Defect detection method for carbon fiber inhaul cable

Abstract

The invention provides a carbon fiber inhaul cable defect detection method which comprises the following steps: S1, establishing a simulation model with the same specification as a detected carbon fiber inhaul cable, and constructing a sensor model on the periphery of the three-dimensional simulation model; s2, applying current excitation to the simulation model to obtain full field voltage and a sensitivity matrix of the tested carbon fiber inhaul cable; s3, sleeving the detection device on the to-be-detected carbon fiber inhaul cable, and moving from one end of the to-be-detected carbon fiber inhaul cable to the other end of the to-be-detected carbon fiber inhaul cable at a preset speed to complete acquisition of detection voltage; s4, performing singular value decomposition on the sensitivity matrix, and calculating an initial gray value matrix; and S5, performing iterative updating on the initial gray value matrix according to the detection voltage and an improved ART algorithm, imaging the section of the detected carbon fiber inhaul cable according to the gray value matrix after iterative updating, and determining the position of the defect of the detected carbon fiber inhaul cable according to an imaging result. According to the method, the weighted TSVD is used for the high-dimensional sensitivity matrix and is combined with the improved ART, so that the accuracy of identifying the position and the size of the defect is improved.

Description

Technical Field

[0001] This invention relates to a method for detecting carbon fiber cables, specifically a method for detecting defects in carbon fiber cables. Background Technology

[0002] Carbon fiber reinforced polymer (CFRP) cables are lightweight, high-strength cable structures made from high-strength carbon fiber as reinforcement and resin as the matrix, manufactured through pultrusion or winding processes. Compared to traditional steel cables, they offer significant advantages such as high strength, light weight, excellent corrosion resistance, and good fatigue resistance, and have been widely used in long-span bridges, building structures, and aerospace applications. However, in practical applications, when CFRP cables are subjected to external impacts or cyclic fatigue loads, they are highly susceptible to damage phenomena such as fiber breakage, matrix cracking, and delamination. These damage behaviors not only reduce the integrity and load-bearing capacity of the structure but may also seriously affect its safety and reliability. Therefore, conducting research on the identification of the location and magnitude of damage in CFRP cables is of great significance for ensuring the safe operation of engineering structures.

[0003] Electromagnetic tomography (EMT) is a non-contact imaging technique based on electromagnetic induction, characterized by real-time performance, low cost, and wide applicability. Its principle involves using an alternating magnetic field to induce eddy currents within the object being measured, forming a secondary magnetic field. Changes in these magnetic fields are detected by external sensors, and image reconstruction algorithms are used to invert the distribution of electrical conductivity or magnetic permeability within the object. This invention employs an EMT system to detect damage to carbon fiber composite cables. However, the quality of the reconstructed image is affected by various factors. The sensitivity matrix is ​​a prerequisite for image reconstruction, and its accuracy directly affects imaging precision. The image reconstruction algorithm is used to solve the inverse problem; both together determine the accuracy and real-time performance of the imaging, forming the core of EMT technology. Therefore, in-depth research into EMT image reconstruction algorithms has significant theoretical and practical value for optimizing imaging quality. In EMT, compared to non-iterative reconstruction algorithms, the ART algorithm can still achieve effective image reconstruction even when dealing with sparse sampling data or missing projection angles. Although this algorithm is fast, it is inaccurate in identifying the shape and location of defects in carbon fiber cables. Summary of the Invention

[0004] The purpose of this invention is to provide a method for detecting defects in carbon fiber cables, so as to solve the problem that existing electromagnetic tomography technology is inaccurate in identifying the shape and location of defects in carbon fiber cables.

[0005] The objective of this invention is achieved in this way:

[0006] A method for detecting defects in carbon fiber cables includes the following steps:

[0007] S1. Establish a three-dimensional simulation model with the same specifications as the carbon fiber cable being tested, and build a sensor model around the three-dimensional simulation model;

[0008] S2. Apply current excitation to the three-dimensional simulation model, use the sensor model to capture the induced signal, and obtain the full-field voltage and the sensitivity matrix of the carbon fiber cable under test;

[0009] S3. Attach the detection device with the same structure as the sensor model to the carbon fiber cable under test, and move it at a constant speed from one end of the carbon fiber cable under test to the other end according to the set moving speed. The time interval for collecting the detection voltage is 200ms-300ms.

