Carbon fiber cable defect detection method based on l1 regularization split constraint

Abstract

The present application relates to a kind of carbon fiber cable defect detection methods based on L1 regularization split constraint, comprising the following steps: S1. according to the specification of the measured carbon fiber cable, construct the electromagnetic simulation model of carbon fiber material cable, calculate sensitivity matrix by field extraction method;S2. Sensor array is constructed;S3. carbon fiber cable is detected, and detection voltage is collected;S4. according to sensitivity matrix, the detection voltage collected and defect-free voltage, calculate the initial gray value matrix of the section of the measured carbon fiber cable;S5. in split Bregman algorithm, introduce lower limit value a, update the initial gray value matrix of the section of the measured carbon fiber cable;S6. according to the gray value matrix of last iteration update, the section of the measured carbon fiber cable is imaged, when imaging result has defect, the position detected by sensor array is defect position.The present application updates initial gray value matrix by split Bregman algorithm, and using lower limit value a to constrain the gray value matrix after updating, improve the accuracy of image reconstruction.

Description

TECHNICAL FIELD

[0001] The application relates to a defect detection method, in particular to a carbon fiber cable defect detection method based on L1 regularization split constraint. BACKGROUND

[0002] Carbon fiber materials have excellent characteristics such as high temperature resistance, corrosion resistance, light weight, high specific strength and high specific stiffness, and are widely used in fields such as aerospace, national defense and military industry, and civil industry. The carbon fiber material cable can be used as a tensile structure of a large-span load-bearing component. Due to factors such as manufacturing process and service environment, the carbon fiber cable is inevitably prone to various initial damages and surface and near-surface damage defects such as debonding and broken strands, which can significantly reduce the mechanical properties of the cable and even cause the fracture of the entire carbon fiber material structure. Therefore, understanding the structural characteristics of carbon fiber materials and how to monitor the damages generated in the production process and service process of the carbon fiber cable to ensure that the carbon fiber cable can stably and reliably work in a high-altitude service environment with large span and long span has become an important problem in the detection technical field.

[0003] Electromagnetic tomography is a non-destructive testing technology that realizes reconstruction of the structure image by measuring and analyzing the electromagnetic field signals inside an object, and has the characteristics of non-contact, low cost, visualization, and can effectively identify non-magnetic materials. The role is to detect defects of the measured object, ensure the safety and reliability of the measured object, and maintain the stability and effectiveness of the measured object in the use process. Therefore, electromagnetic detection provides a clear and feasible way for the detection of high carbon fiber cables with its non-contact, non-invasive, real-time imaging and other advantages. Since carbon fiber materials have low conductivity, the cross section of the carbon fiber cable is not clear when imaging, so it is difficult to accurately determine the position and size of the defects in the carbon fiber cable. SUMMARY

[0004] The purpose of the present application is to provide a carbon fiber cable defect detection method based on L1 regularization split constraint, to solve the problem of inaccurate identification of the position and size of the defects of the carbon fiber material cable in the prior art.

[0005] The purpose of the present application is achieved as follows:

[0006] The carbon fiber cable defect detection method based on L1 regularization split constraint comprises the following steps:

[0007] S1. Constructing an electromagnetic simulation model of the carbon fiber material cable according to the specifications of the measured carbon fiber cable, applying an excitation voltage to the electromagnetic simulation model of the carbon fiber material cable, and establishing a sensitivity matrix of the carbon fiber material cable cross-section object field region by a field quantity extraction method;

[0008] S2. Constructing a sensor array, the structure of which is that a plurality of spiral column coils pointing to the center of the circle are arranged on the inner ring surface of the circular carrier, and an insulator support is used to connect one spiral column coil pointing to the center of the circular carrier at one end of each spiral column coil close to the center of the circle;

[0009] S3. Detecting the carbon fiber cable: the sensor array is sleeved on the measured carbon fiber cable, and is moved from one end to the other end of the measured carbon fiber cable at a speed of 1 mm / s-10 mm / s, and the acquisition of the detection voltage is completed every 300 milliseconds;

[0010] S4. According to the sensitivity matrix, the acquired detection voltage and the defect-free voltage, the initial gray value matrix of the cross section of the measured carbon fiber cable detected by the sensor array is calculated;

[0011] S5. Introducing a lower limit value a in the split Bregman algorithm, and updating the initial gray value matrix of the cross section of the measured carbon fiber cable by using the split Bregman algorithm with the introduction of the lower limit value a;

[0012] S6. According to the gray value matrix of the cross section of the measured carbon fiber cable updated by the last iteration, the cross section of the measured carbon fiber cable is imaged, and when the imaging result has a defect, the position detected by the sensor array is the position of the defect.

