Carbon fiber inhaul cable defect three-dimensional detection method based on alternating vector multiplier method

Abstract

The invention relates to a carbon fiber inhaul cable defect three-dimensional detection method based on an alternating vector multiplier method, and the method comprises the following steps: S1, constructing a three-dimensional electromagnetic simulation model of a carbon fiber inhaul cable according to the specification of a detected carbon fiber inhaul cable, and obtaining a sensitivity matrix and a defect-free voltage; s2, sleeving the detected carbon fiber inhaul cable with a sensor, and collecting the detection voltage of the detected carbon fiber inhaul cable; s3, calculating an initial gray value matrix; s4, introducing an auxiliary variable and a Lagrange multiplier, constructing a Lagrange function, and updating the initial gray value matrix; and S5, performing cross-section image reconstruction according to the updated gray value matrix, and when defects exist, superposing the cross-section images obtained at each time of the detected carbon fiber inhaul cable to obtain a three-dimensional image of the detected carbon fiber inhaul cable, and determining the height of the defects. According to the method, the section images of the detected carbon fiber inhaul cable are reconstructed, the section images are superposed when defects exist, the height of the defects can be obtained, and more comprehensive judgment on the defects of the inhaul cable is achieved.

Description

Technical Field

[0001] The invention relates to a carbon fiber cable defect detection method, in particular to a carbon fiber cable defect three-dimensional detection method based on an alternating vector multiplier method. Background Art

[0002] With the development of bridge technology in my country and the further growth of bridge spans, bridge engineers are faced with the problems brought by traditional steel cables: 1. Traditional steel cables are heavy; 2. Traditional steel cables have a low service life; 3. Traditional steel cables have high maintenance costs and construction difficulties. Based on the above problems, a new material that replaces steel as cables - carbon fiber reinforced composite materials can solve these problems well. Carbon fiber reinforced composite materials are widely used in various large structures, including aerospace industry, industrial buildings and high-pressure vessels, because of their excellent properties such as light weight, high strength, non-magnetic, corrosion resistance and fatigue resistance. These advantages make carbon fiber reinforced composite materials have great advantages in improving the durability of bridge tensile structures and the spanning capacity of bridges. In addition, carbon fiber reinforced composite materials also show great potential in the lightweight design of super-large amusement facilities and aerial passenger ropeways, which can significantly reduce the weight of the overall structure, reduce the load of the supporting structure, meet the load-bearing requirements of long-span cables, and improve the operation efficiency and safety of facilities. However, due to the influence of manufacturing process and service environment, carbon fiber composite cables will inevitably produce various damages and defects such as debonding and broken strands during use. These defects will directly lead to a significant decrease in the mechanical properties of the cables, and may even cause fracture failure, resulting in serious safety accidents. Therefore, effective detection of defects in carbon fiber composite cables is of great practical significance to ensure their safe and reliable service.

[0003] Electromagnetic tomography is a new non-destructive testing technology based on the principle of electromagnetic induction. It has the advantages of non-contact, low cost and visualization. It excites and detects the field of the object under test through multiple coils. The obtained detection data can be visualized after the image reconstruction method is used to calculate the distribution information of the object such as position, shape and size. The various advantages of electromagnetic tomography technology provide a clear and feasible way for the detection of carbon fiber cables.

[0004] However, at present, the research on this technology is mainly focused on two-dimensional planar imaging. However, traditional two-dimensional images have obvious limitations in electromagnetic tomography detection. They can only obtain the defect distribution of the cross section of the object field, which will correspondingly cause some information loss and make it difficult to fully reflect the characteristics of the defects. Summary of the invention

[0005] The object of the present invention is to provide a three-dimensional detection method for defects in carbon fiber cables based on the alternating direction method of multipliers, so as to solve the problem of missing defect information detected by the existing carbon fiber cable defect detection technology.