[0010] S4. Perform singular value decomposition on the sensitivity matrix, and calculate the initial gray value matrix of the carbon fiber cable under test based on the sensitivity matrix after singular value decomposition.

[0011] S5. The initial grayscale matrix is ​​iteratively updated based on the detection voltage and the improved ART algorithm. The cross-section of the carbon fiber cable under test is imaged based on the updated grayscale matrix. When an imaging result shows that the cross-section of the carbon fiber cable under test has a defect, the location of the defect in the carbon fiber cable under test is determined based on the defective cross-section.

[0012] Further, step S4 includes the following steps:

[0013] S4-1. Perform singular value decomposition on the sensitivity matrix to obtain the left singular vector matrix, the diagonal singular value matrix, and the right singular value matrix;

[0014] S4-2. Determine the cutoff value k, and retain the first k largest singular values ​​in the diagonal singular value matrix; determine the weighting factors for the first k largest singular values;

[0015] S4-3. Reconstruct the diagonal singular value matrix that retains the top k largest singular values ​​using a weighted factor;

[0016] S4-4. Retain the first k largest singular values ​​corresponding to the left and right singular vector matrices respectively; use the left and right singular vector matrices with the first k largest singular values ​​retained, as well as the weighted reconstructed diagonal singular value matrix, to calculate the initial gray value matrix.

[0017] Furthermore, the specific method for determining the cutoff value k in step S3-2 is as follows:

[0018] S4-2-1. Traverse the range of values ​​for k and execute steps S3-2-S3-4 to obtain the gray value matrix corresponding to each k value; the range of k is 1-p, k is an integer, and p is the rank of the sensitivity matrix;

[0019] S4-2-2. Calculate the residual norm and the norm of the solution for the gray value matrix corresponding to each k value, and perform a logarithmic transformation on the residual norm and the norm of the solution;

[0020] S4-2-3. Plot the residual norm and the norm of the solution after logarithmic transformation as coordinates on the L-curve, calculate the curvature of each coordinate on the L-curve, and select the point with the largest curvature as the target k.

[0021] Furthermore, the specific method for iteratively updating the grayscale matrix in step S5 is as follows:

[0022] S5-1. Calculate the initial residual vector between the detected voltage and the estimated data;

[0023] S5-2. Calculate the update amount of the gray value matrix in the first iteration based on the initial residual vector;

[0024] S5-3. Calculate the momentum of the first iteration based on the update amount of the gray value matrix in the first iteration;

[0025] S5-4. Update the initial gray value matrix based on the momentum of the first iteration to obtain the updated gray value matrix;

[0026] S5-5. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-9.

[0027] S5-6. Calculate the update amount of the gray value matrix after the m-th iteration;

[0028] S5-7. Based on the update amount of the gray value matrix after the m-th iteration, calculate the momentum of the gray value matrix after the m-th iteration.

[0029] S5-8. Calculate the gray value matrix after the m-th iteration update based on the momentum of the gray value matrix after the m-th iteration update;

[0030] S5-9. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-8.

[0031] Furthermore, the momentum of the grayscale matrix after the m-th iteration update... for:

[0032]

[0033] Among them, momentum (m-1) Let the momentum be the momentum after the (m-1)th iteration. This represents the update amount of the grayscale matrix in the m-th iteration.

[0034] Furthermore, the grayscale matrix after the m-th iteration update is: :

[0035]

[0036]

[0037] in, Let ω be the grayscale matrix after the (m-1)th iteration update, and ω be the relaxation factor. Let be the momentum of the grayscale matrix after the m-th iteration update. This is the grayscale matrix after momentum is superimposed.

[0038] This invention utilizes a weighted TSVD algorithm to reduce the dimensionality of the initial sensitivity matrix. By combining the defect-free voltage value and the detection voltage value, the voltage difference is obtained. Using an improved ART algorithm, the initial conductivity value set of all pixels of the tested carbon fiber cable cross-section is calculated. The initial grayscale value set of all pixels of the tested carbon fiber cable cross-section is iteratively updated using the initial residual and the number of iterations. Using the initial conductivity value set of all pixels of the tested carbon fiber cable cross-section obtained from the last iteration update, the tested carbon fiber cable cross-section is imaged, which can accurately identify the location and shape of defects.

