A method for measuring steel bars in concrete based on magnetization effect

Abstract

The present application discloses a method for measuring steel bars in concrete based on magnetization effect, which relates to the field of magnetic measurement, including: collecting magnetic field data; dividing the concrete member to be measured into a first area and a second area; establishing a magnetic dipole model in the first area; establishing a finite element model in the second field area; establishing a coupling relationship between the magnetic dipole model and the finite element model at the interface between the first area and the second area; obtaining a high-dimensional nonlinear relationship between magnetic field measurement values ​​and steel bar parameters through a numerical fitting method according to a hybrid magnetic field distribution model; obtaining prior distribution information of steel bars; establishing a likelihood function of magnetic field measurement values ​​according to the high-dimensional nonlinear relationship; using Bayes' theorem to calculate the posterior probability distribution of steel bar parameters, and obtaining the optimal estimated value and confidence interval of steel bar parameters. In view of the low measurement accuracy of steel bars in concrete in the prior art, the present application improves the measurement accuracy of concrete steel bars.

Description

Technical Field

[0001] The present application relates to the field of magnetic measurement, and in particular to a method for measuring steel bars in concrete based on magnetization effect. Background Art

[0002] Concrete is one of the most commonly used materials in civil engineering and building construction. In order to improve the bearing capacity and crack resistance of concrete structures, steel bars are usually placed inside the concrete for reinforcement. Parameters such as the diameter, number, and distribution of steel bars directly affect the mechanical properties and durability of concrete structures. Therefore, accurately measuring the parameters of steel bars inside concrete is of great significance for evaluating the safety of existing concrete structures, guiding the maintenance and repair of concrete structures, and accident detection.

[0003] At present, the measurement of steel bars in concrete mainly adopts non-destructive testing methods based on electromagnetic induction, such as eddy current method, pulse induction method and magnetic memory method. These methods measure the secondary magnetic field distribution generated by the magnetization of steel bars and invert the position and diameter of the steel bars. However, due to the influence of factors such as the complex dielectric properties of concrete, the magnetization mechanism of steel bars, and environmental interference, the existing methods have shortcomings such as blind spots, low accuracy, and poor anti-interference ability. Although some schemes have been proposed to measure steel bars in concrete based on the magnetization effect, the measurement accuracy is not high.

[0004] In the related art, for example, a method for measuring the buried depth and diameter of steel bars in concrete based on the magnetization effect is provided in Chinese patent document CN114459331A, including: taking the magnetization effect of ferromagnetic material under the action of an external magnetic field as the theoretical basis, firstly calculating the theoretical value of the spatial magnetic field of the original magnetic field of the cylindrical permanent magnet and the magnetization magnetic field of the steel bar, thereby obtaining the superposition value of the spatial magnetic field intensity under the influence of the steel bar, and then using simulation software to establish a refined model for analysis and calculation, verifying the theoretical calculation results and obtaining the relationship between the steel bar parameters and the detection values, and finally fitting the simulation values ​​according to the least square error formula, and using the fitting function formula to invert the steel bar parameters. However, this scheme only considers the magnetization effect of the steel bar under the excitation of the cylindrical permanent magnet, and establishes a simplified theoretical model. However, the distribution of steel bars inside the actual concrete is complex, resulting in a large deviation between the theoretical calculation value and the actual value, affecting the measurement accuracy. Summary of the invention

[0005] In response to the problem of low measurement accuracy of steel bars in concrete in the prior art, the present application provides a method for measuring steel bars in concrete based on the magnetization effect, which improves the measurement accuracy of concrete steel bars by dividing the far and near field areas, modeling the hybrid magnetic field distribution, and fitting the relationship between high-dimensional nonlinear magnetic field measurement values ​​and steel bar parameters.

[0006] Technical solution, the purpose of this application is achieved through the following technical solution.

[0007] The present application provides a method for measuring steel bars in concrete based on the magnetization effect, including: S1, using a magnetic sensor array arranged on the surface of the concrete component to be measured to collect magnetic field data at multiple preset positions; S2, preprocessing the collected magnetic field data; dividing the concrete component to be measured into a first area and a second area according to the preprocessed magnetic field data; wherein the first area represents the far field area; the second area represents the near field area; specifically, magnetic dipole modeling has high computational efficiency but relatively low accuracy, while finite element modeling has high accuracy but large computational complexity. Magnetic dipole modeling is used in areas far from the steel bars, while finite element modeling is used in key areas near the steel bars. By reasonably dividing the calculation area, the calculation efficiency is improved while ensuring accuracy.

[0008] S3, in the first region, based on the position range and direction of the steel bars, a magnetic dipole model is established, and the magnetic field distribution in the first region is calculated by superimposing the magnetic field contribution of each magnetic dipole; S4, in the second field region, based on the geometric information and material properties of the concrete component to be tested, a finite element model is established, and the preset range of the steel bars is meshed, and the magnetic field distribution in the second region is calculated by solving the Maxwell equations; S5, at the interface between the first region and the second region, a magnetic field continuity condition is set, and a coupling relationship between the magnetic dipole model and the finite element model is established, and a hybrid magnetic field distribution model for measuring the steel bars in the concrete to be tested is obtained by iterative solution; S6, according to the hybrid The magnetic field distribution model is combined with the steel bar parameters to obtain the high-dimensional nonlinear relationship between the magnetic field measurement value and the steel bar parameters through the numerical fitting method; wherein the steel bar parameters include the steel bar diameter; the independent variable of the high-dimensional nonlinear function is the steel bar parameter, and the dependent variable is the magnetic field measurement value; S7, based on the design drawings and construction records of the concrete component to be measured, the prior distribution information of the steel bar is obtained, and the prior distribution information includes the buried depth and diameter of the steel bar; according to the high-dimensional nonlinear relationship, the likelihood function of the magnetic field measurement value is established; the posterior probability distribution of the steel bar parameters is calculated using the Bayesian theorem, and the optimal estimate and confidence interval of the steel bar parameters are obtained through statistical analysis of the posterior probability distribution, which are output as the steel bar measurement value. Among them, the traditional inversion method is usually based on deterministic optimization to obtain a certain parameter estimate. The Bayesian inversion method regards the parameter as a random variable, and estimates the posterior probability distribution of the parameter through the Bayesian theorem, combined with prior knowledge and measurement data. In this way, not only the optimal estimate of the parameter can be obtained, but also the uncertainty of the parameter estimate can be evaluated. Through the analysis of the posterior distribution, the confidence interval of the parameter estimate can be determined, providing a quantitative basis for the reliability of the measurement results.

[0009] Specifically, Bayesian inversion is performed based on the design drawings and construction records of the concrete components to be tested, and the prior distribution information of the steel bars is obtained. The prior distribution information includes the probability distribution p(h, d) of the steel bar burial depth h and diameter d; wherein the steel bar burial depth h and diameter d obey normal distribution or uniform distribution; based on the obtained high-dimensional nonlinear relationship f(d, χ, σ) between the magnetic field measurement value B(x, y, z) and the steel bar parameters d, χ, σ, a likelihood function p(B(x, y, z)|d, χ, σ) of the magnetic field measurement value is established; wherein the magnetic field measurement value B(x, y, z) obeys a mean of f(d, χ, σ) and a variance of Normal distribution; Substitute the prior distribution p(h, d) of the steel bar depth h and diameter d and the likelihood function p(B(x, y, z)|d, χ, σ) of the magnetic field measurement value B(x, y, z) into Bayes' theorem to calculate the joint posterior probability distribution of the steel bar parameters h, d, χ, σ: p(h, d, χ, σ|B(x, y, z)) ∝ p(B(x, y, z)|d, χ, σ) × p(h, d). Numerically integrate the joint posterior probability distribution p(h, d, χ, σ|B(x, y, z)) of the steel bar parameters h, d, χ, σ to calculate the marginal posterior distribution of the steel bar depth h and diameter d:

[0010] p(h|B(x,y,z))=∫∫∫p(h,d,χ,σ|B(x,y,z))dddχdσ;

[0011] p(d|B(x,y,z))=∫∫∫p(h,d,χ,σ|B(x,y,z))dhdχdσ. The marginal posterior distributions p(h|B(x,y,z)) and p(d|B(x,y,z)) of the steel bar depth h and diameter d are statistically analyzed to obtain the maximum posterior estimation value (hMAP, dMAP), posterior mean (hMean, dMean) and confidence intervals [hMin, hMax] and [dMin, dMax] of the steel bar depth h and diameter d; the maximum posterior estimation value (hMAP, dMAP), posterior mean (hMean, dMean) and confidence intervals [hMin, hMax] and [dMin, dMax] of the steel bar depth h and diameter d are output as the estimation results of the steel bar parameters, completing the measurement of steel bars in concrete based on the magnetization effect.

[0012] The present invention uses a hybrid magnetic field distribution simulation method of a magnetic dipole model and a finite element model to establish a high-dimensional nonlinear relationship between magnetic field measurements and steel bar parameters, and combines Bayesian estimation theory to achieve high-precision measurement of key parameters such as steel bar burial depth and diameter. Compared with the existing single model method, the invention uses regional division and model coupling technology to reduce the computational complexity while ensuring near-field accuracy, and uses measurement information and prior knowledge to perform probability estimation of parameters, overcoming the uncertainty and measurement accuracy of traditional point estimation methods.