[0006] The object of the present invention is achieved as follows:

[0007] A three-dimensional detection method for defects in carbon fiber cables based on the alternating direction method of multipliers, comprising the following steps:

[0008] S1. Construct a three-dimensional electromagnetic simulation model of a carbon fiber cable according to the specifications of the carbon fiber cable to be measured, apply an excitation voltage to the electromagnetic simulation model of the carbon fiber cable, and establish a sensitivity matrix and a defect-free voltage of the physical field region of the cross-section of the carbon fiber cable by the field quantity extraction method.

[0009] S2. Sleeve the sensor on the carbon fiber cable to be measured, move it from one end of the carbon fiber cable to the other end, and collect the detection voltage of the carbon fiber cable to be measured once every preset moving interval, and the preset moving interval is less than or equal to 0.25 cm.

[0010] S3. Calculate the initial gray value matrix according to the defect-free voltage, the collected detection voltage, and the sensitivity matrix.

[0011] S4. Introduce auxiliary variables and Lagrange multipliers, construct a Lagrangian function according to the defect-free voltage, the collected detection voltage, and the sensitivity matrix, and update the initial gray value matrix according to the Lagrangian function to obtain an updated gray value matrix.

[0012] S5. Reconstruct the cross-sectional image according to the updated gray value matrix. If there are defects in the cross-sectional image of the carbon fiber cable to be measured, then superimpose the cross-sectional images obtained each time for the carbon fiber cable to be measured to obtain a three-dimensional image of the carbon fiber cable to be measured, and determine the length of the defect according to the position of the defect in the three-dimensional image.

[0013] Further, the structure of the sensor is that a plurality of annular coils pointing to the center are arranged on the inner ring surface of the circular ring carrier, which are divided into detection coils and excitation coils. The number of detection coils is the same as the number of excitation coils, and they are evenly distributed in a double-layer ring shape around the physical field. The inner layer coils are set as detection coils, and the outer layer coils are set as excitation coils.

[0014] Further, the Lagrangian function is:

[0015]

[0016] where S is the sensitivity matrix, g is the gray value matrix, U is the difference between the defect-free voltage value and the collected detection voltage, λ is the L1 regularization parameter, T is the transpose of the matrix, and z is the auxiliary variable.

[0017] Further, the specific method for updating the initial gray value is as follows:

[0018] S4a-1. Update the initial gray value matrix to obtain the updated gray value matrix g 1 as:

[0019] g 1 =(S T S) -1 (S T U + u 0 )

[0020] where S is the sensitivity matrix, S T is the transpose matrix of S, U is the difference between the defect-free voltage and the detected voltage collected, u 0 is the initial value of the Lagrange multiplier, and is a vector of all zeros;

[0021] S4a-2. According to the updated gray value matrix g 1 and the gray value matrix g 0 before the update, determine whether the convergence condition is satisfied. If it is satisfied, output the updated gray value matrix. If not, execute steps S4a-3 - S4a-6;

[0022] S4a-3. Update the auxiliary variable z k to obtain the updated auxiliary variable z k+1 as:

[0023]

[0024] where i is the i-th element in the matrix.

[0025] S4a-4. Update the Lagrange multiplier u k to obtain the updated Lagrange multiplier u k+1 as:

[0026] u k+1 = u k +(g k+1 - z k+1 )

[0027] S4a-5. Update the gray value matrix g k updated last time again to obtain the updated gray value matrix g k+1 as:

[0028] g k+1 =(S T S) -1 (S T U + u k )

[0029] S4a-6. According to the updated gray value matrix g k+1 and the gray value matrix g before updating k , determine whether the convergence condition is satisfied. If it is satisfied, output the updated gray value matrix; if not, loop and execute steps S4a-3 - S4a-5 until the convergence condition is satisfied, and then output the gray value matrix that meets the convergence condition.

[0030] Furthermore, the specific method for determining the length of the defect in step S5 is as follows:

[0031] S5a-1. Set the transparency of the non-defect part of the cross-sectional image to 0;

[0032] S5a-2. Arrange the processed cross-sectional images into a three-dimensional image according to the acquisition time;

[0033] S5a-3. Determine the number of intervals between the cross-sectional image where the defect first appears and the cross-sectional image where the defect last appears;

[0034] S5a-4. Determine the length of the defect based on the moving distance of the sensor and the number of intervals.

