CN116124877A - Three-dimensional irregular defect reconstruction method based on self-adaptive regularized Gaussian Newton method - Google Patents
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Abstract
The invention relates to a three-dimensional irregular defect reconstruction method based on a self-adaptive regularized Gauss Newton method, which comprises the following steps: preprocessing the actually measured magnetic flux leakage signal, and identifying a target area of the defect; initializing a defect depth matrix, and setting relevant parameters of inversion regularization objective functions; determining a predicted magnetic leakage signal of the current defect by adopting a finite element numerical calculation method; comparing the predicted magnetic leakage signal with the actually measured magnetic leakage signal, regularizing an error objective function, and updating related parameters; judging whether the preset termination condition is reached currently, if so, outputting the defect depth, otherwise, updating the defect depth, and returning to iteration for continuous calculation. Compared with the prior art, the Tikhonov regularization method is used for constructing the objective function in the inversion process, regularization parameters are adaptively adjusted along with the iteration times, and the jacobian matrix is solved by finite difference in the iteration process, so that the outline of the irregular defect can be accurately reconstructed, the calculation time is short, and the convergence speed is high.
Description
Technical Field
The invention relates to the technical field of nondestructive testing, in particular to a three-dimensional irregular defect reconstruction method based on a self-adaptive regularized Gaussian Newton method.
Background
Magnetic flux leakage detection (MFL) technology is widely applied in the field of detection of ferromagnetic materials such as long oil and gas pipelines, steel pipes, steel rails and the like, for example, the magnetic flux leakage detection is mainly used for detecting steel structural members, billets, round steels, bars, steel pipes, welding seams and steel cables to confirm the integrity of finished products in the steel industry; in the petrochemical industry for detecting installed oil and gas pipelines (including buried pipelines), tank floors, or recovered oil Tian Gangguan; the device can also be used for carrying out periodic in-service flaw detection on steel cables, steel wire ropes and chains.
The basic principle of magnetic leakage detection is that a ferromagnetic material is magnetized, magnetic field distortion is caused by defects on the surface or near surface of the material, a magnetic leakage field related to geometric characteristics of the defects is generated, and the detection of the defects is realized by acquiring magnetic leakage field signals. The magnetic leakage nondestructive test comprises forward modeling and inversion: forward, i.e., leakage magnetic field analysis of defects, is a distribution of magnetic fields obtained by knowing the source and defect shapes; inversion refers to the reconstruction of defects, and the shape parameters of the defects are estimated by given leakage magnetic field data, so that quantification and visualization of defect detection are realized.
The research work related to the leakage magnetic detection principle at home and abroad mainly comprises a forward calculation model for leakage magnetic detection, a preprocessing of a leakage magnetic signal and an inversion calculation model for leakage magnetic detection. The inversion evaluation and defect imaging of the defect magnetic flux leakage detection signals are key links of magnetic flux leakage detection, and the defect inversion result is an important basis for guiding the operation and maintenance of a detected member or facility, so that the inversion analysis of the detected defect magnetic flux leakage signals is very important.
According to the prior art, inversion algorithms in leakage flux detection are largely divided into mapping-based methods and iteration-based methods. Mapping-based methods attempt to reconstruct defects by using signal processing techniques that aim at establishing a mapping relationship between the signal and the defect geometry, such as reconstructing the defect profile using a swarm intelligence optimization algorithm, but this approach is computationally expensive and difficult to obtain accurate profile information; the iteration-based method generally compares the analog signal with the reference signal to generate a residual error, and minimizes the residual error as an optimization problem of a design strategy, for example, a conjugate gradient method, which is prone to inaccurate results when facing the defect reconstruction problem of complex morphology.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a three-dimensional irregular defect reconstruction method based on a self-adaptive regularized Gaussian Newton method, which can reconstruct irregular defects rapidly and accurately.
The aim of the invention can be achieved by the following technical scheme: a three-dimensional irregular defect reconstruction method based on a self-adaptive regularized Gaussian Newton method comprises the following steps:
s1, collecting a real magnetic leakage detection signal, preprocessing the real magnetic leakage detection signal, and identifying a target area of a defect;
s2, initializing a defect depth matrix according to the identified target area, and setting relevant parameters of an inversion regularization target function;
s3, determining a predicted magnetic flux leakage signal of the current defect by adopting a finite element numerical calculation method;
s4, comparing the predicted magnetic flux leakage signal with the actually measured magnetic flux leakage signal to obtain an error objective function, regularizing the error objective function, and updating related parameters;
s5, judging whether a preset termination condition is met currently, if so, outputting the defect depth obtained by current solving, otherwise, executing the step S6;
s6, updating the defect depth, and returning to the step S3.