[0013] Further, S2, preprocessing the collected magnetic field data; dividing the concrete component to be tested into a first area and a second area according to the preprocessed magnetic field data; wherein the first area represents the far field area; the second area represents the near field area, including: S21, denoising the collected magnetic field data by using wavelet transform; S22, normalizing the denoised magnetic field data by using the maximum and minimum normalization method; S23, feature extraction of the normalized magnetic field data, extracting the gradient amplitude and direction of the magnetic field data, and obtaining magnetic field characteristic data; S24, according to the gradient amplitude in the magnetic field characteristic data, dividing the area with a gradient amplitude greater than a threshold into the second area, otherwise into the first area.

[0014] Further, feature extraction is performed on the normalized magnetic field data to extract characteristic parameters such as the gradient and direction of the magnetic field data to obtain magnetic field characteristic data, including: S231, calculating the gradient vector of the normalized magnetic field data in three-dimensional space by using an improved Sobel operator to obtain the gradient amplitude G mag and the gradient direction G dir ; Among them, the gradient amplitude G mag According to the magnetic field data B x , B y , B z Partial derivatives in three orthogonal directions x, y, and z Calculated, the gradient direction G dir By partial derivative The unit vector representation of the composition; S232. The gradient amplitude G is interpolated by inverse distance weighted interpolation mag Perform spatial interpolation to obtain the gradient amplitude distribution G at each position on the surface of the concrete component to be tested. mag (x, y, z); S233. Perform spatial angle transformation on the gradient direction Gdir through Euler angle transformation, and transform the gradient direction G in the local coordinate system (x', y', z') dir (x', y', z') is converted to the direction angle θ(x, y, z) in the global coordinate system (x, y, z) and Obtain the magnetic field direction distribution at each position on the surface of the concrete component to be tested; S234. According to the gradient amplitude distribution G mag (x,y,z) and magnetic field direction distribution θ(x,y,z), Construct magnetic field characteristic data for subsequent regional division.

[0015] Furthermore, the gradient vector of the normalized magnetic field data in three-dimensional space is calculated by the improved Sobel operator to obtain the gradient amplitude G mag and the gradient direction G dir, including: in three-dimensional space, according to the magnetic field data B x , B y , B z Establish the magnetic permeability μ in three orthogonal directions of x, y, and z respectively x , μ y , μ z The product of the magnetic field data μ x B x , μ y B y , μ z B z Among them, B x , B y , B z Represents the components of magnetic field data in the x, y, and z directions; magnetic permeability μ x , μ y , μ z The product μ is determined in advance or measured in real time according to the material properties and environmental conditions of the concrete component to be tested; the improved Sobel operator is used to calculate the product μ by introducing the magnetic permeability as the weight. x B x , μ y B y , μ z B z Partial derivatives in three orthogonal directions: x, y, and z According to the partial derivative Calculate the gradient magnitude G mag and the gradient direction G dir ; The calculated gradient amplitude G mag (i,j,k) and the gradient direction G dir (i, j, k) is used as the gradient feature of the normalized magnetic field data at the spatial coordinate (i, j, k) for subsequent spatial interpolation and angle transformation.

[0016] Furthermore, the calculation formula of the improved Sobel operator is as follows:

[0017]

[0018] Among them, i, j, and k represent the spatial coordinate indexes in the x, y, and z directions respectively;

[0019] Furthermore, according to the partial derivative Calculate the gradient magnitude G mag and the gradient direction G dir :

[0020]

[0021] Further, S3, in the first region, based on the position range and direction of the steel bars, a magnetic dipole model is established, and the magnetic field distribution of the first region is calculated by superimposing the magnetic field contribution of each magnetic dipole, including: according to the prior position range of the steel bars, a plurality of magnetic dipoles are arranged on the concrete surface along the axial direction of the steel bars in the first region; preferably, according to the design drawings and construction experience of the concrete component, in the first region, the steel bar position (x, y, z) and the magnetic moment direction (mx, my, mz) obey a certain probability distribution, such as uniform distribution, normal distribution, etc., and the parameters of the probability distribution are determined according to the prior information; a certain number of samples are extracted from the above probability distribution using a random sampling technique such as the Monte Carlo method to generate the position (x i ,y i ,z i ) and magnetic moment direction (mx i ,my i ,mz i ), where i is the number of the magnetic dipole; the generated magnetic dipole sample is used as the initial arrangement and substituted into the magnetic dipole model to calculate the magnetic field distribution in the first region. The position and magnetic moment direction of the magnetic dipole are generated by introducing a priori probability distribution and random sampling. At the same time, through multiple random sampling and calculation, the statistical characteristics of the magnetic field distribution in the first region can be obtained, providing richer information for the subsequent estimation of steel bar parameters.

[0022] Using the principle of spatial magnetic field superposition, the magnetic field intensity H generated by each magnetic dipole at the spatial coordinate (x, y, z) is dp (x, y, z) are superimposed to obtain the magnetic field distribution H at any position in the first region under the magnetic dipole model. 1 (x,y,z); where the magnetic field strength H generated by a single magnetic dipole at position (x,y,z) dp (x,y,z) is calculated using the analytical expression for the magnetic dipole.

[0023] Further, S4, in the second field region, based on the geometric information and material properties of the concrete component to be tested, a finite element model is established, and the preset range area of ​​the steel bar is meshed, and the magnetic field distribution of the second region is calculated by solving the Maxwell equations, including: according to the geometric information of the concrete component to be tested, including the size, shape and thickness of the steel bar protective layer, a three-dimensional geometric model of the second region is established; according to the electromagnetic parameters of the concrete and the steel bar, the material properties of the second region are set, and the electromagnetic parameters include magnetic permeability and electrical conductivity; the geometric model of the second region is meshed to generate a finite element network; on the units and nodes of the finite element mesh, the Maxwell equations are discretized to establish a partial differential equation that controls the magnetic field distribution; in combination with the geometric boundary of the second region, the finite element method is used to solve the discretized partial differential equation to obtain the magnetic vector potential A(x, y, z) at the node in the second region; according to the relationship between the magnetic vector potential A(x, y, z) and the magnetic field intensity H(x, y, z) H(x, y, z) = ▽A(x, y, z), the magnetic field distribution H at any position in the second region under the finite element model is calculated. 2 (x,y,z).

[0024] Further, S5, at the interface between the first region and the second region, a magnetic field continuity condition is set, a coupling relationship between the magnetic dipole model and the finite element model is established, and a hybrid magnetic field distribution model for measuring the steel bars in the concrete to be measured is obtained through iterative solution, including: at the interface Γ12 between the first region and the second region, a continuity condition of the magnetic field intensity is established, and the continuity condition is that the magnetic field intensity of the two regions is continuous and equal at the interface:

[0025] H 1 (x,y,z)|Γ12=H 2 (x, y, z)|Γ12, on the interface Γ12 between the first region and the second region, the curl interface condition of the magnetic field is established. The curl interface condition is that the curl of the magnetic field intensity in the normal direction of the interface between the two regions is continuous: n×[▽×H 1 (x,y,z)]|Γ12=n×[▽×H 2 (x, y, z)]|Γ12, where n is the unit normal vector of the interface Γ12; the magnetic field distribution H in the first region calculated by the magnetic dipole model 1 (x, y, z) is used as the boundary condition of the second region of the finite element model, and the magnetic field distribution H in the second region calculated by the finite element model is 2(x, y, z) is used as the source term of the magnetic dipole model. The magnetic dipole model and the finite element model are iteratively solved to make the magnetic field intensity H(x, y, z) satisfy the Maxwell equations and continuity conditions inside the two regions and at the interface. When the iterative calculation converges, the magnetic field distribution H(x, y, z) obtained by combining the magnetic dipole model and the finite element model is used as the hybrid magnetic field distribution model for the steel bar measurement in the concrete to be tested.

[0026] Further, S6, according to the hybrid magnetic field distribution model, combined with the steel bar parameters, a high-dimensional nonlinear relationship between the magnetic field measurement value and the steel bar parameters is obtained by a numerical fitting method; wherein the steel bar parameters include the steel bar diameter; the independent variable of the high-dimensional nonlinear function is the steel bar parameter, and the dependent variable is the magnetic field measurement value, including: according to the steel bar diameter and steel grade in the prior information, determine the value range of the steel bar diameter d [d min ,d max ] and discrete level Δd, generating a series of discrete diameter values ​​{d j |d j =d min +j×Δd,j=0,1,.....,M}; where M is the diameter discrete series; according to the material properties and processing technology of the steel bar, the value range and discrete level of the magnetic susceptibility χ and conductivity σ of the steel bar are determined to generate a series of discrete electromagnetic parameter combinations {(χ k ,σ k )|k=1,2,......,K}; where K is the number of electromagnetic parameter combinations; the orthogonal experimental design method is used to set the discrete steel bar diameter value {d j} and electromagnetic parameter combination {(χ k ,σ k )} to generate a series of reinforcement parameter samples {(d j ,x k ,σ k )|j=0,1,...,M;k=1,2,...,K}.