[0035] Based on the finite element technology, the present invention establishes a simulation model of the electromagnetic tomography imaging system for carbon fiber cables, and images the radial cross-section of the carbon fiber cable, which can visually identify the location of damage and provide an intuitive and reliable basis for the detection of cable damage.

[0036] The present invention develops an image reconstruction method applicable to carbon fiber cables. By using the L1 regularization method and the Lagrangian function, the inverse problem is transformed into an optimization problem, and the alternating direction method of multipliers is used to solve the L1 regularization problem, alleviating the ill-posedness and morbidity of the inverse problem, achieving more accurate defect reconstruction, and ensuring the safe service of the cable.

[0037] The present invention develops a three-dimensional image reconstruction method. The two-dimensional images obtained by the electromagnetic tomography imaging system are stacked in the height direction to obtain the height information of the defect, realizing a more comprehensive and accurate judgment of the cable defect, and achieving a more efficient visual detection of the carbon fiber cable defect. And through the L1 regularization method based on the alternating direction method of multipliers, the ill-posedness and morbidity of the electromagnetic tomography inverse problem are improved, the defect inversion ability of the algorithm is enhanced, and more accurate detection of the defect is realized. Description of the Drawings

[0038] Figure 1 is the flow chart of the present invention.

[0039] Figure 2is the three-dimensional simulation model of the carbon fiber cable under test of the present invention; among them, (a) is the geometric simulation model of the carbon fiber cable under test, and (b) is the conductivity of the carbon fiber cable under test.

[0040] Figure 3 is the simulation model of the sensor.

[0041] Figure 4 is the detected voltage value of single-coil excitation.

[0042] Figure 5 is the defect schematic diagram of the three-dimensional simulation model.

[0043] Figure 6 is the effect diagram of two-dimensional defect transparency processing.

[0044] Figure 7 is the effect diagram of two-dimensional defect superposition.

[0045] Figure 8 is the effect comparison diagram of reconstructing two-dimensional images by the present invention and the Landweber iteration method and the Tikhonov regularization method.

[0046] Figure 9 is the three-dimensional detection imaging diagram of the defects at different positions by the present invention. Detailed implementation manners

[0047] The present invention will be further described in detail below with reference to the accompanying drawings.

[0048] As Figure 1 shown, a three-dimensional detection method for carbon fiber cable defects based on the alternating direction method of multipliers provided by the present invention includes the following steps:

[0049] S1. Construct a three-dimensional 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 a sensitivity matrix and a defect-free voltage of the physical field region of the cross-section of the carbon fiber cable by the field quantity extraction method.

[0050] The carbon fiber cable has conductivity mainly because of the conductive carbon fibers in it, and the magnitude of its conductivity mainly depends on the distribution state of the carbon fibers and the formation of the fiber conductive path. The carbon fiber cable has a transverse conductivity perpendicular to the fiber direction, and at the same time, the carbon fiber composite layers are tightly combined, and there is an interlayer conductivity. The conductivity of the carbon fiber cable shows great anisotropy, with a large conductivity along the fiber direction and a small conductivity perpendicular to the fiber direction. According to the conductivity characteristics of the carbon fiber composite material and the geometric structure of the carbon fiber cable under test, the present invention establishes a simulation model with the same specifications as the carbon fiber cable under test through simulation software.

[0051] For example, as Figure 2As shown in (a), first, a single-strand cylinder with a radius of 3.5 mm and a height of 50 mm is established at the center of the object field, and a cable geometric model composed of seven carbon fiber rods is obtained through replication and rotation.

[0052] As Figure 2 shown in (b), the relative permeability and relative permittivity of the measured carbon fiber cable are 1, and the axial conductivity (along the fiber direction) is set as σ l = 5000 S / m, the transverse conductivity (perpendicular to the fiber direction) σ t = 100 S / m, and the radial conductivity (thickness direction) σ cp = 100 S / m. Before establishing the three-dimensional simulation model, the conductivity of the measured carbon fiber cable in different directions can be measured first.

