Thread defect depth and length detection method based on arc coil

Abstract

The present invention discloses a method for detecting the depth and length of thread defects based on a novel arc coil, comprising the following steps: sensor optimization, feature extraction, parameter fitting, and multi-parameter inversion. The present invention is applicable to the technical field of thread defect detection and adopts an arc-shaped T-R sensor structure to ensure that the lifting distance of each coil is the same, so that the mutual impedance between the coils mainly takes the characteristics of the drill pipe thread being tested. At the same time, a two-excitation and one-receiver working mode is adopted to eliminate background noise and improve the sensitivity of defect detection. Based on a finite element simulation model, a swept frequency excitation measurement method is adopted to extract the characteristic points of the mutual impedance measurement results between the coils, and the relationship between the mutual impedance between the coils and the length and depth of the defect is obtained by a fitting method, thereby reducing costs and improving measurement accuracy and detection efficiency. Based on the swept frequency measurement results of the simulated mutual impedance between the coils, the Newton method is used for inversion to obtain the defect depth and length information of the drill pipe thread.

Description

Technical Field

[0001] The present invention belongs to the technical field of thread defect detection, and in particular is a method for detecting the depth and length of thread defects based on an arc coil. Background Art

[0002] Drill pipe threads are widely used in fields such as petrochemicals, geophysical surveying, and aerospace. Over time, threads inevitably develop defects due to wear. Once defects occur, they pose a serious threat to the safety of the entire equipment. To prevent these hazards, drill pipe threads must undergo nondestructive testing before use.

[0003] Traditionally, thread defect detection involves manual measurement using specialized measuring tools. However, this method is inefficient, consumes significant manpower and material resources, and is subject to relatively large measurement errors. Therefore, this method is not suitable for practical applications.

[0004] Currently, common non-destructive testing methods include ultrasonic testing, X-ray testing, thermal imaging, magnetic flux leakage, and eddy current testing. Ultrasonic testing offers the advantage of fast scanning speeds, but requires coupling agents, and the complex drill pipe thread structure hinders ultrasonic signal analysis. X-ray testing offers the advantage of three-dimensional visualization, but has the disadvantages of high cost and potential harm to the human body. Thermal imaging allows for large-area testing, but the instrumentation used is expensive and insensitive to deeper defects. Magnetic flux leakage can quickly detect defects on the thread surface, but this method is limited to magnetically permeable materials.

[0005] In fact, parallel TR sensors are often used in drill pipe thread defect detection. This structure not only causes the signal detected by the sensor to be interfered by the lift-off distance, but also affects the detection efficiency of the sensor. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and provide a method for detecting the depth and length of thread defects based on an arc coil.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] The method for detecting the depth and length of thread defects based on an arc coil comprises the following steps:

[0009] Step 1: Sensor optimization: Obtain an arc sensor with high sensitivity to the thread defects being measured;

[0010] Step 2: Feature extraction: Use the swept frequency excitation method to obtain thread information and perform feature extraction on the swept frequency measurement signal;

[0011] Step 3: Parameter fitting: Fit the characteristic points and the defect parameters. Based on the fitting results, invert the defect information through the characteristics of the swept frequency signal.

[0012] Step 4: Multi-parameter inversion: Use the Newton iteration method to directly invert the defect information from the frequency sweep results.

[0013] Preferably, in step 1, the arc sensor with higher sensitivity to the measured thread defects includes two excitation coils and one excitation coil, and the three coils have an arc structure. A sensor optimization algorithm combining orthogonal experiment and neural network is adopted, and the optimized parameters include coil height, inner and outer diameters, distance between coils and lifting distance. The range of h is 1mm-3mm, the ranges of r1 and r2 are 1mm-1.2mm and 1.5mm-1.75mm respectively, and the range of w is 0.5mm-1mm. h is the height of the coil, r1 and r2 are the inner and outer diameters respectively, w is the distance between each coil, and l1 is the lifting distance of each coil.

[0014] Preferably, in step 1, the sensor optimization comprises the following steps:

[0015] Determine the main parameters that affect the sensor sensitivity, including coil height, inner and outer diameters, distance between coils, and lift-off distance, and estimate the value range of each parameter based on actual conditions;

[0016] Secondly, according to the value range of each sensor parameter, 5 levels are selected for each parameter to carry out simulation experiments, a total of 5 5 A group of experiments were conducted. According to the simulation results, the basic range of the optimal value of the sensor was determined, and the BP neural network optimized by genetic algorithm was used to establish the functional relationship between the various sensor parameters and the change of the coil mutual impedance.

