A three-dimensional irregular defect reconstruction method based on Armijo-LM algorithm

Abstract

The present invention relates to a three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm, comprising the following steps: S1, obtaining a ferromagnetic material test piece to be detected, collecting and saving a measured magnetic leakage signal; S2, based on the fast finite element principle, establishing a two-dimensional fast finite element forward model for magnetic leakage detection, for calculating and predicting the magnetic leakage signal; S3, slicing the three-dimensional defect contour according to the measured magnetic leakage signal obtained in step S1; using the Armijo-LM algorithm, combined with the two-dimensional fast finite element forward model established in step S2, calculating and correcting the iteration step, and reconstructing the three-dimensional irregular defect; S4, outputting a reconstructed defect contour close to the real defect. Compared with the prior art, the present invention has the advantages of fast reconstruction speed and high reconstruction contour accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of nondestructive testing, and in particular to a three-dimensional irregular defect reconstruction method based on an Armijo-LM algorithm. Background Art

[0002] Ferromagnetic materials are widely used in aerospace, transportation, petrochemical, energy and many other fields due to their good strength, hardness, plasticity and toughness. In practical applications, ferromagnetic materials will inevitably have defects such as damage and corrosion, which will seriously affect the normal operation of equipment and people's life safety. As one of the most commonly used methods of non-destructive testing, magnetic flux leakage detection technology is widely used in defect detection of ferromagnetic materials. After saturation magnetization, the ferromagnetic material detects the leakage magnetic field at the defect position through the sensor to obtain relevant information of the defect. Among them, the method of estimating defect information by inverting and calculating the leakage magnetic signal has always been a difficult point in the research of leakage magnetic detection. The current mainstream inversion algorithm is the iterative method. By using the Newton method, the Levenberg Marquardt method and the improved algorithms of the two, the iterative optimization is performed step by step, so that the predicted leakage magnetic signal is constantly close to the measured leakage magnetic signal, and then the defect contour is reconstructed.

[0003] In the prior art, Chinese patent CN114049428A discloses a three-dimensional irregular defect contour reconstruction method based on an improved trust region projection algorithm. First, a detection area is selected from the ferromagnetic material to be tested, and the magnetic charge density of the detection area is calculated using a cuckoo search algorithm. Then, a unit magnetic dipole band superposition model of a three-dimensional irregular shaped defect is constructed using the magnetic charge density distribution; then, the unit magnetic dipole band superposition model is used to obtain a comparison between an estimated signal and a true signal, and a suitable sampling area is selected; finally, in view of the ill-posedness of the three-dimensional irregular defect reconstruction problem, an improved trust region projection Levenberg-Marquart algorithm is proposed to achieve reconstruction of the irregular defect contour, but this method has the problems of slow defect detection speed and low reconstruction accuracy. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm, which can improve the detection calculation speed and reconstruction accuracy of three-dimensional irregular defects.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm comprises the following steps:

[0007] S1. Obtain a ferromagnetic material specimen to be tested, collect and save the measured leakage magnetic signal;

[0008] S2. Based on the fast finite element principle, a two-dimensional fast finite element forward model for magnetic flux leakage detection is established;

[0009] S3, slicing the three-dimensional defect contour according to the magnetic flux leakage signal obtained in step S1;

[0010] Using the Armijo-LM algorithm, combined with the two-dimensional fast finite element forward model established in step S2, the iteration step size is calculated and corrected to reconstruct the three-dimensional irregular defect;

[0011] S4. Output a reconstructed defect contour close to the real defect.

[0012] Furthermore, the specific contents of step S3 include:

[0013] S31, according to the magnetic flux leakage signal obtained in step S1, slicing the three-dimensional defect contour, initializing the reconstructed contour of the three-dimensional irregular defect, and setting algorithm-related parameters;

[0014] S32, slice the current contour data x of the defect t Input the 2D fast finite element forward model, calculate the predicted magnetic leakage signal and the objective function value, and judge x by the objective function value. t Is it a stable solution? If so, stop iteration, save the current reconstructed contour slice, and execute step S37; otherwise, execute step S33;

[0015] S33, determine whether the current number of iterations reaches the maximum number of iterations, if so, the algorithm stops iterating, saves the current reconstructed contour slice, and executes step S37; otherwise, executes step S34;

[0016] S34, obtain the incremental equation through the LM algorithm and calculate the iteration step Δx t ;

[0017] S35, using Armijo line search method to modify the iteration step Δx′ t =α t Δx t , where α t is the step size factor;

[0018] S36, update the defect contour slice, that is, x t+1 =x t +Δx′ t ;

[0019] S37, if all slice reconstructions are completed, all reconstructed contour slices are spliced ​​to obtain the final three-dimensional defect contour; otherwise, the number of iterations is reset, and the process returns to step S32 to continue the reconstruction of the next defect slice.

