An eddy current sensor for high temperature environment and calibration method thereof

Abstract

The present invention belongs to the technical field of eddy current sensor calibration and discloses an eddy current sensor for use in high-temperature environments and a calibration method thereof. The method comprises: synchronously collecting the operating current, voltage, surface position, temperature, standard displacement signal, and raw output voltage of the eddy current sensor, constructing an equivalent circuit model of the oxide layer, and optimizing and obtaining the thickness distribution; then constructing a thickness growth model and establishing a correlation model to calculate the time-varying impedance; then calculating a sensitivity coefficient function and designing a segmented calibration function to obtain a calibration parameter set; finally, dynamically compensating the raw output voltage using the calibration parameter set to obtain a calibrated displacement. The present invention collects the temperature field, standard displacement signal, and raw voltage signal to establish a three-dimensional dynamic model of temperature-oxide layer-impedance, compensating in real time for the nonlinear effects of oxide layer growth and temperature gradients.

Description

Technical Field

[0001] The present invention relates to the technical field of eddy current sensor calibration, and more particularly to an eddy current sensor for use in a high-temperature environment and a calibration method thereof. Background Art

[0002] In high-temperature environments, the calibration technology of eddy current sensors needs to be systematically optimized to address performance degradation issues under extreme working conditions.

[0003] A Chinese patent with authorization announcement number CN116989651B discloses an eddy current displacement sensor for an offshore platform and its calibration method. The eddy current displacement sensor is first calibrated during calibration, and a three-dimensional surface of the eddy current displacement sensor is drawn for the three coordinates of ambient temperature, spacing distance, and output voltage of different metal objects being measured, and the surface is converted into a calibration function for storage. During use, the eddy current sensor first determines the material of the corresponding metal object being measured based on the initial spacing distance and ambient temperature, so that the calibration function to be used can be determined. Then, during the detection process, the eddy current sensor can input the real-time detected ambient temperature and output voltage into the calibration function for calculation and error calibration, eliminating errors caused by different seawater temperatures or materials of the metal objects being measured. This can greatly improve the detection accuracy of the eddy current displacement sensor and meet the use requirements of the eddy current displacement sensor in the offshore platform automation system.

[0004] Although the above method can meet the application scenarios of marine platforms, research and practical application of the above method and existing technologies have revealed that the above method and existing technologies have at least the following defects:

[0005] Factors such as salt spray corrosion, water pressure fluctuations, and biological adhesion in the marine environment can alter the interface properties between the sensor and the metal being measured. For example, salt spray can easily degrade the sensor's surface insulation or alter the conductivity of the material being measured. Water pressure fluctuations can affect the stability of the sensor's mechanical structure, easily introducing additional measurement errors. On offshore platforms, metals being measured are exposed to seawater for long periods of time, which can lead to electrochemical corrosion or biofouling, causing the material's conductivity and magnetic permeability to change over time. Existing technologies rely on factory-preset three-dimensional surface functions, making it difficult to track the degradation of material properties in real time.

[0006] In view of this, the present invention proposes an eddy current sensor for use in a high temperature environment and a calibration method thereof to solve the above-mentioned problem. Summary of the Invention

[0007] In order to overcome the above-mentioned defects of the prior art and to achieve the above-mentioned purpose, the present invention provides the following technical solution: a method for calibrating an eddy current sensor for a high temperature environment, comprising the following steps:

[0008] Synchronously collect and process the working current and working voltage of the eddy current sensor that has reached the preset temperature to obtain impedance spectrum data; collect the surface position and corresponding temperature data of the eddy current sensor and splice them to obtain two-dimensional temperature field data; collect the standard displacement signal and the original output voltage of the sensor;

[0009] An equivalent circuit model of the oxide layer is constructed based on impedance spectrum data and two-dimensional temperature field data. The oxide layer equivalent circuit model is optimized based on the objective function constructed using the nature-inspired optimization algorithm to obtain the oxide layer thickness distribution.

[0010] Based on the oxide layer thickness distribution and two-dimensional temperature field data, a thickness growth model of the oxide layer was built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models of the time-varying oxide layer thickness and conductivity, and the time-varying oxide layer thickness and dielectric constant were established respectively to calculate the time-varying impedance.

[0011] The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the time-varying impedance and the standard displacement signal are combined to design a segmented calibration function. The sensitivity coefficient function, critical time and segmented calibration function are spliced together to obtain a calibration parameter set.

