Method for measuring wall thickness and conductivity of cladding tube based on stack eddy current

Abstract

The invention relates to the technical field of nondestructive testing, and discloses a cladding tube wall thickness and conductivity measuring method based on stack array eddy current, and the method comprises the steps: firstly constructing a sensor module comprising a plurality of layers of coaxial stack coils, and forming a detection channel with a gradient lift-off distance; obtaining a plurality of self-inductance signals of each channel through broadband frequency sweeping excitation, and extracting a peak frequency corresponding to a signal imaginary part extreme point; establishing a linear function relationship between a peak frequency logarithm value and a coil physical position, and quickly estimating a wall thickness parameter and setting the wall thickness parameter as a prior constraint by utilizing the characteristic that the obtained slope value is sensitive to the wall thickness and is decoupled to the conductivity; and in combination with an eddy current effect analysis theoretical model and a least square optimization algorithm, performing stable iterative solution on the conductivity parameters under constraint conditions. According to the method, through combination of physical feature extraction and model driven inversion, cross sensitivity and discomfort of a multi-parameter inverse problem are effectively overcome, and the precision and convergence efficiency of cladding tube parameter measurement are improved.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, specifically to a method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents. Background Technology

[0002] As a core component of a nuclear reactor, the nuclear fuel cladding tube is the first line of defense against radioactive material leakage. The accuracy of the cladding tube's wall thickness directly affects the reactor's thermo-hydraulic performance, while the material's electrical conductivity is a crucial physical indicator for assessing the uniformity of its alloy composition and the degree of radiation damage. Therefore, high-precision measurement of the cladding tube's wall thickness and electrical conductivity is essential for ensuring the safe operation of nuclear facilities. Eddy current testing technology, with its advantages of being non-contact, fast, and sensitive to surface and near-surface defects in conductive materials, has become a primary means of monitoring cladding tube quality.

[0003] However, eddy current testing of thin-walled tubular conductors such as clad tubes faces complex parameter coupling challenges. Due to the skin effect of eddy currents, the reduction in tube wall thickness and the change in material conductivity often produce similar signal change trajectories on the impedance plane of the detection coil. This overlap of signal characteristics leads to severe cross-sensitivity. Traditional single-frequency or multi-frequency eddy current testing methods typically rely on establishing a large database of standard test blocks or using data-driven models such as neural networks for inversion when dealing with this problem. However, these methods are highly dependent on samples, have limited generalization ability, and are difficult to completely eliminate the mutual interference between parameters from a physical mechanism perspective.

[0004] Furthermore, while parameter inversion methods based on analytical electromagnetic field models have clear physical meaning, they are essentially nonlinear indeterminate inverse problems. In the absence of effective prior information, attempting to simultaneously solve for multiple unknown parameters such as wall thickness, conductivity, and lift-off distance using full-variable iterative methods often results in the objective function exhibiting multi-peak and valley characteristics. This makes the optimization algorithm prone to getting trapped in local optima or failing to converge due to strong correlations between parameters. Especially in actual industrial settings, lift-off noise caused by minute probe movements within the pipe further deteriorates the stability of the inversion, making it difficult for existing detection techniques to achieve high-precision decoupled measurement of wall thickness and conductivity parameters while maintaining computational efficiency. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for measuring the wall thickness and conductivity of clad tubes based on stacked eddy currents. This method solves the problems of parameter decoupling difficulties caused by the cross-sensitivity of wall thickness and conductivity signals in existing eddy current detection of clad tubes, as well as the ill-posedness and poor convergence stability of the multi-parameter inversion solution process.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents, comprising the following steps:

[0007] The configuration includes a stacked eddy current sensor module containing multiple coaxially stacked coils along the axial direction; The reference complex self-inductance signal of each coil in an air environment and the measured complex self-inductance signal on the surface of the casing tube under test are obtained by using a swept frequency eddy current detection module. The difference between the measured complex self-inductance signal and the reference complex self-inductance signal is calculated to obtain the change in the self-inductance of the complex coil. The peak frequency corresponding to the extreme point of the imaginary part of the self-inductance change of each complex coil is determined using the data processing module; The data processing module establishes a linear fitting relationship based on the spatial stacking position of each coil and the logarithm of the peak frequency, and calculates the slope value. The data processing module uses a preset slope-to-wall-thickness mapping relationship to convert the slope value into a priori wall-thickness constraint value. The data processing module is used to construct an analytical theoretical model of the eddy current effect and a least squares optimization objective function that includes conductivity parameters and wall thickness parameters. The prior constraint value of the wall thickness is substituted into the least squares optimization objective function, and the conductivity parameters and the wall thickness parameters are solved iteratively through a numerical optimization algorithm. The wall thickness measurement results and conductivity measurement results are then output.

[0008] Preferably, the step of the configuration including a stacked eddy current sensor module with multiple coaxially stacked coils specifically includes: A rectangular-circular cross-section closely wound coil with consistent geometric dimensions and electrical parameters is selected as the coil; The three coils are stacked coaxially and vertically along the axial direction to form an integrated probe structure; The vertical distance between the bottom surface of the lowest coil in the integrated probe structure and the surface of the casing tube to be tested is defined as the basic lift-off distance; Based on the axial thickness of the coil, the effective lift-off distance of the intermediate layer coil and the top layer coil relative to the surface of the casing tube to be tested is determined.

[0009] Preferably, the step of acquiring the reference complex self-inductance signal of each coil in an air environment and the measured complex self-inductance signal on the surface of the casing tube under test using the swept-frequency eddy current detection module specifically includes: Set sweep frequency excitation parameters, which cover the variation of eddy current skin depth from the full thickness of the pipe wall to the surface of the pipe wall; The stacked eddy current sensor module is placed in an air environment. The impedance analyzer integrated in the swept frequency eddy current detection module is used to collect the air complex impedance signal of each coil at each discrete frequency point. The air complex impedance signal contains a real resistance component and an imaginary reactance component. Based on the ratio of the air complex impedance signal to the product of the imaginary unit and the angular frequency, the reference complex self-inductance value of each coil is calculated to form the reference complex self-inductance signal. The stacked eddy current sensor module is placed on the surface of the cladding tube under test. The impedance analyzer is used to collect the measured complex impedance signals of each coil at each discrete frequency point. The measured complex impedance signal includes a real resistance component and an imaginary reactance component. Based on the ratio of the measured complex impedance signal to the product of the imaginary unit and the angular frequency, the measured complex self-inductance value of each coil is calculated to form the measured complex self-inductance signal.

[0010] Preferably, the step of constructing the analytical theoretical model of the eddy current effect specifically includes: Based on Maxwell's equations and electromagnetic field boundary conditions, an axisymmetric eddy current field analytical model applicable to tubular conductors is established as the analytical theoretical model. The vector magnetic potential equation is solved by the method of separation of variables in cylindrical coordinates. Combining the characteristics of the coil excitation source and the boundary conditions of the medium interface, the integral form analytical solution of the self-inductance change of the complex coil is derived. The analytical solution in integral form is calculated using a numerical integration algorithm to obtain the theoretical value of the change in self-inductance of the coil within a continuous frequency sweep range.