Further, the relevant parameters of the inverse regularization objective function in the step S2 include, but are not limited to, an iteration maximum step ρ and a smoothness matrix L.
Further, the step S4 specifically includes introducing a regularization parameter μ to regularize the error objective function:
wherein, ψ (x k ) Regularized objective function value of kth iteration, d is real leakage detection signal, k is inversion iteration number, x k For the defect depth at the kth iteration, F (x) is the predicted leakage signal,
constraining the deviation term for the model of the kth iteration, wherein L is a smoothness matrix; x is x k-1 Depth of defect, μ at the k-1 th iteration k Is the regularization parameter for the kth iteration.
Further, updating the relevant parameters in the step S4 includes updating the regularization parameter μ, the smoothness matrix L, and the depth correction Δx k And updating.
Further, the updating of the regularization parameter μ is specifically performed by adopting an adaptive method:
wherein mu k For the regularization parameter of the kth iteration,
model constraint bias term for the k-1 th iteration, ψ (x k-1 ) Regularized objective function value for the k-1 th iteration.
Further, the formula for updating the smoothness matrix L is as follows:
L＝[d-F(x k )] 2 。
further, the pair of depth correction amounts Δx k The updating is specifically carried out by adopting a finite difference method to calculate the jacobian matrix and combining with the Hessian matrix.
Further, the pair of depth correction amounts Δx k The formula for updating is:
H(x k )Δx k ＝-g(x k )
wherein g (x k ) Regularizing the gradient matrix of the objective function for the kth iteration, H (x k ) Hessian matrix, x, which is regularized for the k-th iteration of the objective function k For the defect depth of the current kth iteration, jacobian matrix J k For the gradient change of the magnetic leakage signal to the defect parameter, Δt is the step length in the gradient direction.
Further, the preset termination condition in step S5 specifically includes:
wherein ε 1 Is a preset threshold.
Further, the specific process of updating the defect depth in step S6 is as follows:
if Deltax k < ρ, update defect depth is: x is x k+1 ＝x k +Δx k ；
Otherwise, updating the defect depth as follows: x is x k+1 ＝x k +ρ。
Further, the step S2 is specifically to build a finite element forward model to calculate the predicted magnetic leakage signal of the current defect.
Compared with the prior art, the invention has the following advantages:
1. in the defect inversion process, the predicted magnetic leakage signal is compared with the actually measured magnetic leakage signal to obtain an error objective function, regularization processing is carried out on the error objective function by introducing regularization parameters, and the regularization parameters are used for controlling the proportion of data fitting errors and model constraint deviations in the objective function minimization process. Therefore, an inversion objective function is constructed by using a Tikhonov regularization method, and the inversion problem can be converted into an unconstrained optimization problem by combining the introduced regularization parameters, so that the reconstructed defect contour is more similar to the real defect contour, and the three-dimensional irregular defect reconstruction accuracy is effectively improved.
2. The regularization parameter is updated in a self-adaptive mode, so that the regularization parameter can be self-adaptively adjusted along with the change of iteration times, the iteration solving times can be effectively reduced, the calculation time is shortened, and the three-dimensional irregular defect reconstruction speed is improved.
3. According to the invention, the jacobian matrix is calculated by a finite difference method to update the depth correction amount, so that the problem of uncertainty in inversion can be well solved, and the reconstruction defect is continuously close to the real defect until convergence by changing the gradient step length. Compared with the traditional method of directly analyzing and differentiating, the method has the advantages that when large-scale data processing is faced, the calculation time can be effectively shortened, the calculation cost is reduced, the three-dimensional irregular defect reconstruction speed is further improved, and the reconstruction accuracy can be guaranteed.