[0012] The original output voltage of the sensor is dynamically compensated in combination with the calibration parameter set to obtain the calibrated displacement.

[0013] Furthermore, the method for obtaining the oxide layer thickness distribution includes:

[0014] The equivalent impedance is calculated based on the oxide layer equivalent circuit model. Taking the minimization of the weighted residual between the real and imaginary parts of the equivalent impedance and the impedance as the objective function, an iterative optimization algorithm is used to obtain the optimized parameter set. The optimized parameter set includes the optimized base metal resistance, optimized oxide layer resistance, optimized base metal capacitance, optimized oxide layer capacitance, and optimized Warburg diffusion impedance.

[0015] The surface oxide layer of the eddy current sensor is discretized into N×M grid cells, each of which corresponds to an independent oxide layer resistance and oxide layer capacitance, where N and M are the number of rows and columns of the grid cells, respectively. Based on the optimized parameter set, each grid cell is assigned a locally optimized oxide layer resistance, locally optimized oxide layer capacitance, and locally optimized Warburg diffusion impedance.

[0016] According to the locally optimized oxide layer resistance, the first local oxide layer thickness is obtained by combining the oxide layer resistivity and the electrode effective area inversion;

[0017] According to the locally optimized oxide layer capacitance, the second local oxide layer thickness is obtained by combining the vacuum dielectric constant and the oxide layer relative dielectric constant inversion;

[0018] The thickness of the third local oxide layer is obtained based on the locally optimized Warburg diffusion impedance and the Warburg coefficient inversion.

[0019] Performing weighted fusion on the first local oxide layer thickness, the second local oxide layer thickness, and the third local oxide layer thickness to obtain the local oxide layer thickness; wherein the oxide layer resistivity and the oxide layer relative dielectric constant are corrected by using the Arrhenius equation;

[0020] The local oxide layer thickness of each grid cell is calculated to obtain the oxide layer thickness distribution.

[0021] Furthermore, the method for obtaining the time-varying impedance includes:

[0022] Based on a preset material database, the oxidation kinetic parameters, including the oxidation rate constant, activation energy, oxide layer limit thickness, and oxidation inhibition factor, are initialized. The N×M grid cells of the oxide layer on the surface of the eddy current sensor are obtained, and the local temperature and time-varying oxide layer thickness are extracted in each grid cell. The oxidation kinetic equation is solved for each grid cell. The oxide layer thickness distribution is used as the true value, and the oxidation kinetic parameters are optimized using the least squares method.

[0023] The updated value of the time-varying oxide layer thickness is calculated based on the optimized oxidation kinetic parameters. Combined with the porosity correction factor, a relationship model between conductivity and time-varying oxide layer thickness is established. Combined with the oxide layer thickness threshold, a relationship model between dielectric constant and time-varying oxide layer thickness is established. Substituting the updated value of the time-varying oxide layer thickness into the model, the conductivity field and dielectric constant field for each grid cell are obtained.

[0024] According to the conductivity field and dielectric constant field of each grid cell, the corresponding resistance component, capacitance component and Warburg impedance are calculated; based on the conductivity field and dielectric constant field of each grid cell, the time-domain Maxwell equations are constructed; the time-domain Maxwell equations are solved by the time-domain finite difference method to calculate the port time-domain voltage and current of the eddy current sensor at the current moment, and the time-varying impedance is obtained by short-time Fourier transform based on the port time-domain voltage and current of the eddy current sensor at the current moment.

[0025] Furthermore, the method for obtaining the time-varying oxide layer thickness includes:

[0026] The surface oxide layer of the eddy current sensor is divided into N×M grid units. A thickness growth model of the oxide layer of each grid unit is established based on the Arrhenius equation. The model parameters of the thickness growth model are obtained by fitting the oxide layer thickness distribution with the two-dimensional temperature field data through the least squares method. The obtained model parameters are substituted into the thickness growth model to obtain the time-varying oxide layer thickness. The division of the grid units is dynamically adjusted according to the growth of the oxide layer.

[0027] Furthermore, the method for obtaining the calibration parameter set includes:

[0028] According to the time-varying impedance and the oxide layer thickness distribution, an initial sensitivity coefficient function consisting of an initial sensitivity coefficient, an oxide layer thickness attenuation coefficient, an oxide layer thickness distribution, and the imaginary and real parts of the time-varying impedance is constructed. The parameters to be determined in the initial sensitivity coefficient function are obtained by a regression analysis method, including the initial sensitivity coefficient and the oxide layer thickness attenuation coefficient. The sensitivity coefficient function is updated according to the parameters to be determined in the obtained initial sensitivity coefficient function.

