A method for quantitatively detecting conductivity of solid conductive medium by inductive magneto-thermo-acoustic effect

Abstract

This invention discloses a quantitative detection method for the conductivity of solid conductive media using inductive magneto-thermo-acoustic methods, belonging to the field of non-destructive testing technology. It establishes a quantitative mapping relationship between ultrasonic measurement signals and conductivity distribution by deeply analyzing the multi-field coupling relationship of solid conductive media under pulsed electromagnetic excitation; constructs a mathematical model of magneto-acoustic-thermo-acoustic multi-field coupling under solid constraint conditions to accurately solve the forward problem of electromagnetic and acoustic fields; optimizes the excitation and receiving system parameters to improve detection resolution and signal-to-noise ratio; reconstructs the sound source term using a time-inversion method-compressed sensing joint algorithm, and achieves quantitative conductivity inversion using a least-squares iterative algorithm based on Lorentz force divergence-thermal function; quantifies and calibrates the inversion results to ensure detection accuracy; reconstructs the conductivity distribution using imaging technology to identify abnormal regions; and finally generates a standardized detection report.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, specifically to a quantitative detection method for the conductivity of solid conductive media using inductive magnetothermal acoustic methods. Background Technology

[0002] Electrical conductivity, as a core physical parameter characterizing the conductivity, internal defects, material uniformity, and aging state of solid conductive media, plays a crucial role in many key fields. In the aerospace field, the uniformity and stability of the conductivity of various metal components and conductive composite materials used in aircraft directly affect the performance of the aircraft's electrical system and structural safety. In power equipment, the conductivity of conductive components affects power transmission efficiency and equipment reliability. In the precision manufacturing industry, the conductivity of materials such as semiconductor blanks is a key factor determining the performance and quality of electronic devices. Therefore, high-precision, non-contact, and quantitative imaging detection of the internal conductivity of solid conductive media has become an important means to ensure the safe service of these components and the stability of product quality, and is also an urgent need for the continued development of related fields.

[0003] Existing conductivity detection methods have many limitations when dealing with complex practical testing needs. Eddy current detection technology, due to its inherent limitations, can only detect near-surface solid conductive media, and cannot effectively detect the conductivity of the deeper layers within the media. The detection depth is severely limited, making it difficult to meet the need for a comprehensive understanding of the overall conductivity distribution. The four-probe method is a contact detection method. During the detection process, the probe is in direct contact with the sample, which not only easily scratches the sample surface, affecting the integrity of the sample and subsequent use, but also cannot achieve three-dimensional imaging detection of the interior of the solid conductive media, and cannot intuitively present the spatial distribution of conductivity within the medium. Traditional magnetoacoustic imaging or thermoacoustic imaging techniques mostly use a single physical effect and do not fully consider the strong coupling relationship between the static magnetic field, eddy current electric field, Lorentz force field, temperature field and sound field in the solid medium. This neglect of multi-field coupling leads to insufficient accuracy in sound field modeling, a large amount of noise in the detection signal, and a low signal-to-noise ratio, which in turn affects the accuracy of conductivity detection. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an inductive magneto-thermo-acoustic method for quantitative detection of conductivity in solid conductive media. This method establishes a quantitative mapping relationship between ultrasonic measurement signals and conductivity distribution by deeply analyzing the multi-field coupling relationship of solid conductive media under pulsed electromagnetic excitation; constructs a mathematical model of magneto-acoustic-thermo-acoustic multi-field coupling under solid constraints to accurately solve the forward problem of electromagnetic and acoustic fields; optimizes excitation and receiving system parameters to improve detection resolution and signal-to-noise ratio; reconstructs the sound source term using a time-inversion method-compressed sensing joint algorithm, and achieves quantitative conductivity inversion using a least-squares iterative algorithm based on Lorentz force divergence-thermal function; quantifies and calibrates the inversion results to ensure detection accuracy; reconstructs the conductivity distribution through imaging technology to identify abnormal regions; and finally generates a standardized detection report, realizing a full-process quantitative detection from signal excitation, acoustic field coupling, sound source reconstruction, conductivity inversion to result verification, imaging output, and accuracy evaluation.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for quantitative detection of the conductivity of a solid conductive medium using inductive magnetothermal acoustic methods, the method comprising the following specific steps: S1: Analyze the coupling relationship between the internal and external magnetic fields, eddy current electric fields, force fields, temperature fields and response acoustic fields of solid conductive media, and establish the mapping relationship between ultrasonic measurement signals and reconstructed conductivity distribution; S2: Establish a multi-field coupling mathematical model under solid constraint conditions, solve the electromagnetic field and acoustic field forward problems, derive the acoustic field wave equation of magnetoacoustic-thermoacoustic coupling response and study the numerical solution method; S3: Explore the optimal pulsed electromagnetic excitation parameters, static magnetic field parameters, and ultrasonic receiving parameters / layout, and determine the influence of excitation / receiving parameters on detection resolution; S4: Combining the time inversion method and compressed sensing algorithm to reconstruct the sound source term, a least squares iterative reconstruction algorithm for conductivity based on Lorentz force divergence-heat function is proposed to achieve quantitative inversion of conductivity; S5: Quantitatively calibrate the conductivity results obtained from the inversion, compare them with the standard conductivity sample to calculate the detection error, and complete the result correction through repeated detection; S6: Perform imaging reconstruction on the calibrated conductivity data to identify and mark regions of abnormal conductivity. S7: Generates a detection report containing quantitative values, error analysis, imaging spectra, and anomaly information, and outputs the final detection results.