4. The method can well give consideration to overall convergence and rapid local convergence to defect inversion, and can finally obtain the accurate defect profile on the ferromagnetic test piece after iterative solution. In the defect reconstruction process, the given magnetic leakage signal can reflect the approximate range of the defect area, namely the change range of the magnetic leakage signal is larger than the range of the defect area, so that the defect range needing inversion can be determined through the change of the magnetic leakage signal, unnecessary calculation is reduced, and the iterative time of an inversion algorithm is shortened.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an application process of an embodiment;
FIG. 3 is a graph of the results of inverting two objective functions of the same set of defect contours using finite difference based Gauss Newton's method in an embodiment;
FIG. 4 is a graph of the RMSE results inverted for two objective functions in the example;
FIG. 5 is a graph of SSE results for two objective function inversions in the examples;
FIG. 6 is a graph of results using three different optimization algorithms for the same contour using regularized objective functions in an embodiment;
FIG. 7 is a plot of convergence of the inverted RMSE for three different optimization algorithms in the example;
FIG. 8 is a plot of convergence of SSE inverted by three different optimization algorithms in the examples;
FIGS. 9 a-9 d are schematic illustrations of actual profiles of three-dimensional irregular defects in four different slot shapes in an embodiment;
FIGS. 10 a-10 d are the estimated profile reconstruction results for four different slot-like three-dimensional irregularities obtained by the method of the present invention in the examples;
FIG. 11a is a schematic illustration of an actual profile of a crack defect depth of 2mm in an embodiment;
FIG. 11b is a schematic illustration of an actual profile of a crack defect depth of 4mm in an embodiment;
FIG. 11c is a schematic illustration of an actual profile of a crack defect depth of 6mm in an example;
FIG. 11d is a schematic illustration of an actual profile of an embodiment with a crack defect depth of 8 mm;
FIG. 12a is a graph showing the reconstruction result of the crack defect corresponding to FIG. 11a obtained by the method of the present invention in the example;
FIG. 12b is a graph showing the reconstruction result of the crack defect corresponding to FIG. 11b obtained by the method of the present invention in the example;
FIG. 12c is a graph showing the reconstruction result of the crack defect corresponding to FIG. 11c obtained by the method of the present invention in the example;
FIG. 12d is a graph showing the reconstruction result of the corresponding crack defect of FIG. 11d obtained by the method of the present invention in the example.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples.
Examples
As shown in fig. 1, a three-dimensional irregular defect reconstruction method based on a self-adaptive regularized gauss newton method comprises the following steps:
s1, collecting a real magnetic leakage detection signal, preprocessing the real magnetic leakage detection signal, and identifying a target area of a defect;
s2, initializing a defect depth matrix according to the identified target area, and setting relevant parameters of an inversion regularization target function;
s3, determining a predicted magnetic flux leakage signal of the current defect by adopting a finite element numerical calculation method;
s4, comparing the predicted magnetic flux leakage signal with the actually measured magnetic flux leakage signal to obtain an error objective function, regularizing the error objective function, and updating related parameters;
s5, judging whether a preset termination condition is met currently, if so, outputting the defect depth obtained by current solving, otherwise, executing the step S6;
s6, updating the defect depth, and returning to the step S3.
By applying the technical scheme, the specific process is shown in fig. 2, and the main contents are as follows:
step one: preprocessing the actually measured magnetic flux leakage signal, and identifying a target area of the defect;
step two: initializing a defect depth matrix according to the identified target area, and giving relevant parameters in inversion regularization objective functions such as an iteration maximum step length rho, a smoothness matrix L and the like;
step three: calculating a predicted magnetic flux leakage signal of the current defect by using a finite element numerical calculation method;
step three: comparing the predicted magnetic flux leakage signal with the actually measured magnetic flux leakage signal, regularizing the objective function by using the regularization parameter mu, and updating the regularization parameter mu, the smoothness matrix L and the depth correction quantity delta x by referring to a formula k -waiting for relevant parameters;
step five: judging whether a preset termination condition is met, if so, outputting the defect depth solved by the current iteration; otherwise, continuously updating the defect outline by using the self-adaptive regularized Gauss Newton method;
step six: and updating the defect depth according to the condition, and returning to the step three to recalculate the defect prediction magnetic leakage signal.
In the third step, specifically, a finite element forward model is constructed to calculate and obtain a predicted magnetic flux leakage signal.