[0029] According to the oxidation rate equation, the critical time corresponding to half the maximum oxide layer thickness is obtained, a segmented calibration function is constructed, and the parameters to be measured in the segmented calibration function are fitted according to the critical time by the least squares method. The segmented calibration function is then constructed based on the obtained parameters to be measured;

[0030] The sensitivity coefficient function, segmented calibration function and critical time are spliced together to obtain the calibration parameter set.

[0031] Furthermore, the method for obtaining the calibrated displacement includes:

[0032] Obtain the real-time impedance and corresponding time of the eddy current sensor, and calculate the real-time effective impedance based on the real-time impedance;

[0033] The real-time effective oxide layer thickness is calculated through the real-time effective impedance; the critical time is calculated according to the real-time effective oxide layer thickness, the real-time effective displacement signal is obtained according to the real-time effective impedance calculation through the preset conversion function of the eddy current sensor, and the real-time effective displacement signal is calibrated through the segmented calibration function to obtain the calibrated displacement.

[0034] Furthermore, the method of constructing an oxide layer equivalent circuit model includes:

[0035] Obtaining first material data of the base metal and the oxide layer from a preset material database, the first material data including electrical conductivity, length, and cross-sectional area, calculating the base metal resistance and the oxide layer resistance based on the first material data in combination with the two-dimensional temperature field data, obtaining second material data of the base metal and the oxide layer, the second material data including dielectric constant, plate area, and plate spacing, calculating the base metal capacitance and the oxide layer capacitance based on the second material data in combination with the two-dimensional temperature field data;

[0036] The diffusion coefficient is obtained from the preset material database and combined with the two-dimensional temperature field data to calculate the Warburg diffusion impedance;

[0037] An equivalent circuit model of the oxide layer is constructed based on the base metal resistance, oxide layer resistance, base metal capacitance, oxide layer capacitance and Warburg diffusion impedance.

[0038] Furthermore, the method for obtaining impedance spectrum data includes:

[0039] The impedance is obtained by calculating the ratio of the working voltage to the working current, the amplitude and phase difference of the working voltage and the working current are measured synchronously, the complex impedance is calculated, and the impedance and the complex impedance are added to obtain the impedance spectrum data.

[0040] Furthermore, the method for obtaining two-dimensional temperature field data includes:

[0041] Use Kriging interpolation or finite element thermal simulation method to convert discrete temperature measurement points into a continuous two-dimensional temperature field to obtain two-dimensional temperature field data.

[0042] An eddy current sensor for use in a high temperature environment, applied to a calibration method for an eddy current sensor for use in a high temperature environment, comprising:

[0043] Data acquisition module: synchronously collects the working current and working voltage of the eddy current sensor that reaches the preset temperature and processes them to obtain impedance spectrum data; collects the surface position and corresponding temperature data of the eddy current sensor and splices them to obtain two-dimensional temperature field data; collects standard displacement signals and the original output voltage of the sensor;

[0044] Model equivalent module: Constructs an equivalent circuit model of the oxide layer based on impedance spectrum data and two-dimensional temperature field data. Optimizes the oxide layer equivalent circuit model based on the objective function established by the nature-inspired optimization algorithm to obtain the oxide layer thickness distribution.

[0045] Time-varying analysis module: Based on the oxide layer thickness distribution and two-dimensional temperature field data, an oxide layer thickness growth model is built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models between the time-varying oxide layer thickness and conductivity, and between the time-varying oxide layer thickness and dielectric constant are established to calculate the time-varying impedance.

[0046] Calibration analysis module: The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the time-varying impedance and the standard displacement signal are combined to design a segmented calibration function. The sensitivity coefficient function, critical time and segmented calibration function are combined to obtain the calibration parameter set.

[0047] Sensor calibration module: Dynamically compensates the original output voltage of the sensor in combination with the calibration parameter set to obtain the calibrated displacement.