[0020] Furthermore, in step S31, for the collected measured magnetic leakage signal Y∈R M×D , according to the measured leakage magnetic signal, the 3D defect is sliced ​​to obtain a total of M defect slices; the 3D defect contour is initialized, i.e., the depth matrix

[0021] Furthermore, the algorithm-related parameters in step S31 include the maximum number of iterations T max , Armijo constant β∈(0,0.5), and the objective function threshold ε=10 for determining a stable solution -12 .

[0022] Furthermore, the objective function calculation formula in step S32 is:

[0023]

[0024] Among them, G(x t )∈R 1×D is the objective function, y(x t )∈R 1×D To measure the leakage magnetic signal, To predict the magnetic flux leakage signal.

[0025] Furthermore, the incremental equation in step S34 is specifically:

[0026]

[0027] Where t is the number of iterations, Δx t is the iteration step length, E(x t ) is the absolute error between the predicted leakage magnetic signal and the measured leakage magnetic signal, that is, the residual function, H(x t ) is E(x t ), the Hessian matrix of J(x t ) is E(x t )’s Jacobian matrix, μ t is the damping factor, which can be adaptively adjusted according to the change of the residual function, and I is the unit matrix.

[0028] Furthermore, the step length factor α in step S35 is t Satisfies the Armijo-Goldstein criterion:

[0029]

[0030] Among them, g t The function E(x t ), the Armijo constant β∈(0,0.5).

[0031] Furthermore, the step size factor α t Specifically, it is solved by binary search. In order to avoid frequent use of the fast finite element forward model in the S2 step to solve the objective function value during the optimization process, which increases the algorithm calculation time, the Taylor expansion of the objective function is used to obtain a variant of the Armijo-Goldstein criterion:

[0032]

[0033] Among them, the iteration step length Δx t , residual function E(x t ), Jacobian matrix J(x t ) and the Hessian matrix H(x t ) are all known data at the tth iteration, which effectively reduces the algorithm calculation time.

[0034] Furthermore, in step S36, the defect contour slice is updated, that is, x t+1 =x t +Δx′ t , where x t+1 Satisfy the boundary constraints:

[0035]

[0036] Where h is the specimen thickness.

[0037] Furthermore, the step S32 is specifically to determine whether the calculated objective function value is less than the set objective function threshold ε to determine whether x t Is it a stable solution?

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention realizes the reconstruction of three-dimensional defects based on the Armijo-LM algorithm, which can greatly shorten the calculation time and improve the calculation speed. It is verified by the embodiments of the present invention that the calculation time of the present technical solution is less than 2 hours. Taking defect 6 in the embodiment of the present invention as an example, the reconstruction time is reduced by 3% compared with the modified Newton method, 16% compared with the traditional LM algorithm, and 12% compared with the projection LM algorithm based on the trust region.

[0040] 2. The present invention uses the Armijo-goldstein criterion to correct the LM step size, so that the accuracy of the reconstructed contour can be effectively improved. It is verified by the embodiments of the present invention that the mean square error of the reconstruction result and the maximum depth error of the defect do not exceed 0.05 and 0.03, respectively. Taking defect 6 in the embodiment of the present invention as an example, the mean square error of the defect contour reconstruction and the maximum depth error of the defect reconstruction of the present invention are 6% and 4% of the modified Newton method, 10% and 5% of the traditional LM algorithm, and only 4% and 2% of the projection LM algorithm based on the trust region, which fully demonstrates that the technical solution can effectively improve the accuracy of the reconstructed contour.