[0039] This invention proposes a joint optimization method that integrates weighted TSVD sensitivity matrix dimensionality reduction with improved ART to solve the nonlinear inverse problem in electromagnetic tomography. This invention uses weighted TSVD to perform low-rank approximation on the high-dimensional sensitivity matrix to suppress ill-conditioning, and combines it with the improved ART algorithm to achieve high-precision reconstruction of the conductivity distribution of carbon fiber composite cable specimens, effectively locating and quantifying the position, shape and size of defects.

[0040] This invention uses Tikhonov regularization in the improved ART algorithm to effectively suppress the ill-conditioned characteristics of the inverse problem, introduces a momentum term to accumulate historical gradient information, accelerates convergence and suppresses oscillations, and introduces non-negativity constraints to ensure that the results conform to the actual physical scenario.

[0041] This invention improves the Algebraic Reconstruction Technique (ART) by introducing weighted truncated singular value decomposition (TSVD), momentum terms, and non-negativity constraints. This significantly enhances the algorithm's convergence efficiency and its ability to suppress noise interference, while ensuring the non-negativity of the reconstruction results. Traditional ART algorithms are susceptible to measurement noise and ill-conditioned problems during iteration, leading to slow convergence and potential artifacts in the reconstructed images. Weighted TSVD selectively truncates singular values ​​using a weight matrix, effectively reducing the matrix dimension while preserving key feature information. This not only reduces computational complexity but also improves the numerical stability of ill-conditioned problems. The introduction of the momentum term effectively suppresses oscillations during iteration by accumulating historical gradient information, thereby accelerating convergence and improving stability. Furthermore, the application of non-negativity constraints ensures the physical feasibility of the solution vector, avoiding non-physical solutions, which is crucial for reconstructing dielectric constant or conductivity distributions in electromagnetic tomography. Attached Figure Description

[0042] Figure 1 This is a flowchart of the present invention.

[0043] Figure 2 This is a schematic diagram of a ring sensor.

[0044] Figure 3 This is a schematic diagram of electromagnetic tomography detection.

[0045] Figure 4 This is a sensitivity matrix diagram under different excitation conditions.

[0046] Figure 5 These are the L-curves of different flawed simulation models, where (a) is the L-curve corresponding to the first flawed simulation model, (b) is the L-curve corresponding to the second flawed simulation model, (c) is the L-curve corresponding to the third flawed simulation model, and (d) is the L-curve corresponding to the fourth flawed simulation model.

[0047] Figure 6 This is a comparison image of the reconstruction of simulation data using the present invention and other methods.

[0048] Figure 7 This is a comparison image of the reconstruction of actual data using the present invention and other methods. Detailed Implementation

[0049] The invention will now be described in further detail with reference to the accompanying drawings.

[0050] like Figure 1 As shown, the present invention provides a method for detecting defects in carbon fiber cables, comprising the following steps:

[0051] S1. Establish a three-dimensional simulation model with the same specifications as the carbon fiber cable being tested, and build a sensor model around the three-dimensional simulation model.

[0052] like Figure 2 As shown, a three-dimensional simulation model of the tested carbon fiber cable is constructed using COMSOL Multiphysics simulation software. The specifications of the three-dimensional simulation model are the same as those of the tested carbon fiber cable. The established three-dimensional simulation model is a defect-free simulation model. Sensor models can be constructed based on existing sensors, and the sensors are fitted around the periphery of the three-dimensional simulation model. The carbon fiber cable of this invention adopts a "6+1" structure, that is, there are 6 carbon fiber rods around a single carbon fiber rod, and the diameter of a single carbon fiber rod is 8mm. A 16-coil sensor array is used, and its layout is arranged in a concentric ring. The outer diameter of the coil is 10mm, the inner diameter is 5mm, the height is 10mm, and the number of turns is 350.

[0053] S2. Apply current excitation to the three-dimensional simulation model, use the sensor model to capture the induced signal, and obtain the full-field voltage and the sensitivity matrix of the carbon fiber cable under test.

[0054] The sensor model has eight coils evenly distributed on the outer layer as excitation sensors, which form a detection excitation field by precisely applying an alternating electromagnetic field; the eight coils in the inner layer serve as detection sensors. When the outer excitation coil generates an electromagnetic field, the remaining seven detection coils in the inner layer can synchronously capture the induced signal to obtain the full-field voltage.

[0055] The constructed defect-free 3D simulation model was set with an axial conductivity of 10000 S / m and a radial conductivity of 100 S / m, and an alternating excitation current with an amplitude of 1 A and a frequency of 1 MHz was applied. A sequential excitation strategy was adopted, stimulating eight excitation sensors uniformly distributed on the outer layer of the model in turn, and recording the induced voltage signals generated by the remaining seven inner layer detection coils. This yielded 8 × 7 = 56 full-field voltages under defect-free conditions.