[0013] Further, the formula for calculating the initial gray value matrix of the cross section of the measured carbon fiber cable detected by the sensor array is:

[0014] g0=(S T S+γI) -1 S T U

[0015] Wherein, S is the sensitivity matrix, S T is the transpose matrix of S, γ is the first regularization parameter, I is the unit matrix, and U is the difference between the defect-free voltage and the detection voltage.

[0016] Further, the specific way of updating the initial gray value matrix in step S5 is:

[0017] S5-1. Making the initial auxiliary variable d0 and the initial Bregman variable b0 equal to the initial gray value matrix g0;

[0018] S5-2. Updating the initial gray value matrix g0, and constraining the updated gray value matrix g1;

[0019] S5-3. According to the constrained gray value matrix and the initial Bregman variable b0, updating the initial auxiliary variable d0 to obtain the auxiliary variable d1;

[0020] S5-4. Determine whether a preset condition is reached, if yes, output If not, continue to perform steps S5-5-S5-8.

[0021] S5-5. Update the Bregman variable b k-1 .

[0022] S5-6. According to the updated Bregman variable b k and the auxiliary variable d k , update the initial gray value matrix g0 to obtain the gray value matrix g k+1 , constrain the gray value matrix g k+1 using the lower limit value a to obtain the gray value matrix g

[0023] S5-7. According to the constrained gray value matrix g and the updated Bregman variable b k , update the auxiliary variable d k to obtain the auxiliary variable d k+1 .

[0024] S5-8. Determine whether a preset condition is reached, if yes, output If not, repeat steps S5-5-S5-7 until the preset condition is reached.

[0025] Further, the formula for updating the Bregman variable b k-1 in step S5-5 is:

[0026] Further, the formula for updating the initial gray value matrix g0 in step S5-6 is:

[0027]

[0028] Wherein, U is the difference between the defect-free voltage and the detection voltage, S is the sensitivity matrix, d k is the auxiliary variable after the kth update, b k is the Bregman variable after the kth update.

[0029] Further, the condition for constraining the gray value matrix g k+1 in step S5-6 is:

[0030] Further, the formula for updating the auxiliary variable d k in step S5-7 is:

[0031]

[0032] wherein, d k+1 is the k+1th iteration result of the auxiliary variable d, and λ is a second regularization parameter.

[0033] Further, the condition for iterative updating is:

[0034]

[0035] wherein, tol is a set convergence tolerance.

[0036] The electromagnetic tomographic image reconstruction process is converted into an optimization problem of extreme value seeking in the application, the size information of defects is more sensitive, the edge area is clearer, the artifacts around the defect boundary are less, the defect position can be more accurately located, and the reconstruction quality and precision of the defect image are improved. The method combines the L1 regularization term, the split Bregman algorithm and the constraint term, and better solves the ill-conditioned inverse problem. The application provides a defect imaging detection method for carbon fiber composite material inhaul cable based on L1 regularization split constraint, which can automatically remove redundant information while reconstructing the defect image of the carbon fiber inhaul cable, better retain key features, reduce imaging artifacts, and has strong adaptability and robustness in different application scenarios and uncertain noise environments.

[0037] By introducing the L1 regularization term split constraint function, the sparsity of the solution is promoted, the imaging quality is effectively improved, and the spatial resolution of the object edge is improved. The split Bregman algorithm is constructed to decompose the complex optimization problem into a series of simple subproblems, and a step-by-step approximation strategy is used to realize faster convergence, improve the convergence speed of the algorithm, and have good convergence and calculation efficiency. The constraint term is applied to ensure that the value of the solution of the gray value meets the actual physical constraint, improve the reliability and effectiveness of the solution, realize efficient sparse reconstruction, and greatly reduce image artifacts. The combination of L1 regularization balances the algorithm between physical constraints and data-driven characteristics. The gray value is accurately calculated, the defect image is efficiently reconstructed, and the final image presents good defect positioning and denoising effect. The simulation and experimental results show that the image reconstruction effect of the method is better than that of other traditional algorithms, the prediction for different defect positions, quantities and shapes is more accurate, and the reconstruction quality and precision of the defect image can be effectively improved.