[0011] Preferably, the step of establishing a linear fitting relationship and calculating the slope value specifically includes: The physical location number of each coil in the stacked eddy current sensor module is defined as the independent variable; The natural logarithm of the peak frequency corresponding to each coil is used as the dependent variable; The linear regression algorithm is used to perform fitting analysis on the independent variable and the dependent variable to establish the linear fitting function relationship; The slope term is extracted from the linear fitting function relationship and used as the slope value.

[0012] Preferably, the step of converting the slope value into a priori wall thickness constraint value using the data processing module according to a preset slope-wall thickness mapping relationship specifically includes: Multiple sets of forward simulation calculations are performed within a preset parameter space to establish an associated database containing the slope value, the wall thickness parameter, and the conductivity parameter; Sensitivity analysis is performed on the associated database to extract the single-value mapping relationship between the slope value and the wall thickness parameter. The single-value mapping relationship is that the slope value is sensitive to the wall thickness parameter but not sensitive to the conductivity parameter. A quantitative calculation model is established using numerical fitting or interpolation algorithms, with the slope value as the input variable and the wall thickness parameter as the output variable. The slope value obtained from the actual measurement calculation is substituted into the quantitative calculation model to calculate the estimated wall thickness of the cladding tube to be measured, and the estimated wall thickness is set as the prior constraint value of the wall thickness.

[0013] Preferably, the step of constructing the least squares optimization objective function specifically includes: Define the change in self-inductance of the complex coil as the observation vector; The analytical theoretical model is used as the forward calculation kernel to generate the theoretical self-induction change vector; Calculate the Euclidean distance between the theoretical self-influence change vector and the observed vector, construct the residual sum of squares objective function, and use it as the least squares optimization objective function.

[0014] Preferably, the step of iteratively solving for the conductivity parameter and the wall thickness parameter using a numerical optimization algorithm specifically includes: Construct a parameter vector to be solved, which includes the conductivity parameter and the wall thickness parameter; The prior wall thickness constraint value is assigned to the initial wall thickness value in the parameter vector to be solved, and the nominal conductivity of the cladding tube material to be tested is assigned to the initial conductivity value in the parameter vector to be solved. Calculate the sensitivity matrix of the least squares optimization objective function with respect to the parameter vector to be solved, and dynamically adjust the damping factor according to the current residual size; The parameter correction vector is calculated based on the sensitivity matrix and the damping factor, and the parameter vector to be solved is updated. During the iteration process, the wall thickness parameter is finely adjusted within the neighborhood of the prior wall thickness constraint value.

[0015] Preferably, the step of calculating the parameter correction vector employs an improved Levenberg-Marquardt algorithm, specifically including: The Jacobian matrix is ​​calculated as the sensitivity matrix, and the Jacobian matrix represents the first-order partial derivatives of the output of the analytical theoretical model with respect to each physical parameter. By combining the Jacobian matrix, the damping factor, and the current residual vector, the parameter correction vector is obtained by solving the linear equation system. Based on the trend of the objective function value before and after the parameter update, the value of the damping factor is adaptively adjusted, and the search strategy is switched between the characteristics of the gradient descent method and the characteristics of the Gauss-Newton method.

[0016] Preferably, the step of continuing until the preset convergence condition is met specifically includes: The theoretical self-inductance change vector for the current iteration step is generated using the analytical theoretical model, and the objective function value between the theoretical self-inductance change vector and the self-inductance change of the complex coil is calculated. Calculate the magnitude of the parameter change between the current iteration step and the previous iteration step; Determine whether the objective function value is less than a preset residual threshold, or determine whether the magnitude of the parameter change is less than a preset step size threshold; If any of the above conditions are met, or the current number of iterations reaches the preset maximum limit, then the iteration is determined to be converged, and the current parameter estimate is locked and output as the final wall thickness measurement result and conductivity measurement result.

[0017] This invention provides a method for measuring the wall thickness and conductivity of clad tubes based on stacked eddy currents. It has the following advantages: 1. This invention utilizes the spatial slope characteristics of the peak frequency logarithm to achieve effective decoupling of wall thickness and conductivity parameters. By extracting the peak frequencies of different channels in the stacked coil array and establishing a linear fitting relationship between their logarithm values ​​and the physical position of the coils, the obtained slope values ​​have the physical characteristic of being highly sensitive to wall thickness parameters but insensitive to conductivity parameters. This allows the method to quickly and accurately obtain the initial estimate of wall thickness through simple feature extraction before performing complex inversion calculations, effectively solving the technical problem of difficulty in separating wall thickness and conductivity signals due to cross-sensitivity in traditional eddy current detection.

[0018] 2. This invention improves the convergence stability and computational efficiency of multi-parameter iterative solutions by introducing prior constraints on wall thickness. Addressing the nonlinearity and instability typically present in electromagnetic inverse problems, this method does not directly perform a blind full-parameter search, but instead substitutes the previously estimated wall thickness parameters as strong constraints into the eddy current effect analytical model. This reduces the search range of the optimization algorithm in the parameter space, effectively preventing the Levenberg-Marquardt algorithm from getting trapped in local minima during iteration, thus ensuring the high accuracy and reliability of the final wall thickness and conductivity measurement results.

[0019] 3. This invention adopts an integrated sensor structure with axial coaxial stacking, which enhances the diversity of detection information and anti-interference capability; multiple coils stacked along the axis form detection channels with different lift-off distances, enabling the probe to simultaneously acquire broadband response signals of the cladding tube under different electromagnetic coupling strengths without mechanical movement; this tiered coil layout can supplement the information missing of single coil detection from the spatial dimension, and combined with broadband excitation technology, it suppresses random noise interference caused by probe shaking or distance changes, improving the robustness of the system in actual industrial detection environments. Attached Figure Description

[0020] Figure 1 This is an overall method flowchart of an embodiment of the present invention; Figure 2 This is a schematic diagram of the measurement system and probe structure of the present invention; Figure 3 This is a flowchart of a method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to the present invention. Figure 4 This is a schematic diagram of the peak frequency characteristics of the swept-frequency eddy current in an embodiment of the present invention; Figure 5 This is an embodiment of the present invention showing the relationship between the logarithm of the peak frequency and the coil position through linear fitting.

[0021] Among them, 100 is the stacked eddy current sensor module; 200 is the swept frequency eddy current detection module; and 300 is the data processing module. Detailed Implementation

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see the appendix Figure 1 - Appendix Figure 5 This invention provides a method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents, wherein... Figure 3 This is a schematic diagram of the overall process of the measurement method described in this embodiment, as follows: Figure 3 As shown, the method includes the following steps: S1. System setup and frequency sweep data acquisition: Design a coaxial stacked array structure consisting of three coils of the same size as the stacked eddy current sensor module 100, and connect it to the frequency sweep eddy current detection module 200; use the frequency sweep eddy current detection module 200 to drive the stacked eddy current sensor module 100 to perform wideband excitation on the cladding tube, and acquire the self-inductance signals of the three coils at different frequencies; the three coils respectively form detection channels with different lift-off distances.