[0056] like Figure 3 As shown, each element of the sensitivity matrix typically represents the degree of influence of conductivity changes at a specific location in the imaging system on the measured signal. The sensitivity matrix allows for the back-projection of measurement data onto the imaging region, thereby reconstructing the internal structure of the object under test. Sensitivity matrices are generally obtained through field quantity extraction, experimental perturbation, and model perturbation methods. This invention employs the field quantity extraction method. In an empty field, current excitation is sequentially applied to eight excitation sensors, and the corresponding magnetic vector potentials are recorded. The sensitivity matrix S of the measured carbon fiber cable can then be calculated.

[0057]

[0058] Where ω represents the excitation frequency, E represents the excitation coil, and A EM represents the vector magnetic potential of the object field under the action of the excitation signal, and A represents the detection coil. M It represents the vector magnetic potential of the object field under the action of the detection signal.

[0059] S3. Attach the detection device, which has the same structure as the sensor model, to the carbon fiber cable under test. Move it at a constant speed from one end of the carbon fiber cable to the other end according to the set moving speed. The time interval for collecting the detection voltage is 200ms-300ms.

[0060] like Figure 4 As shown, the detection device has the same specifications as the sensor model in step S1. The detection device is fitted onto the carbon fiber cable under test. The host computer generates an excitation signal, which is filtered, denoised, and amplified by the signal processing module before being transmitted to the ring sensor. The carbon fiber cable under test generates an induced signal under the action of the electromagnetic field. After filtering and amplification, the signal is fed back to the host computer system to obtain the detection voltage.

[0061] The detection voltage collected by the detection device each time is the voltage on the cross-section of the carbon fiber cable being tested. By moving the detection device on the carbon fiber cable, the detection voltage of the cross-section of the carbon fiber cable being tested at different positions can be obtained.

[0062] S4. Perform singular value decomposition on the sensitivity matrix, and calculate the initial gray value matrix of the carbon fiber cable under test based on the sensitivity matrix after singular value decomposition.

[0063] Truncated Singular Value Decomposition (TSVD) is a numerical linear algebra method widely used for data dimensionality reduction, noise filtering, and matrix approximation. Its core idea is to achieve a low-rank approximation of a matrix by retaining its principal singular values ​​and corresponding singular vectors while discarding smaller singular values.

[0064] S4-1. Perform singular value decomposition on the sensitivity matrix to obtain the left singular vector matrix, the diagonal singular value matrix, and the right singular value matrix.

[0065] According to singular value decomposition, its SVD can be expressed as:

[0066]

[0067] Where Q is an m×m orthogonal matrix containing left singular vectors; Σ is an m×n diagonal matrix whose diagonal elements are non-negative singular values. , ,..., Arranged in descending order. V is an n×n orthogonal matrix containing right singular vectors.

[0068] The economic SVD of S (i.e., only the non-zero singular value part is calculated) can be used to calculate S using svd(S,'econ'), to obtain Q, Σ and V.

[0069] S4-2. Determine the cutoff value k, and retain the first k largest singular values ​​in the diagonal singular value matrix; determine the weighting factors of the first k largest singular values.

[0070] Choose a truncation threshold k, retain the k largest singular values ​​in the diagonal singular value matrix Σ, and set the remaining singular values ​​to zero. The truncated singular value matrix is ​​denoted as ∑. k :

[0071]

[0072] S4-3. Reconstruct the diagonal singular value matrix by weighting the top k largest singular values ​​according to the weighting factors.

[0073] Exponentially decaying weights are used, where the weights are proportional to the exponential decay function of the singular values. The weighting factors are:

[0074]

[0075] in, This represents the i-th singular value. It is the attenuation coefficient, which controls the attenuation rate of the weight.

[0076] This is achieved by multiplying the weighting factors by the singular values, and then reconstructing the original matrix using the weighted singular values ​​and the corresponding singular vectors. The formula for weighted reconstruction is:

[0077]

[0078] in, For the reason The weight vector is composed of these components.

[0079] In electromagnetic tomography, when using TSVD to reduce the dimensionality of the sensitivity matrix, different weights are applied to different singular values ​​by introducing weighting. During the truncation process, important features related to the target information are enhanced, noise and ill-conditioned components are suppressed, and the preserved subspace more accurately reflects the effective sensitivity distribution, thereby improving the stability and accuracy of image reconstruction.

