Carbon fiber inhaul cable defect detection method based on L1 regularization splitting constraint

Abstract

The invention relates to a carbon fiber inhaul cable defect detection method based on L1 regularization splitting constraint, and the method comprises the following steps: S1, building an electromagnetic simulation model of a carbon fiber inhaul cable according to the specification of a detected carbon fiber inhaul cable, and calculating a sensitivity matrix through a field quantity extraction method; s2, constructing a sensor array; s3, the carbon fiber inhaul cable is detected, and detection voltage is collected; s4, calculating an initial gray value matrix of the section of the detected carbon fiber inhaul cable according to the sensitivity matrix, the collected detection voltage and the defect-free voltage; s5, introducing a lower limit value a into a split Bregman algorithm, and updating an initial gray value matrix of the section of the tested carbon fiber inhaul cable; and S6, according to the gray value matrix updated by the last iteration, imaging the cross section of the detected carbon fiber inhaul cable, and when an imaging result has defects, determining that the position detected by the sensor array is a defect position. According to the method, the initial gray value matrix is updated through the split Bregman algorithm, and the updated gray value matrix is constrained by using the lower limit value a, so that the accuracy of image reconstruction is improved.

Description

Technical Field

[0001] The invention relates to a defect detection method, in particular to a carbon fiber cable defect detection method based on L1 regularized splitting constraints. Background Art

[0002] Carbon fiber materials have excellent properties such as high temperature resistance, corrosion resistance, light weight, high specific strength, and high specific stiffness, and are widely used in aerospace, national defense, military industry, and civil industry. Carbon fiber cables can be used as tensile structures for large-span load-bearing components. Affected by factors such as manufacturing processes and service environments, carbon fiber cables will inevitably produce various initial damages and surface and near-surface damage defects such as debonding and broken strands, resulting in a significant reduction in the mechanical properties of the cables, and even causing the entire carbon fiber material structure to break. Therefore, understanding the structural characteristics of carbon fiber materials and how to monitor the damage caused during the production process and service process to ensure that carbon fiber cables work stably and reliably in large-span and long-span high-altitude service environments has become an important issue in the field of detection technology.

[0003] Electromagnetic tomography is a non-destructive testing technology that reconstructs the image of the structure by measuring and analyzing the electromagnetic field signals inside the object. It is characterized by non-contact, low cost, visualization, and can effectively identify non-magnetic materials. Its function is to detect defects in the object being tested, ensure the safety and reliability of the object being tested, and maintain its stability and effectiveness during use. Therefore, electromagnetic testing, with its advantages of non-contact, non-invasive, and real-time imaging, provides a clear and feasible way for the detection of high carbon fiber cables. Due to the low conductivity of carbon fiber materials, the cross-section of the carbon fiber cable is not clear when imaging, so it is impossible to accurately determine the location and size of the defects in the carbon fiber cable. Summary of the invention

[0004] The purpose of the present invention is to provide a carbon fiber cable defect detection method based on L1 regularized splitting constraint to solve the problem of inaccurate position and size recognition of carbon fiber cable defects in the prior art.

[0005] The object of the present invention is achieved in that:

[0006] The carbon fiber cable defect detection method based on L1 regularized splitting constraint includes the following steps:

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

[0008] S2. construct a sensor array, wherein a plurality of spiral cylindrical coils pointing to the center of the circle are arranged on the inner ring surface of the circular carrier, and a spiral cylindrical coil pointing to the center of the circular carrier is connected to one end of each spiral cylindrical coil close to the center of the circle by using an insulator bracket;

[0009] S3. Detection of carbon fiber cable: The sensor array is mounted on the carbon fiber cable to be tested, and is moved from one end of the carbon fiber cable to the other end at a speed of 1 mm / s-10 mm / s, and the detection voltage is collected every 300 milliseconds;

[0010] S4. Calculate the initial gray value matrix of the cross section of the carbon fiber cable detected by the sensor array according to the sensitivity matrix, the collected detection voltage and the defect-free voltage;

[0011] S5. Introducing a lower limit value a into 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 lower limit value a;

[0012] S6. The gray value matrix of the cross section of the carbon fiber cable under test is obtained according to the last iteration update, and the cross section of the carbon fiber cable under test is imaged. When the imaging result has defects, the position detected by the sensor array is the position of the defect.

