomedicine, multiphase flow measurement, and foreign object monitoring. In recent years, EMT has made considerable progress in visualizing defects in metallic materials. While carbon fiber possesses conductivity, its low conductivity results in unclear imaging, leading to inaccurate identification of the location and shape of defects in carbon fiber cables. This makes the application of EMT in detecting defects in carbon fiber cables challenging. Summary of the Invention

[0004] The purpose of this invention is to provide a defect detection method for carbon fiber cables to solve the problem of inaccurate identification of the location and shape of defects in carbon fiber composite cables.

[0005] The objective of this invention is achieved as follows:

[0006] A defect detection method for carbon fiber cables includes the following steps:

[0007] S1. Construct an electromagnetic simulation model of the carbon fiber cable according to the specifications of the carbon fiber cable under test, apply an excitation voltage to the electromagnetic simulation model of the carbon fiber cable, and establish the sensitivity matrix of the cross-sectional field region of the carbon fiber cable by field quantity extraction method;

[0008] S2. Construct a detection probe, the structure of which is to set several spiral cylindrical coils pointing to the center on the inner ring surface of the circular carrier, and to connect a spiral cylindrical coil pointing to the center of the circular carrier to one end of each spiral cylindrical coil near the center using an insulator bracket.

[0009] S3. Testing carbon fiber cable: The test probe is attached to the carbon fiber cable to be tested. Each spiral columnar coil is aligned with a strand of carbon fiber on the carbon fiber cable to be tested. The probe moves from one end of the carbon fiber cable to the other at a speed of 1mm / s-10mm / s. The test voltage is collected once every 300 milliseconds.

[0010] S4. Based on the collected detection voltage, sensitivity matrix, and defect-free voltage, calculate the initial grayscale value set of all pixels of the carbon fiber cable cross section detected by the detection probe;

[0011] S5. Calculate the initial residual based on the sensitivity matrix, the initial gray value set of all pixels on the cross section of the carbon fiber cable under test, the detection voltage, and the defect-free voltage; update the initial gray value set of all pixels on the cross section of the carbon fiber cable under test using the Krylov subspace algorithm;

[0012] S6. Based on the initial grayscale value set of all pixels of the tested carbon fiber cable cross section obtained from the last iteration update, image the tested carbon fiber cable cross section. When there is a defect in the imaging result, the position detected by the detection probe is the location of the defect.

[0013] Furthermore, the formula for calculating the initial grayscale value set of all pixels of the measured carbon fiber cable cross-section in step S3 is as follows:

[0014] g0=(S T S+γI) -1 S T U

[0015] Where S is the sensitivity matrix, S T Let S be the transpose of S, U be the difference between the defect-free voltage and the detection voltage, and γ be the regularization parameter.

[0016] Furthermore, the specific method for updating the initial grayscale value set of all pixels of the measured carbon fiber cable cross-section in step S5 is as follows:

[0017] S5a-1. Calculate the initial residuals and construct a Krylov subspace based on the initial residuals. The Krylov subspace is an m-dimensional matrix, K = K(A, r0, m) = span(r0, Ar0, A) 2 r0,…,A m-1 r0)m≤n;

[0018] Where K is the Krylov subspace, r0 is the initial residual, r0 = bA·g0, b = S T ·U, A=S T S, g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, and S is the sensitivity matrix. T Let S be the transpose of S, and U be the difference between the defect-free voltage and the detection voltage.

[0019] S5a-2. Calculate the initial search direction P0 and the initial relative residual vector q0;

[0020] S5a-3. Iteratively calculate the initial search direction P0 to obtain the iterated search direction P1, and iteratively calculate the initial relative residual vector q0 to obtain the iterated relative residual vector q1.

[0021] S5a-4. Construct the H2 matrix based on the initial search direction, the initial relative residual vector, and the iteratively calculated search direction and relative residual vector H2. Iteratively update the initial gray value set of all pixels on the cross section according to the H2 matrix.