[0080] S4-4. Retain the first k largest singular values ​​corresponding to the left and right singular vector matrices respectively; use the left and right singular vector matrices with the first k largest singular values ​​retained, as well as the weighted reconstructed diagonal singular value matrix, to calculate the initial gray value matrix.

[0081] Using the truncated singular value matrix ∑ kConstruct an approximate matrix S k :

[0082]

[0083] Among them, Q k Sum of the left singular vectors of the first k columns, V k Let ∑ be the right singular vector of the first k columns. k It is a diagonal matrix composed of the first k singular values.

[0084] Q k and V k The matrix itself remains unchanged; their column vectors are still the result of the singular value decomposition of the sensitivity matrix S. It's just that in constructing the approximate matrix S... k At that time, its effective part was truncated, and only the first k columns of Q and V were used, i.e., Q k and V k .

[0085] The initial grayscale matrix σ of the carbon fiber cable under test (0) for:

[0086]

[0087] in, It means yes The pseudo-inverse matrix, u is the difference between the full-field voltage and the detection voltage of the carbon fiber cable under test.

[0088] In the calculation of the sensitivity matrix using TSVD, choosing a suitable cutoff value k is crucial, as it directly affects the stability and accuracy of the solution. The L-curve method is a commonly used technique to select a suitable cutoff point k by considering the relationship between the residual norm and the solution norm. The L-curve is a curve in a logarithmic coordinate system, with the vertical axis representing the norm of the solution (…). The horizontal axis represents the residual norm ( In the L-curve graph, as the cutoff value k increases, the norm of the solution typically decreases, while the residual norm may increase until a certain point where the rate of increase in residual norm becomes even faster. The optimal value of k usually corresponds to the inflection point of the L-curve, i.e., the point where the curve bends most pronounced, which is also the point where the rate of increase in residual norm accelerates significantly. The inflection point on the L-curve corresponds to the optimal value of k, which is usually the position where the trade-off between solution complexity and residual is optimal. This optimal value of k can be automatically selected by calculating the curvature and finding the point of maximum curvature. By analyzing the inflection points of the L-curve, overfitting can be avoided while maintaining reasonable residuals.

[0089] The following is the process of determining the cutoff value k of TSVD using the L-curve:

[0090] S4-2-1. Traverse the range of values ​​for k, and execute steps S3-2-S3-4 to obtain the grayscale matrix corresponding to each k value. .

[0091] The value of k is set to a range of 1-p, and the value of k is an integer.

[0092] S4-2-2. Calculate the residual norm of the grayscale matrix corresponding to each k value. Norm of reconciliation and the residual norm Norm of reconciliation Perform a logarithmic transformation.

[0093] S4-2-3. Plot the residual norm and the norm of the solution after logarithmic transformation as coordinates on the L-curve, calculate the curvature of each coordinate on the L-curve (i.e., the relationship between the second derivative and the first derivative), and select the point with the largest curvature as the target k.

[0094] The gray value matrix corresponding to the target k is used as the gray value matrix after dimensionality reduction and weighting.

[0095] In image reconstruction, when using the sensitivity coefficient method based on truncated singular values, the appropriate selection of truncated singular values ​​plays a crucial role in image quality. The magnitude of the selected truncated singular values ​​affects the ill-conditioned characteristics of the inverse problem and the degree of loss of important information in the sensitivity coefficient matrix. Therefore, determining the truncated singular values ​​through L-curve analysis based on the singular value distribution characteristics of the sensitivity coefficient matrix has become an efficient and practical strategy. This method allows for more reasonable selection of truncated singular values, thereby improving the quality and stability of the reconstructed image.

[0096] S5. The initial grayscale matrix is ​​iteratively updated based on the detection voltage and the improved ART algorithm. The cross-section of the carbon fiber cable under test is imaged based on the updated grayscale matrix. When an imaging result shows that the cross-section of the cable is defective, the location of the defect in the carbon fiber cable under test is determined based on the defective cross-section of the carbon fiber cable under test.