[0006] Furthermore, in S1, a constant static magnetic field and pulsed electromagnetic excitation are applied to the solid conductive medium under test, generating an eddy current electric field inside the medium. This eddy current electric field forms a Lorentz force field under the action of the static magnetic field. At the same time, the eddy currents generate Joule heat due to the internal resistance loss of the medium and construct a temperature field. The Lorentz force directly drives the medium particles to produce mechanical vibration, while the temperature field induces thermal deformation vibration of the medium through thermoelastic effects. The two types of vibrations are coupled to form a response sound field that radiates outward. In this process, the coupling and transmission law between the magnetic field distribution, eddy current electric field strength, Lorentz force amplitude, temperature field gradient and sound field pressure, propagation delay, and spectral characteristics is comprehensively analyzed. Combined with the medium density, elastic modulus, and thermal expansion coefficient, through multi-physics coupling mechanism analysis and data fitting, a nonlinear quantitative mapping relationship is established between the sound pressure amplitude, phase characteristics, and energy distribution of the ultrasonic measurement signal and the spatial distribution of conductivity inside the medium.

[0007] Furthermore, in S2, a multi-field coupled mathematical model is constructed by combining the elastic mechanical constraints, thermal conductivity characteristics, and electromagnetic response laws of the tested solid conductive medium. This model includes electromagnetic fields, temperature fields, force fields, and sound fields. The distribution of eddy current electric fields and spatial magnetic fields inside the medium under pulsed electromagnetic excitation is solved using Maxwell's equations, completing the quantitative calculation of the electromagnetic field forward problem. The spatiotemporal evolution law of the temperature field inside the medium is obtained from the Joule heating effect and the heat conduction equation. Combining the Lorentz force excitation mechanism and the thermoelastic constitutive equation of the solid medium, the magnetoacoustic-thermoacoustic coupled sound field wave equation integrating mechanical vibration and thermal vibration is derived. On this basis, the finite element method is used to discretize the coupled wave equation in spatial grid and perform iterative calculation in the time domain. By setting boundary conditions and initial field quantities, the efficient numerical solution of the coupled wave equation is achieved, thereby obtaining the solution of the sound field response forward problem corresponding to different conductivity distributions.

[0008] Furthermore, in S2, the expression for Maxwell's equations is: ,in, It is the vector of eddy current electric field intensity induced by pulsed electromagnetic excitation inside the solid conductive medium being measured. It is the magnetic induction intensity vector of the space in which the medium is located, which includes the static magnetic field and the excitation alternating magnetic field components; It is the conductivity of the measured medium. It is the time variable of electromagnetic excitation and acoustic field response. It is the Hamiltonian operator, used to characterize the gradient, divergence, and curl operations of spatial field quantities.

[0009] Furthermore, in S2, the expression for the magnetoacoustic-thermoacoustic coupled sound field wave equation is: ,in, It is the displacement vector generated by the medium particles under the combined action of Lorentz force and thermoelastic effect. It is the density of the solid conductive medium being measured. , Lamé constant is the constant of a solid medium, used to describe the elastic mechanical properties of the medium. It is the vector of magnetic induction intensity of the applied static magnetic field. It is the Lorentz force density vector, which is the direct excitation source of the magnetoacoustic effect; it is the thermal expansion coefficient of the medium, which reflects the ability of the medium to undergo thermal deformation caused by temperature changes. The spatial gradient of the temperature field determines the magnitude and distribution of the thermoelastic force; It is thermoelastic density.

[0010] Furthermore, in S3, the pulse width, peak current, and repetition frequency of the pulsed electromagnetic excitation, the magnetic induction intensity and regional uniformity of the static magnetic field, and the center frequency, receiving bandwidth, number of array elements, arrangement, and spacing of the ultrasonic transducer are selected as key variables. The remaining parameters are fixed by a single-factor variable method, and multiple sets of comparative tests are conducted by changing one parameter individually. Ultrasonic response signals under different conditions are collected, and data such as sound pressure amplitude, signal stability, and defect edge recognition clarity are recorded. The effect of single parameter changes on lateral resolution, longitudinal resolution, and detection depth is analyzed one by one. Based on this, orthogonal experimental design is introduced to optimize and match the combination of multiple parameters. The detection blind zone size and imaging uniformity of different receiving array layouts such as linear and ring arrangements are compared. The coupling effect between parameters is analyzed. A quantitative correlation model between parameters and resolution is constructed through data fitting. Finally, the optimal parameter range and array layout that balances resolution and signal-to-noise ratio are determined.

[0011] Furthermore, in step S4, the magnetoacoustic-thermoacoustic coupling response signal captured by the ultrasonic receiving array is acquired. Through preprocessing operations such as filtering, denoising, and signal synchronization alignment, environmental noise and system interference are eliminated. Then, the time inversion method is used to reverse the time of the preprocessed ultrasonic signal and use it as a boundary condition to carry out back propagation calculation in the magnetoacoustic-thermoacoustic coupling sound field wave equation. This initially realizes the spatial distribution reconstruction of the coupled sound source terms. On this basis, the compressed sensing algorithm is integrated, and a sparse representation model is constructed based on the sparsity characteristics of the sound source terms. The amount of sampled data is reduced by introducing L1 regularization constraints.

[0012] Furthermore, in S4, the reconstructed coupled sound source term is decomposed into a Lorentz force divergence contribution term and a thermal function contribution term based on the multi-field coupling mechanism. The intrinsic relationship between the two terms and the conductivity distribution of the medium is clarified, and an objective function based on the Lorentz force divergence-thermal function is constructed. A least squares iterative algorithm is introduced to continuously reduce the error of the objective function by iteratively updating the conductivity distribution parameters. An iterative convergence threshold and a maximum number of iterations are set to suppress the accumulation of errors during the inversion process, and finally, a high-precision quantitative inversion of the conductivity distribution inside the solid conductive medium is achieved.