[0017] Preferably, in step 2, simulating and determining characteristic points includes:

[0018] Set the corresponding boundary conditions to ensure that the magnetic field intensity H, the tangential component of the magnetic potential A, and the normal component of the eddy current vector J in the metal area and the air area are continuous, which can be expressed as:

[0019] n×(A1-A2)=0(1),

[0020] n×(H1-H2)=0(2),

[0021] n·(J1-J2)=0(3),

[0022] Wherein, magnetic potential A1 and A2 represent the magnetic potential at the surface of the DUT and the air, respectively; H1 and H2 represent the magnetic field strength at the air region and the surface of the DUT, respectively; J1 and J2 represent the eddy current density at the air region and the DUT, respectively;

[0023] In the simulation, the material of the drill pipe thread under test is stainless steel, and the conductivity is 1.1×10 6 S / m, relative magnetic permeability μ r =1, the grid adopts the free meshing method, the excitation current is set to 1A AC current loaded in the TR sensor to generate an alternating magnetic field, the excitation adopts the sweep frequency method, and the maximum eddy current field intensity generated is 1779.32A / m 2 .

[0024] Preferably, in step 3, parameter fitting includes:

[0025] Based on the simulation results, the polynomial fitting method is used to fit the relationship between the characteristic points and the defect parameters. Based on the drill pipe thread defect measurement model, the length of the defect is fixed, and the depth of the defect is set to 2.5mm-0mm, with a step size of 0.5mm. According to the peak characteristic point of the imaginary part of the mutual impedance obtained by simulation, the cubic function fitting is performed using formula (4), where formula (4) is:

[0026] θ=a(d)x 3 +b(d)x 2 +c(d)x+e(4)

[0027] Among them, a, b, c and e are the coefficients of the fitting cubic term, quadratic term, linear term and constant term, respectively, which depend on the electromagnetic characteristics of the drill pipe thread and the length of the defect. The parameter d represents the length of the defect.

[0028] The same method is used, based on the drill pipe thread defect measurement model, with the defect depth fixed and the defect length changed. The defect length is set to 12 mm-22 mm, and the step size is set to 2 mm. According to the peak value of the mutual impedance between the coils obtained by simulation, the function shown in formula (5) is used to fit the characteristic points. Formula (5) is:

[0029] θ=a(d)x 3 +b(d)x 2 +c(d)x+e(5).

[0030] Preferably, in step 4, the multi-parameter inversion includes:

[0031] Find a set of parameters that minimizes the error between the calculated and measured values ​​of the coil's impedance relative increment, i.e.

[0032]

[0033] Where x is the parameter vector to be determined, as well as the length and depth of the defect, which is a 1×2 array. R(x) is the simulation result, and T is the actual result. The purpose of the solution is to make R(x) continuously approach T.

[0034] First, an initial value is selected and iteration is performed. Each iteration requires calculating f(x) to determine whether f(x) is less than a threshold. If so, the iteration ends. Otherwise, the iteration continues. When the iteration ends, the calculated x is the solution, which is the length and depth of the defect. The iteration formula is:

[0035] Δx≈-[R'(x r ) T R'(x r )] -1 ×[R'(x r ) T R'(x r )-T].

[0036] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0037] In the present invention, an arc-shaped TR sensor structure is adopted to ensure that the lifting distance of each coil is the same, so that the mutual impedance between the coils mainly takes the characteristics of the drill pipe thread being measured. At the same time, the two-excitation and one-reception working mode is adopted to eliminate background noise and improve the sensitivity of defect detection.

[0038] In the present invention, based on the finite element simulation model, a swept frequency excitation measurement method is adopted to extract the characteristic points of the mutual impedance measurement results between coils, and the relationship between the mutual impedance between coils and the length and depth of the defect is obtained through a fitting method, which reduces costs and improves measurement accuracy and detection efficiency.