[0027] The steel bar parameter sample {(d j ,x k ,σ k )} as input, substituted into the hybrid magnetic field distribution model, and the corresponding magnetic field measurement value B at the spatial coordinate (x, y, z) was obtained through numerical simulation calculation jk (x, y, z), establish the mapping relationship between the steel bar parameter samples and the magnetic field measurement value samples; take the steel bar diameter d, magnetic susceptibility χ and conductivity σ as independent variables, and the corresponding magnetic field measurement value B(x, y, z) as dependent variable, adopt support vector machine regression method, through training sample data

[0028] {(d j ,xk ,σ k ,B jk The high-dimensional nonlinear function relationship between the magnetic field measurement values ​​and the steel bar parameters is fitted by the K-fold cross-validation method: B(x,y,z)=f(d,χ,σ)+ε, where f(d,χ,σ) is the high-dimensional nonlinear function to be fitted; ε is the fitting error; the K-fold cross-validation method is used to divide the sample data into K subsets, and each subset is used as a validation set in turn, and the remaining subsets are used as training sets. The support vector machine model is trained and validated, the model hyperparameters are optimized, and the fitting accuracy is evaluated; the support vector machine model with the highest validation accuracy is selected as the optimal model, and the high-dimensional nonlinear relationship B(x,y,z)=f(d,χ,σ) between the magnetic field measurement values ​​and the steel bar diameter, magnetic susceptibility, and conductivity is obtained for subsequent steel bar parameter estimation.

[0029] Compared with the prior art, the advantages of this application are:

[0030] The signal-to-noise ratio and feature characterization capability of the magnetic field data are improved by performing wavelet transform denoising, normalization processing and gradient feature extraction on the collected magnetic field data; the concrete is divided into far-field and near-field areas according to the gradient amplitude threshold, realizing adaptive division of the measurement area and improving modeling and calculation efficiency.

[0031] In the far field region, the magnetic dipole model is used to calculate the far field magnetic field distribution by the principle of magnetic field superposition, which reduces the modeling complexity; in the near field region, the finite element model is used to calculate the near field magnetic field distribution by solving the Maxwell equations, which improves the modeling accuracy. The division of the far and near field regions combines the advantages of the two models, taking into account both computational efficiency and accuracy.

[0032] The magnetic field continuity condition was introduced at the interface between the far and near fields, and the coupling relationship between the magnetic dipole model and the finite element model was established. By iteratively solving the magnetic field distribution, a unified hybrid magnetic field distribution model inside the concrete was obtained, realizing the seamless coupling of the far and near field magnetic fields, and ensuring the continuity and accuracy of the magnetic field distribution.

[0033] Key parameters such as steel bar diameter, magnetic susceptibility, and electrical conductivity were introduced, and parameter samples were generated through orthogonal experimental design. Numerical simulation and support vector machine regression methods were used to fit the high-dimensional nonlinear function mapping relationship between magnetic field measurement values ​​and steel bar parameters, and a mapping model from magnetic field measurement values ​​to steel bar parameters was established, which provided a basis for the quantitative estimation of steel bar parameters.

[0034] The prior distribution information of steel bar embedding is combined with the likelihood function of magnetic field measurement values, and the posterior probability distribution of steel bar parameters is calculated based on Bayes' theorem. Through statistical analysis of the posterior distribution, the optimal estimate of parameters such as steel bar diameter and its uncertainty are obtained, thus realizing the probabilistic reasoning of steel bar parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present application will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0036] Figure 1 is an exemplary flow chart of a method for measuring steel bars in concrete based on magnetization effect according to some embodiments of the present application;

[0037] Figure 2 is an exemplary flow chart of dividing the first area and the second area according to some embodiments of the present application;

[0038] Figure 3 is an exemplary flow chart for obtaining magnetic field characteristic data according to some embodiments of the present application;

[0039] Figure 4 is an exemplary flow chart of obtaining a hybrid magnetic field distribution model according to some embodiments of the present application;

[0040] Figure 5 It is an exemplary flow chart for establishing a high-dimensional nonlinear relationship between magnetic field measurement values ​​and steel bar parameters according to some embodiments of the present application. DETAILED DESCRIPTION

[0041] The method and system provided in the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0042] Example 1

[0043] Figure 1The present invention is an exemplary flow chart of a method for measuring steel bars in concrete based on magnetization effect according to some embodiments of the present application, comprising: using a magnetic sensor array arranged on the surface of a concrete member to be measured to collect magnetic field data at multiple preset positions; preprocessing the collected magnetic field data; dividing the concrete member to be measured into a first area and a second area according to the preprocessed magnetic field data; wherein the first area represents a far field area; and the second area represents a near field area; in the first area, a magnetic dipole model is established based on the position range and direction of the steel bars, and the magnetic field distribution of the first area is calculated by superimposing the magnetic field contribution of each magnetic dipole; in the second field area, a finite element model is established based on the geometric information and material properties of the concrete member to be measured, and a preset range area of ​​the steel bars is meshed, and the magnetic field distribution of the second area is calculated by solving the Maxwell equations; in the first area and the second area At the interface of the domain, the magnetic field continuity condition is set, and the coupling relationship between the magnetic dipole model and the finite element model is established. Through iterative solution, a hybrid magnetic field distribution model for measuring the steel bars in the concrete to be tested is obtained; according to the hybrid magnetic field distribution model, combined with the steel bar parameters, the high-dimensional nonlinear relationship between the magnetic field measurement value and the steel bar parameters is obtained through a numerical fitting method; wherein, the steel bar parameters include the steel bar diameter; the independent variable of the high-dimensional nonlinear function is the steel bar parameter, and the dependent variable is the magnetic field measurement value; based on the design drawings and construction records of the concrete component to be tested, the prior distribution information of the steel bar is obtained, and the prior distribution information includes the buried depth and diameter of the steel bar; according to the high-dimensional nonlinear relationship, the likelihood function of the magnetic field measurement value is established; the posterior probability distribution of the steel bar parameters is calculated using the Bayesian theorem, and the optimal estimate and confidence interval of the steel bar parameters are obtained through statistical analysis of the posterior probability distribution, which are output as the steel bar measurement value.

[0044] Specifically, a magnetic sensor array arranged on the surface of the concrete component to be tested is used to collect magnetic field data at multiple preset positions; first, the arrangement scheme of the magnetic sensor array is designed according to the size of the concrete component to be tested. The magnetic sensor array is composed of multiple highly sensitive magnetic sensors, such as Hall sensors, magnetoresistive sensors or fluxgate sensors. The number and spacing of magnetic sensors can be determined according to the required spatial resolution and sampling density. The magnetic sensor array can be arranged in a rectangular, circular or other regular shape to cover the key areas of the concrete component to be tested. Then, the magnetic sensor array is placed close to the surface of the concrete component so that the sensitive axis of the magnetic sensor is perpendicular to the surface of the component. In order to reduce the interference of the environmental magnetic field, a shielding cover can be added to the outside of the magnetic sensor. At the same time, calibration is performed to ensure that the consistency and accuracy of each magnetic sensor meet the requirements.

[0045] Next, a suitable magnetizing device, such as an electromagnetic coil or a permanent magnet, is selected to apply a magnetic field at a preset position of the concrete component to magnetize the steel bars inside the component. The selection of the magnetizing position needs to comprehensively consider factors such as the geometric dimensions of the component, the expected distribution characteristics of the steel bars, and the detection blind area. The magnetization intensity and duration should be sufficient to stimulate the steel bars to produce a significant magnetization effect, but not too large to cause permanent magnetization or hysteresis of the steel bars. Finally, the three-axis magnetic field data at each preset position is synchronously collected using a magnetic sensor array, including magnetic field intensity and direction. During the collection, attention should be paid to reducing the influence of noise sources such as vibration and electromagnetic interference. The collected data is sent to the data collector in real time through a shielded cable or a wireless transmission module, and then transferred to a computer. By controlling the switching of the magnetizing device and the scanning of the magnetic sensor array, the magnetic field distribution data at each preset position on the surface of the concrete component under different magnetization conditions can be obtained.

[0046] Figure 2 According to the exemplary flowchart of dividing the first area and the second area shown in some embodiments of the present application, the collected magnetic field data is preprocessed; according to the preprocessed magnetic field data, the concrete component to be tested is divided into the first area and the second area; wherein the first area represents the far field area; the second area represents the near field area; including: using wavelet transform to denoise the collected magnetic field data. First, select a suitable wavelet basis function and decomposition layer number to perform wavelet decomposition on the magnetic field data. Then, according to the amplitude of the wavelet coefficient, set a suitable threshold to perform soft threshold processing on the wavelet coefficient to filter out high-frequency noise components. Finally, wavelet reconstruction is performed to obtain denoised magnetic field data. Wavelet transform can effectively remove high-frequency random noise in magnetic field data while retaining useful information of steel bar magnetization signal.

[0047] The maximum and minimum normalization method is used to normalize the denoised magnetic field data. The denoised magnetic field data is recorded as B(i, j, k), where i, j, and k represent the coordinate indexes of the sampling points in the x, y, and z directions, respectively. The maximum value Bmax and the minimum value Bmin of B(i, j, k) in the entire sampling space are calculated, and then B(i, j, k) is normalized according to the following formula: Normalization processing can unify magnetic field data of different magnitudes into the range of [0, 1], which facilitates subsequent feature extraction and region division.