[0024] S2. Theoretical Model Construction and Peak Feature Search: The data processing module 300 has a non-magnetic metal tube swept frequency eddy current analytical theoretical model. The data processing module 300 calculates the extreme point of the change of the imaginary part of the self-inductance signal based on the received self-inductance signal, determines the frequency corresponding to the extreme point as the peak frequency, and initializes the conductivity and wall thickness parameters of the cladding tube in the model at the same time.

[0025] S3. Frequency feature extraction and spatial position fitting: The data processing module 300 extracts the peak frequency values ​​corresponding to the three coils and performs logarithmic operations. Then, the data processing module 300 establishes a linear fitting function relationship with the spatial position of the coils as the independent variable and the logarithm of the peak frequency as the dependent variable.

[0026] S4. Prior decoupling of wall thickness based on slope characteristics: The data processing module 300 calculates the slope value of the above linear fitting function and uses the slope value to estimate the wall thickness parameter of the cladding tube. Based on analytical theory, the slope value of the linear fitting function monotonically depends on the wall thickness parameter and is independent of the electrical conductivity property of the material. Therefore, the data processing module 300 directly locks the estimated wall thickness value through the slope value as a prior constraint for subsequent inversion.

[0027] S5. Constructing the inversion model and iteratively solving; The data processing module 300 inputs the eddy current sweep frequency signal into the analytical theoretical model of the eddy current effect, and constructs the least squares optimization objective function of the cladding tube conductivity as the main parameter to be solved; In this process, the data processing module 300 sets the wall thickness estimate obtained in step S4 as a fixed prior constant or a strongly constrained initial value, and uses the improved Levenberg-Marquardt algorithm to iteratively solve the conductivity parameter.

[0028] S6, Convergence Determination; The data processing module 300 determines whether the difference between two consecutive inversion results (objective function residuals or parameter changes) is less than a preset convergence threshold. Alternatively, determine whether the current iteration count has reached the maximum allowed iteration count. .

[0029] S7, iterative control loop; if the result of step S6 is negative (i.e., not converged and not timed out), the data processing module 300 performs an iterative update operation (including adaptive adjustment of the damping factor), setting the iteration count... Then return to step S5 for the next round of calculation until the termination condition is met.

[0030] S8, Result Output and Post-processing. If the result of step S6 is yes, the data processing module 300 locks the current parameter estimate and outputs the final measurement results of the cladding tube wall thickness and conductivity.

[0031] Step S1 of this method mainly involves the structural parameter design of the stacked eddy current sensor, the physical construction of the detection device, and the acquisition of multi-channel scanning data. The core of this step lies in acquiring the electromagnetic response under different spatial coupling states simultaneously without moving the sensor through differentiated physical structural design, providing a data foundation for subsequent elimination of lift-off effect interference. The specific implementation process includes the following sub-steps: S1.1 Construct a three-coil stacked array sensor of the same size.

[0032] Three coils with identical geometric dimensions and electrical parameters were designed and fabricated as sensing units. The coils are tightly wound with a circular cross-section and are coaxially and perpendicularly stacked to form an integrated probe structure. Each coil operates in absolute mode, meaning a single coil simultaneously performs the functions of emitting the excitation magnetic field and receiving the induction signal. Considering the dimensional characteristics of the nuclear fuel cladding tube, the specific geometric parameters of the coils in this embodiment are set as follows: the inner diameter of the coil is denoted as... The value is 1mm; the outer diameter of the coil is denoted as... The value is 3mm; the coil height (i.e., axial thickness) is denoted as... The value is 2mm; the number of coil turns is recorded as... The coils are set to 100 turns, and the three coils are tightly bonded together by an insulating layer with negligible interlayer gaps. In addition, in order to shield against electromagnetic interference from the external environment and focus the detection magnetic field, a cylindrical high-permeability ferrite magnetic shielding shell or a multi-layer permalloy shielding cover is coaxially fitted around the three stacked coils. The inner wall of the shielding cover and the outer diameter of the coil are filled with epoxy resin potting compound to ensure the mechanical rigidity and thermal stability of the sensor structure during high-speed scanning.

[0033] S1.2, Determine the spatial layout of sensors for different lift-off distances.

[0034] A stacked sensor array is placed above the surface of the cladding tube under test. The stacked array structure physically constructs three lift-off distance detection channels with fixed differences. The vertical distance between the bottom surface of the lowest coil (i.e., the first coil) and the outer surface of the cladding tube is defined as the basic lift-off distance, denoted as . Based on coil height Given the parameters, the effective lift-off distance of the intermediate layer coil (i.e., the second coil) relative to the surface of the cladding tube is determined as follows: The effective lift-off distance of the top coil (i.e., the third coil) relative to the surface of the cladding tube is determined as follows: This layout is equivalent to constructing three absolute eddy current sensors with identical parameters except for the lift-off distance. This results in a stepped change in the electromagnetic coupling strength of the three coils to the measured cladding tube, thereby introducing independent information about the spatial position dimension into the measurement data.

[0035] S1.3, Build a frequency sweep detection device.

[0036] Establish a swept-frequency eddy current testing system, which consists of the aforementioned stacked sensor array, a precision impedance analyzer (or broadband eddy current meter), and corresponding signal transmission cables. Connect the three coils to independent channels of the testing instrument. Set the swept-frequency excitation parameters of the instrument. The frequency sweep range covers 100Hz to 1MHz, encompassing the variation of eddy current skin depth from covering the entire thickness of the tube wall to being concentrated only on the tube wall surface; specifically, according to the eddy current skin effect formula... (in For penetration depth, For the excitation frequency, The magnetic permeability of the material, The electromagnetic field, defined as the material's electrical conductivity, is primarily limited by the tube wall's geometry at low frequencies (e.g., 100Hz). At high frequencies (e.g., 1MHz), the penetration depth is much smaller than the tube wall thickness, and the eddy currents are mainly concentrated on the outer surface of the tube wall. This full frequency domain coverage ensures that subsequent inversion algorithms can obtain decoupled information about the wall thickness and conductivity. During the measurement process, the instrument applies a constant-amplitude sinusoidal excitation current to each coil and continuously changes the frequency at logarithmic or linear intervals within the sweep frequency range.

[0037] S1.4, Measure and calculate the coil self-inductance signal.

[0038] The complex impedance signals of each coil at various frequency points are simultaneously acquired using an impedance analyzer. ,in The real part of the resistance component. This represents the imaginary reactance component. To obtain the complete electromagnetic response including phase information, cable phase compensation calibration must be performed on the acquired original complex impedance signal before performing the above calculations. Specifically, this involves measuring the system's inherent impedance under short-circuit conditions at the end of the connecting cable, or performing phase zeroing calibration using a standard resistive load, and eliminating the additional phase shift caused by the transmission cable through a complex rotation algorithm. This step ensures that the phase zero point of the impedance signal in the input data processing module is strictly consistent with the phase reference defined by the analytical theoretical model; this step requires calculating the complex self-inductance signal. Based on the formula... To perform the calculation, that is: ; In the formula, complex self-induction The real part is (Characterizing energy storage), the imaginary part is (Characterizing losses). During the frequency sweep cycle, the complex self-inductance values ​​of the first, second, and third coils at each discrete frequency point are recorded. In addition, in order to obtain the net change caused by the eddy current field, the complex self-inductance of the sensor in air is collected as a reference signal under the same ambient temperature. The complex self-inductance in the active state is subtracted from the air reference signal to form three independent spectral data sequences of self-inductance change.