[0053] As Figure 3 shown, after establishing the three-dimensional electromagnetic simulation model of the measured carbon fiber cable, a sensor model is established according to the sensor. The sensor includes an inner coil and an outer coil. The number of inner coils and outer coils is the same. One inner coil model corresponds to one outer coil model, and the central axes of the corresponding inner coil model and outer coil model are on the same straight line. The number of coils can be defined according to requirements. The structure of each coil is the same. The coil is wound with copper wire. The inner diameter of the coil r = 0.5 cm, the outer diameter R = 1 cm, the longitudinal length L = 1 cm, the thickness H = 0.25 cm, and the number of turns is 350 turns.

[0054] First, set a single coil model, then copy and rotate based on this coil, and finally form a 16-coil array model structure.

[0055] The outer coil is the excitation coil, and the inner coil is the detection coil.

[0056] As Figure 4 shown, place the three-dimensional electromagnetic simulation model of the measured carbon fiber cable at the center of the sensor model. The coil models are used as excitation coils in sequence according to the numbers 1-8. When one of the coils is used as the excitation coil, the current magnitude is 1 A and the frequency is 1 MHz, and the other 7 coil models in the outer circle are used as detection coils. The detection voltage of the three-dimensional electromagnetic simulation model of the measured carbon fiber cable is obtained.

[0057] In an empty field, use the outer No. 1 coil as the excitation coil to apply an excitation signal to it, and then measure the induced voltage values of the inner Nos. 10-16 as detection coils in sequence. According to this rule, use the No. 2 coil as the excitation coil to apply an excitation signal to it until all coils are used as excitation coils in sequence, and extract the object field information under the coil excitation. The sensitivity matrix is obtained by using the field quantity extraction method.

[0058] As Figure 5As shown in the figure, in the simulation model, in order to verify the effectiveness of using electromagnetic tomography technology to detect defects in carbon fiber composite cables, a broken strand defect with a circumferential length of 1mm, a circumferential width of 1mm, and an axial height of 5mm was set on the cable, and the defective and non-defective cables were detected by the detection system. In the corresponding measurement, it can be found that the detection voltage signal can change by up to 1mV compared with the defect-free cable. This shows that the defect will affect the eddy current intensity in the measured cable, resulting in a change in the size of the measurement data. The measurement results show that the induced voltage in the coil is very sensitive to the presence of defects. Therefore, electromagnetic tomography technology can be used to detect whether there are defects in carbon fiber composite cables.

[0059] S2. The sensor is sleeved on the carbon fiber cable to be tested, and is moved from one end of the carbon fiber cable to be tested to the other end, and the detection voltage of the carbon fiber cable to be tested is collected once at every preset movement interval.

[0060] The preset moving interval is less than or equal to 0.25m.

[0061] In addition to the coil, the sensor also has a channel switching module, a signal amplification module, and a signal generation and modulation module. When the sensor is working, the field programmable gate array (FPGA) generates a sinusoidal excitation signal, which is applied to the excitation coil after being processed by digital-to-analog conversion, signal conditioning circuit and amplification circuit, generating induced eddy currents on the surface of the cable. The detection signal of the sensor coil is then differentially amplified and sampled using analog-to-digital conversion. The sampled digital signal is then processed and demodulated by the FPGA and transmitted to the host computer for image reconstruction.

[0062] The sensor collects the detection voltage of the carbon fiber cable being tested, and the voltage collected each time is the detection voltage of the cross section of the carbon fiber cable being tested.