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

[0014] g0=(S T S+γI) -1 S T U

[0015] Among them, S is the sensitivity matrix, S T is the transposed matrix of S, γ is the first regularization parameter, I is the identity matrix, and U is the difference between the defect-free voltage and the detection voltage.

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

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

[0018] S5-2. Update the initial gray value matrix g0 and constrain the updated gray value matrix g1;

[0019] S5-3. Based on the gray value matrix after constraint and the initial Bregman variable b0, update the initial auxiliary variable d0 to obtain the auxiliary variable d1;

[0020] S5-4. Determine whether the preset conditions are met. If so, output If not, continue to execute steps S5-5-S5-8;

[0021] S5-5. For Bregman variable b k-1 Make updates;

[0022] S5-6. Based on the updated Bregman variable b k and auxiliary variable d k , update the gray value matrix g0 to obtain the gray value matrix g k+1 , using the lower limit value a to the gray value matrix g k+1 Constraints are applied to obtain the gray value matrix

[0023] S5-7. According to the gray value matrix after constraint and the updated Bregman variable b k , for the auxiliary variable d k Update to get the auxiliary variable d k+1 ;

[0024] S5-8. Determine whether the preset conditions are met. If so, output If not, repeat steps S5-5-S5-7 until the preset conditions are met.

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

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

[0027]

[0028] Among them, 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] Furthermore, in step S5-6, the gray value matrix g k+1 The constraints are:

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

[0031]

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

[0033] Furthermore, the conditions for iterative updating are:

[0034]

[0035] Among them, tol is the set convergence tolerance.

[0036] The present invention transforms the electromagnetic tomography image reconstruction process into an optimization problem for finding extreme values. It is more sensitive to the size information of the defect, the edge area is clearer, and there are fewer artifacts around the defect boundary. It can locate the defect position more accurately, and improve the reconstruction quality and accuracy of the defect image. The method combines the L1 regularization term, the split Bregman algorithm and the constraint term to better solve the pathological nature of the inverse problem. The present invention proposes a defect imaging detection method for carbon fiber composite cables based on L1 regularization split constraints. While reconstructing the defect image of the carbon fiber cable, it automatically removes redundant information, better retains key features, reduces imaging artifacts, and has strong adaptability and robustness in different application scenarios and uncertain noise environments.

[0037] By introducing the L1 regularization term to split the constraint function, the sparsity of the solution is promoted, the imaging quality is effectively improved, and the spatial resolution of the edge of the object is increased; the split Bregman algorithm is constructed to decompose the complex optimization problem into a series of simple sub-problems, and a faster convergence is achieved through a step-by-step approximation strategy, which improves the convergence speed of the algorithm and has good convergence and computational efficiency; the constraint term is imposed to ensure that the value of the gray value solution conforms to the actual physical constraint, improves the reliability and effectiveness of the solution, realizes efficient and sparse reconstruction, and greatly reduces image artifacts. Combined with L1 regularization, the algorithm achieves a balance between physical constraints and data-driven characteristics. In this way, the gray value is accurately calculated, and efficient reconstruction processing of the defect image is realized. The final image presents a good defect location and denoising effect. The simulation and experimental results show that the image reconstruction effect of this method is better than other traditional algorithms, and the prediction of different defect locations, quantities and shapes is more accurate, which can effectively improve the reconstruction quality and accuracy of the defect image.

[0038] The present invention 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-sectional position, but also greatly reduces the complexity of the problem, so as to carry out subsequent research work more efficiently. Under the influence of complex noise environment, by comparing the image error and structural similarity index data of the reconstructed image, it can be intuitively found that the noise resistance and imaging effect based on the L1 regularization splitting algorithm are better than other methods, and the reconstructed images of different defect distributions under uncertain noise types have higher stability and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the present invention.

[0040] Figure 2 It is an electromagnetic tomography system.

[0041] Figure 3 There are 56 full field voltage measurements.