[0048] Figure 3 This is an exemplary flow chart for obtaining magnetic field characteristic data according to some embodiments of the present application, performing feature extraction on the normalized magnetic field data, extracting the gradient amplitude and direction of the magnetic field data, and obtaining magnetic field characteristic data. In three-dimensional space, according to the magnetic field data B x , B y , B z Establish the magnetic permeability μ in the three orthogonal directions of x, y, and z respectivelyx , μ y , μ z The product of the magnetic field data μ x B x , μ y B y , μ z B z . Magnetic field data B x , B y , B z It represents the components of the magnetic field in the x, y, and z directions, and can be obtained by measuring with a three-axis magnetic sensor. x , μ y , μ z It is predetermined or measured in real time based on the material properties of the concrete component to be tested (such as the type, size, and arrangement of the steel bars) and environmental conditions (such as temperature and humidity), reflecting the degree of influence of the concrete medium on the magnetic field.

[0049] Build the product μ x B x , μ y B y , μ z B z The purpose of this method is to introduce the influence of magnetic permeability into the gradient calculation to more accurately reflect the spatial variation characteristics of the magnetization effect of the steel bar. Then, the improved Sobel operator is used to calculate μ x B x , μ y B y , μ z B z The partial derivatives in the x, y, and z directions. Compared with the traditional Sobel operator, the improved Sobel operator takes the magnetic permeability μ into account during the calculation process. x , μ y , μ z The spatial variation of is calculated as follows:

[0050]

[0051] Among them, i, j, and k represent the spatial coordinate indexes in the x, y, and z directions respectively.

[0052] According to the partial derivative The normalized magnetic field data at the spatial coordinates (i, j, k) can be calculated as mag (i,j,k) and the unit gradient direction vector G dir (i,j,k), as the gradient feature of the point:

[0053]

[0054] The gradient amplitude Gmag(i, j, k) reflects the intensity of the change of the magnetic field intensity at the spatial coordinate (i, j, k). The larger the gradient amplitude, the greater the rate of change of the magnetic field intensity at that location, and the more obvious the magnetization effect of the steel bar. The unit gradient direction vector Gdir(i, j, k) represents the direction of the change of the magnetic field intensity, and its components Corresponding to the rate of change in the x, y, and z directions respectively.

[0055] Since the distribution of measuring points in the actual sampling process is usually uneven and discrete, in order to obtain the gradient amplitude at any position on the surface of the concrete component to be measured, it is necessary to calculate the gradient amplitude G of the discrete sampling points. mag (i, j, k) for spatial interpolation. A commonly used interpolation method is inverse distance weighted interpolation, the basic idea of ​​which is that the gradient amplitude of the interpolation point can be obtained by weighted average of the gradient amplitudes of the sampling points in its neighborhood, and the closer the distance, the greater the weight of the sampling point. Suppose the coordinates of the interpolation point are (x, y, z), then its gradient amplitude G mag (x,y,z) can be calculated by the following formula: Where n is the number of sampling points involved in interpolation, wi is the weight of the i-th sampling point, which is related to its Euclidean distance d(x, y, z; xi, yi, zi) to the point to be interpolated: p is the distance power parameter, which is usually set to 2. Through inverse distance weighted interpolation, the gradient amplitude distribution G at each position on the surface of the concrete component to be tested can be obtained. mag (x,y,z).

[0056] Gradient direction G dir (i, j, k) reflects the direction of the magnetic field in the local coordinate system (x', y', z'), where x', y', z' are orthogonal coordinate systems established along the three axes of the magnetic sensor with the sampling point (i, j, k) as the origin. In order to unify the representation and correspond to the overall geometric shape of the component to be tested, it is necessary to convert the gradient direction in the local coordinate system into the direction angle θ(x, y, z) and This coordinate transformation can be achieved through Euler angle transformation. The basic principle is: by rotating the three coordinate axes of the local coordinate system (x', y', z') in sequence, it coincides with the global coordinate system (x, y, z). Assume that the rotation angle around the z' axis is α, the rotation angle around the y' axis is β, and the rotation angle around the x' axis is γ, then the corresponding transformation matrix R (α, β, γ) can be expressed as:

[0057] R(α,β,γ)=R z (α)×R y (β)×R x (γ); where R x (γ), Ry (β), R z (α) are rotation matrices for rotating around the x', y', and z' axes by angles γ, β, and α, respectively. The specific form is:

[0058]

[0059] Multiply the unit gradient direction vector Gdir(x', y', z') in the local coordinate system by the transformation matrix R(α, β, γ) to get the gradient direction vector in the global coordinate system:

[0060]

[0061] Furthermore, the direction angles θ(x, y, z) and φ(x, y, z) in the global coordinate system can be obtained according to the above components:

[0062]

[0063] Among them, θ is the angle between the gradient direction vector and the z-axis, is the angle between the projection of the gradient direction vector on the xy plane and the x-axis. Through the Euler angle transformation, the local gradient direction can be uniformly converted into the direction angle in the global coordinate system to obtain the magnetic field direction distribution θ(x, y, z) and The gradient amplitude distribution G obtained by inverse distance weighted interpolation mag (x, y, z) and the magnetic field direction distribution θ(x, y, z) obtained by transforming the Euler angle, By combining the gradient amplitude and magnetic field direction information at each position on the surface of the concrete component, the complete magnetic field characteristic data can be constructed. This characteristic data combines the gradient amplitude and magnetic field direction information at each position on the surface of the concrete component, quantitatively describes the spatial distribution characteristics of the magnetization effect of the steel bar, and can be used for subsequent regional division and defect identification. According to the gradient amplitude in the magnetic field characteristic data, the near field area and the far field area are divided. First, the gradient amplitude distribution G is extracted from the obtained magnetic field characteristic data. mag(x, y, z), the distribution reflects the intensity of the change of magnetic field intensity at each position on the surface of the concrete component to be tested. Generally speaking, the area close to the steel bar is more obviously affected by the magnetization effect of the steel bar, and its gradient amplitude is larger; while the magnetic field intensity in the area far from the steel bar changes relatively slowly, and the gradient amplitude is smaller. Then, a gradient amplitude threshold Gth is set, and the area with a gradient amplitude greater than the threshold is divided into the second area, that is, the near field area; the remaining areas with a gradient amplitude less than or equal to the threshold are divided into the first area, that is, the far field area. In this way, the entire surface of the concrete component to be tested is divided into two different areas. The threshold Gth can be pre-determined or adaptively adjusted in the following ways: Empirical formula: Based on a large amount of experimental data and engineering experience, an empirical formula between the threshold and parameters such as the size of the concrete component, the diameter of the steel bar, and the spacing between the steel bars is summarized, and the threshold is calculated using this formula. Simulation analysis: Using numerical simulation methods such as finite element, the electromagnetic field simulation of reinforced concrete components under different parameter conditions is carried out to analyze the spatial distribution law of the magnetic field intensity, and then determine the appropriate threshold. Adaptive adjustment: According to the measured magnetic field data, the statistical distribution characteristics of the gradient amplitude (such as histogram, quantile, etc.) are analyzed, and the threshold is adaptively adjusted to meet the specific near-field area ratio or signal-to-noise ratio requirements.

[0064] The magnetic field distribution model of the first region is established according to the prior position range of the steel bars, including: first, according to the design drawings, construction records and other prior information of the concrete component to be tested, the approximate position range of the steel bars, that is, the range of the first region (far field region) is determined. In actual engineering, the steel bars in the concrete components are usually arranged in rows along a certain direction, and the spacing is relatively fixed, so it can be approximately considered that the axes of the steel bars in the first region are parallel and evenly spaced.

[0065] Then, multiple discrete points are selected along the axial direction of the steel bar in the first region, and these discrete points are used as the positions of magnetic dipoles. A magnetic dipole is an idealized magnetic source model consisting of two magnetic poles of equal size and opposite direction, and is often used to describe the magnetization effect of slender objects (such as steel bars). Simplifying the steel bar into a series of magnetic dipoles distributed along its axis can better approximate the magnetic field distribution of the steel bar as a whole. For each magnetic dipole, the analytical expression in classical electromagnetic theory can be used to calculate the magnetic field intensity Hdp(x, y, z) generated at any position (x, y, z) in space. Assume that the position of the i-th magnetic dipole is (xi, yi, zi), the magnitude of its magnetic moment is mi, and the direction of its magnetic moment is the unit vector ei along the axis of the steel bar. According to the magnetic field distribution formula of the magnetic dipole, the magnetic field intensity H generated at the position (x, y, z) is dpi (x, y, z) can be expressed as:, where μ 0 is the vacuum magnetic permeability, ri is the position vector of the position (x, y, z) relative to the magnetic dipole position (xi, yi, zi), that is, ri =(xx i ,yy i ,zz i ),|r i | is the modulus length of ri, Represents vector dot product.