[0048] The technical effects and advantages of the eddy current sensor for high temperature environment and the calibration method thereof of the present invention are as follows:

[0049] This method establishes a three-dimensional dynamic model of temperature, oxide layer, and impedance by synchronously collecting temperature fields, standard displacement signals, and raw voltage signals. This model compensates for the nonlinear effects of oxide layer growth and temperature gradients in real time. It also uses two-dimensional temperature field data to map the nonuniformity of oxide layer thickness distribution, enabling differentiated calibration of different areas of the sensor surface. Based on time-varying impedance, the compensation parameters are updated in conjunction with real-time data to adapt to material conductivity changes and zero-point drift under high-temperature conditions. This overcomes the challenges of material conductivity changes and zero-point drift in high-temperature environments, providing key technical support for health monitoring of high-temperature equipment such as aircraft engine blades and nuclear reactor components. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a method for calibrating an eddy current sensor for a high temperature environment according to the present invention;

[0051] Figure 2 This is a data flow diagram of the present invention;

[0052] Figure 3 Schematic diagram of the method for obtaining time-varying impedance of the present invention;

[0053] Figure 4 This is a flow chart of a method for calculating temperature field based on quantum thermal sensing according to embodiment 2 of the present invention;

[0054] Figure 5 This is a structural diagram of an eddy current sensor for use in a high-temperature environment according to Example 3 of the present invention. DETAILED DESCRIPTION

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0056] Example 1

[0057] See also Figure 1 and Figure 2 As shown, this embodiment provides a method for calibrating an eddy current sensor for a high temperature environment, comprising the following steps:

[0058] The working current and working voltage of the eddy current sensor that reaches the preset temperature (can be manually defined) are synchronously collected and processed to obtain impedance spectrum data; the surface position and corresponding temperature data of the eddy current sensor are collected and spliced to obtain two-dimensional temperature field data; the standard displacement signal and the original output voltage of the sensor are collected.

[0059] The operating current and operating voltage can be directly measured by an impedance analyzer. By real-time monitoring of the frequency domain response characteristics of the impedance spectrum, the changes in electrical parameters caused by oxide layer growth (such as resistance increase and capacitance attenuation) can be accurately captured, providing core data support for the subsequent establishment of an equivalent circuit model of the oxide layer, inversion of thickness distribution, prediction of time-varying impedance and dynamic compensation, ensuring the measurement accuracy and long-term stability of the sensor under high-temperature and complex working conditions.

[0060] The surface position and corresponding temperature data of the eddy current sensor can be collected through an array temperature sensor. Multiple temperature measurement points are arranged on the surface of the eddy current sensor or the measured area, and spatial positioning is achieved through position coordinate mapping. By collecting spatial temperature distribution data, the oxide layer growth kinetic parameters (such as activation energy and rate constant) can be accurately mapped, and the non-uniform effect of the sensor surface temperature gradient on the oxide layer thickness distribution can be captured, providing key input for establishing a three-dimensional coupled model of temperature-thickness-impedance, thereby realizing spatially differentiated inversion of the oxide layer equivalent circuit parameters, improving the accuracy of time-varying impedance prediction, and ultimately ensuring the adaptability of the dynamic compensation algorithm to temperature drift and oxide layer heterogeneity, and ensuring the measurement reliability of the sensor in complex high-temperature environments.

[0061] The standard displacement signal is obtained through laser interferometer measurement. By providing a reference input of known displacement, it helps to establish a mathematical model of the temperature-displacement response characteristics in the later stage and compensate for the zero drift and sensitivity attenuation caused by high temperature in real time. At the same time, combined with the temperature field distribution data, the nonlinear effect of the temperature gradient on the displacement measurement is separated, and the linearity and range stability of the sensor under extreme working conditions are verified, providing key parameter support for the dynamic compensation algorithm, and ultimately achieving high-precision displacement measurement and long-term reliability of the sensor in high-temperature environments.

[0062] The original output voltage of the sensor is collected through the output port of the preamplifier. The original output voltage of the sensor directly reflects the coupling state between the sensor and the object being measured, and includes the comprehensive influence of multiple physical field parameters such as oxide layer thickness, temperature gradient, and material conductivity. It is the core input of the subsequent displacement calibration. By real-time analysis of the amplitude, phase and waveform characteristics of the original output voltage, combined with temperature field data and standard displacement signals, the interference of temperature drift and oxide layer growth can be separated, and a nonlinear mapping relationship of voltage-displacement-temperature can be established, providing data support for generating sensitivity coefficient functions and segmented calibration parameters, and ultimately realizing adaptive calibration of the sensor under high-temperature and complex working conditions, ensuring displacement measurement accuracy and long-term reliability.