[0042] Figure 4 It is the distribution of different defects of carbon fiber material cables.

[0043] Figure 5 This is the flow chart of the L1 regularized split constraint algorithm.

[0044] Figure 6 It is the electromagnetic finite element model of carbon fiber cable.

[0045] Figure 7 It is the reconstruction result of different defect distribution images based on simulation data.

[0046] Figure 8 It is the reconstruction result of different defect distribution images based on experimental data. DETAILED DESCRIPTION

[0047] The present invention is further described below.

[0048] like Figure 1 As shown, the carbon fiber cable defect detection method based on L1 regularized splitting constraint provided by the present invention comprises the following steps:

[0049] The electromagnetic tomography problem consists of 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 given the distribution of the internal conductivity or magnetic permeability of the sensitive field. The inverse problem is to reconstruct an image showing the internal conductivity or magnetic permeability distribution using the induced voltage and reconstruction algorithm.

[0050] like Figure 2 As shown, 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 reconstructs the image based on the collected voltage.

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

[0052] Finite element simulation software is used to simulate the specifications of carbon fiber cables. The major specifications of carbon fiber cables include materials, the number of carbon fiber rods used to make up the carbon fiber cables, the arrangement of the carbon fiber rods, and the diameter of each carbon fiber rod.

[0053] The sensor array model was constructed, and the size, layout, excitation current, excitation frequency and other parameters of the sensor array model were simulated by finite element simulation software. The sensor array model was mounted on the simulation model of the carbon fiber cable, and the parameters of the sensor array were continuously changed. The simulation model was excited. After each parameter change, the detection voltage was collected, and the image reconstruction algorithm was used to perform imaging based on the detection voltage. The parameters with better imaging effects were determined as the parameters of the sensor array simulation model.

[0054] For example, the fiber volume content of the carbon fiber cable to be tested in the present invention is 72%, and the resin volume content is 28%. It is composed of seven T700 carbon fiber rods in the form of six packages, and the radius of each carbon fiber rod is 4mm. According to the specifications of the carbon fiber cable to be tested, the sensor array model used in the present invention is a 16-coil double-layer planar electromagnetic sensor array, and the distance between the upper and lower relative detection coils and the excitation coils is 0.5mm, and the angle between the centers of the left and right adjacent coils is 45°. The 8 outer coils are used as excitation coils, which are E1-E8, and the 8 inner coils are used as detection coils, which are M1-M8. Each coil is the same size, with an inner diameter of 5mm, an outer diameter of 10mm, a height of 10mm, 350 turns of coils, and 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. A sinusoidal AC signal with an amplitude of 1A and an amplitude of 1MHz is selected as the excitation.

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

[0056] In the empty field, a current of 1A is passed through the excitation coil and the detection coil to ensure that the magnetic vector potential data under grid division are collected from multiple angles, and the sensitivity matrix is ​​obtained by using the field quantity extraction method.

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

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

[0059] Among them, A EX A represents the vector magnetic potential of the excitation coil under the action of the excitation signal. DET It represents the vector magnetic potential when the detection coil is excited, S σ Indicates A EX and A EX The conductivity sensitivity matrix formed.

[0060] S2. Construct a sensor array, the structure of which is that a plurality of spiral cylindrical coils pointing to the center of the circle are arranged on the inner ring surface of the circular carrier, and a spiral cylindrical coil pointing to the center of the circle of the circular carrier is connected to the end of each spiral cylindrical coil close to the center of the circle by an insulator bracket.

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

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

[0063] like Figure 3 As shown, the parameters of the sensor array of the present invention are the same as the parameters of the sensor array simulation model in step S1. The present invention adopts a 16-coil double-layer planar electromagnetic sensor array to apply excitation to the electromagnetic simulation model and collect detection voltage. The present invention adopts a single-coil excitation and multi-coil detection mode. The sensor array is composed of 16 circular copper spiral cylindrical coils. The outer 8 coils are used as excitation coils, which are E1-E8. The outer coils are connected to the ring carrier and point to the center of the circle. An insulator bracket is used to connect a spiral cylindrical coil pointing to the center of the ring carrier at the end of each outer coil close to the center of the circle, that is, the inner coil. The inner 8 coils are used as detection coils, which are M1-M8. The distance between the upper and lower relative detection coils and the excitation coil is 0.5mm, and the angle between the centers of adjacent coils on the left and right is 45°.