[0038] The application constructs a two-dimensional electromagnetic carbon fiber cable finite element model, which not only accurately retains the geometric characteristics of the original three-dimensional structure at the selected cross-section position, but also greatly reduces the complexity of the problem, so as to more efficiently carry out subsequent research work. Under the influence of complex noise environment, by comparing the image error and structure similarity index data of the reconstructed image, it can be found that the anti-noise performance and imaging effect based on the L1 regularization split algorithm are better than those of other methods, and the reconstructed image of different defect distributions under uncertain noise types has high stability and robustness. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a flowchart of the application.

[0040] Figure 2 is an electromagnetic tomography system.

[0041] Figure 3 is 56 full-field voltage measurement values.

[0042] Figure 4 is a carbon fiber material cable with different defect distributions.

[0043] Figure 5 is a L1 regularization split constraint algorithm flowchart.

[0044] Figure 6 is an electromagnetic finite element model of a carbon fiber material cable.

[0045] Figure 7 is an image reconstruction result of different defect distributions based on simulation data.

[0046] Figure 8 is an image reconstruction result of different defect distributions based on experimental data. DETAILED DESCRIPTION

[0047] The application will be further described below.

[0048] As shown in Figure 1 , the carbon fiber cable defect detection method based on L1 regularization split constraint provided by the application comprises the following steps:

[0049] The electromagnetic tomography problem includes two parts: the forward problem and the inverse problem. The forward problem is to obtain the boundary voltage and sensitivity matrix of the sensitive field under the condition that the internal conductivity or magnetic conductivity distribution of the sensitive field is known. The inverse problem is to reconstruct the image showing the internal conductivity or magnetic conductivity distribution by using the induced voltage and reconstruction algorithm.

[0050] As shown in Figure 2 , the sensor array collects the voltage of the carbon fiber cable and sends it to the host computer, the host computer calculates the sensitivity matrix, and performs image reconstruction according to the collected voltage.

[0051] S1. Construct an electromagnetic simulation model of the carbon fiber material cable according to the specifications of the measured carbon fiber cable, apply an excitation current to the electromagnetic simulation model of the carbon fiber material cable, and establish a sensitivity matrix of the carbon fiber material cable cross-section field region by the field extraction method.

[0052] The specifications of the carbon fiber cable are simulated by using a finite element simulation software, and the large specifications of the carbon fiber cable include the material, the number of carbon fiber rods used to form the carbon fiber cable, the arrangement of the carbon fiber rods, and the diameter of each carbon fiber rod.

[0053] A sensor array model is constructed, and the size, layout, excitation current and excitation frequency of the sensor array model are simulated by using a finite element simulation software. The sensor array model is fitted on the simulation model of the carbon fiber cable, and the parameters of the sensor array are continuously changed, and the excitation is applied to the simulation model. After each parameter change, the detection voltage is collected, and imaging is performed according to the detection voltage by using an image reconstruction algorithm. When the imaging effect is good, the parameters are determined as the parameters of the sensor array simulation model.

[0054] For example, the fiber volume content of the measured carbon fiber cable of the present application is 72%, the resin volume content is 28%, and seven T700 carbon fiber rods are combined in the form of six packs. The radius of each carbon fiber rod is 4mm. For the specifications of the measured carbon fiber cable, the sensor array model used by the present application is a 16-coil double-layer planar electromagnetic sensor array. The distance between the upper and lower opposite detection coils and the excitation coil is 0.5mm, and the included angle between the centers of the left and right adjacent coils is 45°. The outer 8 coils are used as excitation coils, E1-E8, and the inner 8 coils are used as detection coils, M1-M8. Each coil has the same size, an inner diameter of 5mm, an outer diameter of 10mm, a height of 10mm, a coil number of 350 turns, and an inner coil center distance from the array center of 17.5mm, which is also the effective detection area radius size of the sensor array. A 1MHz amplitude 1A sinusoidal alternating signal is selected as the excitation.