[0097] To address the inherent limitations of traditional algebraic reconstruction techniques (ART) in electromagnetic tomography (EMT) inverse problems, such as slow convergence, susceptibility to local optima, and sensitivity to noise, this invention proposes an improved ART algorithm that integrates a momentum term and nonnegativity handling. Its core innovation lies in constructing an iterative update rule with "inertia" by adaptively weighting the update direction of the previous iteration onto the current gradient direction. This effectively suppresses the oscillating convergence and local stagnation problems that easily occur in traditional ART algorithms under sparse projection conditions. Furthermore, after each iteration, a nonnegativity constraint is applied to ensure the physical meaning of the reconstruction result, i.e., the conductivity distribution cannot be negative.

[0098] S5-1. First, calculate the initial residual vector between the detected voltage and the estimated data. :

[0099]

[0100] in, Let u be the initial residual vector, and let S represent the difference between the full-field voltage and the detection voltage referred to as the carbon fiber cable. k The reduced sensitivity matrix; σ (0) This is the initial grayscale value matrix. This is the estimated data for the 0th iteration.

[0101] S5-2. Calculate the update amount of the grayscale matrix in the first iteration. :

[0102]

[0103] Where, Δσ (1) This represents the update amount in the first iteration, S(i,:) is the data in the i-th row of the sensitivity matrix, and λ is the regularization parameter, which controls the smoothness of the solution and prevents numerical instability.

[0104] By adopting the Tikhonov regularization framework and introducing stable functional constraints, we can effectively suppress the ill-conditioned characteristics of the inverse problem, improve the singularity of the coefficient matrix, enhance the numerical stability and robustness of the local update calculation, ensure the smooth and efficient iterative convergence process, and reduce the perturbation effect of measurement noise on solution estimation.

[0105] S5-3. Calculate the momentum in the first iteration. (1) :

[0106]

[0107] Among them, momentum (1) The first iteration takes into account both historical and current gradient information. The value is 0, and α is the weight of the momentum term (0 < α < 1), which controls the degree of retention of historical information.

[0108] By introducing a momentum term to accumulate historical gradient information, convergence is accelerated and oscillations are suppressed, thereby improving stability and efficiency.

[0109] S5-4. Update the initial grayscale matrix to obtain the updated grayscale matrix. :

[0110]

[0111] Here, ω represents the relaxation factor, which controls the step size of each iteration. Usually, 0 < λ < 1. If the relaxation factor is too large, the algorithm may be unstable, and if it is too small, the convergence will be slow.

[0112] Apply a nonnegativity constraint to each element in the updated grayscale matrix:

[0113]

[0114] Since the physical nature of conductivity dictates that its value must satisfy non-negativity, non-negativity constraints need to be introduced during the solution process to ensure that the obtained results conform to the actual physical scenario and avoid negative solutions that have no physical meaning.

[0115] S5-5. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-9.

[0116] The residual vector of each row between the first grayscale value matrix update and the detected voltage. for:

[0117]

[0118] The convergence condition is that the number of iterations reaches the upper limit or the residual vector drops below a preset threshold; if either condition is met, the iteration stops.

[0119] S5-6. Calculate the update amount of the grayscale matrix after the m-th iteration. :

[0120]

[0121]

[0122] in, It represents the residual vector between the detected voltage and the estimated data after the (m-1)th iteration update.

[0123] S5-7. Update amount based on the grayscale matrix after the m-th iteration. Calculate the momentum of the grayscale matrix after the m-th iteration update. :

[0124]

[0125] Among them, momentum (m) To comprehensively consider the results of historical gradient information and current gradient information, α is the momentum term weight (0 < α < 1), which controls the degree of retention of historical information.

[0126] S5-8. Momentum of the grayscale matrix after the m-th iteration update. Calculate the grayscale matrix after the m-th iteration update. :

[0127]

[0128]

[0129] in, This is the grayscale matrix after the (m-1)th iteration update. ω is the grayscale matrix after momentum is superimposed, and ω is the relaxation factor.

[0130] S5-9. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-8.

[0131] The convergence condition is that the number of iterations reaches the upper limit or the residual drops below a preset threshold; the process stops when either condition is met.

[0132] The residual vector after the m-th iteration for:

[0133]

[0134] The cross section of the carbon fiber cable under test is imaged based on the gray value matrix. When an imaging result shows that the cross section of the carbon fiber cable under test has a defect, the location of the defective cross section is the position of the defect in the axial direction of the carbon fiber cable under test. The shape of the defect and its position on the cross section can be observed based on the defective cross section of the carbon fiber cable under test.