[0039] The specific process of establishing the frequency sweep eddy current analytical theoretical model for non-magnetic metal tubes in this embodiment is as follows: S2.1, Constructing the physical architecture and parameter definitions of the analytical model of the electromagnetic field.

[0040] This step aims to establish a quantitative mapping relationship between the physical properties (wall thickness, conductivity) of the object under test and the electrical physical quantities (inductance) that the sensor can measure, based on electromagnetic field theory, so as to provide a positive calculation benchmark for subsequent parameter inversion.

[0041] Based on Maxwell's equations and electromagnetic field boundary conditions, an axisymmetric analytical model of eddy current field applicable to tubular conductors is established. This model assumes the cladding tube to be tested is an infinitely long, non-magnetic, hollow cylinder with homogeneous and isotropic material. The physical parameters defined in the model include: the conductivity of the cladding tube. cladding wall thickness , inner diameter of cladding tube Define the outer diameter of the cladding tube as... ,in Air (vacuum) magnetic permeability The geometric parameters of the sensor include: coil inner diameter. outer diameter of the coil axial thickness of the coil and the lift-off distance from the bottom of the coil to the outer surface of the casing tube. Furthermore, the number of coil turns is defined as... The excitation current amplitude is angular frequency is This model neglects displacement current and uses a quasi-static approximation.

[0042] S2.2, Derive and establish the analytical expression for the change in the coil's self-inductance signal.

[0043] In cylindrical coordinates, the vector magnetic potential equation is solved using the method of separation of variables. Combining the characteristics of the coil's excitation source and the boundary conditions at the interfaces of various media (air / pipe wall, pipe wall / air), the change in the coil's self-inductance signal is derived. The integral form of the analytical solution is given. This analytical expression characterizes the increase in self-inductance when the coil is above the pipe, relative to when the coil is in free space. The specific analytical model is as follows: ; In the formula, Denotes the variable of the first integral; This indicates the order of the summation of the series; express The first-order modified Bessel function of the order, express The second-order modified Bessel function; The outer diameter of the cladding tube as defined above .

[0044] S2.3 Calculate the intermediate variables and coefficient matrix in the analytical model.

[0045] The above The specific calculation logic for the coefficients and intermediate variables included in the expression is as follows: Define the structural coefficients related to the coil geometry. and its sub-items , , : ; ; ; ; In the formula, For the second integral variable; and These are the radial and axial coordinate variables during the integration process of the coil cross section, respectively; The axial distance variable during the integration process (corresponding to) ); The coil turns density is defined as follows: N is the number of turns in the coil.

[0046] Define the core coefficient, which reflects the propagation and reflection characteristics of electromagnetic fields in a medium. , and : ; ; ; In the formula, Let be the wave number in the air, and take under the quasi-static approximation. ; is the complex wave number, which characterizes the propagation constant of the eddy current field in a conductive medium; and They represent The derivatives of the first and second kind of modified Bessel functions.

[0047] Define the coefficients of the boundary condition matrix , , , These coefficients describe the continuity condition of the electromagnetic field at the interface between the inner and outer surfaces of the tube wall: ; ; ; ; In the formula, the coefficients Defined here as an integration variable (Right now ).

[0048] Define auxiliary calculation variables and denominator terms : ; ; ; ; ; ; ; ; ; ; S2.4 defines the peak frequency characteristics.

[0049] The analytical model described above is calculated using a numerical integration algorithm (such as the Gauss-Schlauroh integration method) to obtain the change in self-inductance of the coil over a continuous frequency sweep range. .Will The process is decomposed into real and imaginary parts, and the change in the imaginary part is extracted. The excitation frequency corresponding to the maximum value of the change in the imaginary part is defined as the peak frequency. This peak frequency is a key characteristic quantity reflecting the combined effect of the cladding wall thickness and conductivity, and physically corresponds to the frequency point at which the phase lag of the eddy current field within the tube wall reaches a specific equilibrium with energy loss; for example... Figure 4As shown, this is a schematic diagram of the peak frequency characteristics of the swept-frequency eddy current in this embodiment. The horizontal axis represents the excitation frequency (Hz), and the vertical axis represents the change in self-inductance (H). The curves in the figure show the trend of the real and imaginary parts of the change in self-inductance with frequency. The solid line represents the calculated value of the analytical theoretical model, and the dots represent the experimental measured value. The agreement between the two verifies the accuracy of the model. The position marked by the black circle in the figure is the extreme point (peak point) of the curve of the imaginary part of the change in self-inductance. The frequency value of the horizontal axis corresponding to this point is the peak frequency mentioned in this step.

[0050] In this embodiment, the specific process of feature extraction and linear fitting of the swept frequency detection data includes the following sub-steps: S3.1 Extract the peak frequency characteristics of the multi-channel swept frequency signal.

[0051] Based on the self-inductance data sequences of the three coils at different frequencies obtained in step S1, and the peak frequency feature criterion defined in step S2, the data processing module 300 performs a traversal search on the data of the three detection channels. For the first coil, the second coil, and the third coil, the frequency value corresponding to the maximum amplitude point in the imaginary part change curve of their self-inductance signal is identified, and these three frequency values ​​are recorded as the first peak frequency. Second peak frequency and the third peak frequency This step is physically designed to capture the frequency domain response characteristics of the eddy current field at different spatial lift heights when its coupling with the cladding tube is strongest.

[0052] To eliminate the limitation of peak position positioning accuracy on the amplitude of the frequency sweep, after determining the maximum amplitude point, the data processing module 300 further selects this maximum value point and several adjacent frequency points (e.g., 3 or 5 points in total) for local parabolic fitting or Gaussian function fitting. The continuous frequency values ​​corresponding to the extreme points of the fitted curve are calculated and used as the final high-precision peak frequency. This processing can obtain characteristic frequencies higher than the frequency sweep resolution, thereby improving the sensitivity of subsequent wall thickness estimation.

[0053] S3.2, Construct a logarithmic domain feature dataset.

[0054] To transform the nonlinear physical law of peak frequency variation with spatial location into a linear law that is easier to calculate, the three extracted peak frequency values ​​are processed by natural logarithmic operations. Simultaneously, the physical position number of the coil in the stacked array structure is defined as the independent variable. In this embodiment, the position coordinates of the first coil at the bottom layer are set as follows: The position coordinates of the second coil in the middle layer are The position coordinates of the third coil at the top layer are: The coordinates of this location The equidistant discretization level of the coil relative to the surface of the casing tube was characterized. Feature data pairs were constructed by combining the position coordinates with the corresponding logarithmic peak frequencies, resulting in a feature set containing three sets of data.

[0055] S3.3, Establish the linear function relationship and obtain the slope characteristic quantity.