[0022] S5a-5. Determine whether the iteration tolerance has reached the preset condition based on the set of gray values ​​of all pixels on the updated interface. If the preset condition has not been reached, proceed to steps S5a-6-S5a-8.

[0023] S5a-6. Iteratively calculate the search direction and relative residual vector to obtain the iterated search direction and relative residual vector;

[0024] S5a-7. Based on the search direction and relative residual vector calculated iteratively, calculate the elements in the matrix and add them to the H matrix obtained in the previous iteration to obtain H. m Matrix, according to H m The matrix iteratively updates the set of grayscale values ​​of all pixels on the cross section;

[0025] The formula for iteratively updating the set of grayscale values ​​of all pixels on the cross-section of the tested carbon fiber cable is as follows:

[0026] g k =g0+V m ·y

[0027] Among them, V m V is the unit basis vector that is orthogonal to the subspace. m =[v1,v2,...v m ], y = H m -1 (de), d=norm(r0), e=[1,0,0…0] T ;

[0028] Matrix H m The formula for calculating elements in the middle is:

[0029] H(i,j)=q j-1 T ×P i-1 , 1≤i≤j, 1≤j≤m

[0030] Where H(i,j) is H m The element q in the i-th row and j-th column of the matrix j-1 Let P be the relative residual vector after the (j-1)th iteration update. i-1 The search direction after the (i-1)th iteration update is represented by the multiplied relative residual vector q. j-1 and search direction P i-1 Vectors orthogonal are equivalent to A in the Krylov subspace. j-1 r;

[0031] S5a-8. Determine whether the iteration tolerance has reached the preset condition based on the set of grayscale values ​​of all pixels on the updated interface. If the preset condition has not been reached, repeat steps S5a-6-S5a-7 until the preset condition is reached.

[0032] Furthermore, the formula for calculating the initial search direction P0 in step S5a-2 is as follows:

[0033] P0 = r0 / norm(r0)

[0034] Where r0 is the initial residual, and norm(r0) is the second norm of r0;

[0035] The formula for calculating the initial relative residual vector is: q0 = A·P0;

[0036] Furthermore, the formula for calculating the search direction P1 in step S5a-3 is: P1 = r1 / norm(r1), where r1 = r0 - alpha0·P0, alpha0 = r0 T The formula for calculating the search direction P1 is: q1 = A·P1.

[0037] Furthermore, the calculation formula for iteratively updating the set of grayscale values ​​of all pixels on the cross section in step S5a-4 is as follows:

[0038] g1 = g0 + V2·y

[0039] Where g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, AV2 = V2H2, and y = H2 -1 (de), where d = ||r0||2, e = [1,0,0…0] T .

[0040] Further, the formula for iteratively calculating the search direction in step S5a-6 is:

[0041] P k = r k / norm(r k )

[0042] where r k = r k-1 - alpha k-1 ·P k-1 , alpha k = r k T ·q k , r k is the residual of the k-th iteration, r k T is the transpose matrix of r k , P k-1 is the search direction calculated in the (k-1)-th iteration, q k is the relative residual vector calculated in the k-th iteration;

[0043] The formula for iteratively calculating the relative residual vector is: q k = A·P k .

[0044] Further, the preset condition in step S5a-8 is: norm(g k ) < tol*norm(g0), where tol is the set convergence tolerance.

[0045] The present invention constructs a three-dimensional electromagnetic carbon fiber cable model to ensure coil parameters suitable for the measured carbon fiber cable, so as to reduce the influencing factors of the parameters and improve the effect of defect imaging; constructs a Krylov subspace, and can better capture and retain the local features of the image, especially the edge information, by optimizing in the local subspace. The loop mechanism allows the algorithm to iterate multiple times and gradually optimize the quality of the image. Each iteration can make a finer adjustment to the image, thereby gradually approaching the optimal solution. This process of gradual optimization helps to improve the image quality at both the global and local levels.