[0041] 3. The present invention reconstructs three-dimensional regular defects. Compared with existing reconstruction methods, it has the advantages of fast reconstruction speed and high reconstruction accuracy, and has greater potential in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flowchart of the reconstruction method based on the Armijo-LM algorithm of the present invention;

[0043] Figure 2 It is a schematic diagram of the application process of the embodiment;

[0044] Figure 3 It is a comparison diagram of the contours reconstructed for the three-dimensional irregular simulation defect slice 1 by the algorithm of the present invention, the modified Newton method, the traditional LM algorithm and the projection LM algorithm based on the trust region in the embodiment;

[0045] Figure 4 It is a comparison diagram of the reconstructed contour of the three-dimensional irregular simulation defect slice 2 by the algorithm of the present invention, the modified Newton method, the traditional LM algorithm and the projection LM algorithm based on the trust region in the embodiment;

[0046] FIG5( a ) is a true contour diagram of a three-dimensional irregular simulation defect 3 in an embodiment;

[0047] FIG5( b ) is a reconstructed contour diagram of a three-dimensional irregular simulation defect 3 in the embodiment;

[0048] FIG5( c ) is a graph showing an average iteration curve of the objective function of the three-dimensional irregular simulation defect 3 in the embodiment;

[0049] FIG6( a ) is a true contour diagram of a three-dimensional irregular simulation defect 4 in an embodiment;

[0050] FIG6( b ) is a reconstructed contour diagram of a three-dimensional irregular simulation defect 4 in the embodiment;

[0051] FIG6( c ) is a graph showing an average iteration curve of the objective function of the three-dimensional irregular simulation defect 4 in the embodiment;

[0052] FIG. 7( a ) is a true contour diagram of a three-dimensional irregular real defect 5 (a crack with a depth of 2 mm) in the embodiment;

[0053] FIG7( b ) is a reconstructed contour diagram of a three-dimensional irregular real defect 5 (a crack with a depth of 2 mm) in the embodiment;

[0054] FIG7( c ) is a graph showing the average iteration curve of the objective function of the three-dimensional irregular real defect 5 (crack with a depth of 2 mm) in the embodiment;

[0055] FIG8( a ) is a true contour diagram of a three-dimensional irregular real defect 6 (crack with a depth of 6 mm) in the embodiment;

[0056] FIG8( b ) is a reconstructed contour diagram of a three-dimensional irregular real defect 6 (crack with a depth of 6 mm) in the embodiment;

[0057] FIG8( c ) is a graph showing the average iteration curve of the objective function of the three-dimensional irregular real defect 6 (crack with a depth of 6 mm) in the embodiment. DETAILED DESCRIPTION

[0058] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0059] like Figure 1 As shown, a three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm includes the following steps:

[0060] S1. Obtain a ferromagnetic material specimen to be tested, collect and save the measured leakage magnetic signal;

[0061] S2. Based on the fast finite element principle, a two-dimensional fast finite element forward model for magnetic flux leakage detection is established;

[0062] S3, slicing the three-dimensional defect contour according to the magnetic flux leakage signal obtained in step S1;

[0063] Using the Armijo-LM algorithm, combined with the two-dimensional fast finite element forward model established in step S2, the iteration step size is calculated and corrected to reconstruct the three-dimensional irregular defect;

[0064] S4. Output a reconstructed defect contour close to the real defect.

[0065] This embodiment applies the above technical solution. When executing steps S2 to S4, the specific process is as follows: Figure 2 As shown, it mainly includes:

[0066] A) For the collected measured magnetic leakage signal Y∈R M×D, slice the 3D defect according to the measured magnetic leakage signal, a total of M slices, and initialize the 3D defect contour, i.e., the depth matrix Set the maximum number of iterations T max , Armijo constant β∈(0,0.5) and the objective function threshold ε=10 for judging the stable solution -12 .

[0067] B) Slice the current contour of the defect x t Substitute the forward model (t is the number of iterations) to predict the magnetic leakage signal, and calculate the objective function value according to formula (1). If the objective function value is less than ε, the current defect reconstruction contour is judged to be a stable solution, the algorithm stops iterating, saves the current reconstruction contour slice, and goes to step F); otherwise, execute step C).

[0068]

[0069] In the formula, G(x t )∈R 1×D is the objective function, y(x t )∈R 1×D To measure the leakage magnetic signal, To predict the magnetic flux leakage signal.

[0070] C) If the current number of iterations reaches the maximum number of iterations, the algorithm stops iterating, saves the current reconstructed contour slice, and goes to step F); otherwise, the iteration step length is solved by the incremental equation of formula (2).