[0013] Furthermore, in step S5, a standard conductivity sample with the same material and size as the solid conductive medium being tested is selected. The conductivity values ​​of each region of the tested medium obtained by inversion are compared one by one with the calibration values ​​of the corresponding regions of the standard sample. The absolute error, relative error and overall root mean square error of each detection point are calculated respectively to quantify and evaluate the accuracy of the conductivity inversion results.

[0014] Furthermore, in step S6, the calibrated discrete conductivity data is spatially gridded, accurately mapping the conductivity value of each detection point to the actual spatial coordinates of the tested solid conductive medium, thus constructing a complete conductivity spatial distribution dataset. Subsequently, pseudo-color imaging technology is used, and a reasonable gradient color mapping rule is set according to the conductivity value to transform the abstract conductivity value into an intuitive two-dimensional pseudo-color cloud map or three-dimensional stereoscopic imaging model. At the same time, combined with the normal conductivity range of the tested medium, the standard sample calibration range, and industry testing standards, a conductivity anomaly judgment threshold is preset. An abnormal region with conductivity higher or lower than the normal range is screened out through a threshold comparison algorithm. A boundary extraction algorithm is used to accurately delineate the contour range of the abnormal region, marking the spatial coordinates, conductivity extreme values, and abnormal amplitude of the abnormal region, clearly distinguishing different abnormal types of conductivity that are too high or too low.

[0015] Compared with existing technologies, this inductive magnetothermal acoustic method for quantitative detection of the conductivity of solid conductive media has the following advantages: This invention significantly improves the mapping accuracy between ultrasonic response signals and conductivity by establishing a high-precision magnetoacoustic-thermoacoustic coupled wave equation. By optimizing excitation and reception parameters and combining a time-inversion-compressed sensing joint algorithm, it enhances the reconstruction accuracy and noise resistance of the sound source term. Coupled with a least-squares iterative inversion algorithm, it achieves high-precision quantitative calculation of the conductivity of solid conductive media. At the same time, it constructs a complete detection closed loop from inversion calculation to result calibration, imaging recognition, and report output, effectively solving the defects of traditional detection methods that only have inversion without verification, quantification, and standardized output. In addition, this method adopts a non-contact excitation and reception method, which does not damage the tested medium and has the advantages of large detection depth and high resolution. It can be widely used for the detection of internal conductivity uniformity and defect identification of various solid conductive media such as metal components, conductive composite materials, and semiconductor blanks.

[0016] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0018] Figure 1 A flowchart of a quantitative detection method for the conductivity of a solid conductive medium using inductive magnetothermal acoustic methods; Figure 2 This is a flowchart of step S2 in a quantitative detection method for the conductivity of a solid conductive medium using inductive magnetothermal acoustic methods. Figure 3 This is a flowchart of step S4 in a quantitative detection method for the conductivity of a solid conductive medium using inductive magnetothermal acoustic methods. Figure 4 This is a schematic diagram showing the structural dimensions of the solid conductive medium under test and the ultrasonic transducer. Figure 5 The waveform of the current under pulsed electromagnetic excitation; Figure 6 The waveform of the magnetoacoustic-thermoacoustic coupling pressure response at the ultrasonic receiver is shown. Figure 7 The waveform of the original noisy ultrasonic signal before preprocessing; Figure 8 The waveform diagram shows the preprocessed ultrasonic response signal and the synchronous waveform of the pulse excitation. Detailed Implementation

[0019] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0020] This invention provides a quantitative detection method for the conductivity of solid conductive media using inductive magneto-thermo-acoustic methods. By deeply analyzing the multi-field coupling relationship of solid conductive media under pulsed electromagnetic excitation, a quantitative mapping relationship between ultrasonic measurement signals and conductivity distribution is established. A mathematical model of magneto-acoustic-thermo-acoustic multi-field coupling under solid constraint conditions is constructed to accurately solve the forward problem of electromagnetic and acoustic fields. The excitation and receiving system parameters are optimized to improve detection resolution and signal-to-noise ratio. A time-inversion method-compressed sensing joint algorithm is used to reconstruct the sound source term, combined with a least-squares iterative algorithm based on the Lorentz force divergence-thermal function to achieve quantitative conductivity inversion. The inversion results are quantitatively calibrated to ensure detection accuracy. Imaging technology is used to reconstruct the conductivity distribution and identify abnormal regions. Finally, a standardized detection report is generated, realizing a full-process quantitative detection from signal excitation, acoustic field coupling, sound source reconstruction, conductivity inversion to result verification, imaging output, and accuracy evaluation.

[0021] like Figure 1 As shown, for the tested solid conductive medium, a spatially uniform constant static magnetic field and a broadband pulsed electromagnetic excitation are simultaneously applied. The pulsed electromagnetic excitation induces eddy current electric fields on the surface and inside the medium through the principle of electromagnetic induction. These eddy current electric fields interact with the static magnetic field, generating Lorentz force fields perpendicular to the directions of the electric and magnetic fields. Simultaneously, as the eddy currents flow inside the medium, Joule heat loss occurs due to the internal resistance of the medium. Joule heating causes a rapid increase in the local temperature of the medium, forming a temperature gradient field. This, in turn, induces a thermally induced deformation force field in the medium through the thermoelastic effect. The formula for calculating the thermoelastic force density is: ,in, It is thermoelastic force density. The coefficient of thermal expansion of the medium. This represents the temperature field gradient.

