Three-dimensional irregular defect reconstruction method based on adaptive regularized Gauss-Newton method

Abstract

The present invention relates to a three-dimensional irregular defect reconstruction method based on an adaptive regularized Gauss-Newton method, comprising: preprocessing a measured magnetic leakage signal to identify a target area of ​​a defect; initializing a defect depth matrix and setting relevant parameters of an inversion regularization objective function; using a finite element numerical calculation method to determine a predicted magnetic leakage signal of a current defect; comparing the predicted magnetic leakage signal with the measured magnetic leakage signal, and regularizing the error objective function, while updating relevant parameters; judging whether a preset termination condition has been reached, if so, outputting the defect depth, otherwise updating the defect depth and returning to the iteration to continue the calculation. Compared with the prior art, the present invention uses the Tikhonov regularization method to construct an objective function in the inversion process, and the regularization parameter is adaptively adjusted with the number of iterations. Finite differences are used in the iteration process to solve the Jacobian matrix, which can not only accurately reconstruct the contour of the irregular defect, but also has a short calculation time and a fast convergence speed.

Description

Technical Field

[0001] The invention relates to the technical field of nondestructive testing, and in particular to a three-dimensional irregular defect reconstruction method based on an adaptive regularized Gauss-Newton method. Background Art

[0002] Magnetic flux-leakage testing (MFL) technology has been widely used in the field of long-distance oil and gas pipelines, steel pipes, rails and other ferromagnetic material testing. For example, in the steel industry, magnetic flux leakage testing is mainly used to inspect steel structures, steel billets, round steel, bars, steel pipes, welds, and steel cables to confirm the integrity of the finished products; in the petrochemical industry, it is used to inspect installed oil and gas pipelines (including buried pipelines), oil tank bottom plates, or recycled oil field steel pipes; it can also be used for regular in-service flaw detection of steel cables, wire ropes, and chains.

[0003] The basic principle of magnetic flux leakage detection is to magnetize ferromagnetic materials, and defects on the surface or near the surface of the material cause magnetic field distortion, generate leakage magnetic fields related to the geometric characteristics of the defects, and detect defects by acquiring leakage magnetic field signals. Nondestructive magnetic flux leakage testing includes forward modeling and inversion: forward modeling is the analysis of the leakage magnetic field of defects, which is to find the distribution of the magnetic field when the source and defect shape are known; inversion refers to the reconstruction of defects, and the shape parameters of the defects are evaluated by given leakage magnetic field data, so as to achieve quantification and visualization of defect detection.

[0004] The research work on the principle of magnetic flux leakage detection at home and abroad mainly includes the forward calculation model of magnetic flux leakage detection, the preprocessing of magnetic flux leakage signals and the inversion calculation model of magnetic flux leakage detection. Among them, the inversion evaluation of defect magnetic flux leakage detection signals and defect imaging are the key links of magnetic flux leakage detection. The defect inversion results are an important basis for guiding the operation and maintenance of the tested components or facilities. Therefore, it is very important to perform inversion analysis on the detected defect magnetic flux leakage signals.

[0005] According to the existing technology, the inversion algorithm in magnetic flux leakage detection is mainly divided into mapping-based method and iteration-based method. The mapping-based method attempts to reconstruct the defect by using signal processing technology, which aims to establish a mapping relationship between the signal and the defect geometry, such as using a swarm intelligence optimization algorithm to reconstruct the defect contour, but the computational complexity of this method is too large and it is difficult to obtain accurate contour information; the iteration-based method usually compares the simulated signal with the reference signal to generate a residual error, and then minimizes the residual error as an optimization problem of the design strategy, such as the conjugate gradient method. This method is prone to problems such as inaccurate results when faced with complex morphological defect reconstruction problems. Summary of the invention

[0006] 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 adaptive regularized Gauss-Newton method, which can reconstruct irregular defects quickly and accurately.

[0007] The purpose of the present invention can be achieved by the following technical solution: A three-dimensional irregular defect reconstruction method based on an adaptive regularized Gauss-Newton method comprises the following steps:

[0008] S1. Collect the measured magnetic flux leakage signal, pre-process the measured magnetic flux leakage signal, and identify the target area of ​​the defect;

[0009] S2. Initialize the defect depth matrix according to the identified target area and set the relevant parameters of the inversion regularization objective function;

[0010] S3. Use finite element numerical calculation method to determine the predicted magnetic leakage signal of the current defect;

[0011] S4, comparing the predicted magnetic leakage signal with the measured magnetic leakage signal to obtain an error objective function, performing regularization on the error objective function, and updating relevant parameters at the same time;

[0012] S5, judging whether the preset termination condition has been reached, if so, outputting the defect depth currently solved, otherwise executing step S6;

[0013] S6. Update the defect depth, and then return to step S3.