[0064] Each coil is the same size, with an inner diameter of 5mm, an outer diameter of 10mm, a height of 10mm, 350 turns, and 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 constructing 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. Detection of carbon fiber cables: The sensor array is mounted on the carbon fiber cables to be tested, and is moved from one end of the carbon fiber cables to be tested to the other end at a speed of 1 mm / s-10 mm / s, and the detection voltage is collected every 300 milliseconds.

[0067] The electrical properties of the carbon fiber cable are anisotropic, and its conductivity varies in different directions. The conductivity in the x direction is set to 100, the conductivity in the y direction is set to 100, and the conductivity in the z direction is set to 10000. The lift-off between the electromagnetic simulation model of the carbon fiber composite cable and the coil array is 0.5 mm.

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

[0069] Table 1. Excitation-detection coil sequence

[0070]

[0071]

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

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

[0074] S4. Calculate the initial gray 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] Among them, S is the sensitivity matrix, S T is the transposed matrix of S, γ is the first regularization parameter, I is the identity 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 carbon fiber cable being tested. The specific method of obtaining the defect-free voltage through the actual object is: use the sensor array to measure the different positions of the carbon fiber cable several times, subtract the obtained detection voltages, and make a bar graph of the subtraction results. If there is no U-shaped curve in the bar graph, it proves that the two detected voltages measured are defect-free voltages.

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

[0080] S5. A lower limit value a is introduced into the split Bregman algorithm, and the initial gray value matrix of the cross section of the measured carbon fiber cable is updated by using the split Bregman algorithm with the lower limit value a.

[0081] The inverse problem of electromagnetic tomography is to reconstruct the conductivity or magnetic permeability in the measured field based on the known boundary voltage measurement and the prior sensitivity matrix, thereby reconstructing the distribution of the conductive or magnetic permeable material in the measured object field. The inverse EMT problem seeks the internal conductivity distribution based on the sensitivity matrix. The relationship between the voltage measurement and the conductivity distribution in the imaging area is nonlinear and is expressed as follows:

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

[0083] Where V is the coil induced voltage, F is the sensitive field distribution function, D is 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 is subdivided into enough tiny regions, the change of conductivity on these tiny scales becomes extremely small. In this case, the nonlinear relationship of the electromagnetic tomography (EMT) inverse problem can be approximately linearized and converted into the following formula:

[0085] U=Sg

[0086] First, build the model function. The main principle is to transform the original linear problem into a problem of least squares residual. At the same time, the L1 regularization term is introduced to transform the original problem into an optimization problem containing a regularization term. The converted expression is as follows:

[0087]

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

[0089] like Figure 5 As shown, the split Bregman algorithm is then used to decompose the original problem into sub-problems that are easy to solve, reducing the computational complexity. By splitting ||g||1, the optimization problem is converted into an equivalent constraint form. An auxiliary variable d is introduced to make 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 the penalty term and using Bregman iteration, the constrained problem is transformed into an unconstrained problem:

[0093]

[0094] Among them, μ is the penalty parameter that controls the closeness between g and d, b is the Bregman variable, and d is the auxiliary variable.

[0095] The split Bregman method achieves faster convergence through a step-by-step approximation strategy and is more efficient than traditional optimization methods.

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

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

[0098] The updated gray value g1 is constrained again using the lower limit constraint. The constraint formula is:

[0099]

[0100] Among them, max is the maximum value function, a is the lower limit value, and the value of a is obtained by manual parameter adjustment, 0≤a≤0.1.

[0101] Compare the value of each element in g1 with a, and replace the elements with values ​​less than a with a to avoid elements with negative grayscale values.

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

[0103]

[0104] in, d1 is the first iteration result of the auxiliary variable d, λ is the second regularization parameter, and μ and λ are both manually adjusted.

[0105] S5-4. Determine whether the preset conditions are met. When the preset conditions are met, stop iteration and output the gray value matrix g1. When the preset conditions are not met, continue to execute steps S5-5-S5-8.