[0055] The electrical properties of the carbon fiber cable are anisotropic, and the electrical conductivity differs in different directions, with the x-direction electrical conductivity set to 100, the y-direction electrical conductivity set to 100, and the z-direction electrical conductivity set to 10000. The lift-off between the carbon fiber composite cable electromagnetic simulation model and the coil array is 0.5mm.

[0056] When the field is empty, the excitation coil and the detection coil are passed through 1A current value, and the magnetic vector potential data under grid division is collected from multiple angles, and the sensitivity matrix is obtained by using the field extraction method.

[0057] The solution of sensitivity is usually divided into experimental perturbation method, simulation perturbation method and field quantity formula extraction method. The field quantity extraction method is adopted to obtain the sensitivity matrix in the application, and the calculation formula of the sensitivity matrix is:

[0058] S σ =E A ·E B =-ω 2 A EX ·A DET

[0059] Wherein, A EX represents the vector magnetic potential of the excitation coil under the action of the excitation signal, A DET represents the vector magnetic potential of the detection coil when the excitation is applied, S σ represents the conductivity sensitivity matrix formed by A EX and A EX .

[0060] S2. Constructing a sensor array, the structure is that a plurality of spiral columnar coils pointing to the center of the circle are arranged on the inner ring surface of the circular carrier, and an insulator support is used to connect a spiral columnar coil pointing to the center of the circular carrier at one end of each spiral columnar coil close to the center of the circle.

[0061] The sensor array comprises at least two outer coils and two inner coils.

[0062] In the construction of the sensor array, the existing sensor array can be directly used, or the sensor array can be continuously changed through the simulation model, and the sensor array parameters with better imaging results are selected to construct the sensor array.

[0063] As shown in Figure 3 , the parameters of the sensor array of the application are the same as those of the sensor array simulation model in step S1. The application adopts a 16-coil double-layer planar electromagnetic sensor array to excite the electromagnetic simulation model and collect detection voltages. The application adopts a single-coil excitation and multi-coil detection mode, and the sensor array is composed of 16 circular copper spiral columnar coils. Eight outer coils are used as excitation coils, which are E1-E8. The outer coils are connected to the circular carrier and point to the center of the circle. An insulator support is used to connect a spiral columnar coil pointing to the center of the circular carrier at one end of each outer coil close to the center of the circle, that is, an inner coil. Eight inner coils are used as detection coils, which are M1-M8. The distance between the upper and lower detection coils and the excitation coil is 0.5 mm, and the included angle between the centers of the left and right adjacent coils is 45°.

[0064] Each coil is the same size, with an inner diameter of 5mm, an outer diameter of 10mm, a height of 10mm, and 350 turns. The center of the inner coil is 17.5mm away from the center of the array, which is also the radius of the effective detection area of ​​the sensor array.

[0065] Before building the sensor array, simulation software is used to simulate the sensor array through parameters such as coil size, excitation current, and excitation frequency to determine the parameters of the sensor array in order to reduce the influence of simulation hardware on the simulation and improve the accuracy of defect imaging.

[0066] S3. Detecting the carbon fiber cable: The sensor array is placed on the carbon fiber cable to be tested and moved from one end of the carbon fiber cable to the other at a speed of 1 mm / s-10 mm / s, with the detection voltage collected every 300 milliseconds.

[0067] The electrical properties of carbon fiber cables are anisotropic, with conductivity varying in different directions. The conductivity in the x-direction, y-direction, and z-direction was set to 100, 100, and 10,000, respectively. The liftoff between the electromagnetic simulation model of the carbon fiber composite cable and the coil array was 0.5 mm.

[0068] As shown in Table 1, based on the parameters used in step S1 when measuring the carbon fiber cable, the same parameters are also used in the actual test to collect the voltage of the carbon fiber cable under test. When using the sensor array to measure the voltage of the carbon fiber cable, 16 coils are evenly wrapped around the outside of the carbon fiber cable. One outer coil is selected as the excitation coil, and a 1MHz, 1A amplitude sinusoidal AC signal is passed through. The inner coils except those directly below the outer coil are used to collect the detection voltage, and all other coils are grounded.

[0069] Table 1. Excitation-detection coil order

[0070]

[0071]

[0072] like Figure 4 As shown, 56 induced voltage values ​​are obtained after the outer coils are excited in sequence.