[0014] Furthermore, the relevant parameters of the inversion regularization objective function in step S2 include but are not limited to the maximum iteration step size ρ and the smoothness matrix L.

[0015] Furthermore, the step S4 specifically introduces a regularization parameter μ to regularize the error objective function:

[0016]

[0017]

[0018] Among them, ψ(x k ) is the regularized objective function value of the kth iteration, d is the measured magnetic leakage signal, k is the number of inversion iterations, x k is the defect depth at the kth iteration, F(x) is the predicted magnetic leakage signal, is the model constraint deviation term of the kth iteration, L is the smoothness matrix; x k-1 is the defect depth at the k-1th iteration, μ k is the regularization parameter for the kth iteration.

[0019] Furthermore, the updating of the relevant parameters in step S4 includes the regularization parameter μ, the smoothness matrix L, the depth correction value Δx k to update.

[0020] Furthermore, the updating of the regularization parameter μ is specifically performed by adopting an adaptive method:

[0021]

[0022] Among them, μ k is the regularization parameter for the kth iteration, is the model constraint deviation term of the k-1th iteration, ψ(x k-1 ) is the regularized objective function value of the k-1th iteration.

[0023] Furthermore, the formula for updating the smoothness matrix L is:

[0024] L=[dF(x k )] 2 .

[0025] Furthermore, the depth correction value Δx k The update is performed by using the finite difference method to calculate the Jacobian matrix and then combining it with the Hessian matrix.

[0026] Furthermore, the depth correction value Δx k The formula for updating is:

[0027] H(x k )Δx k =-g(x k )

[0028]

[0029]

[0030]

[0031]

[0032] Among them, g(x k ) is the gradient matrix of the regularized objective function at the kth iteration, H(x k ) is the Hessian matrix of the regularized objective function at the kth iteration, x k is the defect depth of the current k-th iteration, the Jacobian matrix J k is the gradient change of the leakage magnetic signal to the defect parameters, and Δt is the step size in the gradient direction.

[0033] Furthermore, the preset termination condition in step S5 is specifically:

[0034]

[0035] Among them, ε1 is the preset threshold.

[0036] Furthermore, the specific process of updating the defect depth in step S6 is as follows:

[0037] If Δx k <ρ, then the updated defect depth is: x k+1 =x k +Δx k ;

[0038] Otherwise update the defect depth to: x k+1 =x k +ρ.

[0039] Furthermore, the step S2 specifically calculates the predicted magnetic leakage signal of the current defect by establishing a finite element forward model.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. In the defect inversion process, the present invention compares the predicted magnetic leakage signal with the measured magnetic leakage signal to obtain an error objective function, and introduces a regularization parameter to regularize the error objective function, and uses the regularization parameter to control the proportion of data fitting error and model constraint deviation in the objective function minimization process. Thus, the Tikhonov regularization method is used to construct the inversion objective function, and combined with the introduced regularization parameter, the inversion problem can be converted into an unconstrained optimization problem, so that the reconstructed defect contour is closer to the real defect contour, and the accuracy of three-dimensional irregular defect reconstruction is effectively improved.

[0042] 2. The present invention adopts an adaptive method to update the regularization parameter, so that the regularization parameter can be adaptively adjusted as the number of iterations changes, which can effectively reduce the number of iterative solutions, thereby shortening the calculation time and improving the speed of three-dimensional irregular defect reconstruction.

[0043] 3. The present invention calculates the Jacobian matrix through the finite difference method to update the depth correction value, which can well solve the ill-posed problem in the inversion. By changing the gradient step size, the reconstructed defect is constantly close to the real defect until convergence. Compared with the traditional method of direct analysis and differentiation, when facing large data processing, it can effectively shorten the calculation time and reduce the calculation cost, further improve the speed of three-dimensional irregular defect reconstruction, and ensure the accuracy of reconstruction.