[0022] The Lorentz force directly drives the medium particles to produce mechanical vibrations, while the thermoelastic force induces thermal vibrations of the medium particles through the thermal expansion and contraction effect. The two types of vibrations superimpose and couple with each other inside the medium, forming a magnetoacoustic-thermoacoustic coupled response sound field that radiates and propagates to the outside of the medium. In this process, the coupling and transmission laws between the spatial distribution of the magnetic field, the intensity distribution of the eddy current electric field, the density distribution of the Lorentz force, the spatiotemporal evolution of the temperature field, and the sound pressure amplitude, propagation delay, spectral characteristics, and energy attenuation characteristics of the response sound field are comprehensively collected and analyzed.

[0023] The inherent physical properties of the measured medium are introduced, including density ρ = 2700 kg / m³, elastic modulus E = 70 GPa, Poisson's ratio ν = 0.33, Lamé constant λ = 56.5 GPa, μ = 26.3 GPa, and coefficient of thermal expansion β = 2.3 × 10⁻⁶. -5 With a specific heat capacity of c=900J / (kg·K), a nonlinear quantitative mapping relationship between the sound pressure amplitude, phase characteristics, and spectral distribution of ultrasonic measurement signals and the spatial distribution of conductivity within the medium was established through derivation of the multi-physics coupling mechanism and fitting of multiple sets of experimental data. Specifically, a third-order polynomial fitting combined with a multilayer perceptron neural network (12 nodes in the input layer, 24 nodes in the hidden layer, and 1 node in the output layer) was adopted. The training method is as follows: a multi-input multi-output mapping model is constructed. The input consists of 12-dimensional features of the ultrasound signal, including sound pressure, phase, and spectrum. The output is the conductivity value at the corresponding spatial location. The coefficient of determination R for the mapping model is [missing information]. 2 =0.998.

[0024] Combining the elastic mechanical boundary constraints, isotropic thermal conductivity, and quasi-static electromagnetic response of the tested solid conductive medium, a four-dimensional multi-field coupled mathematical model is constructed, incorporating electromagnetic, temperature, force, and acoustic fields. The solution domain is divided into an internal region of the medium and an external air propagation region. The dimensions of the solution domain are: 50mm × 50mm × 20mm for the tested medium and 100mm × 100mm × 50mm for the air region. The structural dimensions of the tested medium and the ultrasonic transducer are as follows. Figure 4 As shown, the spacing parameters of each key position are marked, including the inner circle diameter of 0.1cm, the distance between the transducer and the outer circle of 0.03cm, the distance between the outer circle and the inner circle of 0.08cm, the distance between the left side of the inner circle and the left side of the outer circle of 0.18cm, and the total width of the outer circle of 0.23cm.

[0025] like Figure 2 As shown, under quasi-static approximation conditions (pulse electromagnetic excitation frequency on the order of 1kHz-10MHz, displacement current much smaller than conduction current, displacement current term can be ignored), the distribution of eddy current electric field and spatial magnetic field inside the medium under pulse electromagnetic excitation is solved using the complete simplified Maxwell's equations. The equations are expressed as follows: Where E is the eddy current electric field intensity vector generated by pulsed electromagnetic excitation inside the solid conductive medium under test; B is the magnetic induction intensity vector of the space in which the medium is located, which includes the constant static magnetic field component and the alternating magnetic field component generated by pulsed excitation; σ is the conductivity distribution function of the medium under test; t is the time variable of electromagnetic excitation and acoustic field response; ∇ is the Hamiltonian operator.

[0026] Electromagnetic field boundary conditions are set as follows: the tangential electric field and the normal magnetic induction intensity are continuous at the interface between the medium and the air; the electromagnetic field intensity at infinity is 0. The solution domain is spatially discretized using the finite difference method with a spatial grid step size of Δx = 0.1 mm. The distribution of eddy current electric and magnetic fields inside the medium at different times is iteratively calculated using the time step method with a time step size of Δt = 1 ns, thus completing the quantitative calculation of the electromagnetic field forward problem.

[0027] Based on the Joule heating effect and the Joule heat power density inside the medium, and combined with the three-dimensional transient heat conduction equation, the spatiotemporal evolution of the temperature field is solved. The heat conduction equation is as follows: ,in, q is the thermal conductivity of the medium, q is the Joule heat power density, and T is the temperature inside the solid conductive medium being measured. The temperature field boundary conditions are set as follows: the surface of the medium undergoes natural convection heat transfer with the air. At the initial moment, the temperature inside the medium is uniform and equal to the ambient temperature T0=25℃. The heat conduction equation is solved by the finite element method to obtain the temperature distribution and temperature gradient distribution inside the medium at different times. The temperature field calculation error is <0.1℃.

[0028] Combining the Lorentz force excitation mechanism with the thermoelastic constitutive equation of solid media, and substituting the Lorentz force and thermoelastic force as volume force terms into the elasticity wave equation, a complete magnetoacoustic-thermoacoustic coupled sound field wave equation integrating mechanical vibration and thermally induced vibration is derived, expressed as: Where u is the displacement vector of the medium particles under the combined action of Lorentz force and thermoelastic effect; λ and μ are the Lamé constants of the solid medium; The vector of magnetic induction intensity of the applied constant static magnetic field; β is the Lorentz force density vector, which is the direct excitation source of the magnetoacoustic effect; β is the thermal expansion coefficient of the medium. The spatial gradient of the temperature field; It is the thermoelastic force density vector.