[0063] When the sensor is detecting, an excitation current is passed through the excitation coil, and the excitation coil will generate an alternating excitation magnetic field in the measured space. If there is a conductive or magnetic material in the measured space, the distribution of the excitation magnetic field will change, thereby forming a changing magnetic field related to the distribution of the conductivity and magnetic permeability of the measured material space. Then the detection coils distributed at the boundary of the measured space obtain the change information of the magnetic field through electromagnetic induction to obtain "projection" data. By controlling the excitation unit to change the excitation coil, that is, changing the direction of the excitation magnetic field, the detection information of the object field information in multiple projection directions can be obtained. The detection information is combined with the prior information, that is, the sensitivity matrix, and the gray value matrix of the object field distribution is calculated using the image reconstruction algorithm, and the distribution image of the conductive or magnetic material in the measured space is reconstructed on the computer.

[0064] S3. Calculate the initial gray value matrix based on the defect-free voltage, the collected detection voltage, and the sensitivity matrix.

[0065] Calculate the initial gray value matrix g 0 using the formula:

[0066] g 0 = S T U

[0067] where S T is the transpose matrix of the sensitivity matrix S, and U is the difference between the defect-free voltage and the collected detection voltage.

[0068] S4. Introduce auxiliary variables and Lagrange multipliers, construct a Lagrangian function based on the defect-free voltage, the collected detection voltage, and the sensitivity matrix, and update the initial gray value matrix according to the Lagrangian function to obtain the updated gray value matrix.

[0069] To solve the problems existing in the inverse problem of electromagnetic tomography, the present invention converts the inverse problem into an optimization problem through the L1 regularization method. And the alternating direction method of multipliers (ADMM) is used to solve the L1 regularization problem, alleviating the ill-posedness and ill-conditioning of the inverse problem and achieving more accurate defect reconstruction.

[0070] The mathematical expression of the inverse problem of electromagnetic tomography can be expressed as: U = Sg, where U is the difference between the defect-free voltage and the collected detection voltage, S is the sensitivity matrix, and g is the gray value matrix. However, there is still a problem to be solved when solving the inverse problem, that is, the sensitivity matrix S obtained by solving the forward problem is an irreversible matrix and its inverse matrix usually does not exist. Therefore, in order to be able to perform the calculation of the inverse problem, the least squares method is usually introduced to minimize the error between the observed data and the model prediction data (usually the sum of the squares of the data residuals) to obtain an optimal solution, and its expression is as follows:

[0071]

[0072] L1 regularization is a method used in regression analysis to reduce the model complexity and perform feature selection. Its principle is to add a penalty term of the L1 norm to the least squares loss function, thereby shrinking the regression coefficients of the model to achieve the purpose of reducing the number of features and improving the model performance, and converting the ill-posed inverse problem into a well-posed minimization problem. Specifically, for the given sensitivity matrix S and the difference U between the defect-free voltage and the collected detection voltage, the present invention hopes to solve the vector g to minimize the following objective function:

[0073]

[0074] Among them, || ||2 is the 2-norm, || ||1 is the 1-norm. The former term in the above formula represents the data item, and the latter term represents the regularization item. λ is the L1 regularization parameter.

[0075] The present invention uses the alternating direction method of multipliers to solve the above formula, decomposes the complex optimization problem into multiple easily solvable sub-problems, and approximates the optimal solution of the original problem by alternately optimizing these sub-problems.

[0076] To solve the mathematical problem of the above formula, the present invention introduces an auxiliary variable z to replace g, and transforms the problem into a new optimization problem:

[0077]

[0078] Introduce the constraint g = z, construct the Lagrangian function, and introduce the constraint g = z into the Lagrangian function through the Lagrange multiplier u. The Lagrangian function is:

[0079]

[0080] Solve this Lagrangian function by alternately optimizing the grayscale value matrix g, the auxiliary variable z, and the Lagrange multiplier u. The specific steps are as follows:

[0081] S4a-1. Update the initial grayscale value matrix by minimizing the part related to the grayscale value matrix in the Lagrangian function to obtain the updated grayscale value matrix g 1 , and the calculation formula is:

[0082] g 1 =(S T S) -1 (S T U + u 0 )

[0083] Among them, u 0 is a matrix of all zeros.

[0084] S4a-2. According to the updated grayscale value matrix g 1 and the grayscale value matrix g 0 before the update, judge whether the convergence condition is satisfied. If it is satisfied, output the updated grayscale value matrix. If it is not satisfied, execute steps S4a-3 - S4a-5.