[0044] Fourth, the present invention can well balance the overall convergence and fast local convergence for defect inversion, and can finally obtain the accurate defect contour on the ferromagnetic specimen after iterative solution. In the process of defect reconstruction, since the given leakage magnetic signal can reflect the approximate range of the defect area, that is, the range of change of the leakage magnetic signal is larger than the range of the defect area, the defect range that needs to be inverted can be determined by the change of the leakage magnetic signal, reducing unnecessary calculations and shortening the iteration time of the inversion algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0046] Figure 2 It is a schematic diagram of the application process of the embodiment;

[0047] Figure 3 This is a result diagram of inverting two objective functions of the same set of defect profiles using the finite difference-based Gauss-Newton method in the embodiment;

[0048] Figure 4 RMSE result diagram of the inversion of two objective functions in the embodiment;

[0049] Figure 5 The SSE result diagram of the inversion of two objective functions in the embodiment;

[0050] Figure 6 The results of using three different optimization algorithms for the same contour using a regularized objective function in the embodiment are shown in FIG.

[0051] Figure 7 It is the convergence curve of RMSE inverted by three different optimization algorithms in the embodiment;

[0052] Figure 8 It is the convergence curve of SSE inverted by three different optimization algorithms in the embodiment;

[0053] Figures 9a to 9d Schematic diagram of actual outlines of four three-dimensional irregular defects with different groove shapes in the embodiment;

[0054] Figures 10a to 10d The estimated contour reconstruction results of four three-dimensional irregular defects of different groove shapes obtained by the method of the present invention in the embodiment;

[0055] Fig.11a This is a schematic diagram of the actual outline of a crack defect with a depth of 2 mm in the embodiment;

[0056] Fig.11b This is a schematic diagram of the actual outline of a crack defect with a depth of 4 mm in the embodiment;

[0057] Fig.11cThis is a schematic diagram of the actual outline of a crack defect with a depth of 6 mm in the embodiment;

[0058] Fig.11d This is a schematic diagram of the actual outline of a crack defect with a depth of 8 mm in the embodiment;

[0059] Fig.12a The method of the present invention is used in the embodiment to obtain Fig.11a Corresponding crack defect reconstruction result map;

[0060] Figure 12b The method of the present invention is used in the embodiment to obtain Fig.11b Corresponding crack defect reconstruction result map;

[0061] Fig.12c The method of the present invention is used in the embodiment to obtain Fig.11c Corresponding crack defect reconstruction result map;

[0062] Fig.12d The method of the present invention is used in the embodiment to obtain Fig.11d Corresponding crack defect reconstruction result diagram. DETAILED DESCRIPTION

[0063] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Example

[0065] like Figure 1 As shown, a three-dimensional irregular defect reconstruction method based on an adaptive regularized Gauss-Newton method comprises the following steps:

[0066] S1. Collect the measured magnetic flux leakage signal, pre-process the measured magnetic flux leakage signal, and identify the target area of ​​the defect;

[0067] S2. Initialize the defect depth matrix according to the identified target area and set the relevant parameters of the inversion regularization objective function;

[0068] S3. Use finite element numerical calculation method to determine the predicted magnetic leakage signal of the current defect;

[0069] S4, comparing the predicted magnetic leakage signal with the measured magnetic leakage signal to obtain an error objective function, performing regularization on the error objective function, and updating relevant parameters at the same time;

[0070] S5, judging whether the preset termination condition has been reached, if so, outputting the defect depth currently solved, otherwise executing step S6;

[0071] S6. Update the defect depth, and then return to step S3.

[0072] This embodiment applies the above technical solution, and the specific process is as follows Figure 2 As shown, the main contents are:

[0073] Step 1: Preprocess the measured magnetic flux leakage signal and identify the target area of ​​the defect;

[0074] Step 2: Initialize the defect depth matrix according to the identified target area, and give the relevant parameters in the inversion regularization objective function such as the maximum iteration step size ρ and the smoothness matrix L;

[0075] Step 3: Use the finite element numerical calculation method to calculate the predicted magnetic leakage signal of the current defect;

[0076] Step 3: Compare the predicted magnetic flux leakage signal with the measured magnetic flux leakage signal, use the regularization parameter μ to regularize the objective function, and update the regularization parameter μ, the smoothness matrix L and the depth correction Δx according to the formula k And other related parameters;

[0077] Step 5: Determine whether the preset termination condition is met. If so, output the defect depth solved by the current iteration; otherwise, continue to use the adaptive regularized Gauss-Newton method to update the defect contour;

[0078] Step 6: Update the defect depth according to the conditions, and return to step 3 to recalculate the defect prediction leakage magnetic signal.