[0066] By vector superposition of the magnetic field intensities generated by all magnetic dipoles at positions (x, y, z), the magnetic field distribution H at any position in the first region under the magnetic dipole model can be obtained: 1 (x,y,z):

[0067] H 1 (x,y,z)=∑H dpi (x,y,z),i=1,2,.....,N, where N is the total number of magnetic dipoles in the first region. This magnetic field superposition method based on the analytical expression of magnetic dipoles can quickly calculate the theoretical magnetic field distribution at any position in the first region, providing a reference for subsequent defect identification. Compared with magnetic field modeling based on numerical methods such as finite element, this method has higher computational efficiency and does not rely on meshing, making it suitable for real-time or rapid detection.

[0068] The finite element method is used to establish the magnetic field distribution model of the second region. First, the geometric information of the component is obtained according to the design drawings of the concrete component to be tested, physical measurements, etc., including the external size and shape of the component and the thickness of the protective layer of the internal steel bars. Using this geometric information, a three-dimensional geometric model of the second region (near field region) is established on the computer. In the modeling process, it is necessary to reasonably simplify the detailed features of the component and extract the main geometric parameters to facilitate the subsequent meshing and calculation.

[0069] Then, according to the material properties of concrete and steel bars, the corresponding electromagnetic parameters are set for the geometric model of the second region. The key parameters of concrete and steel bars in the electromagnetic field include magnetic permeability and electrical conductivity. Magnetic permeability reflects the magnetization ability of the material under an external magnetic field, and the magnetic permeability of steel bars is usually much greater than that of concrete; electrical conductivity reflects the material's ability to conduct current, and the electrical conductivity of steel bars is also much greater than that of concrete. In the finite element model, steel bars and concrete can be set as different material property areas based on these parameter differences. For the setting of steel bar material properties, the nonlinear magnetization characteristics of steel bars need to be considered. The magnetic permeability of steel bars is not a constant, but a nonlinear function that changes with the strength of the external magnetic field. In order to improve the calculation accuracy, the nonlinear magnetization characteristics of steel bars can be introduced into the finite element model by using methods such as piecewise linearization and BH curve fitting. For the setting of concrete material properties, since its magnetic permeability and electrical conductivity are much smaller than those of steel bars, it can be approximated as an isotropic linear material to simplify the calculation. However, when concrete has defects such as cracks and voids, its local electromagnetic parameters may change significantly. In order to consider this situation, some possible defect areas can be preset in the geometric model and the corresponding electromagnetic parameters can be set according to the defect type.

[0070] After completing the geometric modeling and setting the material properties, the geometric model of the second region needs to be meshed to generate a discretized mesh suitable for finite element calculation. The purpose of meshing is to discretize the continuous geometric region into a finite number of units and nodes so that the partial differential equations controlling the field distribution can be approximately solved on each unit. The effect of meshing directly affects the accuracy and efficiency of the calculation results. In the second region, due to the drastic change of the magnetic field near the steel bars, it is necessary to perform dense meshing around the steel bars; while in the area far away from the steel bars, the magnetic field changes relatively slowly, and a relatively sparse mesh can be used. In addition, the type and shape of the mesh unit also need to be selected according to the characteristics of the problem to be solved. For example, tetrahedral units are more suitable for describing complex geometric shapes than hexahedral units, but the calculation accuracy is relatively low. After the mesh is generated, the Maxwell equations controlling the magnetic field distribution can be approximately discretized on each unit and node. The Maxwell equations are the basic equations that describe the spatiotemporal evolution of the electromagnetic field, including Gauss's law, Ampere's loop law, Faraday's law of electromagnetic induction, and magnetic Gauss's law.

[0071] Under quasi-static conditions, the displacement current can be neglected and Maxwell's equations simplify to: ▽×B(x,y,z)=J(x,y,z); where B(x,y,z) is the magnetic induction intensity, H(x,y,z) is the magnetic field intensity, and J(x,y,z) is the current density. and ▽× represent the divergence and curl operators, respectively. In order to facilitate finite element solution, the magnetic vector potential A(x, y, z) is usually introduced so that B(x, y, z) = ▽×A(x, y, z). Substituting into Maxwell's equations and considering the material constitutive relations B(x, y, z) = μH(x, y, z), J(x, y, z) = σE(x, y, z), we can obtain the elliptic partial differential equation for the magnetic vector potential: Where μ is the magnetic permeability, σ is the electrical conductivity, and J s (x, y, z) is the source current density and t is the time.

[0072] In the cells and nodes of the grid, the magnetic vector potential A(x, y, z) is approximated by shape functions and substituted into the above partial differential equations to obtain a discretized set of algebraic equations. Combined with the geometric boundary conditions of the second region, the algebraic equations are transformed into linear matrix equations using weighted residual methods such as the Galerkin method and the least squares method, and then solved using numerical algorithms such as Gaussian elimination and conjugate gradients to finally obtain the numerical solution of the magnetic vector potential at each node. According to the relationship between the magnetic vector potential and the magnetic field intensity H(x, y, z) = ▽ × A(x, y, z), the node magnetic vector potential is numerically differentiated and interpolated to obtain the magnetic field distribution H at any position in the second region. 2 (x, y, z). This finite element method-based magnetic field modeling can more accurately consider the complex geometric shape of concrete components and the nonlinear magnetization characteristics of steel bars, calculate the refined magnetic field distribution in the near field area, and provide an important basis for subsequent defect identification.

[0073] Figure 4 This is an exemplary flow chart for obtaining a hybrid magnetic field distribution model according to some embodiments of the present application. By coupling the magnetic dipole analytical model of the first region and the finite element numerical model of the second region, a hybrid magnetic field distribution model for measuring steel bars in a concrete component is established. First, at the interface Γ12 between the first region (far field region) and the second region (near field region), a continuity condition of the magnetic field intensity H(x, y, z) needs to be established. The continuity condition requires that the magnetic field intensity of the two regions is continuous and equal at the interface, that is: H 1 (x,y,z)|Γ12=H 2 (x,y,z)|Γ12; where H 1 (x, y, z) is the magnetic field distribution in the first region calculated by the magnetic dipole model, H 2(x, y, z) is the magnetic field distribution of the second region calculated by the finite element model, and Γ12 represents the value taken on the interface Γ12. This continuity condition reflects the continuous characteristics of the magnetic field as a macroscopic physical quantity in space, and is a basic requirement to ensure the physical rationality of the magnetic field distribution model. In actual calculations, the continuity condition can be implemented as a boundary condition or constraint condition of the two regional models.

[0074] Secondly, on the interface Γ12 between the first region and the second region, it is also necessary to establish the curl interface condition of the magnetic field intensity H(x, y, z). The curl interface condition requires that the curl of the magnetic field intensity in the normal direction of the interface between the two regions is continuous, that is: n×[▽×H 1 (x,y,z)]|Γ12=n×[▽×H 2 (x, y, z)]|Γ12; where n is the unit normal vector of the interface Γ12, and ▽× represents the curl operator. This curl interface condition reflects the passivity of the magnetic induction intensity B(x, y, z) at the interface, and is a necessary condition for the magnetic field to satisfy Gauss's law. In actual calculations, the curl interface condition can be converted into the boundary condition of the magnetic vector potential A(x, y, z) to achieve this. Then, the magnetic field distribution H in the first region calculated by the magnetic dipole model is 1 (x, y, z) is used as the boundary condition of the second region of the finite element model, and the magnetic field distribution H in the second region calculated by the finite element model is 2 (x, y, z) is used as the source term of the magnetic dipole model. By iteratively solving the models of the two regions, the magnetic field intensity H(x, y, z) satisfies Maxwell's equations and continuity conditions both inside the region and at the interface.

[0075] Specifically, in each iterative calculation, the magnetic field distribution H in the first region is fixed. 1 (x, y, z), and use it as the Dirichlet boundary condition of the finite element model of the second region. Solve the finite element model to obtain the magnetic field distribution H in the second region. 2 (x, y, z); then, the magnetic field distribution in the second region H 2 The normal derivative of (x, y, z) is used as the source term of the magnetic dipole model to recalculate the magnetic field distribution H in the first region 1 (x, y, z). Repeat this process for multiple iterations until the magnetic field distributions of the two regions meet the continuity condition at the interface and satisfy their respective control equations inside the regions, i.e., convergence is achieved. In actual calculations, appropriate convergence criteria can be set, such as the change in magnetic field intensity between two iterative calculations is less than a certain threshold, or the number of iterations reaches a preset maximum value.

[0076] Finally, when the iterative calculation converges, the magnetic field distribution H in the first region obtained by combining the magnetic dipole model is 1(x, y, z) and the magnetic field distribution H in the second region obtained by the finite element model 2 (x, y, z), the hybrid magnetic field distribution model H(x, y, z) of the steel bar measurement in the entire concrete component to be tested can be obtained. This hybrid modeling method that combines the magnetic dipole analytical model with the finite element numerical model combines the advantages of the two models. It can not only quickly calculate the far-field magnetic field distribution of large-scale components, but also finely analyze the near-field magnetic field details of key parts, which can significantly improve the efficiency and accuracy of magnetic field forward calculation.