In step four, the inversion problem in the general leakage flux reconstruction can be described as:
d＝F(x)+e
wherein d is a real magnetic leakage signal, x is the defect depth in the current model, F (x) is a predicted magnetic leakage signal, and is a forward result of the defect depth x in the current model, e is an error term, and obtaining the defect depth x in the model according to the real magnetic leakage signal d is an inversion problem. In practice, a very accurate model defect depth x cannot be found in the leakage reconstruction so that the model predicted signal is exactly identical to the true signal. It is desirable to make the forward data as close as possible to the real data, i.e. to make the predicted leakage signal as close as possible to the real leakage signal, so the inversion problem is defined as:
wherein d is a true magnetic leakage signal, x is the defect depth in the current model, F (x) is a predicted magnetic leakage signal of the current model,
for the data fitting error term, the solution x can be obtained by minimizing the objective function psi (x), and as a plurality of solutions meeting the requirement are possible, the solution meeting the characteristics of magnetic flux leakage signals and initializing depth information (namely prior information) is required to be searched in a plurality of solutions, the depth parameters in the model are limited by the technical scheme, and the constraint deviation term of the model is set in iteration>
And (3) making:
wherein L is a smoothness matrix, k is the inversion iteration number, x k For the depth of the defect at the kth iteration, x k-1 Is the defect depth at the k-1 th iteration. The inversion problem is actually a constraint optimization problem, and regularization parameter mu is introduced in the technical scheme, so that the inversion problem is converted into an unconstrained optimization problem:
the regularization parameter is updated by adopting an adaptive method:
the regularization parameter mu is used for controlling the proportion of the data fitting error and the model constraint deviation in the process of minimizing the objective function. When mu is larger, the specific gravity of the model constraint is increased, and the influence of the data fitting deviation is reduced; conversely, as μ decreases, the specific gravity of the data fitting deviation increases, and as μ approaches 0, the inversion problem is a sick least squares problem, the solution of which is unstable.
The smoothness matrix L is a variance matrix of the data in the model, expressed as:
L＝[d-F(x k )] 2
correction amount Deltax of defect depth k Expressed as:
H(x k )Δx k ＝-g(x k )
g (x) k ) Regularizing the objective function ψ (x) for the kth iteration k ) Gradient of H (x) k ) Regularizing the objective function ψ (x) for the kth iteration k ) Is a Hessian matrix of (c).
The expressions of the gradient matrix and the Hessian matrix are:
wherein, jacobian matrix J k To better solve the problem of uncertainty in inversion for gradient change of magnetic leakage signal to defect parameter, jacobian matrix J k Is represented by a finite difference method:
wherein Δt is the step size in the gradient direction.
In the gauss newton method, the jacobian matrix needs to be effectively calculated, a direct analysis derivative form is generally adopted, a chained rule is applied to obtain the jacobian matrix, and a large amount of calculation time is needed for large-scale data processing. According to the technical scheme, the jacobian matrix can be solved by adopting a finite difference method, so that the problem of inappropriateness in inversion can be solved well, and the reconstruction defect is continuously close to the real defect until convergence is achieved by changing the gradient step length.
Let ψ (x) be x k Performing Taylor series expansion nearby, and ignoring higher-order terms more than twice to obtain:
to make psi (x) Take the minimum value, then
After simplification, let Deltax k ＝(x-x k ) The following steps are:
H(x k )Δx k ＝-g(x k )
differentiating x on two sides of psi (x), the simplification process is as follows:
due to the Hessian matrix H (x k ) Is a symmetric matrix, i.e. H (x k )＝H(x k ) T The method can obtain:
H(x k )+H(x k ) T ＝2H(x k )
thus, H (x) k )Δx k ＝-g(x k )。
Solving to obtain correction quantity delta x of defect depth in model k Then, in the defect depth update in the sixth step, if Δx k < ρ, x k+1 ＝x k +Δx k Otherwise x k+1 ＝x k +ρ。
In step five, when the correction amount Deltax of the defect depth in the model k And stopping iteration after enough time, wherein the preset termination condition is specifically as follows:
and judging whether the depth correction value is small enough, if the termination condition is met, stopping iteration, and outputting an inversion result of the obtained defect depth. In the modelDefect depth parameter x k Boundary constraint conditions need to be satisfied: />
Wherein D is the maximum depth.