[0039] In the present invention, based on the swept frequency measurement results of the mutual impedance between coils simulated by Ansys Maxwell, the Newton method is used for inversion to obtain the defect depth and length information of the drill rod thread, thereby improving the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the method for detecting the depth and length of thread defects based on arc coils of the present invention;

[0041] Figure 2 This is a structural diagram of a TR drill rod thread sensor in the arc coil-based thread defect depth and length detection method of the present invention;

[0042] Figure 3 This is an overall flow chart of sensor optimization in the arc coil-based thread defect depth and length detection method of the present invention;

[0043] Figure 4 This is a diagram showing the results of frequency sweep measurement of mutual impedance (imaginary part) between coils in the method for detecting thread defect depth and length based on arc coils of the present invention;

[0044] Figure 5This is a diagram showing the results of frequency sweep measurement of mutual impedance (real part) between coils in the thread defect depth and length detection method based on arc coils of the present invention;

[0045] Figure 6 This is a defect depth fitting result diagram based on feature point extraction in the thread defect depth and length detection method based on arc coil of the present invention;

[0046] Figure 7 This is a defect length fitting result diagram based on feature point extraction in the thread defect depth and length detection method based on arc coil of the present invention. DETAILED DESCRIPTION

[0047] The following is combined with Figure 1-7 , further illustrating the specific implementation of the thread defect depth and length detection method based on the arc coil of the present invention. The thread defect depth and length detection method based on the arc coil of the present invention is not limited to the description of the following embodiments.

[0048] Example 1:

[0049] This embodiment provides a specific implementation method of the thread defect depth and length detection method based on the arc coil, such as Figure 1-7 As shown, the following steps are included:

[0050] Step 1: Sensor optimization: Obtain an arc sensor with high sensitivity to the thread defects being measured;

[0051] Step 2: Feature extraction: Use the swept frequency excitation method to obtain thread information and perform feature extraction on the swept frequency measurement signal;

[0052] Step 3: Parameter fitting: Fit the characteristic points and the defect parameters. Based on the fitting results, invert the defect information through the characteristics of the swept frequency signal.

[0053] Step 4: Multi-parameter inversion: Use the Newton iteration method to directly invert the defect information from the frequency sweep results.

[0054] Furthermore, in step 1, the arc sensor with higher sensitivity to the measured thread defects includes two excitation coils and one excitation coil, and the three coils have an arc structure. The sensor optimization algorithm combining orthogonal experiment and neural network is adopted. The optimized parameters include coil height, inner and outer diameters, distance between coils and lifting distance. The range of h is 1mm-3mm, the ranges of r1 and r2 are 1mm-1.2mm and 1.5mm-1.75mm respectively, and the range of w is 0.5mm-1mm. h is the height of the coil, r1 and r2 are the inner and outer diameters respectively, w is the distance between each coil, and l1 is the lifting distance of each coil.

[0055] Furthermore, in step 1, sensor optimization includes the following steps:

[0056] Determine the main parameters that affect the sensor sensitivity, including coil height, inner and outer diameters, distance between coils, and lift-off distance, and estimate the value range of each parameter based on actual conditions;

[0057] Secondly, according to the value range of each sensor parameter, 5 levels are selected for each parameter to carry out simulation experiments, a total of 5 5 A group of experiments were conducted. According to the simulation results, the basic range of the optimal value of the sensor was determined, and the BP neural network optimized by genetic algorithm was used to establish the functional relationship between the various sensor parameters and the change of the coil mutual impedance.

[0058] Furthermore, in step 2, the feature points are determined by simulation, including:

[0059] Set the corresponding boundary conditions to ensure that the magnetic field intensity H, the tangential component of the magnetic potential A, and the normal component of the eddy current vector J in the metal area and the air area are continuous, which can be expressed as:

[0060] n×(A1-A2)=0(1),

[0061] n×(H1-H2)=0(2),

[0062] n·(J1-J2)=0(3),

[0063] Wherein, magnetic potential A1 and A2 represent the magnetic potential at the surface of the DUT and the air, respectively; H1 and H2 represent the magnetic field strength at the air region and the surface of the DUT, respectively; J1 and J2 represent the eddy current density at the air region and the DUT, respectively;

[0064] In the simulation, the material of the drill pipe thread under test is stainless steel, and the conductivity is 1.1×10 6 S / m, relative magnetic permeability μ r =1, the grid adopts the free meshing method, the excitation current is set to 1A AC current loaded in the TR sensor to generate an alternating magnetic field, the excitation adopts the sweep frequency method, and the maximum eddy current field intensity generated is 1779.32A / m 2 .