[0046] This invention constructs a Krylov subspace to better reconstruct defect feature information. While reconstructing the image, it also effectively preserves image edge information, resulting in a high-quality defect reconstruction image. By adding noise intensity to simulate noise signals, the Krylov subspace algorithm demonstrates strong noise resistance, exhibiting excellent noise adaptability and robustness. Comparing the correlation coefficients and image errors of the reconstructed images using the methods provided allows for a direct and reliable assessment of the reconstruction quality. This provides an intuitive and reliable basis for evaluating the effectiveness of defect reconstruction. Attached Figure Description

[0047] Figure 1 This is a flowchart of the present invention.

[0048] Figure 2 (a) is a structural diagram of the detection probe. Figure 2 (b) is a schematic diagram of the testing of the carbon fiber cable being tested.

[0049] Figure 3 This is a comparison diagram of the cross-sectional images constructed by the present invention and the methods of Tikhonov, Landweber, and TSVD.

[0050] Figure 4 This is a comparison image of the cross-sectional images constructed by the present invention and the methods of Tikhonov, Landweber, and TSVD under a noise intensity of 20dB. Detailed Implementation

[0051] The present invention will now be described in further detail.

[0052] like Figure 1 As shown, the defect detection method for carbon fiber cables provided by the present invention includes the following steps:

[0053] S1. Construct an electromagnetic simulation model of the carbon fiber cable according to the specifications of the carbon fiber cable under test. Apply an excitation voltage to the electromagnetic simulation model of the carbon fiber cable and establish the initial sensitivity matrix of the cross-sectional field region of the carbon fiber cable by field quantity extraction method.

[0054] The constructed simulation model is an ideal, undamaged model with the same specifications and dimensions as the carbon fiber cable under test.

[0055] like Figure 2As shown, the electromagnetic simulation model establishment and excitation detection process were implemented using COMSOL Multiphysics software. The electromagnetic simulation model of the carbon fiber cable mainly consists of a carbon fiber cable, an outer coil, and an inner coil. The carbon fiber cable 1 is composed of 7 carbon fiber rods, each 100mm long and 7mm in diameter, with an axial conductivity of 10000 (S / m) and a radial conductivity of 100 (S / m). The outer coil is the excitation coil, and the inner coil is the detection coil. Both the inner and outer coils have an inner diameter of 5mm and an outer diameter of 10mm. Both the outer and inner coils are made of wound copper wire, with one inner coil corresponding to one outer coil. The central axes of the corresponding inner and outer coils are on the same straight line.

[0056] The excitation voltage of the excitation coil is set to 24V and the excitation frequency is 1MHz. When each excitation coil is excited, the voltage of the seven detection coils (excluding those below the excitation coil) is collected. During each detection process, the eight excitation coils are excited in a clockwise rotation, so 56 voltage values ​​can be obtained in one detection process.

[0057] In the simulation model, a unit current is applied to each excitation coil and detection coil to extract the vector magnetic potential distribution of the measured object field region. The extracted independent vector magnetic potential distribution data are then combined sequentially with the excitation coil and detection coil to calculate the conductivity sensitivity matrix, as shown in the following formula:

[0058] S=-ω 2 A A A B

[0059] Where ω represents the operating frequency of the electromagnetic detection system, and A A Let A be the vector magnetic potential distribution of the object field under excitation A. B Let be the vector magnetic potential distribution of the object field under excitation B.

[0060] S2. The detection probe is configured such that several spiral cylindrical coils pointing towards the center are arranged on the inner ring surface of the circular carrier, and an insulator bracket is used to connect a spiral cylindrical coil pointing towards the center of the circular carrier to one end of each spiral cylindrical coil near the center.

[0061] The circular carrier can be a circuit board.

[0062] like Figure 2As shown in (a), the spiral columnar coils arranged on the annular carrier are all made of copper wire. Several spiral columnar coils pointing towards the center are arranged on the inner ring surface of the annular carrier, forming the outer coils, which are the excitation coils. An insulator bracket connects one spiral columnar coil pointing towards the center of the annular carrier to the end of each spiral columnar coil near the center, forming the inner coil, which is the detection coil. The excitation and detection coils are positioned opposite each other. Both the detection and excitation coils have an inner diameter of 5 mm and an outer diameter of 10 mm. The outer excitation coil is fixed to the circuit board. An insulating material passes through the annular detection and excitation coils, fixing their central axes on the same straight line. The carbon fiber cable to be measured can be placed in the intermediate object field area surrounding the coil arrangement.