[0085] The convergence condition is that the difference between the grayscale value matrix updated in the previous iteration and the grayscale matrix updated in this iteration is less than 1e-4 or 1e-6.

[0086] S4a-3. Minimize the part related to the auxiliary variable in the Lagrangian function to update the auxiliary variable z kUpdate to obtain the updated auxiliary variable z k+1 , and the calculation formula is:

[0087]

[0088] where u k is the Lagrange multiplier obtained from the k-th update, and i is the i-th element in the matrix.

[0089] That is,

[0090] S4a-4. Update the Lagrange multiplier u k to obtain the updated Lagrange multiplier u k+1 as:

[0091] u k+1 = u k + (g k+1 - z k+1 )

[0092] S4a-5. Update the grayscale value matrix g k from the previous update again to obtain the updated grayscale value matrix g k+1 as:

[0093] g k+1 = (S T S) -1 (S T U + u k )

[0094] S4a-6. According to the updated grayscale value matrix g k+1 and the grayscale value matrix g k before the update, determine whether the convergence condition is satisfied. If it is satisfied, output the updated grayscale value matrix. When it is not satisfied, loop through steps S4a-3 - S4a-5 until the convergence condition is satisfied, and output the grayscale value matrix that satisfies the convergence condition.

[0095] Judge whether the calculation result meets the condition by calculating the size relationship between the Frobenius norm of the iteration result and the set value tol. The convergence condition is that the difference between the grayscale value matrix updated in the previous iteration and the grayscale matrix updated in this iteration is less than 1e-4 or 1e-6.

[0096] The present invention gradually approaches the optimal solution by alternately updating the grayscale value matrix g, the auxiliary variable z, and the Lagrange multiplier u. By optimizing each variable, the present invention ensures that the solution converges gradually in each iteration, and finally obtains the optimal solution of the original problem.

[0097] The quality of the reconstructed image using the present invention depends on the selection of the regularization parameter λ and the number of iterations. The parameter values usually need to be carefully adjusted and optimized according to the specific application and experimental data to determine the optimal parameter combination.

[0098] S5. Perform cross-sectional image reconstruction based on the updated grayscale value matrix. When there are defects in the cross-sectional image of the measured carbon fiber cable, stack the cross-sectional images obtained for the measured carbon fiber cable each time to obtain a three-dimensional image of the measured carbon fiber cable, and determine the length of the defect according to the position of the defect in the three-dimensional image.

[0099] Reconstruct the defect image based on the grayscale value matrix obtained after iterative update. First, use a function to perform triangulation on the input grayscale value coordinates. Divide the input two-dimensional point set into a series of non-overlapping triangles, with the vertices of each triangle determined by the points in the coordinates, generating a mesh composed of triangular patches. Then, use the patch function to draw the reconstructed image of the defect according to the triangular data and coordinates.

[0100] To solve the limitations of traditional two-dimensional cross-sectional imaging in detection, when there are defects, the present invention performs post-processing operations of transparency and stacking on the cross-sectional image to generate a three-dimensional image. By stacking the two-dimensional images obtained by the electromagnetic tomography system detection in the height direction, the height information of the defect is obtained, realizing a more accurate judgment of the cable defect.

[0101] When there are no defects, there is no need to perform post-processing on the measured carbon fiber cable.

[0102] As Figure 6 shown, first perform transparency processing on the system two-dimensional detection image to remove or reduce the significance of the non-defect area, making the defect area more prominent and easy to observe. This process first identifies the defect area through a threshold processing method, and then sets the transparency of the non-defect part to zero, ensuring that only the defect information is clearly retained.

[0103] By setting the RGB color threshold, with the minimum value yellow_min = [200, 200, 0] and the maximum value yellow_max = [255, 255, 50], identify the area in the image where the pixel values fall within this range as the "yellow area", that is, the defect area, and set the Alpha channel of the yellow area to 255 (completely opaque), and the Alpha of the non-yellow area to 0 (completely transparent), and apply Gaussian blur to the Alpha channel to achieve a smooth transition between the transparent and opaque areas.