[0073] The sensor array is moved from one end of the carbon fiber cable to the other at a speed of 1 mm / s-10 mm / s, and the detection voltage is collected every 300 milliseconds.

[0074] S4. Calculate the initial grayscale value matrix of the cross section of the carbon fiber cable detected by the sensor array based on the sensitivity matrix, the collected detection voltage, and the defect-free voltage.

[0075] The formula for calculating the initial gray value matrix is:

[0076] g0=(S T S+γI) -1 S T U

[0077] wherein S is a sensitivity matrix, S T is the transpose matrix of S, γ is a first regularization parameter, I is a unit matrix, and U is the difference between the defect-free voltage and the detection voltage.

[0078] The defect-free voltage can be obtained in the established simulation model or in the actual measured carbon fiber cable. The specific way to obtain the defect-free voltage from the actual object is to use the sensor array to measure several times at different positions of the carbon fiber cable, subtract the obtained detection voltages, and make a column chart of the subtraction result. If there is no U-shaped curve in the column chart, it is proved that the two measured detection voltages are defect-free voltages.

[0079] The initial gray value matrix is a normalized matrix, so the value of each element in the initialization gray matrix is between 0 and 1.

[0080] S5. Introducing a lower limit value a in the split Bregman algorithm, and using the split Bregman algorithm with the introduction of the lower limit value a to update the initial gray value matrix of the measured carbon fiber cable section.

[0081] The electromagnetic tomography inverse problem is to reconstruct the conductivity or magnetic permeability in the measured field according to the known boundary voltage measurement and the prior sensitivity matrix, so as to reconstruct the distribution of the conductivity or magnetic permeability material in the measured object field. The EMT inverse problem seeks the internal conductivity distribution according to the sensitivity matrix. The relationship between the voltage measurement value and the conductivity distribution in the imaging area is nonlinear, which is denoted as follows:

[0082] V=∫∫ D σ(x,y)·F(x,y,μ(x,y),σ(x,y)))dxdy

[0083] wherein V represents the coil induced voltage, F represents the sensitive field distribution function, D indicates the cross section of the imaging area, σ(x,y) is the permeability distribution of the detection area, and μ(x,y) is the conductivity distribution of the detection area.

[0084] When the object field area is subdivided into a sufficient number of micro areas, the change of the conductivity in these fine scales will become extremely small. In this case, the nonlinear relationship of the electromagnetic (EMT) inverse problem can be approximately linearized and can be converted to the following formula:

[0085] U=Sg

[0086] Firstly, the model function is constructed. The main principle is to transform the original linear problem into a residual problem by using the least square method. At the same time, the L1 regularization term is introduced to transform the original problem into an optimization problem containing a regularization term, and the transformed expression is as follows:

[0087]

[0088] Wherein, U is the voltage difference between the defect-free voltage and the detection voltage, which is an m x 1 matrix, S is the sensitivity matrix, m x n can be obtained by finite element simulation, g represents the conductivity or permeability distribution of the detection area, which is an n x 1 gray value matrix. λ is the second regularization parameter, m is the number of single detection voltage, and n is the number of divided grid elements.

[0089] As shown in Figure 5 Secondly, the original problem is decomposed into sub-problems which are easy to solve by using the split Bregman algorithm, and the computational complexity is reduced. By splitting ||g||1, the optimization problem is converted into an equivalent constraint form. An auxiliary variable d is introduced, so that g = d, and the original problem can be expressed as:

[0090]

[0091] g0=d0=b0=(S T S+γI) -1 S T U

[0092] Finally, by introducing a penalty term, the Bregman iteration is used, and the constrained problem is transformed into an unconstrained problem:

[0093]

[0094] Wherein, μ is the penalty parameter, which controls the approximation degree between g and d, b is the Bregman variable, and d is the auxiliary variable.

[0095] The split Bregman method realizes faster convergence through step-by-step approximation strategy, and is more efficient than the traditional optimization method.

[0096] S5-1. First, let d0 = b0 = g0.

[0097] S5-2. Update the initial gray value matrix by using the initial auxiliary variable d0 and the initial Bregman variable b0 to obtain the updated gray value matrix g1, and the update formula is:

[0098] The lower bound constraint term is used to constrain the updated gray value g1 again, and the constraint formula is:

[0099]

[0100] Wherein, max is the maximum function, a is the lower limit value, the value of a is obtained by manual parameter tuning, 0≤a≤0.1.