[0071]

[0072] In the formula, Δx t is the iteration step length, E(x t ) is the absolute error between the predicted leakage magnetic signal and the measured leakage magnetic signal, that is, the residual function, H(x t ) is E(x t ), the Hessian matrix of J(x t ) is E(x t )’s Jacobian matrix, μ t is the damping factor and I is the unit matrix.

[0073] D) Modify the iteration step size Δx using Armijo line search t '=α t Δx t , where the compensation factor α t The Armijo-Goldstein criterion in formula (3) is satisfied.

[0074]

[0075] Where gt The function E(x t )’s gradient.

[0076] E) Update the defect contour slice, i.e. x t+1 =x t +Δx′ t , x t+1 Satisfy the boundary constraints:

[0077]

[0078] Where h is the thickness of the specimen. Increase the number of iterations by 1 and return to step B).

[0079] F) If all slices are reconstructed, all reconstructed contour slices are spliced ​​to obtain the final three-dimensional defect contour, otherwise the number of iterations is reset and the process returns to step B) to reconstruct the next defect slice.

[0080] For further detailed description, this embodiment is first described from the following aspects:

[0081] 1. 3D irregular defect reconstruction method based on Armijo-LM algorithm

[0082] The LM algorithm is a nonlinear optimization method between the Newton method and the gradient descent method. It is mainly used to solve nonlinear least squares problems. When used for defect reconstruction in magnetic flux leakage detection, it reduces the error between the measured magnetic flux leakage signal and the predicted magnetic flux leakage signal through iterative optimization so that the reconstructed contour of the defect is constantly close to the real contour. It is essentially a nonlinear least squares problem, which is solved by the Armijo-LM algorithm. The theoretical method is as follows:

[0083]

[0084] Where t is the number of iterations, G(x t )∈R 1×D is the objective function, y(x t )∈R 1×D To measure the leakage magnetic signal, To predict the magnetic flux leakage signal, E(x t )∈R 1×D is the residual function, x t ∈R 1×N is the defect contour depth matrix at the tth iteration, that is, the defect contour slice.

[0085] Perform a first-order Taylor expansion on the residual function:

[0086] E(x t +Δx t )≈E(x t )+J(x t )T Δx t (6)

[0087] Where J(x t )∈R D×N is the Jacobian matrix of the residual function, which is calculated as follows:

[0088]

[0089]

[0090] J(x t ) into the objective function:

[0091]

[0092] The least squares problem requires finding the iteration step size Δx t , so that G(x t +Δx t ) is the smallest. Therefore, the objective function is t Find the first-order derivative and set the derivative to 0 to obtain the incremental equation:

[0093] Δx t =-[H(x t )] -1 J(x t ) T E(x t ) (10)

[0094] Where H(x t )∈R N×N is the Hessian matrix. In the LM algorithm, its calculation method is:

[0095] H(x t )=J(x t )J(x t ) T +μ t I (11)

[0096] Where μ t is the damping factor, which is used to ensure that the Hessian matrix is ​​positive; I∈R N×N is the identity matrix.

[0097] It can be seen from this that if the damping factor μ t is very small, the influence of the unit matrix I is much smaller than that of the Hessian matrix, and the LM algorithm is closer to the Gauss-Newton method. t Very large, the influence of the unit matrix I is much greater than that of the Hessian matrix.

[0098] Damping factor μ t The value of is uncertain, which will lead to the iteration step length Δx t The instability and uncertainty of the defect contour update lead to uncertainty. Therefore, the damping factor μ t Make improvements.

[0099] The present invention improves the damping factor from two aspects. On the one hand, the damping factor μ is defined as t =||E(x t )||2, so that it can be adaptively adjusted according to the change of the residual function to reduce the iteration step size Δx t Instability and uncertainty; on the other hand, the introduction of Armijo line search for the iteration step Δx t The correction is made so that the objective function value decreases sufficiently in each iteration, and the algorithm is accelerated to obtain the minimum value of the objective function.

[0100] Armijo line search uses the Armijo-goldstein criterion, which requires that: given a constant β∈(0,0.5), if the step size factor α t Satisfies the Armijo-Goldstein criterion:

[0101]

[0102] Among them, g t The function E(x t ), Armijo constant β∈(0,0.5), then the iteration step length Δx t Corrected to α t Δx t The first inequality in the above formula is used to ensure that the objective function value has a sufficient decrease, that is, G(x t +α t Δx t )<G(x t ), the second inequality is used to prevent the step size factor α t If it is too small, the Armijo-Goldstein criterion will be easily satisfied and lose its effect.