[0079] In step three, a finite element forward model is constructed to calculate and obtain the predicted magnetic flux leakage signal.

[0080] In step 4, the inversion problem in leakage magnetic reconstruction can usually be described as:

[0081] d=F(x)+e

[0082] In the formula, d is the real magnetic leakage signal, x is the defect depth in the current model, F(x) is the predicted magnetic leakage signal, which is the forward modeling result of the defect depth x in the current model, and e is the error term. The inversion problem is to obtain the defect depth x in the model based on the real magnetic leakage signal d. In fact, it is impossible to find a very accurate model defect depth x in magnetic leakage reconstruction so that the model predicted signal is completely consistent with the real signal. Therefore, it is necessary to make the forward modeling data as close to the real data as possible, that is, to make the predicted magnetic leakage signal as close to the real magnetic leakage signal as possible, so the inversion problem is defined as:

[0083]

[0084] Where d is the real magnetic flux leakage signal, x is the defect depth in the current model, and F(x) is the predicted magnetic flux leakage signal of the current model. is the data fitting error term, and the solution x can be obtained by minimizing the objective function ψ(x). Since there may be multiple solutions that meet the requirements, it is necessary to find a solution that meets the leakage magnetic signal characteristics and the initialization depth information (i.e., prior information) among many solutions. This technical solution restricts the depth parameters in the model and sets the model constraint deviation term in the iteration. make:

[0085]

[0086] Among them, L is the smoothness matrix, k is the number of inversion iterations, and x k is the defect depth at the kth iteration, x k-1 is the defect depth at the k-1th iteration. The above inversion problem is actually a constrained optimization problem. This technical solution introduces a regularization parameter μ to transform the inversion problem into an unconstrained optimization problem:

[0087]

[0088] The regularization parameter is updated using an adaptive method:

[0089]

[0090] The role of the regularization parameter μ is to control the proportion of data fitting error and model constraint deviation in the process of minimizing the objective function. When μ is large, the proportion of model constraints increases and the influence of data fitting deviation decreases; conversely, when μ decreases, the proportion of data fitting deviation increases. When μ approaches 0, the inversion problem is an ill-conditioned least squares problem and its solution is unstable.

[0091] The smoothness matrix L is the variance matrix of the data in the model, expressed as:

[0092] L=[dF(x k )] 2

[0093] Defect depth correction Δx k It is expressed as:

[0094] H(x k )Δx k =-g(x k )

[0095] In the formula, g(x k ) is the regularized objective function ψ(x k ), H(x k ) is the regularized objective function ψ(x k ) is the Hessian matrix of .

[0096] The expressions of gradient matrix and Hessian matrix are:

[0097]

[0098]

[0099] Among them, the Jacobian matrix J k is the gradient change of the leakage magnetic signal to the defect parameters. In order to better solve the ill-posed problem in the inversion, the Jacobian matrix J k The calculation of is represented by the finite difference method:

[0100]

[0101]

[0102] Among them, Δt is the step size in the gradient direction. The Jacobian matrix is ​​the one that needs to be effectively calculated in the Gauss-Newton method. Usually, the Jacobian matrix is ​​obtained by direct analytical differentiation and chain rule. This method requires a lot of computing time for large data processing. This technical solution uses the finite difference method to solve the Jacobian matrix, which can solve the ill-posed problem in the inversion. By changing the gradient step size, the reconstructed defect is constantly close to the real defect until convergence.

[0103] Set ψ(x) at x k Performing Taylor series expansion around , and ignoring higher-order terms above the second order, we get:

[0104]

[0105] To minimize ψ(x), After simplification, let Δx k =(xx k ), then:

[0106] H(x k )Δx k =-g(x k )

[0107] Differentiate both sides of ψ(x) with respect to x and simplify as follows:

[0108]

[0109]

[0110]

[0111] Since the Hessian matrix H(x k) is a symmetric matrix, that is, H(x k )=H(x k ) T , we can get:

[0112] H(x k )+H(x k ) T =2H(x k )

[0113] So we get H(x k )Δx k =-g(x k ).

[0114] Solve to obtain the correction value Δx of the defect depth in the model k Then, when the defect depth is updated in step 6, if Δx k <ρ, then x k+1 =x k +Δx k , otherwise x k+1 =x k +ρ.