[0063] The number of detection coils and excitation coils can be defined by the user, depending on the imaging accuracy of the object field, the size of the object field, and the coil arrangement. This invention uses eight detection coils and eight excitation coils.

[0064] S3. Testing carbon fiber cable: The testing probe is attached to the carbon fiber cable to be tested. Each spiral columnar coil is aligned with a strand of carbon fiber on the carbon fiber cable to be tested. The probe moves from one end of the carbon fiber cable to the other at a speed of 1mm / s-10mm / s. The voltage is collected once every 300 milliseconds.

[0065] like Figure 2 As shown in (b), the detection probe is placed on the carbon fiber cable under test, the excitation voltage of the excitation coil is set to 24V, the excitation frequency is 1MHz, and the voltage of the detection coil is collected and recorded as the detection voltage. The detection probe moves from one end of the carbon fiber cable under test to the other end at a preset speed, and the detection voltage is collected once every 300 milliseconds.

[0066] The preset speed of the present invention can be 10 mm / s.

[0067] S4. Based on the collected detection voltage, sensitivity matrix, and defect-free voltage, calculate the initial grayscale value set of all pixels of the cross section detected by the detection probe at the position of the carbon fiber cable being tested.

[0068] The defect-free voltage can be obtained from a simulation model with the same specifications as the carbon fiber cable being tested, or from an actual carbon fiber cable with the same specifications. The specific method for obtaining the defect-free voltage from an actual cable is as follows: use a detection probe to measure the carbon fiber cable at different locations several times, subtract the obtained detection voltages, and plot the subtraction results in a bar graph. If the bar graph does not show a U-shaped curve, it proves that the two measured detection voltages are defect-free voltages.

[0069] A regularization function is constructed. The main principle is to transform the original linear problem into a problem of finding the residual using the least squares method. Simultaneously, a regularization parameter is introduced to correct the objective function. The original problem has been transformed into a problem of finding an extremum. The regularization parameter is modified to shorten the distance between the calculated and actual values, thereby approximating the solution to the original problem infinitely.

[0070]

[0071] Where g is the set of gray values ​​of all pixels on the cross section, U is the difference between the defect-free voltage value and the detection voltage, S is the sensitivity matrix, and γ is the regularization parameter.

[0072] g = argmin(||SU|| 2 +γ‖g|| 2 )

[0073]

[0074] Among them, S T Let S be the transpose of S.

[0075] Based on the above analysis, the regularization formula can be expressed as:

[0076] g0=(S T S+γI) -1 S T U

[0077] Where I is the identity matrix.

[0078] S5. Calculate the initial residual vector based on the sensitivity matrix, the initial gray value set of all pixels on the cross section of the carbon fiber cable under test, the detection voltage, and the defect-free voltage. Then, update the initial gray value set of all pixels on the cross section of the carbon fiber cable under test using the Krylov subspace algorithm.

[0079] S5a-1. Calculate the initial residuals. Based on the initial residuals, construct the Krylov subspace. The Krylov subspace is an m-dimensional matrix. The Krylov subspace is as follows:

[0080] K = K(A, r0, m) = span(r0, Ar0, A) 2 r0,…,A m-1 r0)m≤n

[0081] Where K is the Krylov subspace, r0 is the initial residual, r0 = bA·g0, b = S T ·U, A=S T S, g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, and S is the sensitivity matrix. TLet S be the transpose of S, and U be the difference between the defect-free voltage and the detection voltage.

[0082] The matrix A is increased in dimensionality to form an M-order matrix, which adds more effective information about the solution and reduces the impact of ill-posed parameters.