[0063] Methods for obtaining impedance spectroscopy data include:

[0064] The impedance is obtained by calculating the ratio of the working voltage to the working current, the amplitude and phase difference of the working voltage and the working current are measured synchronously, the complex impedance is calculated, and the impedance and the complex impedance are added to obtain the impedance spectrum data.

[0065] Methods for obtaining two-dimensional temperature field data include:

[0066] Use Kriging interpolation or finite element thermal simulation method to convert discrete temperature measurement points into a continuous two-dimensional temperature field to obtain two-dimensional temperature field data.

[0067] An equivalent circuit model of the oxide layer is constructed based on impedance spectrum data and two-dimensional temperature field data. The objective function is built based on the nature-inspired optimization algorithm to optimize the equivalent circuit model of the oxide layer and obtain the oxide layer thickness distribution.

[0068] Methods for constructing an oxide layer equivalent circuit model include:

[0069] Obtaining first material data of the base metal and the oxide layer from a preset material database, the first material data including electrical conductivity, length, and cross-sectional area, calculating the base metal resistance and the oxide layer resistance based on the first material data in combination with the two-dimensional temperature field data, obtaining second material data of the base metal and the oxide layer, the second material data including dielectric constant, plate area, and plate spacing, calculating the base metal capacitance and the oxide layer capacitance based on the second material data in combination with the two-dimensional temperature field data;

[0070] The diffusion coefficient is obtained from the preset material database and combined with the two-dimensional temperature field data to calculate the Warburg diffusion impedance;

[0071] An equivalent circuit model of the oxide layer is constructed based on the base metal resistance, oxide layer resistance, base metal capacitance, oxide layer capacitance and Warburg diffusion impedance.

[0072] Methods for obtaining oxide layer thickness distribution include:

[0073] The equivalent impedance is calculated based on the oxide layer equivalent circuit model. Taking the minimization of the weighted residual between the real and imaginary parts of the equivalent impedance and the impedance as the objective function, an iterative optimization algorithm is used to obtain the optimized parameter set. The optimized parameter set includes the optimized base metal resistance, optimized oxide layer resistance, optimized base metal capacitance, optimized oxide layer capacitance, and optimized Warburg diffusion impedance.

[0074] The surface oxide layer of the eddy current sensor is discretized into N×M grid cells, each of which corresponds to an independent oxide layer resistance and oxide layer capacitance, where N and M are the number of rows and columns of the grid cells, respectively. Based on the optimized parameter set, each grid cell is assigned a locally optimized oxide layer resistance, locally optimized oxide layer capacitance, and locally optimized Warburg diffusion impedance.

[0075] According to the locally optimized oxide layer resistance, the first local oxide layer thickness is obtained by combining the oxide layer resistivity and the electrode effective area inversion;

[0076] According to the locally optimized oxide layer capacitance, the second local oxide layer thickness is obtained by combining the vacuum dielectric constant and the oxide layer relative dielectric constant inversion;

[0077] The thickness of the third local oxide layer is obtained based on the locally optimized Warburg diffusion impedance and the Warburg coefficient inversion.

[0078] Performing weighted fusion on the first local oxide layer thickness, the second local oxide layer thickness, and the third local oxide layer thickness to obtain the local oxide layer thickness; wherein the oxide layer resistivity and the oxide layer relative dielectric constant are corrected by using the Arrhenius equation;

[0079] The local oxide layer thickness of each grid cell is calculated to obtain the oxide layer thickness distribution.

[0080] Based on the oxide layer thickness distribution and two-dimensional temperature field data, a thickness growth model of the oxide layer was built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models of the time-varying oxide layer thickness and conductivity, and the time-varying oxide layer thickness and dielectric constant were established respectively to calculate the time-varying impedance.

[0081] Methods for obtaining time-varying oxide thickness include:

[0082] The surface oxide layer of the eddy current sensor is divided into N×M grid cells, and a thickness growth model of the oxide layer of each grid cell is established based on the Arrhenius equation. The model parameters in the thickness growth model are obtained by fitting the oxide layer thickness distribution with the two-dimensional temperature field data using the least squares method. The obtained model parameters are substituted into the thickness growth model to obtain the time-varying oxide layer thickness. The division of the grid cells is dynamically adjusted according to the growth of the oxide layer. For example, when the oxide layer thickness exceeds a preset thickness threshold, the grid cells are refined (e.g., from 10μm to 5μm).