[0101] The value of each element in g1 is compared with a, and the element whose value is less than a is replaced by a, so as to avoid the element with negative gray value.

[0102] S5-3. The initial auxiliary variable d0 is updated to obtain the auxiliary variable d1, and the update formula is:

[0103]

[0104] Wherein, d1 is the first iteration result of the auxiliary variable d, λ is the second regularization parameter, and μ and λ are obtained by manual parameter tuning.

[0105] S5-4. Determine whether the preset condition is reached, when the preset condition is reached, stop iteration, and output the gray value matrix g1, when the preset condition is not reached, continue to execute steps S5-5-S5-8.

[0106] S5-5. The Bregman variable b k-1 is updated to obtain the Bregman variable b k , and the update formula is:

[0107] S5-6. The initial gray value matrix g0 is updated to obtain the gray value matrix g k+1 , and the update formula is:

[0108]

[0109] Wherein, g k+1 is the result of updating the initial gray value g0 matrix for the k+1 time, d k is the result of updating the auxiliary variable d for the k time, and b k is the result of updating the Bregman variable for the k time.

[0110] The gray value matrix is constrained, and the constraint formula is:

[0111] Wherein, 0≤a≤0.1.

[0112] Because the carbon fiber cable has low conductivity, it is easy to have negative gray value, which leads to the false image of the carbon fiber cable interface. The lower limit value is used to constrain the gray value matrix, so as to ensure that the value of the variable g solution is not less than the lower limit value, which meets the actual physical constraint, thereby improving the reliability and interpretability of the solution.

[0113] The lower limit value a is used to constrain the gray value, which reduces the dependence of the split Bregman algorithm on the second regularization parameter λ, so that the second regularization parameter can work in a large interval range, and the practicability of the algorithm is increased.

[0114] S5-7. Update the auxiliary variable d k to obtain the auxiliary variable d k+1 , and the update formula is:

[0115]

[0116] wherein d k+1 is the result of the k+1th update of the auxiliary variable.

[0117] S5-8. Determine whether a preset condition is reached, if yes, output the gray value matrix If not, repeat steps S5-5-S5-7 until the preset condition is reached.

[0118] The preset condition is an iteration tolerance wherein tol is a preset convergence tolerance.

[0119] When the preset condition is reached, the gray value matrix calculated by the last update is output.

[0120] The split Bregman method realizes faster convergence through a step-by-step approximation strategy, and is more efficient than traditional optimization methods. The split Bregman method combines the advantages of L1 regularization and lower limit constraint, which balances optimization efficiency, sparsity, physical constraint and numerical stability, and can meet the needs of various practical problems.

[0121] S6. According to the gray value matrix of the measured carbon fiber cable section obtained by the last iteration update, the measured carbon fiber cable section is imaged, and when the imaging result has a defect, the position detected by the sensor array is the position of the defect.

[0122] The output gray value matrix is normalized, and the cross section of the measured carbon fiber cable is imaged according to the normalized gray value matrix, and when the imaging result has a defect, the position detected by the sensor array is the position of the defect, and the size of the defect is more consistent with the original distribution of the defect. The position of the defect in the imaging result can be observed in the cross section of the measured carbon fiber cable.

[0123] S7. Carbon fiber cable defect reconstruction image evaluation.

[0124] S7-1. The method of the present application is evaluated by using a simulation model.

[0125] For example Figure 6As shown, different positions of the simulation model established in step S1 are set with a broken strand defect with a depth of 1 mm, a cuboid structure of a preset specification is set difference with the carbon fiber cable geometry, internal boundaries are saved, and a carbon fiber composite cable structure model containing a defect is formed. Through the set defect, a corresponding image is drawn, and whether the image reconstructed by the method of the application is consistent with the drawn image is judged.

[0126] The circles outside the defect model in the figure are blue, representing the imaging area, which is also the detection range of the sensor array; the structure inside the blue color is a carbon fiber composite cable, Figure 7 The middle red part represents a broken strand defect with a depth of 1 mm on the surface of the carbon fiber composite cable.

[0127] Through Figure 7 The comparison results show that the reconstructed image based on the L1 regularization split constraint algorithm is most consistent with the original defect model in defect distribution. The algorithm can realize accurate positioning of the defect, the defect size and shape in the reconstructed image are clear, the artifact phenomenon is minimal, and the overall image quality exceeds the performance of the traditional algorithm.