[0077] Figure 5 This is an exemplary flow chart of establishing a high-dimensional nonlinear relationship between magnetic field measurement values ​​and steel bar parameters according to some embodiments of the present application. By constructing a high-dimensional nonlinear relationship model between magnetic field measurement values ​​and steel bar parameters, the steel bar diameter, magnetic susceptibility and conductivity estimation are realized. First, according to the steel bar diameter and steel grade in the prior information, the value range of the steel bar diameter d is determined [d min ,d max ] and discrete level Δd, generating a series of discrete diameter values ​​{d j |d j =d min +j×Δd,j=0,1,.....,M}. Among them, d min and d max are the minimum and maximum values ​​of the steel bar diameter, Δd is the step size of the diameter discretization, and M is the number of diameter discretization levels. For example, for a steel bar with a diameter of 18 mm and a steel grade of HRB400 in the prior information, the diameter value range can be set to [16 mm, 20 mm], and the discrete step size can be set to 0.5 mm, then a diameter value sequence of {16, 16.5, 17, 17.5, 18, 18.5, 19, 19.5, 20} can be generated, with a total of 9 discrete levels.

[0078] Then, according to the material properties and processing technology of the steel bar, the value range and discrete level of the magnetic susceptibility χ and electrical conductivity σ of the steel bar are determined to generate a series of discrete electromagnetic parameter combinations {(χ k ,σ k )|k=1,2,......,K}. Among them, χ is the magnetic susceptibility of the steel bar, σ is the electrical conductivity of the steel bar, and K is the number of electromagnetic parameter combinations. For example, for ordinary carbon steel materials, the value range of the magnetic susceptibility χ can be set to [50, 300], and the value range of the electrical conductivity σ can be set to [5×10^6, 6×10^6]. According to 5 and 3 levels of discretization respectively, the electromagnetic parameter combination sequence {(50, 5×10^6), (50, 5.5×10^6), (50, 6×10^6), ..., (300, 6×10^6)} can be generated, with a total of 15 combinations.

[0079] Then, the orthogonal experimental design method is used to combine the discrete steel bar diameter value {dj} and the electromagnetic parameter combination {(χk, σk)} to generate a series of steel bar parameter samples.

[0080] {(d j ,x k ,σ k )|j=0,1,......,M;k=1,2,.....,K}. Orthogonal experimental design can reduce the number of experiments while ensuring the uniform distribution of samples in the parameter space, thereby improving the efficiency and reliability of subsequent model training. For example, using the L18 (2^1×3^7) orthogonal table, the above 9 levels of diameter values ​​and 15 electromagnetic parameter combinations can be arranged into 18 groups of experiments, covering different level combinations of each parameter, and generating 18 steel bar parameter samples.

[0081] The steel bar parameter sample {(d j ,x k ,σ k )} as input, substitute into the hybrid magnetic field distribution model constructed in step S5, and obtain the magnetic field measurement value B corresponding to the spatial coordinate (x, y, z) through numerical simulation calculation jk (x, y, z), establish the mapping relationship between the steel bar parameter sample and the magnetic field measurement value sample. Among them, the magnetic field measurement value B jk (x, y, z) can be the component value of physical quantities such as magnetic induction intensity and magnetic field intensity at a certain point or line in space. Numerical simulation calculations can use finite element method, boundary element method and other numerical methods to solve Maxwell's equations and obtain discrete solutions to magnetic field distribution.

[0082] With the steel bar diameter d, magnetic susceptibility χ and conductivity σ as independent variables and the corresponding magnetic field measurement value B(x, y, z) as dependent variable, the support vector machine regression method is used to train the sample data {(d j ,x k ,σ k ,B jk The high-dimensional nonlinear function relationship between the magnetic field measurement value and the steel bar parameters is fitted as follows: B(x,y,z)=f(d,χ,σ)+ε, where f(d,χ,σ) is the high-dimensional nonlinear function to be fitted and ε is the fitting error.

[0083] Support vector machine regression is a nonlinear regression method based on statistical learning theory. It maps low-dimensional input space to high-dimensional feature space by finding the optimal classification hyperplane, and realizes the modeling of complex nonlinear relationships. Compared with traditional methods such as polynomial regression and neural network, support vector machine regression has the advantages of global optimization, strong generalization ability, and less dimensionality disaster. In the training process of the support vector machine regression model, the K-fold cross-validation method is used to divide the sample data into K subsets, and each subset is used as a validation set in turn, and the remaining subsets are used as training sets. The model is trained and validated, the model hyperparameters are optimized, and the fitting accuracy is evaluated. Among them, K-fold cross-validation can make full use of limited sample data, reduce the risk of model overfitting, and improve the accuracy of the evaluation of the model's generalization ability. Through grid search, random search and other methods, the hyperparameters of the support vector machine model such as kernel function type, kernel function parameters, and penalty factor are optimized to improve the fitting accuracy and robustness of the model.

[0084] Finally, the support vector machine model with the highest K-fold cross-validation accuracy is selected as the optimal model, and the high-dimensional nonlinear relationship B(x,y,z)=f(d,χ,σ) between the magnetic field measurement value and the steel bar diameter, magnetic susceptibility, and electrical conductivity is obtained for subsequent steel bar parameter estimation. The trained support vector machine model is used to quickly invert the magnetic field measurement value of the concrete component to be tested, estimate the diameter, magnetic susceptibility and electrical conductivity parameters of the steel bar, and realize quantitative non-destructive testing of steel bars. Specifically, the magnetic field measurement value B(x,y,z) of the component to be tested is input into the support vector machine model, and the steel bar parameters (d,χ,σ) corresponding to the magnetic field measurement value are obtained through model inversion calculation, thereby realizing the quantitative characterization of the steel bar diameter and material properties. This steel bar parameter estimation method based on support vector machine regression can effectively overcome the complex coupling effect and nonlinear interference in the steel bar magnetic measurement process by constructing a nonlinear relationship model between the magnetic field measurement value and the steel bar parameters, and improve the accuracy and reliability of parameter estimation.

[0085] S7, according to the design drawings and construction records of the concrete component to be measured, obtain the prior distribution information of the steel bar, the prior distribution information includes the probability distribution p(h, d) of the steel bar buried depth h and diameter d; wherein the steel bar buried depth h and diameter d obey normal distribution or uniform distribution; according to the high-dimensional nonlinear relationship f(d, χ, σ) between the obtained magnetic field measurement value B(x, y, z) and the steel bar parameters d, χ, σ, establish the likelihood function p(B(x, y, z)|d, χ, σ) of the magnetic field measurement value. The maximum a posteriori estimate (hMAP, dMAP), the a posteriori mean (hMean, dMean) and the confidence interval [hMin, hMax] and [dMin, dMax] of the steel bar buried depth h and diameter d are output as the estimation results of the steel bar parameters, and the steel bar measurement in concrete based on the magnetization effect is completed.

[0086] Example 2

[0087] A certain project needs to inspect the steel bars of a concrete beam component. The beam component is 6m long, 0.4m wide and 0.6m high. According to the design drawings, the beam component uses C40 concrete, the longitudinal force reinforcement is 4 HRB400 grade hot-rolled ribbed steel bars with a diameter of 25mm, and the thickness of the concrete protective layer is 30mm. An 8×6 magnetic sensor array is arranged on the surface of a reinforced concrete beam component with a length of 6m and a cross-sectional size of 0.4m×0.6m. The sensor array covers a range of 5.6m×0.36m, the size of a single sensor is 0.04m×0.04m, and the distance between adjacent sensors is 0.1m. The sensor array is used to collect the three-axis magnetic field data Bx(i, j), By(i, j), and Bz(i, j) at different positions of the beam component, where i=8, j=6, and a total of 48×3=144 magnetic field data are obtained.

[0088] The collected magnetic field data were preprocessed: the 5-level db4 wavelet was used to perform wavelet denoising on Bx, By, and Bz respectively. The wavelet coefficient threshold was set to 0.3 times the maximum wavelet coefficient of each. Smooth magnetic field data were obtained after denoising. The maximum and minimum values ​​of the denoised Bx, By, and Bz were normalized respectively, and the data were mapped to the interval [0, 1] to eliminate the dimension effect. The improved Sobel operator with anisotropic permeability was used to calculate the gradient amplitude Gmag(i, j) and gradient direction Gdir(i, j) of the normalized Bx, By, and Bz respectively. The improved Sobel operator uses the vacuum permeability μ0 as the weight in the x and y directions, and 0.5μ0 as the weight in the z direction. The gradient amplitude distribution Gmag(x, y, z) of the entire beam component surface was obtained by inverse distance weighted interpolation, and the power parameter p=1.5 was used for interpolation. Perform Euler angle transformation on Gdir(i, j) to obtain the magnetic field direction distribution angle θ(x, y, z) at each position on the beam surface. (6) Put Gmag(x, y, z), θ(x, y, z), Combined into magnetic field characteristic data. Take Gmax as the maximum value of Gmag(x, y, z), take 0.25Gmax as the threshold, define the area where Gmag(x, y, z)>0.25Gmax as the near field area (the second area), and the rest of the area as the far field area (the first area).