In summary, the technical scheme uses a Tikhonov regularization method to construct an inversion objective function, and the regularization parameter mu is introduced to convert inversion problems into unconstrained optimization problems, so that the reconstructed defect profile is closer to the real defect profile. The regularization and self-adaptive parameters are used for constructing an objective function in inversion, so that the objective function can be more close to a real defect through an inversion algorithm, a common objective function construction method is a least square method, and for verifying the effectiveness of the objective function, the finite difference Gaussian Newton method is used for carrying out inversion comparison on the same group of defect outlines by using the self-adaptive regularization objective function and the least square objective function. The reconstructed defect profile is shown in fig. 3, and fig. 4 and 5 are convergence curves of two objective functions at different iteration times. As shown in fig. 3, the solid line represents a real defect, the dotted line represents an initial defect, the dotted line represents an inversion result of the least squares objective function, and the dotted line represents an inversion result of the adaptive regularized objective function. As can be seen from fig. 3, the inversion result based on the adaptive regularized objective function is closer to the true defect profile. The reconstruction error is shown in fig. 4 and 5, the dashed line represents the error of the least squares objective function, and the solid line represents the error of the adaptive regularized objective function. From fig. 4 and 5, it can be seen that both SSE and RMSE based on the inversion result of the adaptive regularization objective function are smaller than based on the inversion result of the least squares, and in 15 iterations, the inversion based on the adaptive regularization objective function is already optimal at the third iteration, whereas the least squares optimization requires at least 10 iterations to be optimal. The method shows that the addition of the self-adaptive parameters can reduce errors, shorten iteration times and finally shorten calculation time, so that inversion based on the self-adaptive regularization objective function is effective.
In addition, the technical scheme adopts a Gaussian Newton method based on finite difference, and utilizes the finite difference method to solve the jacobian matrix. In order to verify the effectiveness of the optimization algorithm in the technical scheme, the same group of defect contours are inverted by using an objective function of a Tikhonov regularization method, the reconstructed defect contours are shown in fig. 6, and fig. 7 and 8 are convergence curves of 3 optimization algorithms, namely a Gaussian Newton method, a conjugate gradient method and a Gaussian Newton method based on finite difference. In fig. 6, the solid line represents a real defect, the dotted line represents an initial defect, the circle line is an inversion result of the gaussian newton method based on finite difference, and the triangle line and the square line are inversion results of the gaussian newton method and the conjugate gradient method, respectively. As can be seen from fig. 6, the finite difference gaussian newton inversion result is closest to the real defect, and the inversion results of the gaussian newton method and the conjugate gradient method are inferior to those of the finite difference gaussian newton method. In fig. 7 and 8, the dot-dashed line represents the inversion error of the gaussian newton method, the dashed line represents the inversion error of the conjugate gradient method, and the solid line represents the inversion error of the gaussian newton method based on finite difference. From fig. 7 and fig. 8, it can be seen that both SSE and RMSE of the finite difference-based gaussian newton inversion result are close to 0, which indicates that the prediction effect of the method is good, and the inversion errors of the gaussian newton method and the conjugate gradient are larger than those of the adaptive regularized gaussian newton method, which indicates that the finite difference-based gaussian newton inversion algorithm is effective.
The four groove-shaped irregular defects shown in fig. 9a to 9d are respectively used for carrying out defect reconstruction calculation by using the method provided by the invention, and fig. 10a to 10d show corresponding reconstruction profiles, which show that the actual profile of the defect can be better approximated to reflect the main body shape after iteration.
In this embodiment, the measured data is preprocessed to obtain a measured signal, and then a predicted signal of the crack defect is obtained through a finite element forward model. The actual profile of the crack is shown in figures 11 a-11 d, the crack defects are reconstructed by using the inversion algorithm provided by the invention, and the final reconstructed profile is shown in figures 12 a-12 d.
Comparing fig. 11a to 11d with fig. 12a to 12d, it can be seen that the predicted profile is substantially consistent with the actual profile, which indicates that for the actual measurement signal, the inversion algorithm used in the present invention can better approximate the actual profile of the crack defect, and can meet the actual requirement.
In order to further verify the effectiveness of the present technical solution, because of the discomfort of reconstructing the three-dimensional irregular defect, the present embodiment defines the reconstruction error as a root mean square error, that is:
in the middle of
For predicting defect profile +.>
Is the true defect profile.
Meanwhile, the maximum depth of the defect affects the safety and service life of the ferromagnetic material, so that the maximum depth error is also given:
wherein m is the thickness of the ferromagnetic material.
For simulation and actual defects, reconstruction was performed using gaussian newton method (GN), conjugate gradient method (CG) and adaptive regularized gaussian newton method, respectively, and the results are shown in table 1.