[0128] In order to evaluate the image quality of the L1 regularization split constraint algorithm (i.e. the present application) compared with the LBP, Landweber iterative algorithm and Tikhonov regularization algorithm, the present application uses image error (IE) and structural similarity index (SSIM) as evaluation indexes. The image error reflects the difference between the reconstructed image and the original image, and the structural similarity index measures the brightness, contrast and structural information to evaluate the similarity between the original image and the reconstructed image. The smaller the image error, the better the quality of the reconstructed image and the higher the imaging accuracy; the larger the structural similarity index, the higher the degree of agreement between the structural information of the reconstructed image and the original image. Through these two indexes, the reconstruction effect of different algorithms can be comprehensively evaluated.

[0129] The calculation formula of IE is:

[0130]

[0131] Wherein, g represents the true conductivity distribution, represents the calculated conductivity distribution.

[0132] The calculation formula of SSIM is:

[0133]

[0134] Wherein, is the average value of g, is The average value of , i is the i-th element in the matrix.

[0135] Table 2. Image errors of different defect distributions based on simulation data

[0136]

[0137] Table 3. Structural similarity index of different defect distributions based on simulation data

[0138]

[0139] As shown in Tables 2 and 3, as the algorithm transitions from LBP to the L1 regularized split constraint algorithm, the image error gradually decreases, while the structural similarity index increases accordingly. This significant change demonstrates that the L1 regularized split constraint algorithm has a significant effect in improving image accuracy, making the location and size of defects in the resulting image more consistent with the original model.

[0140] S7-2. Evaluate the method of the present invention using actual carbon fiber cables.

[0141] In order to verify the performance of the proposed electromagnetic tomography method in a complex noise environment, an experiment was designed and implemented. In order to verify the effectiveness of the proposed method, a Figure 2 The electromagnetic detection system for defects in carbon fiber composite cables consists of a multi-coil electromagnetic sensor array module, a coil excitation array module, and a host computer module. The sensor array consists of 16 circular copper coils, each of which is the same size, with an inner diameter of 5mm, an outer diameter of 10mm, and a height of 10mm. The coils are wound 350 times with a copper wire of 0.2mm diameter. The center of the inner coil of the sensor array is 12.5mm away from the center of the array. This layout not only defines the radius range of the effective detection area and imaging area of ​​the sensor array, but also ensures that they together form a precise circular detection area with a diameter of 25mm. The detection voltage values ​​of the full field and the field containing defects were extracted using the constructed electromagnetic tomography system. During the experiment, there are many potential noise sources, such as electromagnetic interference, internal system noise, and environmental noise. These noise factors may have an adverse effect on the accuracy of the detection results.

[0142] like Figure 8 As shown in the figure, a 2mm deep broken strand defect is created at different locations on the surface of the carbon fiber cable, and the image of the carbon fiber cable with the defect is reconstructed using different methods. Figure 8The defect image in the figure is an image drawn according to the manufactured defect. Due to the soft field characteristics of the EMT electromagnetic induction field, the reconstructed image quality of a single defect distribution is better than that of multiple defects, and the reconstructed images of several algorithms cannot well identify the number of defect distributions F. This may be because the spacing between two defects of the defect distribution F is small, and the defect boundary may overlap, resulting in a continuous long strip-shaped defect.

[0143] As shown in Tables 4 and 5, the image error and structural similarity of the cross-sectional image reconstructed by each method and the real interface image of the carbon fiber cable are calculated.

[0144] Table 4. Image error of different defect distributions based on experimental data

[0145]

[0146] Table 5. Structural similarity index of different defect distributions based on experimental data

[0147]

[0148] By comparing the image error and structural similarity index of different algorithms in Tables 4 and 5, it can be seen that the anti-noise performance and imaging effect of the present application are better than those of other methods, verifying the anti-noise performance of the method in a complex noise environment. The experimental results show that the method has strong robustness and stability, and can accurately identify the surface defects of the object in a high noise environment, providing strong support for the practical application of electromagnetic tomography technology.