[0065] Furthermore, in step 3, parameter fitting includes:

[0066] Based on the simulation results, the polynomial fitting method is used to fit the relationship between the characteristic points and the defect parameters. Based on the drill pipe thread defect measurement model, the length of the defect is fixed, and the depth of the defect is set to 2.5mm-0mm, with a step size of 0.5mm. According to the peak characteristic point of the imaginary part of the mutual impedance obtained by simulation, the cubic function fitting is performed using formula (4), where formula (4) is:

[0067] θ=a(d)x 3+b(d)x 2 +c(d)x+e(4)

[0068] Among them, a, b, c and e are the coefficients of the fitting cubic term, quadratic term, linear term and constant term, respectively, which depend on the electromagnetic characteristics of the drill pipe thread and the length of the defect. The parameter d represents the length of the defect.

[0069] The same method is used, based on the drill pipe thread defect measurement model, with the defect depth fixed and the defect length changed. The defect length is set to 12 mm-22 mm, and the step size is set to 2 mm. According to the peak value of the mutual impedance between the coils obtained by simulation, the function shown in formula (5) is used to fit the characteristic points. Formula (5) is:

[0070] θ=a(d)x 3 +b(d)x 2 +c(d)x+e(5).

[0071] Furthermore, in step 4, multi-parameter inversion includes:

[0072] Find a set of parameters that minimizes the error between the calculated and measured values ​​of the coil's impedance relative increment, i.e.

[0073]

[0074] Where x is the parameter vector to be determined, as well as the length and depth of the defect, which is a 1×2 array. R(x) is the simulation result, and T is the actual result. The purpose of the solution is to make R(x) continuously approach T.

[0075] First, an initial value is selected and iteration is performed. Each iteration requires calculating f(x) to determine whether f(x) is less than a threshold. If so, the iteration ends. Otherwise, the iteration continues. When the iteration ends, the calculated x is the solution, which is the length and depth of the defect. The iteration formula is:

[0076] Δx≈-[R'(x r ) T R'(x r )] -1 ×[R'(x r ) T R'(x r )-T].

[0077] Example 2:

[0078] This embodiment provides a specific implementation method of the thread defect depth and length detection method based on the arc coil, such as Figure 1-7 As shown, the following steps are included:

[0079] Step 1: The proposed arc sensor includes two excitation coils and one excitation coil, and the three coils present an arc structure, such as Figure 2 As shown in the figure. The height of the coil is h, the inner and outer diameters are r1 and r2 respectively, and the distance between each coil is w. In addition, the coil adopts an arc structure, so the lifting distance is l1, eliminating the influence of the coil lifting distance. The sensor optimization algorithm combining orthogonal test and neural network is used. The overall basic flow chart of the optimization process is shown in the figure. Figure 3 As shown in the figure, the optimized parameters include coil height, inner and outer diameters, inter-coil distance, and lift-off distance. The range of h is 1mm-3mm, the ranges of r1 and r2 are 1mm-1.2mm and 1.5mm-1.75mm, respectively, and the inter-coil distance w is 0.5mm-1mm. The target value is the change in impedance between the coils.

[0080] Through prior knowledge, we determined that the main factors affecting the sensitivity of the sensor are coil height, inner and outer diameters, distance between coils and lift-off distance, and estimated the approximate value range of each parameter based on the actual situation. Secondly, according to the value range of each parameter of the sensor, 5 levels were selected for each parameter to carry out simulation experiments, with a total of 5 5 A set of experiments were conducted. Based on the simulation results, the optimal range of sensor values ​​can be determined. Within this range, the neural network has good fitting accuracy due to its excellent ability to approximate nonlinear functions. Therefore, a BP neural network optimized by a genetic algorithm was used to establish the functional relationship between the sensor parameters and the changes in the coil's mutual impedance.