[0056] Linear regression algorithms (such as least squares) are used to fit and analyze the above feature set to establish the logarithmic peak frequency. Regarding the coil position The linear functional relationship is expressed as: ; In the formula, The natural logarithm of the peak frequency; The stacking position number represents the coil; The slope of the fitted line; The intercept of the fitted line; such as Figure 5 As shown, this is a schematic diagram illustrating the relationship between the logarithm of the peak frequency and the coil position in this embodiment. The horizontal axis represents the lift-off distance (corresponding to different spatial positions of the stacked coils), and the vertical axis represents the natural logarithm of the peak frequency. The figure shows the measurement data points and their corresponding linear fitting lines for cladding tube wall thicknesses of 1mm, 1.5mm, and 2mm. The data points and the fitted lines highly overlap, visually verifying the good linear relationship between the logarithm of the peak frequency and spatial position. Simultaneously, there are significant differences in the slope of the lines (i.e., the degree of inclination) corresponding to different wall thicknesses, indicating that the slope k is highly sensitive to the wall thickness parameter. The slope value is obtained through fitting calculations. Simultaneously, the determination coefficient (R-squared, denoted as ) of the linear regression model is calculated. The linearity threshold (e.g., 0.98) is used as an evaluation index for goodness of fit. The data processing module 300 sets the linearity threshold (e.g., 0.98). If the calculated linearity... If the value is less than the threshold, the sensor coupling state at the current location is determined to be abnormal (such as the presence of local crack interference or probe tilt). The system automatically marks the measurement point as invalid or triggers a retest mechanism to prevent wall thickness estimation errors caused by physical model mismatch.

[0057] The physical principle underlying this step is that, due to the edge and diffusion effects of the eddy current field, the peak frequency decreases exponentially with increasing coil lift-off distance, exhibiting a linear relationship after logarithmic transformation. The intercept... Simultaneously affected by the material's electrical conductivity and wall thickness, the slope... The rate of decay was characterized; since the wall thickness is the geometric boundary condition restricting the radial diffusion of the eddy current field, the decay rate is mainly determined by the wall thickness and is insensitive to the electrical conductivity of the material itself. Therefore, by extracting the slope... This allows us to obtain an independent characteristic parameter that is only sensitive to wall thickness and approximately decoupled from conductivity.

[0058] In this embodiment, the specific process of independently estimating the wall thickness using the slope characteristic of the peak frequency changing with the coil position includes the following sub-steps: S4.1, Construct a slope-wall-thickness feature mapping database.

[0059] Using the frequency-sweeping eddy current analytical model of the non-magnetic metal tube established in step S2, multiple sets of forward simulation calculations are performed within a preset parameter space that covers the physical properties of the object under test. In specific implementation, the wall thickness of the cladding tube is set. The range of variation (e.g., 0.5 mm to 0.8 mm for a typical zirconium alloy clad tube) and conductivity Range of variation (e.g., set as a baseline value) For each group The parameters are combined, and the peak frequencies of the three coils are calculated using an analytical model. The corresponding linear fitting slope is then calculated according to the method in step S3. The calculated slope With corresponding wall thickness and conductivity Stored in the database to form a sample set.

[0060] S4.2, verify the independence of the slope characteristic from conductivity.

[0061] Sensitivity analysis was performed on the generated database. The results show that, in the case of wall thickness... Even if the conductivity is fixed as an arbitrary constant, The slope is calculated by varying the slope over the entire range. The value remains constant or only exhibits negligible fluctuations. From a physical perspective, this is because the rate at which the peak frequency decays with increasing lift-off distance (i.e., coil position) essentially depends on the geometric boundary constraints imposed on the eddy current field during radial diffusion. For non-magnetic metal tubes, this geometric boundary constraint is the tube wall thickness, while the material's conductivity only affects the intensity and absolute phase of the eddy current, without altering its geometric decay with spatial position. Based on this, the slope is confirmed. It is a decoupled characteristic that is only sensitive to wall thickness and not to electrical conductivity.

[0062] S4.3, Establish a quantitative mapping relationship between slope and wall thickness.

[0063] Based on the physical laws verified by S4.2, and ignoring the slight influence of conductivity, the multivariate relationships in the database are simplified to slope. With wall thickness The single-valued mapping relationship between them. Numerical fitting algorithms (such as polynomial fitting) or interpolation algorithms are used to establish the slope. Input variables, wall thickness This is a quantitative calculation model for the output variables. In this embodiment, the least squares method is used to establish a second-order polynomial fitting model, whose mathematical expression is denoted as: ,in , , These are the fitting coefficients obtained through training on the sample set. This polynomial model can accurately approximate the nonlinear monotonic relationship between slope and wall thickness, and compared to linear interpolation, it has better noise resistance and computational smoothness. This model reflects the slope... With wall thickness The monotonic correspondence between the two ensures that for each given slope input, a unique wall thickness output value can be obtained.

[0064] S4.4 performs online estimation of wall thickness parameters.

[0065] During the actual measurement process, the data processing module 300 reads the linear fitting slope calculated from the measured data in step S3. The measured slope Substituting the values ​​into the quantitative calculation model established in step S4.3, the estimated wall thickness of the cladding tube to be measured can be directly retrieved or calculated. This step, by introducing information about the spatial dimension, pre-determines the range of wall thickness parameters before solving for conductivity, thereby transforming the subsequent conductivity measurement problem from a two-parameter coupled inversion to a single-parameter solution or a two-parameter fine-tuning under strong constraints, reducing the ill-conditioned nature of the inversion problem.

[0066] In this embodiment, the wall thickness estimation result is used as a priori constraint, and the specific process of inverting the conductivity using the improved numerical optimization algorithm is as follows: S5.1, construct the least squares objective function for conductivity inversion.

[0067] Based on the theory of inverse problem solving, a residual minimization model is established between the physical parameters to be inverted and the observed data. The coil self-inductance signals at each frequency obtained through experimental measurement in step S1 are defined as the observation vectors. Simultaneously, the analytical theoretical model of the eddy current effect established in step S2 is used as the forward calculation kernel. The mathematical objective of the inversion is to find an optimal combination of physical parameters (including conductivity). and wall thickness This makes the theoretical output value of the analytical model under the current parameters consistent with the observed vectors of the actual measurements. The Euclidean distance (i.e., the sum of squared residuals) between the two sides is minimized; to further suppress the influence of measurement noise on the inversion results, this step introduces a frequency weighting matrix when constructing the objective function. Based on the signal-to-noise ratio characteristics of the frequency sweep detection system, differentiated weighting coefficients are assigned to data at different frequency points (e.g., reducing the weight of the ultra-high frequency band with greater signal jitter and increasing the weight of the mid-frequency band with stable signal). At this point, the optimization objective function is modified to minimize the weighted sum of squared residuals, i.e. This forces the inversion algorithm to prioritize fitting high-confidence frequency band data.

[0068] S5.2 introduces prior wall thickness information and initializes the parameter vector.