[0083] S5a-2. Calculate the initial search direction P0 and the initial relative residual vector q0.

[0084] The formula for calculating the initial search direction P0 is:

[0085] P0 = r0 / norm(r0)

[0086] Here, norm(r0) is the second norm of r0.

[0087] The initial relative residual vector q0 is calculated as follows: q0 = A·P0;

[0088] S5a-3. Iteratively calculate the initial search direction P0 to obtain the iteratively calculated search direction P1: P1 = r1 / norm(r1), where r1 = r0 - alpha0·P0, alpha0 = r0 T ·q0; Iteratively calculate the initial relative residual vector q0 to obtain the iterated relative residual vector q1: q1=A·P1.

[0089] S5a-4. Construct an H2 matrix based on the initial search direction, the initial relative residual vector, and the search direction and residual vector calculated iteratively. Iteratively update the initial grayscale value set of all pixels on the cross section according to the H2 matrix.

[0090] The elements in the first row and first column of the H2 matrix are: H(1,1)=q0 T ×P0, the element in the first row and second column is H(1,2)=q1 T ×P0, the element in the second row and first column is: H(2,1)=q0 T ×P1, the element in the second row and second column is: H(2,2)=q1 T ×P1.

[0091] The orthogonality of vectors q0 and P0, and the orthogonality of vectors q0 and P1, are equivalent to r0. Similarly, the orthogonality of vectors q1 and P0, and the orthogonality of vectors q1 and P1, are equivalent to A. 1 r.

[0092] The formula for iteratively updating the initial grayscale value set of all pixels on the cross section is:

[0093] g1 = g0 + V2·y

[0094] Where g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, AV2 = V2H2, and y = H2 -1 (de), where d = ||r0||2, e = [1,0,0…0] T .

[0095] S5a-5. Determine whether the iteration tolerance meets the preset conditions based on the set of grayscale values ​​of all pixels on the updated interface. If the preset conditions are not met, proceed to steps S5a-6-S5a-8.

[0096] Set the convergence tolerance tol, with the preset condition: iteration tolerance norm(g1). <tol*norm(g0)

[0097] S5a-6. Perform iterative calculations on the search direction and the relative residual vector respectively to obtain the iterated search direction and the relative residual vector.

[0098] The formula for iteratively calculating the search direction is:

[0099] P k =r k / norm(r k )

[0100] Where, r k =r k-1 -alpha k-1 ·P k-1 alpha k =r k T ·q k .

[0101] The formula for iteratively calculating the relative residual vector is: q k =A·P k .

[0102] S5a-7. Based on the search direction and relative residual vector calculated iteratively, calculate the elements in the matrix and add them to the H matrix obtained in the previous iteration to obtain H. m Matrix, according to H m The matrix calculates the set of grayscale values ​​of all pixels on the cross section.

[0103] The formula for calculating the set of grayscale values ​​of all pixels on the cross section is:

[0104] g k =g0+V m ·y

[0105] Among them, V m V is the unit basis vector that is orthogonal to the subspace. m =[v1,v2,...vm ], y = H m -1 (de), d=norm(r0), e=[1,0,0…0] T .

[0106] Based on the search direction and relative residual vector calculated in this iteration, as well as the search direction and relative residual vector calculated in previous iterations, calculate H. m The elements of the matrix, the element in the i-th row and j-th column of matrix Hm, are: H(i,j) = q j-1 T ×P i-1 , 1≤i≤j, 1≤j≤m, where q j-1 Let P be the relative residual vector after the (j-1)th iteration update. i-1 Let q be the search direction after the (i-1)th iteration update. The subscript of the relative residual vector plus 1 indicates the column number of the element after multiplication, and the subscript of the search direction plus 1 indicates the row number of the element after multiplication. j-1 and relative residual vector P i-1 The vectors orthogonal to each other are equal to A in the Krylov subspace. j-1 r, that is, the superscript of A is the same as the subscript of the relative residual vector q.