[0089] The calculation results show that the magnetic field gradient amplitude in the near field area within 0.2m from the surface of the beam component is large, and the magnetic field lines are severely bent, which is the main impact area of ​​the steel bars and defects. The magnetic field gradient amplitude in the far field area is small, the magnetic field lines are nearly parallel, and the defects are less affected. Further analysis found that the magnetic field gradient amplitude at certain positions in the near field area showed abnormal mutations, and combined with the magnetic field direction, it can be judged that there is a steel bar fracture defect at this location. In the far field area, the local magnetic field gradient amplitude was also observed to increase, and combined with the magnetic field direction, it was judged that there was a steel bar corrosion and thinning defect at this location. Finally, through the defect location algorithm, it was determined that the steel bar fracture defect was located at 0.1m from the bottom of the beam in the middle of the beam span, and the fracture length was about 0.08m. The corrosion and thinning defect was located at the end of the beam 0.15m away from the top of the beam, with a corrosion area of ​​about 0.05m^2 and a maximum corrosion depth of 0.02m.

[0090] In the far field region, 10 magnetic dipoles are arranged longitudinally along the beam component, with a distance of 0.6m between adjacent dipoles. The dipole moment direction of the magnetic dipole is parallel to the axis of the steel bar, and the magnitude is estimated based on the theoretical magnetization intensity of the steel bar, with a value of m = 1.2 × 10^6A·m^2. Using the magnetic dipole analytical model, the spatial magnetic field distribution H1 (x, y, z) generated by the superposition of 10 dipoles is calculated. The calculation results show that the magnetic field intensity in the far field is in the range of 0.5 to 2.5A / m, the magnetic lines of force are approximately parallel, and the direction is consistent with the axis of the steel bar.

[0091] A geometric model was established for the near-field region. The model size was consistent with the actual beam component, with a length of 6m and a cross-sectional size of 0.4m×0.6m. The electromagnetic parameters of concrete and steel bars were imported into the model. The relative magnetic permeability μr=1 and the electrical conductivity σ=0.01S / m were taken for concrete; the relative magnetic permeability μr=300 and the electrical conductivity σ=6×10^6S / m were taken for steel bars. According to the estimated position of the steel bars, 9 scanning lines were generated along the length of the beam in the near-field region model, with a scanning line spacing of 0.05m. Scanning sections with a spacing of 0.1m were generated along each scanning line, and a total of 450 scanning sections were obtained. Tetrahedral meshing was performed on each scanning section, and the mesh size was adaptively adjusted according to local characteristics, taking 2mm near the steel bars and 5mm away from the steel bars. About 1.2 million tetrahedral units and 250,000 nodes were generated in the entire near-field region. At the mesh units and nodes, the Maxwell equations of static magnetic field were discretized, and the Coulomb specification was used to determine the unique solution. The finite element method was used to solve the discrete equations, with a total of 86 iterations, and the final residual was <1e-6, reaching the convergence condition. The magnetic vector potential distribution A2(x, y, z) in the near field was calculated, and the magnetic induction intensity B2(x, y, z) was calculated by B=▽×A, and the magnetic field intensity H2(x, y, z) was calculated by H2=B2 / μ0-M, where M is the magnetization intensity of the steel bar.

[0092] The magnetic field intensity H1 (x, y, z) on the boundary of the far field is used as the first boundary condition of the near field, and the magnetic field intensity H2 (x, y, z) on the boundary of the near field is used as the charge source term of the far field, and the Maxwell equations of the two regions are iteratively solved. After 18 iterations, the relative residual of the magnetic field intensity on both sides of the interface is <1e-3, and it is considered that the coupling calculation results of the two regions have converged. Finally, the hybrid magnetic field distribution H (x, y, z) of the entire region is obtained. The hybrid magnetic field H (x, y, z) is analyzed, and it is found that the magnetic field intensity distribution in the far field is in good agreement with the initial dipole model calculation results, indicating that the far field is reasonable. In the near field, the magnetic field intensity decays rapidly within 0.01m near the steel bar, and the maximum value reaches 50A / m, and the magnetic lines are severely bent, with an obvious magneto-induced elongation effect, which is consistent with the finite element calculation results. Further comparative analysis of the simulated magnetic field and the measured magnetic field in the near field shows that the spatial distribution morphology and numerical consistency of the two are high, and the relative error is within 10%, which proves the accuracy of the hybrid magnetic field model. However, near the defect, the gradient of the simulated magnetic field change is smaller than the measured magnetic field, indicating that the size and properties of the actual defect are somewhat different from the simulation model and need to be further optimized. Finally, the hybrid magnetic field model is embedded in the defect quantitative identification algorithm. By repeatedly adjusting the defect parameters to make the simulated magnetic field match the measured magnetic field as much as possible, the optimal estimated parameters of the defect are obtained. The results show that the length of the broken steel bar segment is 0.086m, and the average thinning of the corroded steel bar is 12.8%, which is basically consistent with the destructive detection results. The quantitative identification accuracy meets the requirements of engineering applications.

[0093] The diameter of the steel bar varies in the range of 20 to 32 mm, with a discrete interval of 2 mm, and the number of diameter discrete levels M = 6. The relative magnetic permeability of the steel bar is in the range of 200 to 400 and takes 5 levels: {200, 250, 300, 350, 400}; the electrical conductivity of the steel bar is in the range of 5 to 7MS / m and takes 5 levels: {5.0, 5.5, 6.0, 6.5, 7.0}, so the number of electromagnetic parameter combinations K = 5×5 = 25.

[0094] The orthogonal table L50 (2^1×5^6) was used to generate 50 representative combinations of steel bar parameters. Each parameter set includes 1 diameter value and 1 electromagnetic parameter combination, for a total of 50×(1+2)=150 parameters. These 50 parameter sets were substituted into the hybrid magnetic field model to calculate the corresponding magnetic field distribution data, and each set of data contained 48×3=144 magnetic field intensity values.

[0095] Thirty groups of data were randomly selected as SVM training sets, and the remaining 20 groups were used as validation sets. A 5-fold cross-validation was performed on the training set data to optimize the kernel function type and hyperparameters of the SVM model. The results show that the regression fitting effect of the model is optimal when the RBF kernel function is combined with the hyperparameters C=100 and g=0.1. In the training set, the determination coefficient R^2=0.95; in the validation set, the determination coefficient R^2=0.92. This result proves that the SVM model can accurately characterize the nonlinear correspondence between the magnetic field measurement value and the steel bar diameter, magnetic permeability, and electrical conductivity.

[0096] According to the design drawings, the diameters of the four longitudinal stress-bearing steel bars follow the normal distribution N(25, 1), and the thickness of the protective layer follows the normal distribution N(30, 2). The probability density function of the normal distribution is used to calculate the prior probability distribution of the steel bar diameter in the range of 2032 mm and the protective layer thickness in the range of 2634 mm. The measured magnetic field data was collected using an 8×6 magnetic sensor array arranged on the surface of the beam component, and a total of 144 magnetic field intensity measurements were obtained. These 144 measurements were input into the trained SVM model to calculate the likelihood probability of the steel bar diameter and electromagnetic parameters corresponding to each measurement value.

[0097] Combining the prior probability and likelihood probability, the Bayesian inference formula is used to calculate the posterior probability distribution of the steel bar diameter and the protective layer thickness. The mathematical expectation of the posterior distribution is taken as the optimal estimate of the steel bar diameter and the protective layer thickness, and the 95% confidence interval is calculated. The final measurement results show that the average diameters of the four longitudinal force-bearing steel bars are 24.6mm, 25.2mm, 24.9mm, and 25.5mm, respectively. The overall average is 24.8mm, and the standard deviation is 1.2mm, which is basically consistent with the design value of 25mm. The average height of the center of the four steel bars from the bottom of the beam is 33.2mm, 34.5mm, 33.7mm, and 35.1mm, respectively. The overall average is 34.1mm, and the standard deviation is 1.8mm, which meets the specification requirements for the design protective layer thickness of 30mm.

[0098] Further analysis of the 95% confidence interval shows that the confidence interval radius of the steel bar diameter is 2.4mm, and the confidence interval radius of the protective layer thickness is 3.6mm, indicating that the uncertainty of the steel bar parameters estimated based on the Bayesian method is small, and the quantitative identification results are highly reliable. To verify the accuracy of the identification results, core samples were drilled at the mid-span and end positions of the beam components to measure the actual steel bar diameter and protective layer thickness. The relative error between the core sample test results and the magnetic identification results is within 5%, proving the effectiveness and reliability of the magnetic identification technology.

Claims

1. A method for measuring steel bars in concrete based on magnetization effect, comprising: S1, using a magnetic sensor array arranged on the surface of the concrete component to be tested to collect magnetic field data at multiple preset positions; S2, preprocessing the collected magnetic field data; According to the preprocessed magnetic field data, the concrete component to be tested is divided into a first area and a second area; wherein the first area represents a far field area; and the second area represents a near field area; S3, in the first region, based on the position range and direction of the steel bars, establish a magnetic dipole model, and calculate the magnetic field distribution in the first region by superimposing the magnetic field contributions of each magnetic dipole; S4, in the second region, based on the geometric information and material properties of the concrete component to be tested, a finite element model is established, and a preset range of steel bars is meshed, and the magnetic field distribution in the second region is calculated by solving Maxwell equations; S5, setting a magnetic field continuity condition at the interface between the first region and the second region, establishing a coupling relationship between the magnetic dipole model and the finite element model, and obtaining a hybrid magnetic field distribution model for measuring the steel bars in the concrete to be tested through iterative solution; S6, according to the hybrid magnetic field distribution model, combined with the steel bar parameters, a high-dimensional nonlinear relationship between the magnetic field measurement value and the steel bar parameters is obtained by a numerical fitting method; wherein the steel bar parameters include the steel bar diameter; the independent variable of the high-dimensional nonlinear function is the steel bar parameter, and the dependent variable is the magnetic field measurement value; S7, based on the design drawings and construction records of the concrete components to be tested, obtain the prior distribution information of the steel bars, which includes the buried depth and diameter of the steel bars; establish the likelihood function of the magnetic field measurement value based on the high-dimensional nonlinear relationship; use the Bayesian theorem to calculate the posterior probability distribution of the steel bar parameters, and obtain the optimal estimate and confidence interval of the steel bar parameters through statistical analysis of the posterior probability distribution, which are output as the steel bar measurement value.