[0104] The distance between adjacent cross-sectional images is the preset moving interval of the sensor. The height of the defect is determined based on the number of intervals between the cross-sectional image where the defect first appears and the interface image where the defect last appears, and the preset moving interval. For example, if the number of intervals between the cross-sectional image where the defect first appears and the interface image where the defect last appears is 2, and the preset moving interval is 0.25 cm, then the height of the defect is 0.5 cm.

[0105] As Figure 7 shown, after performing image processing on the two-dimensional image and then superimposing the images, 3D image reconstruction is achieved. The defect information of each layer can be displayed more clearly, and the spatial position and morphological characteristics of the defects are accurately presented. This image processing and superimposition technology significantly improves the observation accuracy of defects and provides more intuitive data support for subsequent defect analysis and evaluation.

[0106] S6. Method evaluation.

[0107] To evaluate the image reconstruction effect of the method proposed in the present invention, the Landweber iterative method, the Tikhonov regularization method, and the method of the present invention were used to perform two-dimensional cross-sectional defect image reconstruction on the detected voltage data obtained from the 3D model.

[0108] As Figure 8 shown, first, four types of defects with different sizes were set on the carbon fiber composite cable. As Figure 6 shown in the first column, the axial height of the defects is 5 mm, the circumferential length of the defects in the first and third rows is 1 mm, the circumferential length of the defects in the second and fourth rows is 3 mm, the circumferential width of the defects in the first and second rows is 1 mm, and the circumferential width of the defects in the second and fourth rows is 2 mm. Figure 8 It also shows the two-dimensional reconstruction results of the cable defects obtained by the Tikhonov regularization method, the Landweber iterative method, and the method proposed in the present invention. In the reconstructed image, the yellow part is the low-conductivity area with defects, and the blue part is the high-conductivity area without damage.

[0109] From Figure 8From the reconstructed images, it can be seen that when the defect size is very small, the Tikhonov regularization method performs poorly and cannot accurately reconstruct a defect with a length of 1 mm, a width of 1 mm, and a height of 5 mm. This is because a core feature of the Tikhonov regularization method is that it tends to generate smooth solutions, which means that in the reconstruction process, high-frequency components in the image, such as sharp edges or small defects, will be smoothed by the method, resulting in the inability to reconstruct the defects. The Landweber iterative method can detect four different sizes of defects, but there are too many artifacts in the reconstructed images and the size of the reconstructed defects is too large, resulting in inaccurate reconstruction results. This is because the Landweber iterative method lacks a built-in mechanism to suppress high-frequency noise, and when faced with complex image reconstruction tasks, it will generate images containing artifacts. The L1 regularization method based on the alternating direction method of multipliers proposed in this paper can not only reconstruct defects with small volumes, but also obtain image reconstruction results with fewer artifacts, effectively overcoming the disadvantages of the above two methods, and the overall image quality exceeds the performance of traditional methods.

[0110] As Figure 9 shown, in order to verify the effectiveness of the algorithm proposed in the present invention, defects with a circumferential length of 2.5 mm, a circumferential width of 6 mm, and an axial height of 5 mm were set on the carbon fiber composite cable, and the defects were placed at different positions in the object field for three-dimensional image reconstruction. From Figure 9 the image reconstruction results, it can be clearly seen that the reconstructed three-dimensional image successfully reflects the specific position and height of the cable defects and reconstructs the spatial distribution of the defects.