[0029] The coupled wave equation was discretized using the finite element method, and the solution domain was divided into a hexahedral structured mesh with a total of 5 × 10⁵ mesh elements, a mesh quality > 0.95, and a mesh size less than 1 / 6 of the ultrasonic wave length to ensure computational accuracy. The time domain was calculated iteratively using the central difference method, with the time step satisfying the Courant-Friedrichs-Lewy stability condition. Initial conditions were set as follows: at t=0, the displacement and velocity of the medium particles were both 0, and the electromagnetic field and temperature field were both 0. Boundary conditions: the outer surface of the medium was a free boundary, and the sound pressure at infinity was 0.

[0030] Through iterative calculations, with a total of 1×10⁶ iterations and a numerical calculation time of approximately 2 hours, the vibration law of internal particles and the response of external radiated sound field corresponding to different conductivity distributions were obtained, thus completing the solution of the coupled sound field forward problem.

[0031] Pulsed electromagnetic excitation parameters, static magnetic field parameters, and ultrasonic receiving parameters / layout were selected as key optimization variables. By combining the single-factor variable method with orthogonal experimental design, the influence of each parameter on the detection resolution and the optimal parameter combination were determined.

[0032] With all other parameters kept constant, multiple control tests were conducted by changing only one parameter. Ultrasonic response signals were collected under different conditions, and characteristic indicators such as sound pressure amplitude, signal-to-noise ratio, and defect edge recognition clarity were extracted. The corresponding lateral resolution (the minimum distance between two adjacent conductivity anomaly regions that can be distinguished), longitudinal resolution (the minimum distance between conductivity anomalies of different depths that can be distinguished), and effective detection depth were calculated. The specific single-factor experimental data are as follows: In the pulse electromagnetic excitation parameters, the pulse width was successively taken as 1μs, 5μs, 10μs, 50μs, 100μs, 1ms, 5ms, and 10m. The corresponding signal-to-noise ratios are 12dB, 28dB, 35dB, 32dB, 25dB, 18dB, 10dB, and 5dB, respectively; the peak currents are 1A, 10A, 20A, 50A, and 100A, respectively, corresponding to sound pressure amplitudes of 0.5Pa, 5Pa, 10Pa, 25Pa, and 50Pa, respectively; the repetition frequencies are 1Hz, 10Hz, 100Hz, and 1kHz, respectively, with detection efficiencies of 1 time / s, 10 times / s, 100 times / s, and 50 times / s, respectively. Heat accumulation will lead to a decrease in detection efficiency at high repetition frequencies. The actual current waveform of the pulsed electromagnetic excitation is as follows: Figure 5 As shown, the peak current reaches 1000A, and the pulse period is approximately 6×10⁻⁶. -7 The parameters satisfy the broadband pulse excitation requirements. In the static magnetic field parameters, the magnetic induction intensity is taken as 0.1T, 0.5T, 1T, 1.5T, and 2T respectively; the Lorentz force density is taken as 100N / m³, 500N / m³, 1000N / m³, 1500N / m³, and 2000N / m³ respectively; the magnetic field region uniformity is taken as 1%, 3%, 5%, and 10% respectively; and the imaging distortion rate is taken as 0.5%, 1%, 3%, and 10% respectively.

[0033] In the ultrasonic receiving parameters, the center frequency of the ultrasonic transducer is 0.5MHz, 1MHz, 5MHz, and 10MHz respectively; the longitudinal resolution is 0.8mm, 0.4mm, 0.08mm, and 0.04mm respectively; the detection depth is 50mm, 30mm, 10mm, and 5mm respectively; the receiving bandwidth is 50%, 100%, and 150% of the center frequency respectively; the imaging contrast is 15dB, 30dB, and 25dB respectively; the number of array elements is 16, 64, 128, and 256 respectively; and the lateral resolution is 0.5mm, 0.2mm, 0.1mm, and 0.08mm respectively.

[0034] Based on the univariate analysis, four main influencing factors were selected: pulse width, peak current, static magnetic field magnetic induction intensity, and ultrasound center frequency. Each factor was set to four levels, and an L16(4) model was designed. 4 Orthogonal experiment, the factor level table for the orthogonal experiment is as follows: 1 10 20 0.5 1 2 50 50 1 5 3 100 80 1.5 8 4 1000 100 2 10 The weighted composite score of lateral resolution, longitudinal resolution, and signal-to-noise ratio (weights 0.3:0.3:0.4) was used as the evaluation index. Range analysis was used to determine the order of influence of each factor. The range values ​​were: ultrasound center frequency 21.3 μs, static magnetic field 18.7 μs, peak current 15.2 μs, and pulse width 12.5 μs, indicating that ultrasound center frequency had the greatest impact, followed by static magnetic field, peak current, and pulse width. Analysis of variance was used to determine the significance of each factor's influence. Ultrasound center frequency and static magnetic field were highly significant, peak current was significant, and pulse width was insignificant. The optimal parameter combination was finally determined to be a pulse width of 50 μs, a peak current of 50 A, a static magnetic field of 1 T, and an ultrasound center frequency of 5 MHz. Under this combination, the lateral resolution was 0.08 mm, the longitudinal resolution was 0.08 mm, and the signal-to-noise ratio was 38 dB.

[0035] Meanwhile, the detection performance of three different ultrasonic receiving array layouts—linear, circular, and planar array—was compared. The detection blind zone size, imaging uniformity, and edge detection accuracy of different layouts were analyzed. The linear array had a detection blind zone of 15% and an imaging uniformity of 75%, the circular array had a detection blind zone of 3% and an imaging uniformity of 96%, and the planar array had a detection blind zone of 8% and an imaging uniformity of 88%. The results show that the circular array has the highest resolution, the smallest detection blind zone, and the best imaging uniformity in the central region, making it more suitable for conductivity imaging detection of solid conductive media.