[0081] Step 2: Determine the characteristic points by simulation. The optimized TR sensor is analyzed using ANASYS Maxwell finite element simulation software. In order to ensure the continuity of the magnetic field intensity H, the tangential component of the magnetic potential A, and the normal component of the eddy current vector J in the metal area and the air area under test, the corresponding boundary conditions are set, which are expressed as Equations (1)-(3). In the simulation, the material of the drill rod thread under test is stainless steel, that is, the electrical conductivity is 3×10 8 S / m, relative magnetic permeability μ r =1, the grid adopts the free splitting method, the excitation current is set to 1A AC loaded in the TR sensor to generate an alternating magnetic field, the excitation adopts the sweep frequency method, and the maximum eddy current field intensity generated can reach 1779.32A / m 2 The real and imaginary parts of the simulation are as follows: Figure 4 and 5 As shown in Figure 4, there is a peak point in the frequency sweep result, which serves as the characteristic point of the frequency sweep measurement.

[0082] n×(A1-A2)=0(1),

[0083] n×(H1-H2)=0(2),

[0084] n·(J1-J2)=0(3),

[0085] Where A1 and A2 represent the magnetic potentials at the surface of the DUT and the air, respectively; H1 and H2 represent the magnetic field intensities at the air region and the surface of the DUT, respectively; J1 and J2 represent the eddy current densities at the air region and the DUT, respectively.

[0086] Step 3: Based on the simulation results, the relationship between the characteristic points and the defect parameters is fitted using the polynomial fitting method. Based on the drill pipe thread defect measurement model, the length of the defect is fixed, and the depth of the defect is set to 2.5mm-0mm, with a step size of 0.5mm. According to the peak characteristic point of the imaginary part of the mutual impedance obtained by simulation, the cubic function fitting method of formula (4) is used, and the results are as follows: Figure 7 shown.

[0087] θ=a(d)x 3 +b(d)x 2 +c(d)x+e (4),

[0088] Where a, b, c and e are the coefficients of the cubic term, quadratic term, linear term and constant term respectively, which depend on the electromagnetic characteristics of the drill pipe thread and the length of the defect. The parameter d represents the length of the defect. Figure 6 The fitting results shown are R 2 =0.9381, proving the accuracy of the fitting results.

[0089] In addition, the same method is used, based on Figure 1 The drill rod thread defect measurement model shown in the figure fixes the defect depth and changes the defect length. The defect length is set to 12mm-22mm and the step size is set to 2mm. According to the peak value of the mutual impedance between the coils obtained by simulation, the function shown in formula (5) is used to fit the characteristic points, R 2 =0.9903, the result is as follows Figure 7 shown.

[0090] θ=a(d)x 3 +b(d)x 2 +c(d)x+e (5)

[0091] Step 4: Propose a method that can simultaneously calculate the defect length and depth information. This method is based on the optimization method, which requires finding a set of parameters that minimizes the error between the calculated value and the measured value of the relative increment of the coil impedance, that is,

[0092]

[0093] Where x is the parameter vector to be determined, as well as the length and depth of the defect, which is a 1×2 array. R(x) is the calculation result of the simulation, and T is the actual result. The purpose of the solution is to make R(x) continuously approach T.

[0094] This patent proposes a Newton-based inversion method to obtain the length and depth of the defect. In order to find the optimal defect size to minimize the f(x) value. According to Taylor expansion, f'(x) can be approximately expressed as:

[0095] f'(x)≈f'(x r )+f”(x r )×[Δx](7)

[0096] Where x r Indicates the actual size of the defect (optimal solution), Δx=xx r .

[0097] In x r In the vicinity of , f' can be approximately calculated as:

[0098] f”(x)≈[R'(x r )] T [R'(x r )](8)

[0099] Substituting (8) into (7), we can obtain:

[0100] Δx≈-[R'(x r ) T R'(x r )] -1 ×[R'(x r ) T R'(x r )-T](9)

[0101] Therefore, the iterative algorithm first selects an initial value and iterates according to formula (9). Each iteration requires calculating f(x) to determine whether f(x) is less than a threshold. If so, the iteration ends; otherwise, the iteration is continued. When the iteration ends, the calculated x is the solution, which is the length and depth of the defect.