[0069] To address the multi-value problem caused by the strong coupling between electrical conductivity and wall thickness in the eddy current effect, this embodiment utilizes the wall thickness value obtained through independent estimation in step S4. Physical constraints are imposed on the inversion process. The parameter vector to be solved is constructed. ,in This is the conductivity estimate for the current iteration step. This is the wall thickness estimate for the current iteration step. At the initial moment of the iteration calculation (step 0), the wall thickness estimate obtained in step S4 is directly used. Assign to The initial value is set, and the nominal conductivity of the material to be tested (e.g., the empirical conductivity value of zirconium alloy) is also set as the initial value. The initial value of conductivity is calculated using a physical feature decoupling initialization strategy. This strategy ensures that the algorithm's search starting point is within the convergence region of the true solution, thus avoiding the common pitfalls of gradient algorithms. This embodiment employs the characteristic frequency correlation method to calculate a more accurate initial value for conductivity. Instead of directly using fixed empirical values, this is based on the eddy current characteristic equation. (in (Constants related to the coil structure), using the measured peak frequency extracted in step S3. and the wall thickness value estimated in step S4 The approximate conductivity is calculated by reverse derivation. This dynamic initial value assignment strategy fully utilizes the implicit information in the measurement data, making the initial parameter vector... By being close to the true solution, the average number of iterations required for subsequent convergence can be reduced by more than 30%.

[0070] S5.3, perform iterative correction calculation.

[0071] The Levenberg-Marquardt algorithm is used to solve the aforementioned nonlinear least squares problem. This algorithm achieves adaptive switching between gradient descent and Gauss-Newton methods by introducing a damping term into the iteration direction. In each iteration, the sensitivity matrix (i.e., the Jacobian matrix) of the objective function with respect to the parameters to be inverted is calculated, and the damping factor is dynamically adjusted based on the current residual magnitude. The formula for calculating the parameter correction based on this algorithm is as follows: ; In the formula, Denotes the correction vector for the parameters, where This is a correction factor for conductivity. This is the amount of fine-tuning correction for the wall thickness; The Jacobian matrix is ​​represented by its elements, which are the first-order partial derivatives of the analytical model output with respect to various physical parameters. Physically, it characterizes the sensitivity of the self-inductance signal to changes in conductivity and wall thickness. It is the transpose of the Jacobian matrix; is the damping factor, a non-negative real number used to adjust the condition number of the coefficient matrix and the search step size of the algorithm; Represents the identity matrix; This represents the theoretical self-inductive response vector calculated after substituting the current parameter estimates into the analytical model in step S2; This is the actual measured sweep frequency self-inductance signal vector.

[0072] S5.4, update the physical parameters and determine convergence.

[0073] The correction vector calculated in step S5.3 is used to update the current parameter estimates, approximating the true physical parameters. The parameter update formula is as follows: ; In the formula, This represents the updated parameter vector, which will serve as the current parameter estimate in the next iteration. ; The current parameter estimate before the update; This is the correction vector obtained from the above calculation. Repeat steps S5.3 and S5.4 until the theoretical self-inductance response vector matches the observed vector. The residuals between the two values ​​are less than the preset convergence threshold. The final output is the converged conductivity. This is the precise conductivity value of the cladding tube under test. Through this process, the algorithm utilizes the prior value of the wall thickness. By locking the search range, the model error is compensated by fine-tuning the wall thickness parameter, thereby achieving high-precision conductivity inversion.

[0074] In this embodiment, the specific process of determining the convergence of the inversion process and outputting the final measurement result includes the following sub-steps: S6.1 Calculate the fitting error and parameter stability index of the current iteration step.

[0075] After each iteration completes the parameter update, the data processing module 300 evaluates the inversion state based on the updated parameters. First, it calculates the theoretical self-induced response vector obtained in step S5.3. The observation vector obtained from the actual measurement in step S1 The statistical deviation between the vector differences, typically characterized by the Euclidean norm of the vector difference or the sum of squared residuals, is used as the objective function value. Next, calculate the correction vector generated in step S5.3. The vector magnitude represents the relative magnitude of the parameter change in the current iteration step.

[0076] S6.2, execute the dual convergence criterion for determination.

[0077] The index calculated in step S6.1 is compared with the preset convergence conditions. This embodiment adopts a dual judgment logic that combines fitting accuracy and numerical stability to ensure that the inversion result is both physically consistent with the measurement data and mathematically stable.

[0078] Judgment condition 1: Objective function value Less than the preset residual threshold This condition indicates that the theoretical output curve of the analytical model and the actual frequency sweep data curve have reached a high degree of overlap.

[0079] Judgment condition two: The magnitude of the corrected vector is less than the preset step size threshold. This condition indicates that the update magnitude of the parameters to be inverted is negligible, and the algorithm has searched to the vicinity of the extreme point.

[0080] in, and The minimum positive number pre-set based on the signal-to-noise ratio and required accuracy of the measurement system ( Set to 10 -6 , Set to 10 4 ).

[0081] If any of the above conditions are met, or the number of iterations reaches the preset maximum limit (e.g., set to 50 times), the algorithm is considered to have converged, and the iteration loop terminates. If the conditions are not met, the process returns to step S5.3 to continue the next round of calculation.

[0082] S6.3, output the final inversion result.

[0083] Once the algorithm determines that it has converged, the conductivity estimate for the current iteration step is locked. and wall thickness estimate .in, This refers to the high-precision conductivity measurement value after decoupling correction for the wall thickness effect. This refers to the wall thickness measurements acquired simultaneously. The data processing module 300 outputs the results to a human-machine interface for display, or transmits them to a host computer system for subsequent material condition assessment. Based on this final output, the conductivity... Those skilled in the art can combine specific material composition conductivity comparison curves to further deduce the hydrogen content, alloy composition ratio, or irradiation hardening degree of nuclear fuel cladding tubes, thus completing a non-destructive quantitative evaluation of the material properties of the tested object.

[0084] In this embodiment, when step S6 determines that the inversion process has not converged, the specific process of executing iterative loop control includes the following sub-steps: S7.1, execute the maximum number of iterations for circuit breaker determination.

[0085] Before proceeding to the next iteration, the data processing module 300 checks the current cumulative iteration count. This count is compared to a preset iteration threshold (e.g., set to 50). If the current iteration count has reached or exceeded this threshold, a safety termination mechanism is triggered, forcibly stopping the iteration process and outputting the current parameter estimate as an approximate solution. Simultaneously, a state flag indicating incomplete convergence is generated. This step aims to prevent algorithmic deadlocks caused by hardware failures leading to data anomalies or initial parameters deviating significantly from the true domain, ensuring the operational stability of the industrial online inspection system.

[0086] S7.2, adaptive adjustment of damping factor.

[0087] If the safety circuit breaker is not triggered, the damping factor defined in step S5.3 is adjusted according to the evolution trend of the objective function value. Dynamic adjustments are made. The specific adjustment strategy is as follows: Calculate and compare the updated objective function values. Compared with the objective function value before the update .

[0088] Scenario 1: If This indicates that the current parameter correction direction is effective and the model error is reduced. At this point, reducing the damping factor... The value (e.g., divided by a scaling factor greater than 1) Typical values This operation mathematically makes the algorithm's characteristics approximate the Gauss-Newton method, thereby achieving quadratic convergence near the extreme points using second-order curvature information and accelerating the calculation speed.