Claims

1. A method for defect detection of carbon fiber cables based on L1-regularized split constraints, characterized by, The method comprises the following steps: S1. Constructing an electromagnetic simulation model of the carbon fiber material cable according to the specifications of the measured carbon fiber cable, applying an excitation voltage to the electromagnetic simulation model of the carbon fiber material cable, and establishing a sensitivity matrix of the cross-section field region of the carbon fiber material cable by field extraction method; S2. Constructing a sensor array, the structure of which is that a plurality of spiral column coils pointing to the center are arranged on the inner ring surface of the circular ring carrier, and an insulator support is used to connect a spiral column coil pointing to the center of the circular ring carrier at one end of each spiral column coil close to the center; S3. Detecting the carbon fiber cable: the sensor array is sleeved on the measured carbon fiber cable, and the detection voltage is collected every 300 milliseconds at a speed of 1-10 mm / s from one end to the other end of the measured carbon fiber cable; S4. Calculating the initial gray value matrix of the cross-section of the measured carbon fiber cable detected by the sensor array according to the sensitivity matrix, the collected detection voltage and the defect-free voltage; S5. Introducing a lower limit value a in the split Bregman algorithm, and updating the initial gray value matrix of the cross-section of the measured carbon fiber cable by using the split Bregman algorithm with the introduction of the lower limit value a; S6. According to the gray value matrix of the cross-section of the measured carbon fiber cable obtained by the last iteration update, the cross-section of the measured carbon fiber cable is imaged, and when the imaging result has defects, the position detected by the sensor array is the position of the defects.

2. The L1-regularization based split constraints based carbon fiber cable defect detection method according to claim 1, characterized in that, The formula for calculating the initial gray value matrix of the cross-section of the measured carbon fiber cable detected by the sensor array is: g0 = (S T S + γI) -1 S T U where S is a sensitivity matrix, S T is the transpose matrix of S, γ is a first regularization parameter, I is an identity matrix, and U is the difference between the defect-free voltage and the detection voltage.

3. The L1-regularization based split constraints based carbon fiber cable defect detection method according to claim 1, characterized in that, The specific way of updating the initial gray value matrix in step S5 is: S5-1. Making the initial auxiliary variable d0 and the initial Bregman variable b0 equal to the initial gray value matrix g0; S5-2. Updating the initial gray value matrix g0, and constraining the updated gray value matrix g1; S5-3. Update the initial auxiliary variable d0 with the constrained gray value matrix and the initial Bregman variable b0, to obtain the auxiliary variable d1. S5-4. Determine whether a preset condition is reached, if yes, output If not, continue to perform steps S5-5-S5-8; S5-5. Update the Bregman variable b k-1 ; S5-6. Update the Bregman variable b according to the updated Bregman variable b k and the auxiliary variable d k , and obtain the gray value matrix g k+1 , and constrain the gray value matrix g k+1 using the lower limit value a, to obtain the gray value matrix S5-7. The matrix of constrained gray values and the updated Bregman variable b k The auxiliary variable d k is updated to obtain the auxiliary variable d k+1 ; S5-8. Determine whether a preset condition is reached, if yes, output If not, repeat steps S5-5-S5-7 until the preset condition is reached.

4. The L1-regularization based split constraints based carbon fiber cable defect detection method according to claim 3, characterized in that, The Bregman variable b is updated in step S5-5 k-1 The formula for updating is:

5. The L1-regularization based split constraints based carbon fiber cable defect detection method according to claim 3, characterized in that, The formula for updating the initial gray value matrix g0 in step S5-6 is: where U is the difference between the defect-free voltage and the detected voltage, S is the sensitivity matrix, μ is the penalty parameter, d k is the kth updated auxiliary variable, b k is the kth updated Bregman variable.

6. The L1-regularization based split constraint based carbon fiber cable defect detection method according to claim 3, characterized in that, The gray value matrix g in step S5-6 is subjected to a constraint condition k+1 The constraint condition is:

7. The L1-regularization based split constraints based carbon fiber cable defect detection method according to claim 3, characterized in that, The auxiliary variable d is updated in step S5-7 k The formula for updating is: wherein, d k+1 is the result of the k+1 iteration of the auxiliary variable d and λ is a second regularization parameter.

8. The L1 -regularization based split constraints based carbon fiber cable defect detection method according to claim 3, characterized in that, The condition for iteration update is: Wherein, tol is the set convergence tolerance.

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