[0115] In step 5, when the correction value Δx of the defect depth in the model k If the value is small enough, the iteration is stopped. The preset termination condition is as follows: That is, it is determined whether the depth correction value is small enough. If the termination condition is met, the iteration is stopped and the inversion result of the defect depth is output. k The boundary constraints must be met:

[0116]

[0117] Where D is the maximum depth.

[0118] In summary, this technical solution uses the Tikhonov regularization method to construct the inversion objective function. By introducing the regularization parameter μ, the inversion problem is transformed into an unconstrained optimization problem, so that the reconstructed defect contour is closer to the real defect contour. Regularization and adaptive parameters are both used to construct the objective function in the inversion, so that it can be closer to the real defect through the inversion algorithm. The common objective function construction method is the least squares method. To verify the effectiveness of the objective function, the finite difference Gauss-Newton method is used to invert and compare the same set of defect contours using the adaptive regularization objective function and the least squares objective function. The reconstructed defect contour is as follows: Figure 3 As shown, Figure 4 and Figure 5 are the convergence curves of the two objective functions at different numbers of iterations. Figure 3As shown in the figure, the solid line represents the real defect, the dotted line represents the initial defect, the dotted line represents the inversion result of the least squares objective function, and the dotted line represents the inversion result of the adaptive regularization objective function. Figure 3 It can be seen that the inversion result based on the adaptive regularization objective function is closer to the real defect contour. Figure 4 and Figure 5 As shown in , the dotted line represents the error of the least squares objective function, and the solid line represents the error of the adaptive regularization objective function. Figure 4 and Figure 5 It can be seen that the SSE and RMSE of the inversion results based on the adaptive regularization objective function are smaller than those based on the least squares inversion results. In 15 iterations, the inversion based on the adaptive regularization objective function is optimal at the third iteration, while the least squares optimization requires at least 10 iterations to reach the optimal value. This shows that the addition of adaptive parameters can reduce errors, shorten the number of iterations, and ultimately shorten the calculation time, so the inversion based on the adaptive regularization objective function is effective.

[0119] In addition, this technical solution uses the Gauss-Newton method based on finite differences to solve the Jacobian matrix. To verify the effectiveness of the optimization algorithm in this technical solution, the objective function of the Tikhonov regularization method is used to invert the same set of defect contours. The reconstructed defect contours are as follows: Figure 6 As shown, Figure 7 and Figure 8 These are the convergence curves of three optimization algorithms: Gauss-Newton method, conjugate gradient method, and Gauss-Newton method based on finite differences. Figure 6 In the figure, the solid line represents the real defect, the dotted line represents the initial defect, the circle line is the inversion result of the Gauss-Newton method based on finite difference, and the triangle line and the square line are the inversion results of the Gauss-Newton method and the conjugate gradient method, respectively. Figure 6 It can be seen that the inversion results of the finite difference Gauss-Newton method are closest to the real defects, and the inversion results of the Gauss-Newton method and the conjugate gradient method are worse than the inversion results of the finite difference Gauss-Newton method. Figure 7 and Figure 8 In the figure, the dotted line represents the inversion error of the Gauss-Newton method, the dashed line represents the inversion error of the conjugate gradient method, and the solid line represents the inversion error of the Gauss-Newton method based on finite differences. Figure 7 and Figure 8 It can be seen that the SSE and RMSE of the inversion results based on the finite difference Gauss-Newton method are close to 0, indicating that the prediction effect of this method is very good, while the inversion errors of the Gauss-Newton method and conjugate gradient are larger than those of the adaptive regularized Gauss-Newton method, indicating that the inversion algorithm based on the finite difference Gauss-Newton method is effective.

[0120] like Figures 9a to 9dThe four irregular groove defects shown in the figure are respectively subjected to defect reconstruction calculation using the method proposed in the present invention. Figures 10a to 10d The corresponding reconstructed contour is shown, indicating that after iterations, the actual contour of the defect can be well approximated to reflect its main shape.

[0121] In this embodiment, the measured data is preprocessed to obtain the measured signal, and then the prediction signal of the crack defect is obtained through the finite element forward model. The crack defects with depths of 2mm, 4mm, 6mm, and 8mm are selected. The actual contour of the crack is as follows Figures 11a to 11d As shown, the crack defect is reconstructed using the inversion algorithm proposed in the present invention, and the final reconstructed contour is as follows: Figures 12a to 12d shown.