[0106] S5-5. For Bregman variable b k-1 Update and get the Bregman variable b k , the update formula is:

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

[0108]

[0109] Among them, g k+1 is the result of updating the initial gray value g0 matrix for the k+1th time, d k is the result of the kth update of the auxiliary variable d, b k is the result of the k-th update of the Bregman variable.

[0110] Constrain the gray value matrix, the constraint formula is:

[0111] Among them, 0≤a≤0.1.

[0112] Due to the low conductivity of carbon fiber cables, negative gray values ​​are prone to occur, resulting in artifacts in the constructed carbon fiber cable interface image. The gray value matrix is ​​constrained by using a lower limit value to ensure that the value of the variable g solution is not less than the lower limit value, which meets the actual physical constraints, thereby improving the reliability and interpretability of the solution.

[0113] The lower limit 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 range, thereby increasing the practicality of the algorithm.

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

[0115]

[0116] Among them, d k+1 It is the result of updating the auxiliary variables for the k+1th time.

[0117] S5-8. Determine whether the preset conditions are met. If so, output If not, repeat steps S5-5-S5-7 until the preset conditions are met.

[0118] The default condition is iteration tolerance Among them, tol is the preset convergence tolerance.

[0119] When the preset conditions are met, the gray value matrix calculated by the last update is output.

[0120] The split Bregman method achieves faster convergence through a stepwise approximation strategy, which is more efficient than traditional optimization methods. The advantage of the split Bregman method combined with L1 regularization and lower bound constraints is that it balances optimization efficiency, sparsity, physical constraints, and numerical stability, and can meet the needs of a variety of practical problems.

[0121] S6. The gray value matrix of the cross section of the carbon fiber cable under test is obtained according to the last iteration update, and the cross section of the carbon fiber cable under test is imaged. When the imaging result has defects, 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 tested carbon fiber cable is imaged according to the normalized gray value matrix. When the imaging result has defects, the position detected by the sensor array is the location of the defect. The size of the defect is more consistent with the original distribution of the defect. The position of the defect in the cross section of the tested carbon fiber cable can be observed in the imaging result.

[0123] S7. Evaluation of defect reconstruction images of carbon fiber cables.

[0124] S7-1. Evaluate the method of the present invention using a simulation model.

[0125] like Figure 6As shown, a strand-broken defect with a depth of 1 mm is set at different positions of the simulation model established in step S1, and a difference set is made between the rectangular structure of the preset specification and the geometric structure of the carbon fiber cable, and the internal boundary is saved to form a defective carbon fiber composite cable structure model. The corresponding image is drawn through the set defect to determine whether the image reconstructed by the method of the present application is consistent with the drawn image.

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

[0127] pass Figure 7 From the comparison results, it can be seen that the reconstructed image based on the L1 regularized split constraint algorithm is most consistent with the original defect model in terms of defect distribution. The algorithm can accurately locate the defects. The defect size and shape in its reconstructed image are clear, the artifact phenomenon is minimal, and the overall image quality exceeds the performance of traditional algorithms.

[0128] In order to evaluate the image quality of the L1 regularized split constraint algorithm (i.e., the present invention) compared with LBP, Landweber iterative algorithm, and Tikhonov regularization algorithm, the present invention uses image error (IE) and image structural similarity index (SSIM) as evaluation indicators. The image error reflects the degree of difference between the reconstructed image and the original image, and the structural similarity index evaluates the similarity between the original image and the reconstructed image by measuring brightness, contrast, and structural information. 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 consistency between the structural information of the reconstructed image and the original image. Through these two indicators, the reconstruction effects of different algorithms can be comprehensively evaluated.

[0129] The calculation formula for IE is:

[0130]

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

[0132] The calculation formula of SSIM is:

[0133]

[0134] in, is the average value of g, for 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 gradually transitions from LBP to L1 regularized split constraint algorithm, the image error shows a trend of gradual reduction, while the structural similarity index gradually increases accordingly. This significant change shows that the L1 regularized split constraint algorithm has a significant effect in improving image accuracy, making the location and size of defects in the obtained image more consistent with the original model.