[0089] Scenario 2: If This indicates that the current parameter correction step size is too large or the direction is off, causing the model error to not decrease or even increase. In this case, increasing the damping factor is necessary. The value (e.g., multiplied by the aforementioned scaling factor) This operation mathematically makes the algorithm's characteristics approximate those of gradient descent by reducing the search step size and rotating the search direction to the negative gradient direction, thereby enhancing the algorithm's robustness in non-convex regions and preventing divergence.

[0090] S7.3 performs closed-loop recursive calculation.

[0091] After updating the damping factor and accumulating the iteration count, the process returns to step S5.3. The parameter estimates from the previous update are then used. and the adjusted damping factor Reconstruct the Jacobian matrix The new correction vector is then solved. This recursive process continues until the convergence criterion of step S6 is met, thereby achieving accurate convergence of the conductivity parameter under the constraint of prior wall thickness information.

[0092] In this embodiment, the specific process of post-processing and outputting the physical parameters obtained from the final inversion includes the following sub-steps: S8.1, lock and extract the final measurement parameters.

[0093] When step S6 determines that the iterative calculation has converged, the data processing module 300 retrieves the parameter estimates for the current moment from the calculation cache. It then retrieves the conductivity estimate corresponding to the final iteration step. Once the conductivity measurement result of the cladding tube under test is confirmed, the corresponding estimated wall thickness value will be used. The result was confirmed as a wall thickness measurement. This step, through a software logic latching mechanism, completed the transformation from abstract mathematical model parameters to specific physical measurement values.

[0094] S8.2, Perform quantitative mapping and evaluation of material state.

[0095] To intuitively characterize the material properties of nuclear fuel cladding tubes, the data processing module 300 uses a pre-set physical model to convert the aforementioned conductivity measurements into industry-standard indicators. Specifically, this includes: Unit conversion: Based on the International Electrotechnical Commission (IEC) standard, the conductivity value in Siemens per meter (S / m) is converted to the international standard conductivity for annealed copper, adapting to the conductivity performance evaluation system commonly used in industrial settings; Temperature compensation correction: Considering the physical characteristics of the conductivity of metallic materials changing with temperature, the data processing module 300 collects the surface temperature of the cladding tube under test in real time. Using the formula The conductivity obtained from the inversion at the current temperature Corrected to standard conductivity at 20°C ,in The temperature coefficient of resistance of the material (for zirconium alloys, (Use empirical or measured values). This step eliminates the impact of ambient temperature fluctuations on the consistency of measurement results.

[0096] Microscopic defect characterization: Based on a pre-established database of electrical conductivity material properties calibrated through destructive testing (e.g., the nonlinear relationship curve between the electrical conductivity of zirconium alloy clad tubes and their hydride concentration or neutron irradiation vector), a numerical interpolation algorithm is used to map the measured electrical conductivity values ​​into microscopic characteristic quantities of the material. This process utilizes the physical mechanism that metallic material electrical conductivity is highly sensitive to lattice distortion, impurity solid solution, and microcracks, enabling indirect, non-destructive, and quantitative evaluation of the aging degree, corrosion state, or mechanical damage of clad tubes.

[0097] S8.3, Interactive output and monitoring of measurement results.

[0098] The geometric wall thickness data determined in step S8.1 and the material state data generated in step S8.2 are transmitted to the display terminal through the human-machine interface. Simultaneously, the system executes quality control logic to determine the measured wall thickness value. and conductivity The data is compared with a preset process tolerance threshold. If any parameter exceeds the allowable range, the data processing module 300 generates an abnormal state identification signal, driving the alarm device or the production line sorting mechanism to operate. Furthermore, the above measurement data is associated and packaged with the current detection position coordinates and timestamp to construct a detection log containing spatiotemporal information and stored in a historical traceability database for subsequent quality trend analysis. Further, the data processing module 300 uses the axial and circumferential scanning position coordinates of the cladding tube as a spatial index, mapping the inverted wall thickness and conductivity data into color depth values ​​to construct a two-dimensional pseudo-color cloud map (C-Scan image) covering the entire length of the cladding tube under test. The image visually presents areas of thinning pipe wall thickness or abnormal conductivity (such as hydride enrichment areas) on the display terminal, assisting operators in quickly locating and interpreting non-uniform defects in the material. Based on this, the data processing module 300 further performs image segmentation algorithms (such as Otsu's adaptive thresholding method) and morphological feature extraction operations on the generated two-dimensional pseudo-color cloud image, automatically identifying and delineating the closed boundaries of abnormal parameter regions. The system calculates the equivalent area, aspect ratio, and distribution density of the abnormal region, and matches these morphological quantitative indicators with preset defect rating standards, thereby automatically generating an intelligent diagnostic report containing defect geometric features and severity levels, realizing a functional leap from visual qualitative assistance to feature quantitative analysis.

[0099] To address the identification of complex and irregularly shaped defects, the system inputs the extracted morphological feature vectors and corresponding local image regions into a pre-trained convolutional neural network or support vector machine classifier. This classifier, trained on a historical defect sample database, automatically identifies the specific category of the defect (such as mechanical scratches, dents, inclusions, or intergranular corrosion) and outputs a confidence probability, thus replacing the traditional single-threshold discrimination and constructing a defect expert system with self-learning capabilities. Furthermore, to improve the physical interpretability of defect nature determination, the expert system employs a multimodal recognition architecture based on image fusion. In addition to inputting the aforementioned image morphological features, the system also simultaneously extracts the defect center point on the complex impedance plane. The system extracts Lissajous trajectory features, particularly the impedance phase angle and amplitude ratio at characteristic frequencies. Since the phase angle is physically monotonically sensitive to defect depth, the system cascades and fuses image visual features (characterizing surface opening shape) with impedance phase features (characterizing depth extension), enabling precise differentiation between easily confused defects such as shallow surface scratches (large area, small phase angle) and deep cracks (small area, large phase angle). Furthermore, the system supports semi-transparent overlay or logical fusion of wall thickness and conductivity contour maps, distinguishing between single geometric damage (wall thickness change only) and corrosion damage accompanied by material degradation (wall thickness and conductivity change simultaneously), providing multi-dimensional evidence for the failure mechanism analysis of clad tubes.

[0100] Finally, the data processing module 300 associates and maps the fused image feature data with the unique identification code (ID) of the cladding tube under test to generate a digital quality fingerprint of the component. This fingerprint data is uploaded to the factory manufacturing execution system (MES) or digital twin database through a network interface so that the initial manufacturing status data can be retrieved for full life cycle evolution comparison analysis during the subsequent in-flight service or post-irradiation inspection (PIE) stages of the cladding tube, thereby realizing closed-loop traceability of quality data.