[0107] H M The matrix is ​​in the form of:

[0108]

[0109] Calculate H m For each element in the matrix, only the element at the corresponding position in the m-th row and n-th column needs to be calculated, including the search direction, relative residual vector, and H. m The elements in the first m-1 rows and the first m-1 columns of the matrix have been calculated and saved in previous iterations. For example, when m=3 in this iteration, the matrix when m=2 has been calculated in the previous iteration, i.e., H2. We only need to calculate the elements of the third column and the third row based on the search direction and relative residual vector calculated in this iteration, as well as the search direction and relative residual vector calculated in the previous iteration, and add the elements of the third column and the third column to the matrix when m=2 to form the matrix when m=3, i.e., H3.

[0110] Through H m Matrix calculation V m :

[0111] h j，j v j =Av j -h 1,j v1-h 2,j v2-…-h j-1,jv j-1

[0112] Among them, h j，j For H m The element in the j-th row and j-th column of the matrix, v j For V m The column element of the j-th column in the data.

[0113] From the above formula, we can obtain: AV m =V m H m

[0114] Therefore, through We can obtain Vm. y = H m -1 (de) is the linear coefficient H m The solution to y = de.

[0115] The Krylov subspace algorithm is used to calculate residuals, construct search directions, update step size, retain effective projection data to the maximum extent, and search for the optimal solution in the constructed space to reduce the impact of outliers.

[0116] S5a-8. Determine whether the iteration tolerance has reached the preset condition based on the set of grayscale values ​​of all pixels on the updated interface. If the preset condition has not been reached, repeat steps S5a-6-S5a-7 until the preset condition is reached.

[0117] Set the convergence tolerance tol, with the preset condition: iteration tolerance norm(g) k ) <tol*norm(g0)

[0118] S6. Based on the initial grayscale value set of all pixels of the tested carbon fiber cable cross section obtained from the last iteration update, image the tested carbon fiber cable cross section. When there is a defect in the imaging result, the position detected by the detection probe is the location of the defect.

[0119] The output is the grayscale value of the tested carbon fiber cable cross section after iterative update. When there is a defect in the imaging result, the position detected by the detection probe is the location of the defect. When there is no defect in the imaging result, the position detected by the detection probe is normal.

[0120] S7. Method Evaluation.

[0121] Based on the simulation model established in step S1, a defect is set at the cross-section of the carbon fiber cable surrounded by the detection coil in the simulation model. The difference between the cuboid structure of the preset specification and the geometric structure of the carbon fiber cable is calculated, and the internal boundary is preserved to form a carbon fiber composite cable structure model with defects.

[0122] The defect shape and location of a three-dimensional carbon fiber cable simulation model are randomly set. Detection voltage data from multiple coils in turn are collected to obtain the detection voltage. Based on the set defect shape and location, a cross-sectional defect image of the simulation model is plotted, ensuring a correspondence between the detection voltage and the defect image. Initial grayscale values ​​on the simulation model cross-section corresponding to the set defect are obtained. The initial grayscale value set on the simulation model cross-section is iteratively updated each time using the Krylov subspace algorithm of this invention, resulting in an updated grayscale value set for the simulation model cross-section.

[0123] The image correlation coefficient and image error are calculated to evaluate the image reconstruction capabilities of the Tikhonov, Landweber, and TSVD methods compared to the method proposed in this invention.

[0124] The mathematical expression for the image correlation coefficient is:

[0125]

[0126] Where g is the set of grayscale values ​​of all pixels on the cross section of the simulation model with the defect set, g i Let g be the i-th element. This is the set of grayscale values ​​of all pixels on the cross-section of the tested carbon fiber cable after iterative updates. The average value of g is... for The average value.

[0127] The mathematical expression for image error is:

[0128]

[0129] The smaller the error value, the smaller the error between the reconstructed image and the original image, and the better the reconstruction effect. The closer the reconstructed image is to the original image, the higher the correlation coefficient.