[0135] Simulation models with four different defect locations were constructed for carbon fiber composite cables. In the defective simulation model, a defect was introduced into the carbon fiber composite cable at the interface between the excitation and detection coils. A cuboid structure with dimensions of 8mm long, 4mm wide, and 1mm high was used to subtract the carbon fiber cable geometry from the original structure, retaining the subtracted geometry to form the defective carbon fiber composite cable simulation model. A sequential excitation strategy was employed. Eight excitation sensors uniformly distributed on the outer layer of the model at two different defect locations were excited by applying an alternating excitation current with an amplitude of 1A and a frequency of 1MHz. The induced voltage signals generated by the remaining seven inner layer detection coils were recorded sequentially to obtain the detection voltage corresponding to the defect location.

[0136] like Figure 5As shown, based on four simulation models, this invention uses the sensitivity matrix and voltage difference combined with the TSVD algorithm to plot L-curves. With the increase in the number of solution paradigms, the residual paradigm continuously decreases. Near the inflection point, the rate of decrease in the residual paradigm gradually slows down, indicating that the effect of further increasing the solution paradigm on improving the residual has become less pronounced. Choosing a regularization parameter corresponding to the inflection point ensures the stability of the solution while avoiding overfitting noise. For the same sensitivity matrix S, the optimal cutoff point k calculated by the TSVD algorithm varies with different voltage differences u. This phenomenon indicates that the selection of the cutoff point k depends not only on the sensitivity matrix S but also closely related to the characteristics of the measured data u. By simulating and analyzing the variation of k values ​​under different voltage differences, the performance of the TSVD algorithm can be further optimized to improve the approximation effect under different conditions. The simulation results provide guidance for experimental design, helping to determine a suitable voltage difference range, thereby obtaining a more accurate k value in the experiment. Figure 4 The solid circle in the diagram represents the point of maximum curvature of the L-curve.

[0137] Figure 5 The curve in Figure (a) corresponds to the simulation model with defects and Figure 6 The simulation model in the first row is the same. Figure 5 The curve in Figure (b) corresponds to the simulation model with defects and Figure 6 The simulation model in the second row is the same. Figure 5 The curve in Figure (c) corresponds to the simulation model with defects and Figure 6 The simulation model in the third row is the same. Figure 5 The curve in figure (d) corresponds to the simulation model with defects and Figure 6 The simulation model in the fourth row is the same.

[0138] like Figure 6 As shown, four algorithms—Tikhonov regularization, Landweber iteration, ART, and WTSVD-IART—were used to reconstruct images of four different defects in carbon fiber composite cables. The red areas represent the defects. Figure 5As can be seen, the WTSVD-IART algorithm exhibits the best overall performance in both single-defect and dual-defect models. Its reconstructed images not only accurately reproduce the geometric features of the defect but also demonstrate outstanding artifact suppression. In contrast, traditional algorithms have significant limitations: for the single-defect model, while the Tikhonov regularization algorithm, Landweber iterative algorithm, and ART algorithm can locate the defect, they produce relatively more artifacts, especially in the defect edge region, which may lead to exaggeration or underestimation of the defect size; for the dual-defect model, the ART algorithm shows a relative advantage in defect identification, but it is still inferior to the WTSVD-IART algorithm. Overall, the images reconstructed by the WTSVD-IART algorithm are closest to the true size and shape of the carbon fiber composite cable defect, achieving the best imaging effect on the defect target.

[0139] like Figure 7 As shown, the Tikhonov regularization, Landweber iteration, and Algebraic Reconstruction Technique (ART) algorithms can all effectively identify the spatial distribution characteristics of five different defects in carbon fiber composite cables. However, due to the significant influence of experimental noise, all three methods exhibit certain limitations in the quantitative characterization of defect size. The reconstructed boundaries are significantly diffuse, and geometric distortion and cross-sectional area shrinkage effects are obvious, resulting in a systematic scale deviation between the actual defects and the experimental results. The noise interference introduced during the experiment amplifies the reconstruction error, leading to obvious artifacts in the reconstructed images. These artifacts mainly manifest as non-physical false structural features, severely affecting the signal-to-noise ratio and spatial resolution of the images. In contrast, the WTSVD-IART algorithm proposed in this invention shows significant advantages. This algorithm not only outperforms traditional methods in defect localization accuracy but, more importantly, significantly improves defect size reconstruction and noise suppression capabilities. Its reconstruction results show clearer defect boundaries and more accurate size characterization, while exhibiting stronger robustness to experimental noise.