Claims

1. A three-dimensional detection method for carbon fiber cable defects based on the alternating direction method of multipliers, characterized in that It includes the following steps: S1. Construct a three-dimensional electromagnetic simulation model of a carbon fiber material cable according to the specifications of the carbon fiber cable to be measured. Apply an excitation voltage to the electromagnetic simulation model of the carbon fiber material cable, and establish a sensitivity matrix and a defect-free voltage of the physical field region of the cross-section of the carbon fiber material cable by the field quantity extraction method; S2. Sleeve the sensor on the carbon fiber cable to be measured, move from one end of the carbon fiber cable to be measured to the other end, and collect the detection voltage of the carbon fiber cable to be measured once every preset moving interval, and the preset moving interval is less than or equal to 0.25 cm; S3. Calculate the initial gray value matrix according to the defect-free voltage, the collected detection voltage, and the sensitivity matrix; S4. Introduce auxiliary variables and Lagrange multipliers, construct a Lagrangian function according to the defect-free voltage, the collected detection voltage, and the sensitivity matrix, and update the initial gray value matrix according to the Lagrangian function to obtain an updated gray value matrix; S5. Perform cross-sectional image reconstruction according to the updated gray value matrix. If there are defects in the cross-sectional image of the carbon fiber cable to be measured, then superimpose the cross-sectional images obtained each time of the carbon fiber cable to be measured to obtain a three-dimensional image of the carbon fiber cable to be measured, and determine the length of the defect according to the position of the defect in the three-dimensional image.

2. According to the three-dimensional detection method for defects in carbon fiber cables based on the alternating direction method of multipliers described in claim 1, the structure of the sensor is that a number of annular coils pointing to the center are arranged on the inner ring surface of the ring carrier, which are divided into detection coils and excitation coils. The number of detection coils is the same as the number of excitation coils, and they are evenly distributed in a double-layer ring shape around the physical field. The inner layer coil is set as the detection coil, and the outer layer coil is set as the excitation coil.

3. The three-dimensional defect detection method for carbon fiber cables based on the alternating direction method of multipliers according to claim 1, wherein The Lagrangian function is: Where S is the sensitivity matrix, g is the gray value matrix, U is the difference between the defect-free voltage value and the collected detection voltage, λ is the L1 regularization parameter, T is the transpose of the matrix, and z is the auxiliary variable.

4. The three-dimensional detection method for carbon fiber cable defects based on the alternating direction method of multipliers according to claim 1, characterized in that The specific method for updating the initial gray value is: S4a-1. Update the initial grayscale value matrix to obtain the updated grayscale value matrix g 1 as follows: g 1 = (S T S) -1 (S T U + u 0 ) where S is the sensitivity matrix, and S T is the transpose matrix of S, U is the difference between the defect-free voltage and the detected voltage collected, and u 0 is the initial value of the Lagrange multiplier, which is a vector of all zeros; S4a-2. Determine whether the convergence condition is satisfied according to the updated grayscale value matrix g 1 and the grayscale value matrix g before the update 0 . If the convergence condition is satisfied, output the updated grayscale value matrix; if not, execute steps S4a-3 to S4a-6; S4a-3. Update the auxiliary variable z k to obtain the updated auxiliary variable z k+1 as follows: Where i is the i-th element in the matrix. S4a-4. Update the Lagrange multiplier u k to obtain the updated Lagrange multiplier u k+1 as follows: u k+1 = u k +(g k+1 - z k+1 ) S4a-5. Update the grayscale value matrix g of the last update k Perform the update again to obtain the updated grayscale value matrix g k+1 as follows: g k+1 = (S T S) -1 (S T U + u k ) S4a-6. According to the updated gray value matrix g k+1 and the gray value matrix g before the update k , determine whether the convergence condition is satisfied. If it is satisfied, output the updated gray value matrix. If not, loop and execute steps S4a-3 - S4a-5 until the convergence condition is satisfied, and then output the gray value matrix that meets the convergence condition.

5. The three-dimensional defect detection method for carbon fiber cables based on the alternating direction method of multipliers according to claim 1, wherein The specific method for determining the length of the defect in step S5 is: S5a-1. Set the transparency of the non-defect part of the cross-sectional image to 0; S5a-2. Arrange the processed cross-sectional images into a three-dimensional image according to the collected time; S5a-3. Determine the number of intervals between the cross-sectional image where the defect first appears and the cross-sectional image where the defect last appears; S5a-4. Determine the length of the defect according to the moving distance of the sensor and the number of intervals.

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