[0122] contrast Figures 11a to 11d and Figures 12a to 12d It can be seen that the predicted contour is basically consistent with the actual contour, indicating that for the measured signal, the inversion algorithm used in the present invention can better approximate the true contour of the crack defect and can meet the actual requirements.

[0123] To further verify the effectiveness of this technical solution, due to the ill-posedness of the reconstruction of three-dimensional irregular defects, this embodiment defines the reconstruction error as the root mean square error, that is:

[0124]

[0125] In the formula To predict the defect contour, is the actual defect outline.

[0126] At the same time, because the maximum depth of the defect will affect the safety and service life of the ferromagnetic material, the maximum depth error is also given:

[0127]

[0128] Where m is the thickness of the ferromagnetic material.

[0129] For the simulation and actual defects, Gauss-Newton method (GN), conjugate gradient method (CG) and adaptive regularized Gauss-Newton method are used for reconstruction respectively, and the results are shown in Table 1.

[0130] Table 1 Reconstruction results of different algorithms

[0131]

[0132] It can be seen from the data in Table 1 that, for the reconstruction problem of three-dimensional irregular defects, the method proposed in the present invention has shown excellent performance in terms of both reconstruction speed and reconstruction accuracy.

Claims

1. A three-dimensional irregular defect reconstruction method based on adaptive regularized Gauss-Newton method, characterized in that: The following steps are involved: S1. Collect the measured magnetic flux leakage signal, pre-process the measured magnetic flux leakage signal, and identify the target area of ​​the defect; S2. Initialize the defect depth matrix according to the identified target area and set the relevant parameters of the inversion regularization objective function; S3. Use finite element numerical calculation method to determine the predicted magnetic leakage signal of the current defect; S4, comparing the predicted magnetic leakage signal with the measured magnetic leakage signal to obtain an error objective function, performing regularization on the error objective function, and updating relevant parameters at the same time; S5, judging whether the preset termination condition has been reached, if so, outputting the defect depth currently solved, otherwise executing step S6; S6, update the defect depth, and then return to step S3; The relevant parameters of the inversion regularization objective function in step S2 include but are not limited to the maximum iteration step length ρ and the smoothness matrix L; The step S4 specifically introduces a regularization parameter μ to regularize the error objective function: Among them, ψ(x k ) is the regularized objective function value of the kth iteration, d is the measured magnetic leakage signal, k is the number of inversion iterations, x k is the defect depth at the kth iteration, F(x) is the predicted magnetic leakage signal, is the model constraint deviation term of the kth iteration, L is the smoothness matrix; x k-1 is the defect depth at the k-1th iteration, μ k is the regularization parameter for the kth iteration.

2. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 1 is characterized in that: The updating of the relevant parameters in step S4 includes updating the regularization parameter μ, the smoothness matrix L, the depth correction value Δx k to update.

3. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 2 is characterized in that: The updating of the regularization parameter μ is specifically performed by using an adaptive method: Among them, μ k is the regularization parameter for the kth iteration, is the model constraint deviation term of the k-1th iteration, ψ(x k-1 ) is the regularized objective function value of the k-1th iteration.

4. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 2 is characterized in that: The formula for updating the smoothness matrix L is: L=[d-F(x k )] 2 。 5. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 2, characterized in that: The depth correction value Δx k The update is specifically carried out by using the finite difference method to calculate the Jacobian matrix and then combining it with the Hessian matrix; Depth correction Δx k The formula for updating is: H(x k )Δx k =-g(x k ) Among them, g(x k ) is the gradient matrix of the regularized objective function at the kth iteration, H(x k ) is the Hessian matrix of the regularized objective function at the kth iteration, x k is the defect depth of the current k-th iteration, the Jacobian matrix J k is the gradient change of the leakage magnetic signal to the defect parameters, and Δt is the step size in the gradient direction.

6. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 2, characterized in that: The preset termination condition in step S5 is specifically: Among them, ε1 is the preset threshold.

7. The three-dimensional irregular defect reconstruction method based on the adaptive regularized Gauss-Newton method according to claim 2 is characterized in that: The specific process of updating the defect depth in step S6 is as follows: If Δx k < ρ, then update the defect depth to: x k+1 = x k + Δx k ; Otherwise update the defect depth to: x k+1 =x k +ρ.

8. A three-dimensional irregular defect reconstruction method based on adaptive regularized Gauss-Newton method according to any one of claims 1 to 7, characterized in that: The step S2 specifically calculates the predicted magnetic flux leakage signal of the current defect by establishing a finite element forward model.

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