Claims

1. A method for detecting defects in carbon fiber cables, characterized in that, Includes the following steps: S1. Establish a three-dimensional simulation model with the same specifications as the carbon fiber cable being tested, and build a sensor model around the three-dimensional simulation model; S2. Apply current excitation to the three-dimensional simulation model, use the sensor model to capture the induced signal, and obtain the full-field voltage and the sensitivity matrix of the carbon fiber cable under test; S3. Attach the detection device with the same structure as the sensor model to the carbon fiber cable under test, and move it at a constant speed from one end of the carbon fiber cable under test to the other end according to the set moving speed. The time interval for collecting the detection voltage is 200ms-300ms. S4. Perform singular value decomposition on the sensitivity matrix, and calculate the initial gray value matrix of the carbon fiber cable under test based on the sensitivity matrix after singular value decomposition. S5. The initial grayscale matrix is ​​iteratively updated based on the detection voltage and the improved ART algorithm. The cross-section of the carbon fiber cable under test is imaged based on the updated grayscale matrix. When an imaging result shows that the cross-section of the carbon fiber cable under test has a defect, the location of the defect in the carbon fiber cable under test is determined based on the defective cross-section.

2. The method for detecting defects in carbon fiber cables according to claim 1, characterized in that, Step S4 includes the following steps: S4-1. Perform singular value decomposition on the sensitivity matrix to obtain the left singular vector matrix, the diagonal singular value matrix, and the right singular value matrix; S4-2. Determine the cutoff value k, and retain the first k largest singular values ​​in the diagonal singular value matrix; determine the weighting factors for the first k largest singular values; S4-3. Reconstruct the diagonal singular value matrix that retains the top k largest singular values ​​using a weighted factor; S4-4. Retain the first k largest singular values ​​corresponding to the left and right singular vector matrices respectively; use the left and right singular vector matrices with the first k largest singular values ​​retained, as well as the weighted reconstructed diagonal singular value matrix, to calculate the initial gray value matrix.

3. The method for detecting defects in carbon fiber cables according to claim 2, characterized in that, The specific method for determining the cutoff value k in step S3-2 is as follows: S4-2-1. Traverse the range of values ​​for k and execute steps S3-2-S3-4 to obtain the gray value matrix corresponding to each k value; the range of k is 1-p, k is an integer, and p is the rank of the sensitivity matrix; S4-2-2. Calculate the residual norm and the norm of the solution for the gray value matrix corresponding to each k value, and perform a logarithmic transformation on the residual norm and the norm of the solution; S4-2-3. Plot the residual norm and the norm of the solution after logarithmic transformation as coordinates on the L-curve, calculate the curvature of each coordinate on the L-curve, and select the point with the largest curvature as the target k.

4. The method for detecting defects in carbon fiber cables according to claim 1, characterized in that, The specific method for iteratively updating the grayscale matrix in step S5 is as follows: S5-1. Calculate the initial residual vector between the detected voltage and the estimated data; S5-2. Calculate the update amount of the gray value matrix in the first iteration based on the initial residual vector; S5-3. Calculate the momentum of the first iteration based on the update amount of the gray value matrix in the first iteration; S5-4. Update the initial gray value matrix based on the momentum of the first iteration to obtain the updated gray value matrix; S5-5. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-9. S5-6. Calculate the update amount of the gray value matrix after the m-th iteration; S5-7. Based on the update amount of the gray value matrix after the m-th iteration, calculate the momentum of the gray value matrix after the m-th iteration. S5-8. Calculate the gray value matrix after the m-th iteration update based on the momentum of the gray value matrix after the m-th iteration update; S5-9. Determine if the convergence condition is met. If it is met, stop the iteration and output the updated grayscale matrix. If it is not met, repeat steps S5-6-S5-8.

5. The method for detecting defects in carbon fiber cables according to claim 1, characterized in that, Momentum of the grayscale matrix after the m-th iteration update for: Among them, momentum (m-1) Let the momentum be the momentum after the (m-1)th iteration. This represents the update amount of the grayscale matrix in the m-th iteration.

6. The method for detecting defects in carbon fiber cables according to claim 1, characterized in that, The grayscale matrix after the m-th iteration update is: : in, Let ω be the grayscale matrix after the (m-1)th iteration update, and ω be the relaxation factor. Let be the momentum of the grayscale matrix after the m-th iteration update. This is the grayscale matrix after momentum is superimposed.

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