[0103] To obtain the step size factor α that satisfies the Armijo-Goldstein criterion t , using the binary search method. In the optimization process, each time the step size factor changes, the objective function value needs to be re-solved, which will lead to the frequent use of the fast finite element forward model and increase the algorithm calculation time. Therefore, G(x t +α t Δx t )After Taylor's second-order expansion, we get the following inequality:

[0104]

[0105] Substituting the inequality into the Armijo-goldstein criterion, we get the variant of the Armijo-goldstein criterion:

[0106]

[0107] Since at the tth iteration, the iteration step length Δx t , residual function E(x t ), Jacobian matrix J(x t ) and the Hessian matrix H(x t ) are all known, so the step size factor α can be calculated t , thereby avoiding the frequent use of the two-dimensional fast finite element forward model for calculations and effectively reducing the algorithm calculation time.

[0108] That is to say, when performing reconstruction calculation, the present technical solution first uses the LM algorithm to obtain the iteration step; secondly, the iteration step is corrected by Armijo line search; and finally, the reconstructed contour of the magnetic leakage signal is obtained.

[0109] In this embodiment, the thickness of the ferromagnetic material specimen to be detected is 10 mm, and the maximum depth of the defect does not exceed 80% of the wall thickness. By saturating the specimen, the measured leakage magnetic signal Y∈R is collected and saved. M×D ;

[0110] Then, based on the fast finite element principle, a two-dimensional fast finite element forward model for predicting magnetic flux leakage signals was established;

[0111] The Armijo-LM algorithm is then used in combination with the established two-dimensional fast finite element forward model to reconstruct the three-dimensional irregular defects. Specifically:

[0112] 1.1: Slice the 3D defect according to the collected measured magnetic leakage signal, a total of M slices, and initialize the reconstructed contour of the 3D irregular defect, that is, the total depth matrix Let the maximum number of iterations T max , Armijo constant β∈(0,0.5) and the objective function threshold ε=10 -12 .

[0113] 1.2: Slice the contour of the current defect x t Substitute into the fast finite element forward model, calculate the predicted magnetic leakage signal, use formula (15) to calculate the objective function value, and judge x by the objective function value t Is it a stable solution? tIf it is a stable solution, stop the iteration, save the current reconstructed contour slice, and execute step 1.6; otherwise, execute the next step.

[0114]

[0115] Among them, G(x t )∈R 1×D is the objective function, y(x t )∈R 1×D To measure the leakage magnetic signal, To predict the magnetic flux leakage signal.

[0116] 1.3: If the current number of iterations reaches the maximum number of iterations, the algorithm stops iterating, saves the current reconstructed contour slice, and executes step 1.6; otherwise, the incremental equation is solved by formula (16) to calculate the iteration step length Δx t .

[0117] Δx t =-[H(x t )] -1 J(x t ) T E(x t ) (16)

[0118] 1.4: Modify the iteration step length Δx′ using the Armijo line search method t =α t Δx t .

[0119] 1.5: Update the defect contour slice, i.e. x t+1 =x t +Δx′ t , x t+1 Satisfy the boundary constraints:

[0120] Where h is the thickness of the specimen. Increase the number of iterations by 1 and return to step 1.2.

[0121] 1.6: If all slices are reconstructed, all reconstructed contour slices are spliced ​​to obtain the final three-dimensional defect contour and proceed to the next step; otherwise, the number of iterations is reset, the next defect slice is reconstructed, and return to step 1.2.

[0122] 1.7: To verify the effectiveness of this technical solution, this embodiment uses formula (17) to calculate the mean square error E of the reconstruction result: R Since the maximum depth of a defect in actual applications directly affects the safety and service life of the equipment, this embodiment also uses formula (18) to calculate the error E between the current maximum depth of the reconstructed defect and the actual maximum depth of the defect MD .

[0123]

[0124] Where M and N represent the number of rows and columns of the depth matrix respectively, X is the actual depth matrix of the defect, is the reconstructed depth matrix of the defect.

[0125]

[0126] Where h is the specimen thickness.