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

[0141] In order to verify the performance of the proposed electromagnetic tomography method in a complex noise environment, experiments were 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 cable is composed 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 coil is made of 350 turns of copper wire with a diameter of 0.2mm. 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 defective field 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, which may have an adverse effect on the accuracy of the detection results.

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

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

[0144] Table 4. Image errors 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 errors and structural similarity indexes of different algorithms in Table 4 and Table 5, it can be seen that the noise resistance and imaging effect of the present invention are better than those of other methods, which verifies the noise resistance of the method in a complex noise environment. The experimental results show that the method has strong robustness and stability, can accurately identify surface defects of objects in a high noise environment, and provides strong support for the practical application of electromagnetic tomography technology.

Claims

1. A carbon fiber cable defect detection method based on L1 regularized splitting constraint, characterized in that: The steps include: S1. Construct an electromagnetic simulation model of the carbon fiber cable according to the specifications of the tested carbon fiber cable, apply an excitation voltage to the electromagnetic simulation model of the carbon fiber cable, and establish a sensitivity matrix of the material field region of the cross section of the carbon fiber cable by a field quantity extraction method; S2. construct a sensor array, wherein a plurality of spiral cylindrical coils pointing to the center of the circle are arranged on the inner ring surface of the circular carrier, and a spiral cylindrical coil pointing to the center of the circular carrier is connected to one end of each spiral cylindrical coil close to the center of the circle by using an insulator bracket; S3. Detection of carbon fiber cable: The sensor array is mounted on the carbon fiber cable to be tested, and is moved from one end of the carbon fiber cable to the other end at a speed of 1 mm / s-10 mm / s, and the detection voltage is collected every 300 milliseconds; S4. Calculate the initial gray value matrix of the cross section of the 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 into 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 lower limit value a; S6. The gray value matrix of the cross section of the carbon fiber cable under test is obtained according to the last iterative update, and the cross section of the carbon fiber cable under test is imaged. When the imaging result has defects, the position detected by the sensor array is the position of the defect.

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

3. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 1 is characterized in that: The specific method of updating the initial gray value matrix in step S5 is: S5-1. Make the initial auxiliary variable d0 and the initial Bregman variable b0 equal to the initial gray value matrix g0; S5-2. Update the initial gray value matrix g0 and constrain the updated gray value matrix g1; S5-3. Based on the gray value matrix after constraint and the initial Bregman variable b0, update the initial auxiliary variable d0 to obtain the auxiliary variable d1; S5-4. Determine whether the preset conditions are met. If so, output If not, continue to execute steps S5-5-S5-8; S5-5. For Bregman variable b k-1 Make updates; S5-6. Based on the updated Bregman variable b k and auxiliary variable d k , update the gray value matrix g0 to obtain the gray value matrix g k+1 , using the lower limit value a to the gray value matrix g k+1 Constraints are applied to obtain the gray value matrix S5-7. According to the gray value matrix after constraint and the updated Bregman variable b k , for the auxiliary variable d k Update to get the auxiliary variable d k+1 ; S5-8. Determine whether the preset conditions are met. If so, output If not, repeat steps S5-5-S5-7 until the preset conditions are met.

4. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 3 is characterized in that: In step S5-5, the Bregman variable b k-1 The formula for updating is:

5. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 3 is characterized in that: The formula for updating the initial gray value matrix g0 in step S5-6 is: Among them, U is the difference between the defect-free voltage and the detection voltage, S is the sensitivity matrix, μ is the penalty parameter, and d k is the auxiliary variable after the kth update, b k is the Bregman variable after the kth update.

6. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 3 is characterized in that: In step S5-6, the gray value matrix g k+1 The constraints are:

7. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 3 is characterized in that: In step S5-7, the auxiliary variable d k The formula for updating is: in, d k+1 is the k+1th iteration result of the auxiliary variable d, and λ is the second regularization parameter.

8. The carbon fiber cable defect detection method based on L1 regularized splitting constraint according to claim 3 is characterized in that: The conditions for iterative updating are: Among them, tol is the set convergence tolerance.

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