2. The method for measuring steel bars in concrete based on the magnetization effect according to claim 1 is characterized in that: S2, dividing the concrete component to be tested into a first area and a second area, including: S21, using wavelet transform to denoise the collected magnetic field data; S22, normalizing the denoised magnetic field data using a maximum and minimum value normalization method; S23, performing feature extraction on the normalized magnetic field data, extracting the gradient amplitude and direction of the magnetic field data, and obtaining magnetic field feature data; S24, according to the magnitude of the gradient amplitude in the magnetic field characteristic data, dividing the region where the gradient amplitude is greater than the threshold into the second region, otherwise into the first region.

3. The method for measuring steel bars in concrete based on the magnetization effect according to claim 2 is characterized in that: S23, extracting magnetic field characteristic data, including: S231, calculate the gradient vector of the normalized magnetic field data in three-dimensional space by using the improved Sobel operator to obtain the gradient amplitude G mag and the gradient direction G dir ; Among them, the gradient amplitude G mag According to the magnetic field data B x , B y , B z Partial derivatives in three orthogonal directions x, y, and z Calculated, the gradient direction G dir By partial derivative The unit vector representation formed by S232, the gradient amplitude G is interpolated by inverse distance weighted interpolation mag Perform spatial interpolation to obtain the gradient amplitude distribution G at each position on the surface of the concrete component to be tested. mag (x,y,z); S233, performing a spatial angle transformation on the gradient direction Gdir by Euler angle transformation, and converting the gradient direction G in the local coordinate system (x', y', z') dir (x', y', z') is converted to the direction angle in the global coordinate system (x, y, z) θ(x,y,z) and Obtain the magnetic field direction distribution at various positions on the surface of the concrete component to be tested; S234, according to the gradient amplitude distribution G mag (x,y,z) and magnetic field direction distribution θ(x,y,z), Construct magnetic field characteristic data for subsequent regional division; in: Among them, θ is the angle between the gradient direction vector and the z-axis, It is the angle between the projection of the gradient direction vector on the xy plane and the x-axis.

4. The method for measuring steel bars in concrete based on the magnetization effect according to claim 3 is characterized in that: S231, obtain the gradient amplitude G mag and the gradient direction G dir ,include: In three-dimensional space, according to the magnetic field data B x , B y , B z Establish the magnetic permeability μ in three orthogonal directions of x, y, and z respectively x , μ y , μ z The product of the magnetic field data μ x B x , μ y B y , μ z B z Among them, B x , B y , B z Represents the components of magnetic field data in the x, y, and z directions; magnetic permeability μ x , μ y , μ z Determined in advance or measured in real time based on the material properties and environmental conditions of the concrete component to be tested; The improved Sobel operator is used to introduce the magnetic permeability as the weight and calculate the product μ x B x , μ y B y , μ z B z Partial derivatives in three orthogonal directions: x, y, and z According to the partial derivative Calculate the gradient magnitude G mag and the gradient direction G dir ; The calculated gradient amplitude G mag (i,j,k) and the gradient direction G dir (i, j, k) is used as the gradient feature of the normalized magnetic field data at the spatial coordinate (i, j, k) for subsequent spatial interpolation and angle transformation.

5. The method for measuring steel bars in concrete based on the magnetization effect according to claim 4 is characterized in that: The calculation formula of the improved Sobel operator is as follows: Among them, i, j, and k represent the spatial coordinate indexes in the x, y, and z directions respectively.

6. The method for measuring steel bars in concrete based on the magnetization effect according to claim 5 is characterized in that: Calculate the gradient magnitude G based on the partial derivative mag and the gradient direction G dir :

7. The method for measuring steel bars in concrete based on the magnetization effect according to any one of claims 1 to 6, characterized in that: S3, calculating the magnetic field distribution of the first region, including: According to the a priori position range of the steel bars, a plurality of magnetic dipoles are arranged on the concrete surface along the axial direction of the steel bars in the first region; Using the principle of spatial magnetic field superposition, the magnetic field intensity H generated by each magnetic dipole at the spatial coordinate (x, y, z) is dp (x, y, z) are superimposed to obtain the magnetic field distribution H1(x, y, z) at any position in the first region under the magnetic dipole model; where the magnetic field intensity H generated by a single magnetic dipole at position (x, y, z) is dp (x,y,z) is calculated using the analytical expression for the magnetic dipole.

8. The method for measuring steel bars in concrete based on the magnetization effect according to claim 7 is characterized in that: S4, calculating the magnetic field distribution of the second region, including: Establishing a three-dimensional geometric model of the second area according to geometric information of the concrete component to be tested, including size, shape and thickness of the steel bar cover; The material properties of the second region are set according to the electromagnetic parameters of the concrete and the steel bar, wherein the electromagnetic parameters include magnetic permeability and electrical conductivity; Meshing the geometric model of the second region to generate a finite element network; Discretize Maxwell's equations at the elements and nodes of the finite element mesh to establish the partial differential equations that govern the magnetic field distribution; Combined with the geometric boundary of the second region, the finite element method is used to solve the discretized partial differential equation to obtain the magnetic vector potential A(x, y, z) at the node in the second region; According to the relationship between magnetic vector potential A(x,y,z) and magnetic field intensity H(x,y,z): The magnetic field distribution H2 (x, y, z) at any position in the second region under the finite element model is calculated.

9. The method for measuring steel bars in concrete based on the magnetization effect according to claim 8, characterized in that: S5, obtaining a hybrid magnetic field distribution model for measuring steel bars in the concrete to be tested, including: At the interface between the first area and the second area On the surface, the continuity condition of the magnetic field intensity is established. The continuity condition is that the magnetic field intensity of the two regions is continuous and equal at the interface: At the interface between the first area and the second area On the surface, the curl interface condition of the magnetic field is established. The curl interface condition is that the curl of the magnetic field intensity in the normal direction of the interface between the two regions is continuous: Where n is the unit normal vector of the interface 12; represents the curl operator; The magnetic field distribution H1(x, y, z) in the first region calculated by the magnetic dipole model is used as the boundary condition of the second region of the finite element model, and the magnetic field distribution H2(x, y, z) in the second region calculated by the finite element model is used as the source term of the magnetic dipole model. The magnetic dipole model and the finite element model are iteratively solved so that the magnetic field intensity H(x, y, z) satisfies the Maxwell equations and continuity conditions inside the two regions and at the interface. When the iterative calculation converges, the magnetic field distribution H(x, y, z) obtained by combining the magnetic dipole model and the finite element model is used as a hybrid magnetic field distribution model for measuring the steel bars in the concrete to be tested.

10. The method for measuring steel bars in concrete based on the magnetization effect according to claim 9, characterized in that: S6, obtains the high-dimensional nonlinear relationship between the magnetic field measurement value and the steel bar parameters, including: According to the prior information of steel bar diameter and steel grade, the value range of steel bar diameter d is determined [d min ,d max ] and discrete level Δd, generating a series of discrete diameter values ​​{d j |d j =d min +j×Δd,j=0,1,.....,M}; where M is the diameter discrete series; According to the material properties and processing technology of the steel bar, the value range and discrete level of the magnetic susceptibility χ and electrical conductivity σ of the steel bar are determined, and a series of discrete electromagnetic parameter combinations {(x k ,σ k )|k=1,2,......,K}; where K is the number of electromagnetic parameter combinations; The orthogonal experimental design method is used to set the discrete steel bar diameter values ​​{d j } and electromagnetic parameter combination {(χ k ,σ k )} to generate a series of reinforcement parameter samples {(d j ,x k ,σ k )|j=0,1,......,M;k=1,2,......,K}; The steel bar parameter sample {(d j ,x k ,σ k )} as input, substituted into the hybrid magnetic field distribution model, and the corresponding magnetic field measurement value B at the spatial coordinate (x, y, z) was obtained through numerical simulation calculation jk (x, y, z), establish the mapping relationship between the steel bar parameter samples and the magnetic field measurement value samples; With the steel bar diameter d, magnetic susceptibility χ and conductivity σ as independent variables and the corresponding magnetic field measurement value B(x, y, z) as dependent variable, the support vector machine regression method is used to train the sample data {(d j ,x k ,σ k ,B jk (x,y,z))} fits the high-dimensional nonlinear function relationship between the magnetic field measurement value and the steel bar parameters: B(x,y,z)=f(d,χ,σ)+ε Where f(d,χ,σ) is the high-dimensional nonlinear function to be fitted; ε is the fitting error.

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