[0127] 2. Reconstruction Experiment and Result Analysis of the Present Invention

[0128] In order to verify the effectiveness of the method proposed in the present invention, the defect model was established using COMSOL finite element simulation software, and the simulation results were used as the measured magnetic leakage signals of the simulated defects. First, slices of three-dimensional irregular simulated defects (defect 1 and defect 2), i.e., two-dimensional irregular defects, were used to reconstruct defects 1 and 2 using the present invention, the modified Newton method, the traditional LM algorithm, and the trust region projection LM algorithm. The results are shown in FIG. Figure 3 and Figure 4 shown. Figure 3 and Figure 4 In the figure, the solid lines represent the true contours, the circled solid lines represent the reconstructed contours of the modified Newton method, the dotted lines represent the reconstructed contours of the traditional LM algorithm, the dot-dashed lines represent the reconstructed contours of the trust region projection LM algorithm, and the dotted lines represent the reconstructed contours of the algorithm of the present invention. Figure 3 and Figure 4 It can be seen that the reconstruction result of the present invention is closest to the real defect and has the highest reconstruction accuracy.

[0129] The present invention is used to reconstruct three-dimensional irregular simulation defects (defect 3 and defect 4) and compared with the other three algorithms. The results are shown in Figures 5 and 6, where Figures 5(a) and 6(a) are the real contours of the defects, Figures 5(b) and 6(b) are the reconstructed contours of the defects using the algorithm of the present invention, and Figures 5(c) and 6(c) are the average iteration curves of the objective functions of the defects using the four algorithms under the condition that the initial solution and the number of iterations are the same. The average here refers to the average iteration curves of the objective function of all slices of a defect. It can be seen from Figures 5(c) and 6(c) that under the same conditions, the algorithm of the present invention converges the fastest and has the smallest convergence value of the objective function.

[0130] Table 1 is a comparison of the mean square error of the reconstructed contour, the maximum depth error and the calculation time of the four algorithms for three-dimensional irregular simulation defects under the same initial value conditions. It can be seen from Table 1 that the proposed method takes the shortest time and the E of the reconstructed defect is R and E MDThe reconstruction effect is the best, while the reconstruction results of the modified Newton method, the traditional LM algorithm and the trust region projection LM algorithm are relatively poor. Therefore, for three-dimensional simulation defects, the present invention has a good reconstruction effect, fast reconstruction speed and high precision.

[0131] Table 1 Reconstruction results of different algorithms for simulation defects

[0132]

[0133] To further verify the effectiveness of the present invention, it is applied to three-dimensional irregular real defects (defects 5 and 6), and compared with the modified Newton method, the traditional LM algorithm and the trust region projection LM algorithm. The measured leakage magnetic signal of the real defect is measured by a leakage magnetic detection device, which consists of three two-wheel magnetizers, a digital encoder and a measurement module. Each magnetizer consists of two neodymium magnets to magnetize the steel plate. The digital encoder provides displacement information of the leakage magnetic device, and thus also provides its speed information. The measurement module consists of ten units, each of which contains a linear Hall effect sensor A1324 to measure the leakage magnetic signal.

[0134] The reconstruction results are shown in Figures 7 and 8. Figures 7(a) and 8(a) are both the real contours of the defect, Figures 7(b) and 8(b) are both the reconstructed contours of the defect using the algorithm of the present invention, and Figures 7(c) and 8(c) are the average iteration curves of the objective function when the four algorithms perform contour reconstruction under the condition that the initial solution and the number of iterations are the same. The calculation time is shown in Table 2 (confirm whether the calculation time is for the entire defect or a slice).

[0135] It can be seen from FIG. 6(c), FIG. 7(c) and Table 2 that, for the same three-dimensional irregular defect, the present invention has the shortest calculation time, the fastest convergence speed, and the smallest convergence of the objective function value, indicating that the present invention has a fast reconstruction speed and high reconstruction accuracy.

[0136] It can be seen from Table 2 that compared with the other three methods, the mean square error and maximum depth error of the defect reconstruction of the present invention are the smallest. Therefore, for three-dimensional irregular real defects, the reconstruction speed of the present invention is fast and the accuracy is high, which shows that the present invention is effective in practical applications.