[0102] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for detecting thread defect depth and length based on an arc coil, characterized in that: The following steps are involved: Step 1: Sensor optimization to obtain an arc sensor with high sensitivity to the thread defects being measured; The arc sensor with high sensitivity to the thread defects under test includes two excitation coils and one receiving coil. The three coils have an arc structure. A sensor optimization algorithm combining orthogonal test and neural network is used. The optimized parameters include coil height, inner and outer diameters, distance between coils, and lift-off distance. h is the coil height, r1 and r2 are the inner and outer diameters respectively, w is the distance between each coil, and the lift-off distance of each coil is l1. The range of h is 1mm-3mm, the ranges of r1 and r2 are 1mm-1.2mm and 1.5mm-1.75mm respectively, and the range of w is 0.5mm-1mm. The method includes the following steps: Determine the parameters that affect the sensitivity of the sensor, including h, r1, r2, w, and l1, and estimate the value range of each parameter based on actual conditions; According to the value range of each sensor parameter, 5 levels are selected for each parameter to carry out simulation experiments, with a total of 5 5 A group of experiments were conducted to determine the optimal value range of the sensor based on the simulation results. The BP neural network optimized by genetic algorithm was used to establish the functional relationship between the various sensor parameters and the change of the coil mutual impedance. Step 2: Feature extraction, simulation to determine feature points, including: Set the corresponding boundary conditions to ensure that the magnetic field intensity H, the tangential component of the magnetic potential A, and the normal component of the eddy current vector J in the metal area and the air area are continuous, which can be expressed as: n×(A1-A2)=0 (1), n×(H1-H2)=0 (2), n·(J1-J2)=0 (3), Wherein, magnetic potential A1 and A2 represent the magnetic potential at the surface of the DUT and the air, respectively; H1 and H2 represent the magnetic field strength at the air region and the surface of the DUT, respectively; J1 and J2 represent the eddy current density at the air region and the DUT, respectively; In the simulation, the material of the drill pipe thread under test is stainless steel, and the conductivity is 1.1×10 6 S / m, relative magnetic permeability μ r =1, the grid adopts the free splitting method, the excitation current is set to 1A AC loaded in the arc sensor to generate an alternating magnetic field, the excitation adopts the sweep frequency method, and the maximum eddy current field intensity generated is 1779.32A / m 2 ; The result of the frequency sweep has a peak point, which is used as the characteristic point of the frequency sweep measurement; Step 3: Parameter fitting, including: Based on the simulation results, the polynomial fitting method is used to fit the relationship between the characteristic points and the defect parameters. Based on the drill rod thread defect measurement model, the defect length l is fixed, and the defect depth x is set to 0mm-2.5mm, with a step size of 0.5mm. According to the peak characteristic point of the imaginary part of the mutual impedance between the coils obtained by simulation, the cubic function fitting is performed using formula (4): θ=a(l)x 3 +b(l)x 2 +c(l)x+e (4), The same method is used to fix the depth d of the defect and change the length of the defect. The length x of the defect is set to 12 mm to 22 mm, and the step size is set to 2 mm. According to the peak characteristic point of the imaginary part of the mutual impedance between the coils obtained by simulation, the fitting is performed using formula (5): θ=A(d)x 3 +B(d)x 2 +C(d)x+E (5), Wherein, a(l) or A(d), b(l) or B(d), c(l) or C(d), and e or E are the coefficients of the fitting cubic term, quadratic term, linear term, and constant term, respectively, which depend on the electromagnetic characteristics of the drill pipe thread and the length or depth of the defect; Step 4: Multi-parameter inversion, using the Newton iteration method, directly inverts the depth and length of the defect based on the frequency sweep results, so that the error between the simulated calculated value and the measured value of the relative increment of the coil impedance is minimized.

2. The method for detecting thread defect depth and length based on arc coil according to claim 1, characterized in that: In step 4, the multi-parameter inversion includes: Find a set of parameters that minimizes the error between the simulated value and the measured value of the relative increment of the coil impedance, that is: Where x is the parameter vector to be determined, i.e., the length l and depth d of the defect, which is a 1×2 array. R(x) is the simulation result, and T is the actual result. The purpose of the solution is to make R(x) continuously approach T. First, an initial value is selected and iteration is performed. Each iteration requires calculating f(x) to determine whether f(x) is less than a threshold. If so, the iteration ends. Otherwise, the iteration continues. When the iteration ends, the calculated x is the solution, which is the length and depth of the defect. The iteration formula is: Δx≈-[R'(x r ) T R'(x r )] -1 ×[R'(x r ) T R'(x r )-T], Among them, x r Indicates the actual length and actual depth of the defect.

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