[0036] like Figure 3 As shown, the magnetoacoustic-thermoacoustic coupling response signals captured by each element of the ultrasonic receiving array are acquired and then subjected to refined preprocessing operations in sequence: A fourth-order Butterworth bandpass filter is used, with a cutoff frequency of 0.1MHz-10MHz, to filter out power frequency interference and high-frequency random noise, with a noise suppression ratio of 20dB; A 5-level decomposition of the db4 wavelet combined with soft thresholding denoising (threshold 0.01) was used to further remove inherent system noise and electromagnetic interference noise, achieving a signal fidelity of 98%. A cross-correlation algorithm is used to synchronize and align the signals received by different array elements, correcting the phase error to <0.1, thus eliminating the phase error caused by array element position differences and signal propagation delay.

[0037] The original noisy ultrasonic signal waveform before preprocessing is as follows: Figure 7 As shown, the preprocessed ultrasonic response signal and the pulse excitation synchronization waveform are as follows: Figure 8As shown, the noise suppression effect and signal fidelity of the preprocessing operation are intuitively verified.

[0038] The spatial distribution of the coupled sound source terms is initially reconstructed using the time-inversion method: the signal of each pre-processed array element is time-inverted, and the inverted signal is used as the boundary condition for the corresponding array element position. The boundary sound pressure amplitude is normalized to 1 Pa and substituted into the derived magnetoacoustic-thermoacoustic coupled sound field wave equation for back propagation calculation. When all back-propagated signals are coherently superimposed at the sound source position, the preliminary spatial distribution of the coupled sound source terms can be obtained. The preliminary reconstruction positioning error is less than 0.1 mm.

[0039] Building upon this foundation, compressed sensing algorithms are incorporated, and the sparsity characteristics of conductivity anomaly regions are utilized to construct a sparse representation model for coupled sound source terms. A discrete cosine transform basis is selected as the overcomplete dictionary, representing the sound source terms as a linear combination of dictionary atoms with a sparsity of K=50. L1 regularization constraints are introduced to transform the reconstruction problem into a convex optimization problem. The alternating direction multiplier method (ADMM) is employed to solve this optimization problem. This method can maintain the accuracy and resolution of sound source reconstruction with a reconstruction error of less than 2% even with a 60% reduction in the amount of sampled data.

[0040] For the reconstructed coupled sound source term, based on the multi-field coupling mechanism, it is decomposed into a magnetoacoustic sound source term and a thermoacoustic sound source term, both of which are linearly positively correlated with the dielectric conductivity, with a correlation coefficient r > 0.99. A least-squares objective function based on the Lorentz force divergence-thermal function is constructed. The gradient descent method least-squares iterative algorithm is introduced to solve this objective function, and the conductivity distribution is initialized to 1 × 10⁻⁶. 7 S / m, gradient descent step size 1×10 -9 The conductivity parameter is updated iteratively using the gradient descent formula. In each iteration, the predicted sound source term is calculated using a forward problem, and the objective function error is calculated. The iteration convergence threshold is set to 10. -4 The maximum number of iterations is 100, and convergence is achieved in 86 iterations. When the error of the objective function is less than the convergence threshold or the maximum number of iterations is reached, the iteration stops, and finally a high-precision quantitative distribution of the internal conductivity of the solid conductive medium is obtained, with an inversion relative error of less than 1.5%.

[0041] A standard conductivity sample identical in material, size, and heat treatment process to the solid conductive medium being tested was selected. A high-precision contact conductivity meter was used to perform multi-point grid calibration on the standard sample, with a calibration point spacing of 0.04 mm. The resulting spatial distribution calibration values ​​of the standard sample's conductivity were 1.0 × 10⁻⁶. 7 S / m, 1.5×10 7 S / m, 2.0×10 7 S / m.

[0042] The conductivity values ​​at each detection point of the tested medium obtained by inversion were compared one by one with the calibration values ​​at the corresponding spatial positions of the standard sample. The accuracy was quantified according to the calculation formulas for absolute error, relative error, and root mean square error. The inversion values ​​were 1.02 × 10⁻⁶. 7 S / m, 1.48×10 7 S / m, 2.01×10 7 S / m, with an absolute error of 0.02×10 7 S / m, -0.02×10 7 S / m, 0.01×10 7 S / m, with relative errors of 2%, 1.33%, and 0.5% respectively, and a root mean square error of 0.018 × 10⁻⁶. 7 S / m is used to quantify and evaluate the accuracy of the conductivity inversion results.

[0043] Five independent and repeated tests were performed on the same test medium. The mean and standard deviation of each test result were calculated, with the standard deviation being 0.005 × 10⁻⁶. 7 S / m, outliers are removed using the Grubbs criterion, with a critical value of G0. 05 ,5=1.672, the results were corrected by weighted average method, with the weights set equally to 0.2 to reduce the impact of random errors; at the same time, a piecewise systematic error compensation model was established, and systematic error compensation was performed on the inversion results according to the error distribution law of different conductivity ranges and different detection depths. Through 5 independent repeated detections, outlier removal by Grubbs criterion, weighted average correction and iterative optimization of systematic error compensation model, and verification by multiple sets of standard sample calibration experiments, the overall detection relative error was controlled within 3%.

[0044] The calibrated discrete conductivity data were spatially meshed. Based on the actual size of the measured medium and the required detection resolution, the detection area was divided into 625×625×250 three-dimensional mesh units, with each mesh unit corresponding to a conductivity value. A cubic spline interpolation algorithm was used to map the discrete detection point data onto the three-dimensional mesh units, with an interpolation error of less than 0.01×10⁻⁶. 7 S / m, construct a complete spatial distribution dataset of electrical conductivity.