[0137] Table 2. Reconstruction results of different algorithms for real defects

[0138]

[0139] Based on the above results, the method proposed in the present invention can effectively realize the contour reconstruction of various three-dimensional irregular defects, has the advantages of high reconstruction accuracy and high speed, and can well meet practical requirements.

[0140] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm, characterized in that: The following steps are involved: S1. Obtain a ferromagnetic material specimen to be tested, collect and save the measured leakage magnetic signal; S2. Based on the fast finite element principle, a two-dimensional fast finite element forward model for magnetic flux leakage detection is established; S3, slicing the three-dimensional defect contour according to the magnetic flux leakage signal obtained in step S1; Using the Armijo-LM algorithm, combined with the two-dimensional fast finite element forward model established in step S2, the iteration step size is calculated and corrected to reconstruct the three-dimensional irregular defect; S4, outputting a reconstructed defect contour close to the real defect; The specific contents of step S3 include: S31, according to the magnetic flux leakage signal obtained in step S1, slicing the three-dimensional defect contour, initializing the reconstructed contour of the three-dimensional irregular defect, and setting algorithm-related parameters; S32, slice the current contour data x of the defect t Input the 2D fast finite element forward model, calculate the predicted magnetic leakage signal and the objective function value, and judge x by the objective function value. t Is it a stable solution? If so, stop iteration, save the current reconstructed contour slice, and execute step S37; otherwise, execute step S33; S33, determine whether the current number of iterations reaches the maximum number of iterations, if so, the algorithm stops iterating, saves the current reconstructed contour slice, and executes step S37; otherwise, executes step S34; S34, obtain the incremental equation through the LM algorithm and calculate the iteration step Δx t ; S35, using Armijo line search method to correct the iteration step Δx t '=α t Δx t , where α t is the step size factor; S36, update the defect contour slice, that is, x t+1 =x t +Δx t '; S37, if all slice reconstructions are completed, all reconstructed contour slices are spliced ​​to obtain the final three-dimensional defect contour; otherwise, the number of iterations is reset, and the process returns to step S32 to continue the reconstruction of the next defect slice.

2. A three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 1, characterized in that: In the step S31, the collected measured magnetic leakage signal Y∈R M×D , according to the measured leakage magnetic signal, the 3D defect is sliced ​​to obtain a total of M defect slices; the 3D defect contour is initialized, i.e., the depth matrix 3. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 1 is characterized in that: The algorithm-related parameters in step S31 include the maximum number of iterations T max , Armijo constant β∈(0,0.5), and the objective function threshold ε=10 for determining a stable solution -12 .

4. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 1, characterized in that: The objective function calculation formula in step S32 is: Among them, G(x t )∈R 1×D is the objective function, y(x t )∈R 1×D To measure the leakage magnetic signal, To predict the magnetic flux leakage signal.

5. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 4 is characterized in that: The incremental equation in step S34 is specifically: Where t is the number of iterations, Δx t is the iteration step length, E(x t ) is the absolute error between the predicted leakage magnetic signal and the measured leakage magnetic signal, that is, the residual function, H(x t ) is E(x t ), the Hessian matrix of J(x t ) is E(x t )’s Jacobian matrix, μ t is the damping factor, which can be adaptively adjusted according to the change of the residual function, and I is the unit matrix.

6. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 1, characterized in that: The step length factor α in step S35 is t Satisfies the Armijo-Goldstein criterion: Among them, g t The function E(x t ), the Armijo constant β∈(0,0.5).

7. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 6 is characterized in that: The step size factor α t Specifically, it is solved by binary search. In order to avoid frequent use of the fast finite element forward model in the S2 step to solve the objective function value during the optimization process, which increases the algorithm calculation time, the Taylor expansion of the objective function is used to obtain a variant of the Armijo-Goldstein criterion: Among them, the iteration step length Δx t , residual function E(x t ), Jacobian matrix J(x t ) and the Hessian matrix H(x t ) are all known data at the tth iteration, which can effectively reduce the algorithm calculation time.

8. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 1, characterized in that: In step S36, the defect contour slice is updated, that is, x t+1 =x t +Δx t ', where x t+1 Satisfy the boundary constraints: Where h is the specimen thickness.

9. The three-dimensional irregular defect reconstruction method based on the Armijo-LM algorithm according to claim 3, characterized in that: The step S32 is specifically to determine whether the calculated objective function value is less than the set objective function threshold ε, so as to determine whether x t Is it a stable solution?

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