[0130] like Figure 3 As shown, this invention more closely approximates the cross-sectional distribution of the simulation model than other algorithms. This algorithm can accurately detect the location and number of defects. The reconstructed image exhibits clear defect edges, fewer artifacts, and superior image quality compared to traditional algorithms.

[0131] Table 1 shows the comparison results of the correlation coefficients between the present invention and the methods of Tikhonov, Landweber, and TSVD.

[0132] Table 1. Image Correlation Coefficients

[0133] Model Tikhonov Landweber TSVD Krylov A 0.8115 0.8552 0.8634 0.8901 B 0.7615 0.7951 0.8116 0.8593

[0134] Table 2 shows the comparison results of image errors between the present invention and the methods of Tikhonov, Landweber, and TSVD.

[0135] Table 2. Image Errors

[0136] Model Tikhonov Landweber TSVD Krylov A 0.3261 0.2753 0.2704 0.2395 B 0.3771 0.3392 0.328 0.2729

[0137] As shown in Tables 1 and 2, data analysis reveals that the method of the present invention improves the correlation coefficient to varying degrees and reduces image error to varying degrees compared with traditional methods.

[0138] like Figure 4 As shown, the noise immunity and imaging performance of this invention are superior to other methods. The noise immunity of this invention remains stable under different carbon fiber cable strand breakage defects, demonstrating strong adaptability and robustness in various application scenarios and uncertain noise environments.

Claims

1. A method for defect detection in carbon fiber cables, characterized in that, Includes the following steps: S1. Construct an electromagnetic simulation model of the carbon fiber cable according to the specifications of the carbon fiber cable under test, apply an excitation voltage to the electromagnetic simulation model of the carbon fiber cable, and establish the sensitivity matrix of the cross-sectional field region of the carbon fiber cable by field quantity extraction method; S2. Construct a detection probe, the structure of which is to set several spiral cylindrical coils pointing to the center on the inner ring surface of the circular carrier, and to connect a spiral cylindrical coil pointing to the center of the circular carrier to one end of each spiral cylindrical coil near the center using an insulator bracket. S3. Testing carbon fiber cable: The test probe is attached to the carbon fiber cable to be tested. Each spiral columnar coil is aligned with a strand of carbon fiber on the carbon fiber cable to be tested. The probe moves from one end of the carbon fiber cable to the other at a speed of 1mm / s-10mm / s. The test voltage is collected once every 300 milliseconds. S4. Based on the collected detection voltage, sensitivity matrix, and defect-free voltage, calculate the initial grayscale value set of all pixels of the carbon fiber cable cross section detected by the detection probe; S5. Calculate the initial residual based on the sensitivity matrix, the initial gray value set of all pixels on the cross section of the carbon fiber cable under test, the detection voltage, and the defect-free voltage; update the initial gray value set of all pixels on the cross section of the carbon fiber cable under test using the Krylov subspace algorithm; S6. Based on the initial grayscale value set of all pixels of the carbon fiber cable cross section to be tested obtained from the last iteration update, the cross section of the carbon fiber cable to be tested is imaged. When there is a defect in the imaging result, the position detected by the detection probe is the location of the defect.

2. The defect detection method for carbon fiber cables according to claim 1, characterized in that, The formula for calculating the initial grayscale value set of all pixels of the measured carbon fiber cable cross-section in step S3 is as follows: g0=(S T S+γI) -1 S T U Where S is the sensitivity matrix, S T Let S be the transpose of S, U be the difference between the defect-free voltage and the detection voltage, and γ be the regularization parameter.