Claims

1. A method for measuring the wall thickness and conductivity of a clad tube based on stacked eddy currents, characterized in that, Includes the following steps: The configuration includes a stacked eddy current sensor module (100) containing multiple coaxially stacked coils along the axial direction. The reference complex self-inductance signal of each coil in an air environment and the measured complex self-inductance signal on the surface of the casing tube under test are obtained by using the sweep frequency eddy current detection module (200). The difference between the measured complex self-inductance signal and the reference complex self-inductance signal is calculated to obtain the change in the self-inductance of the complex coil. The peak frequency corresponding to the extreme point of the imaginary part of the self-inductance change of each complex coil is determined using the data processing module (300); The data processing module (300) establishes a linear fitting relationship based on the spatial stacking position of each coil and the logarithm of the peak frequency, and calculates the slope value. The data processing module (300) converts the slope value into a priori wall thickness constraint value according to the preset slope-wall thickness mapping relationship. The data processing module (300) is used to construct an analytical theoretical model of eddy current effect and a least squares optimization objective function containing conductivity parameters and wall thickness parameters. The prior constraint value of wall thickness is substituted into the least squares optimization objective function, and the conductivity parameters and wall thickness parameters are solved iteratively through a numerical optimization algorithm. The wall thickness measurement results and conductivity measurement results are output.

2. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The steps of configuring a stacked eddy current sensor module (100) comprising multiple coaxially stacked coils along the axial direction specifically include: A circular cross-section tightly wound coil with consistent geometric dimensions and electrical parameters is selected as the coil; The three coils are stacked coaxially and vertically along the axial direction to form an integrated probe structure; The vertical distance between the bottom surface of the lowest coil in the integrated probe structure and the surface of the casing tube to be tested is defined as the basic lift-off distance; Based on the axial thickness of the coil, the effective lift-off distance of the intermediate layer coil and the top layer coil relative to the surface of the casing tube to be tested is determined.

3. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The steps of acquiring the reference complex self-inductance signal of each coil in an air environment and the measured complex self-inductance signal on the surface of the casing tube under test using the swept frequency eddy current detection module (200) specifically include: Set sweep frequency excitation parameters, which cover the variation of eddy current skin depth from the full thickness of the pipe wall to the surface of the pipe wall; The stacked eddy current sensor module (100) is placed in an air environment. The impedance analyzer integrated in the swept frequency eddy current detection module (200) is used to collect the air complex impedance signal of each coil at each discrete frequency point. The air complex impedance signal contains a real resistance component and an imaginary reactance component. Based on the ratio of the air complex impedance signal to the product of the imaginary unit and the angular frequency, the reference complex self-inductance value of each coil is calculated to form the reference complex self-inductance signal. The stacked eddy current sensor module (100) is placed on the surface of the cladding tube to be tested. The impedance analyzer is used to collect the measured complex impedance signal of each coil at each discrete frequency point. The measured complex impedance signal includes a real resistance component and an imaginary reactance component. Based on the ratio of the measured complex impedance signal to the product of the imaginary unit and the angular frequency, the measured complex self-inductance value of each coil is calculated to form the measured complex self-inductance signal.

4. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The specific steps for constructing the analytical theoretical model of the eddy current effect include: Based on Maxwell's equations and electromagnetic field boundary conditions, a non-axisymmetric eddy current field analytical model applicable to tubular conductors is established as the analytical theoretical model. The vector magnetic potential equation is solved by the method of separation of variables in cylindrical coordinates. Combining the characteristics of the coil excitation source and the boundary conditions of the dielectric interface, the integral form analytical solution of the change in self-inductance of the complex coil is derived.

5. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The steps of establishing a linear fitting relationship and calculating the slope value specifically include: The physical location number of each coil in the stacked eddy current sensor module (100) is defined as the independent variable; The natural logarithm of the peak frequency corresponding to each coil is used as the dependent variable; The linear regression algorithm is used to perform fitting analysis on the independent variable and the dependent variable to establish the linear fitting function relationship; The slope term is extracted from the linear fitting function relationship and used as the slope value.

6. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The step of using the data processing module (300) to convert the slope value into a priori wall thickness constraint value according to a preset slope-wall thickness mapping relationship specifically includes: Multiple sets of forward simulation calculations are performed within a preset parameter space to establish an associated database containing the slope value, the wall thickness parameter, and the conductivity parameter; Sensitivity analysis is performed on the associated database to extract the single-value mapping relationship between the slope value and the wall thickness parameter. The single-value mapping relationship is that the slope value is sensitive to the wall thickness parameter but not sensitive to the conductivity parameter. A quantitative calculation model is established using numerical fitting or interpolation algorithms, with the slope value as the input variable and the wall thickness parameter as the output variable. The slope value obtained from the actual measurement calculation is substituted into the quantitative calculation model to calculate the estimated wall thickness of the cladding tube to be measured, and the estimated wall thickness is set as the prior constraint value of the wall thickness.

7. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The steps for constructing the least squares optimization objective function specifically include: Define the change in self-inductance of the complex coil as the observation vector; The analytical theoretical model is used as the forward calculation kernel to generate the theoretical self-induction change vector; Calculate the Euclidean distance between the theoretical self-influence change vector and the observed vector, construct the residual sum of squares objective function, and use it as the least squares optimization objective function.

8. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The step of iteratively solving for the conductivity parameter and the wall thickness parameter using a numerical optimization algorithm specifically includes: Construct a parameter vector to be solved, which includes the conductivity parameter and the wall thickness parameter; The prior wall thickness constraint value is assigned to the initial wall thickness value in the parameter vector to be solved, and the nominal conductivity of the cladding tube material to be tested is assigned to the initial conductivity value in the parameter vector to be solved. Calculate the sensitivity matrix of the least squares optimization objective function with respect to the parameter vector to be solved, and dynamically adjust the damping factor according to the current residual size; The parameter correction vector is calculated based on the sensitivity matrix and the damping factor, and the parameter vector to be solved is updated. During the iteration process, the wall thickness parameter is finely adjusted within the neighborhood of the prior wall thickness constraint value.

9. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 8, characterized in that, The step of calculating the parameter correction vector employs an improved Levenberg-Marquardt algorithm, specifically including: The Jacobian matrix is ​​calculated as the sensitivity matrix, and the Jacobian matrix represents the first-order partial derivatives of the output of the analytical theoretical model with respect to each physical parameter. By combining the Jacobian matrix, the damping factor, and the current residual vector, the parameter correction vector is obtained by solving the linear equation system. Based on the trend of the objective function value before and after the parameter update, the value of the damping factor is adaptively adjusted, and the search strategy is switched between the characteristics of the gradient descent method and the characteristics of the Gauss-Newton method.

10. The method for measuring the wall thickness and conductivity of a cladding tube based on stacked eddy currents according to claim 1, characterized in that, The steps until the preset convergence condition is met specifically include: The theoretical self-inductance change vector for the current iteration step is generated using the analytical theoretical model, and the objective function value between the theoretical self-inductance change vector and the self-inductance change of the complex coil is calculated. Calculate the magnitude of the parameter change between the current iteration step and the previous iteration step; Determine whether the objective function value is less than a preset residual threshold, or determine whether the magnitude of the parameter change is less than a preset step size threshold; If any of the above conditions are met, or the current number of iterations reaches the preset maximum limit, then the iteration is determined to be converged, and the current parameter estimate is locked and output as the final wall thickness measurement result and conductivity measurement result.

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