Table 1 different algorithm reconstruction results
As can be seen from the data in table 1, the method according to the present invention shows excellent performance in terms of the reconstruction speed and the reconstruction accuracy, with respect to the reconstruction problem of the three-dimensional irregular defect.
Claims (10)
1. The three-dimensional irregular defect reconstruction method based on the self-adaptive regularized Gaussian Newton method is characterized by comprising the following steps of:
s1, collecting a real magnetic leakage detection signal, preprocessing the real magnetic leakage detection signal, and identifying a target area of a defect;
s2, initializing a defect depth matrix according to the identified target area, and setting relevant parameters of an inversion regularization target function;
s3, determining a predicted magnetic flux leakage signal of the current defect by adopting a finite element numerical calculation method;
s4, comparing the predicted magnetic flux leakage signal with the actually measured magnetic flux leakage signal to obtain an error objective function, regularizing the error objective function, and updating related parameters;
s5, judging whether a preset termination condition is met currently, if so, outputting the defect depth obtained by current solving, otherwise, executing the step S6;
s6, updating the defect depth, and returning to the step S3.
2. The three-dimensional irregular defect reconstruction method based on the adaptive regularized gauss newton method according to claim 1, wherein the relevant parameters of the inverse regularized objective function in the step S2 include, but are not limited to, iterative maximum step ρ, smoothness matrix L.
3. The three-dimensional irregular defect reconstruction method based on the adaptive regularized gauss newton method according to claim 2, wherein the step S4 is specifically to introduce a regularization parameter μ to regularize the error objective function:
wherein, ψ (x k ) Regularized objective function value of kth iteration, d is real leakage detection signal, k is inversion iteration number, x k For the defect depth at the kth iteration, F (x) is the predicted leakage signal,
constraining the deviation term for the model of the kth iteration, wherein L is a smoothness matrix; x is x k-1 Depth of defect, μ at the k-1 th iteration k Is the regularization parameter for the kth iteration.
4. The method for three-dimensional irregular defect reconstruction based on adaptive regularized gauss-newton method according to claim 3, wherein updating the relevant parameters in step S4 comprises updating regularized parameters μ, smoothness matrix L, depth correction Δx k And updating.
5. The three-dimensional irregular defect reconstruction method based on the self-adaptive regularized gauss-newton method according to claim 4, wherein the updating of the regularized parameter μ is specifically performed by adopting the self-adaptive method:
wherein mu k For the regularization parameter of the kth iteration,
model constraint bias term for the k-1 th iteration, ψ (x k-1 ) Regularized objective function value for the k-1 th iteration.
6. The method for reconstructing three-dimensional irregular defects based on adaptive regularized gauss-newton method according to claim 4, wherein the formula for updating the smoothness matrix L is:
L＝[d-F(x k )] 2 。
7. the method for reconstructing three-dimensional irregular defects based on adaptive regularized gauss-newton method according to claim 4, wherein the pair of depth correction amounts Δx k The updating is specifically carried out by adopting a mode of calculating a jacobian matrix by a finite difference method and combining a Hessian matrix;
for depth correction amount Deltax k The formula for updating is:
H(x k )Δx k ＝-g(x k )
wherein g (x k ) Regularizing the gradient matrix of the objective function for the kth iteration, H (x k ) Hessian matrix, x, which is regularized for the k-th iteration of the objective function k For the defect depth of the current kth iteration, jacobian matrix J k For the gradient change of the magnetic leakage signal to the defect parameter, Δt is the step length in the gradient direction.
8. The three-dimensional irregular defect reconstruction method based on the adaptive regularized gauss-newton method according to claim 4, wherein the preset termination condition in step S5 is specifically:
wherein ε 1 Is a preset threshold.
9. The three-dimensional irregular defect reconstruction method based on the adaptive regularized gauss-newton method according to claim 4, wherein the specific process of updating the defect depth in step S6 is as follows:
if Deltax k < ρ, update defect depth is: x is x k+1 ＝x k +Δx k ；
Otherwise, updating the defect depth as follows: x is x k+1 ＝x k +ρ。
10. The method for reconstructing three-dimensional irregular defects based on adaptive regularized gauss-newton method according to any one of claims 1-9, wherein step S2 is specifically to calculate the predicted magnetic leakage signal of the current defect by establishing a finite element forward model.
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