[0045] Pseudo-color imaging technology is employed, and gradient color mapping rules are set according to the conductivity value range, 0-1×10 7 S / m corresponds to blue, 1-2×10 7 S / m corresponds to green, 2-3×10 7 S / m corresponds to yellow, greater than 3×10 7S / m corresponds to red, transforming the abstract conductivity value into an intuitive two-dimensional pseudo-color cloud map. For three-dimensional detection needs, a ray projection volume rendering technique is used to generate a three-dimensional stereoscopic imaging model with a resolution of 1024×768. It supports rotation, translation, and sectioning operations at any angle, comprehensively displaying the spatial distribution characteristics of conductivity within the medium. It also includes an example image of two-dimensional pseudo-color conductivity imaging and an image showing the extraction effect of abnormal region boundaries. The imaging resolution is 0.08mm, and the imaging contrast is 30dB. The magnetoacoustic-thermoacoustic coupling pressure response waveform acquired by the ultrasonic receiver is shown below. Figure 6 As shown, the waveform includes a main response peak and multiple reflection peaks, with a peak pressure of 6 Pa, which is consistent with the theoretical calculation results.

[0046] Based on the technical requirements of the tested medium, the normal conductivity range, and industry testing standards, a threshold for judging abnormal conductivity is preset, with the normal range being 1.0 × 10⁻⁶. 7 -2.0×10 7 S / m, the upper threshold is greater than 2.0 × 10 7 S / m, lower than the threshold of 1.0 × 10 7 S / m, using a threshold comparison algorithm to filter out grid cells with conductivity higher or lower than the normal range, and using the Canny edge detection algorithm (low threshold 20, high threshold 50) to accurately extract the contour boundary of the abnormal area, calculate the area, volume, center spatial coordinates, maximum, minimum and average conductivity of the abnormal area, etc., with an abnormal area positioning accuracy of ±0.05mm, use different color marks to distinguish between abnormal types of conductivity that are too high and too low, and mark the location and severity of the abnormal area on the imaging atlas.

[0047] The system automatically generates standardized test reports, which include: basic information of the tested medium (name, material, size, number, test date), parameter settings of the testing system (pulse electromagnetic excitation parameters, static magnetic field parameters, ultrasonic receiving parameters, array layout), quantitative conductivity test results (conductivity values ​​of each region, overall average value, standard deviation), error analysis results (absolute error, relative error, root mean square error), conductivity imaging spectrum (two-dimensional pseudo-color cloud map, three-dimensional stereoscopic imaging map), detailed information of abnormal areas (spatial coordinates, size, conductivity extreme values, anomaly type), test conclusions, and handling suggestions.

[0048] The test report is output in both electronic and paper formats. At the same time, the raw conductivity data, preprocessed signal data, imaging data and test report files are stored in a unified database to establish a test data traceability system, which facilitates subsequent query, statistics and analysis.

[0049] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for quantitatively detecting the conductivity of a solid conductive medium using inductive magnetothermal acoustic methods, characterized in that, The method includes the following specific steps: S1: Analyze the coupling relationship between the internal and external magnetic fields, eddy current electric fields, force fields, temperature fields and response acoustic fields of solid conductive media, and establish the mapping relationship between ultrasonic measurement signals and reconstructed conductivity distribution; S2: Combining the elastic mechanical constraints, thermal conductivity characteristics, and electromagnetic response laws of the tested solid conductive medium, a multi-field coupled mathematical model including electromagnetic field, temperature field, force field, and sound field is constructed. The distribution of eddy current electric field and spatial magnetic field inside the medium under pulsed electromagnetic excitation is solved by Maxwell's equations, and the quantitative calculation of the electromagnetic field forward problem is completed. The spatiotemporal evolution law of the temperature field inside the medium is obtained from the Joule heating effect and the heat conduction equation. Combining the Lorentz force excitation mechanism and the thermoelastic constitutive equation of the solid medium, the magnetoacoustic-thermoacoustic coupled sound field wave equation integrating mechanical vibration and thermal vibration is derived. The finite element method is used to perform spatial grid discretization and time domain iterative calculation on the magnetoacoustic-thermoacoustic coupled sound field wave equation. By setting boundary conditions and initial field quantities, the efficient numerical solution of the coupled wave equation is achieved, thereby obtaining the solution of the sound field response forward problem corresponding to different conductivity distributions. The expression for the magnetoacoustic-thermoacoustic coupled sound field wave equation is as follows: ,in, It is the displacement vector generated by the medium particles under the combined action of Lorentz force and thermoelastic effect. It is the density of the solid conductive medium being measured. , Lamé constant is the constant of a solid medium, used to describe the elastic mechanical properties of the medium. It is the vector of magnetic induction intensity of the applied static magnetic field. It is the Lorentz force density vector, which is the direct excitation source of the magnetoacoustic effect; It is the coefficient of thermal expansion of the medium, which reflects the ability of the medium to undergo thermal deformation caused by temperature changes; The spatial gradient of the temperature field determines the magnitude and distribution of the thermoelastic force; It is thermoelastic force density; S3: Explore the optimal pulsed electromagnetic excitation parameters, static magnetic field parameters, and ultrasonic receiving parameters / layout, and determine the influence of excitation / receiving parameters on detection resolution; S4: Combining the time inversion method and compressed sensing algorithm to reconstruct the sound source term, a least squares iterative reconstruction algorithm for conductivity based on Lorentz force divergence-heat function is proposed to achieve quantitative inversion of conductivity; S5: Quantitatively calibrate the conductivity results obtained from the inversion, compare them with the standard conductivity sample to calculate the detection error, and complete the result correction through repeated detection; S6: Perform imaging reconstruction on the calibrated conductivity data to identify and mark regions of abnormal conductivity. S7: Generates a detection report containing quantitative values, error analysis, imaging spectra, and anomaly information, and outputs the final detection results.

2. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S1, a constant static magnetic field and pulsed electromagnetic excitation are applied to the solid conductive medium under test, generating an eddy current electric field inside the medium. This eddy current electric field forms a Lorentz force field under the action of the static magnetic field. At the same time, the eddy currents generate Joule heat due to the internal resistance loss of the medium and construct a temperature field. The Lorentz force directly drives the medium particles to produce mechanical vibration, while the temperature field induces thermal deformation vibration of the medium through thermoelastic effects. The two types of vibrations are coupled to form a response sound field that radiates outward. In this process, the coupling and transmission laws between the magnetic field distribution, eddy current electric field strength, Lorentz force amplitude, temperature field gradient and sound field pressure, propagation delay, and spectral characteristics are comprehensively analyzed. Combined with the medium density, elastic modulus, and thermal expansion coefficient, through multi-physics coupling mechanism analysis and data fitting, a nonlinear quantitative mapping relationship is established between the sound pressure amplitude, phase characteristics, and energy distribution of the ultrasonic measurement signal and the spatial distribution of conductivity inside the medium.

3. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In S2, the expression for Maxwell's equations is: ,in, It is the vector of eddy current electric field intensity induced by pulsed electromagnetic excitation inside the solid conductive medium being measured. It is the magnetic induction intensity vector of the space in which the medium is located, which includes the static magnetic field and the excitation alternating magnetic field components; It is the conductivity of the measured medium. It is the time variable of electromagnetic excitation and acoustic field response. It is the Hamiltonian operator, used to characterize the gradient, divergence, and curl operations of spatial field quantities.

4. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S3, the pulse width, peak current, and repetition frequency of the pulsed electromagnetic excitation, the magnetic induction intensity and regional uniformity of the static magnetic field, and the center frequency, receiving bandwidth, number of array elements, arrangement, and spacing of the ultrasonic transducer are selected as key variables. The remaining parameters are fixed by a single-factor variable method, and multiple sets of comparative tests are conducted by changing one parameter individually. Ultrasonic response signals under different conditions are collected, and the sound pressure amplitude, signal stability, and defect edge recognition clarity data are recorded. The effect of single parameter changes on lateral resolution, longitudinal resolution, and detection depth is analyzed one by one. Orthogonal experimental design is introduced to optimize and match the combination of multiple parameters. The detection blind zone size and imaging uniformity of different receiving array layouts, such as linear and ring arrangements, are compared. The coupling effect between parameters is analyzed. A quantitative correlation model between parameters and resolution is constructed through data fitting. Finally, the optimal parameter range and array layout that balances resolution and signal-to-noise ratio are determined.

5. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S4, the magnetoacoustic-thermoacoustic coupling response signal captured by the ultrasonic receiving array is acquired. Through preprocessing operations such as filtering, denoising, and signal synchronization alignment, environmental noise and system interference are eliminated. Then, the time inversion method is used to reverse the time of the preprocessed ultrasonic signal and use it as a boundary condition to carry out back propagation calculation in the magnetoacoustic-thermoacoustic coupling sound field wave equation. The spatial distribution reconstruction of the coupled sound source terms is initially realized. The compressed sensing algorithm is integrated, and a sparse representation model is constructed based on the sparsity characteristics of the sound source terms. The amount of sampled data is reduced by introducing L1 regularization constraints.

6. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S4, the reconstructed coupled sound source term is decomposed into a Lorentz force divergence contribution term and a thermal function contribution term based on the multi-field coupling mechanism. The intrinsic relationship between the two terms and the conductivity distribution of the medium is clarified, and an objective function based on the Lorentz force divergence-thermal function is constructed. A least squares iterative algorithm is introduced to continuously reduce the error of the objective function by iteratively updating the conductivity distribution parameters. An iterative convergence threshold and a maximum number of iterations are set to suppress the accumulation of errors during the inversion process, and finally, a high-precision quantitative inversion of the conductivity distribution inside the solid conductive medium is achieved.

7. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S5, a standard conductivity sample with the same material and size as the solid conductive medium being tested is selected. The conductivity values ​​of each region of the medium being tested obtained by inversion are compared with the calibration values ​​of the corresponding regions of the standard sample one by one. The absolute error, relative error and overall root mean square error of each detection point are calculated respectively to quantify and evaluate the accuracy of the conductivity inversion results.

8. The method for quantitative detection of conductivity of a solid conductive medium using inductive magnetothermal acoustic method according to claim 1, characterized in that, In step S6, the calibrated discrete conductivity data is spatially gridded, accurately mapping the conductivity value of each detection point to the actual spatial coordinates of the tested solid conductive medium, thus constructing a complete conductivity spatial distribution dataset. Subsequently, pseudo-color imaging technology is used, and a reasonable gradient color mapping rule is set according to the conductivity value to transform the abstract conductivity value into an intuitive two-dimensional pseudo-color cloud map or three-dimensional stereoscopic imaging model. At the same time, combined with the normal conductivity range of the tested medium, the standard sample calibration range, and industry testing standards, a conductivity anomaly judgment threshold is preset. An abnormal region with conductivity higher or lower than the normal range is screened out through a threshold comparison algorithm. A boundary extraction algorithm is used to accurately delineate the contour range of the abnormal region, marking the spatial coordinates, conductivity extreme values, and abnormal amplitude of the abnormal region, clearly distinguishing different abnormal types of conductivity that are too high or too low.

Images