3. The defect detection method for carbon fiber cables according to claim 1, characterized in that, The specific method for updating the initial grayscale value set of all pixels of the measured carbon fiber cable cross-section in step S5 is as follows: S5a-1. Calculate the initial residuals and construct a Krylov subspace based on the initial residuals. The Krylov subspace is an m-dimensional matrix, K = K(A, r0, m) = span(r0, Ar0, A) 2 r0,…,A m-1 r0)m≤n; Where K is the Krylov subspace, r0 is the initial residual, r0 = bA·g0, b = S T ·U, A=S T S, g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, and S is the sensitivity matrix. T Let S be the transpose of S, and U be the difference between the defect-free voltage and the detection voltage. S5a-2. Calculate the initial search direction P0 and the initial relative residual vector q0; S5a-3. Iteratively calculate the initial search direction P0 to obtain the iterated search direction P1, and iteratively calculate the initial relative residual vector q0 to obtain the iterated relative residual vector q1. S5a-4. Construct an H2 matrix based on the initial search direction, the initial relative residual vector, and the iteratively calculated search direction and relative residual vector. Iteratively update the initial grayscale value set of all pixels on the cross section according to the H2 matrix. S5a-5. Determine whether the iteration tolerance has reached the preset condition based on the set of gray values ​​of all pixels on the updated interface. If the preset condition has not been reached, proceed to steps S5a-6-S5a-8. S5a-6. Iteratively calculate the search direction and relative residual vector to obtain the iterated search direction and relative residual vector; S5a-7. Based on the search direction and relative residual vector calculated iteratively, calculate the elements in the matrix and add them to the H matrix obtained in the previous iteration to obtain H. m Matrix, according to H m The matrix iteratively updates the set of grayscale values ​​of all pixels on the cross section; The formula for iteratively updating the set of grayscale values ​​of all pixels on the cross-section of the tested carbon fiber cable is as follows: g k =g0+V m ·y Among them, V m V is the unit basis vector that is orthogonal to the subspace. m =[v1,v2,...v m ], y = H m -1 (de), d=norm(r0), e=[1,0,0…0] T ; Matrix H m The formula for calculating elements in the middle is: H(i,j)=q j-1 T ×P i-1 ,1≤i≤j,1≤j≤m Where H(i,j) is H m The element q in the i-th row and j-th column of the matrix j-1 Let P be the relative residual vector after the (j-1)th iteration update. i-1 The search direction after the (i-1)th iteration update is represented by the multiplied relative residual vector q. j-1 and search direction P i-1 Vectors orthogonal are equivalent to A in the Krylov subspace. j-1 r; S5a-8. Determine whether the iteration tolerance has reached the preset condition based on the set of grayscale values ​​of all pixels on the updated interface. If the preset condition has not been reached, repeat steps S5a-6-S5a-7 until the preset condition is reached.

4. The defect detection method for carbon fiber cables according to claim 3, characterized in that, The formula for calculating the initial search direction P0 in step S5a-2 is: P0 = r0 / norm(r0) Where r0 is the initial residual, and norm(r0) is the second norm of r0; The formula for calculating the initial relative residual vector is: q0=A·P0.

5. The defect detection method for carbon fiber cables according to claim 3, characterized in that, The formula for calculating the search direction P1 in step S5a-3 is: P1 = r1 / norm(r1), where r1 = r0 - alpha0·P0, alpha0 = r0 T The formula for calculating the search direction P1 is: q1 = A·P1.

6. The defect detection method for carbon fiber cables according to claim 3, characterized in that, The calculation formula for iteratively updating the grayscale value set of all pixels on the cross section in step S5a-4 is as follows: g1 = g0 + V2·y Where g0 is the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable being measured, AV2 = V2H2, and y = H2 -1 (de), where d = ||r0||2, e = [1,0,0…0] T .

7. The defect detection method for carbon fiber cables according to claim 3, characterized in that, The formula for iteratively calculating the search direction in steps S5a-6 is as follows: P k =r k / norm(r k ) Where, r k =r k-1 -alpha k-1 ·P k-1 alpha k =r k T ·q k r k Let r be the residual of the k-th iteration. k T For r k The transpose of P k-1 Let q be the search direction calculated in the (k-1)th iteration. k Let be the relative residual vector calculated in the k-th iteration; The formula for iteratively calculating the relative residual vector is: q k =A·P k .

8. The defect detection method for carbon fiber cables according to claim 3, characterized in that, The preset condition in step S5a-8 is: norm(g k ) < tol * norm(g0), where tol is the set convergence tolerance.

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