[0083] See also Figure 3 , methods for obtaining time-varying impedance include:

[0084] Initialize the oxidation kinetic parameters based on the preset material database. The oxidation kinetic parameters include the oxidation rate constant, activation energy, oxide layer limit thickness, and oxidation inhibition factor. Obtain the N×M grid cells of the oxide layer on the surface of the eddy current sensor. Extract the local temperature and time-varying oxide layer thickness in each grid cell.

[0085] Solve the oxidation kinetics equation for each grid cell (e.g., using a fourth-order Runge-Kutta method for time integration);

[0086] Taking the oxide layer thickness distribution as the true value, the oxidation kinetic parameters are optimized by the least square method;

[0087] The updated value of the time-varying oxide layer thickness is obtained based on the optimized oxidation kinetic parameters;

[0088] Combined with the porosity correction factor, a relationship model between conductivity and time-varying oxide layer thickness is constructed. Combined with the oxide layer thickness threshold, a relationship model between dielectric constant and time-varying oxide layer thickness is constructed. Substituting the updated value of the time-varying oxide layer thickness into the model, the conductivity field and dielectric constant field for each grid cell are obtained.

[0089] According to the conductivity field and dielectric constant field of each grid cell, the corresponding resistance component, capacitance component and Warburg impedance are calculated;

[0090] The time-domain Maxwell equations are constructed based on the conductivity field and dielectric constant field of each grid cell;

[0091] The time-domain finite-difference method is used to solve the time-domain Maxwell equations, and the time-domain voltage and current of the port of the eddy current sensor at the current moment are calculated. According to the time-domain voltage and current of the port of the eddy current sensor at the current moment, the time-varying impedance is obtained by short-time Fourier transform calculation.

[0092] The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the segmented calibration function is designed in combination with the time-varying impedance and the standard displacement signal. The sensitivity coefficient function, the critical time and the segmented calibration function are spliced together to obtain the calibration parameter set.

[0093] Methods for obtaining a calibration parameter set include:

[0094] According to the time-varying impedance and the oxide layer thickness distribution, an initial sensitivity coefficient function consisting of an initial sensitivity coefficient, an oxide layer thickness attenuation coefficient, an oxide layer thickness distribution, and the imaginary and real parts of the time-varying impedance is constructed. The parameters to be determined in the initial sensitivity coefficient function are obtained by a regression analysis method, including the initial sensitivity coefficient and the oxide layer thickness attenuation coefficient. The sensitivity coefficient function is updated according to the parameters to be determined in the obtained initial sensitivity coefficient function.

[0095] According to the oxidation rate equation, the critical time corresponding to half the maximum oxide layer thickness is obtained, a segmented calibration function is constructed, and the parameters to be measured in the segmented calibration function are fitted according to the critical time by the least squares method. The segmented calibration function is then constructed based on the obtained parameters to be measured;

[0096] The sensitivity coefficient function, segmented calibration function and critical time are spliced together to obtain the calibration parameter set.

[0097] The original output voltage of the sensor is dynamically compensated in combination with the calibration parameter set to obtain the calibrated displacement.

[0098] Methods for obtaining calibrated displacements include:

[0099] Obtain the real-time impedance and corresponding time of the eddy current sensor, and calculate the real-time effective impedance based on the real-time impedance;

[0100] The real-time effective oxide layer thickness is calculated through the real-time effective impedance; the critical time is calculated according to the real-time effective oxide layer thickness, the real-time effective displacement signal is obtained according to the real-time effective impedance calculation through the preset conversion function of the eddy current sensor, and the real-time effective displacement signal is calibrated through the segmented calibration function to obtain the calibrated displacement.

[0101] Example 2

[0102] See also Figure 4 As shown, this embodiment provides a method for calculating temperature field based on quantum thermal sensing applied to Example 1, including the following steps:

[0103] In a high-temperature stable diamond substrate, a nitrogen vacancy color center array is embedded through ion implantation and annealing processes to form a nanoscale temperature-sensitive unit; each nitrogen vacancy color center generates a fluorescence signal through laser excitation, and its zero-field splitting effect varies with temperature.

[0104] A 532nm laser pulse is used to initialize the electron spin state of the nitrogen vacancy color center, and a dynamic decoupling microwave sequence is applied to suppress magnetic noise and lattice vibration interference in a high-temperature environment, extending the coherence time from the microsecond level at room temperature to the hundreds of nanoseconds at high temperatures (such as 800°C).

[0105] Entangled photon pairs are used to create quantum entangled states of adjacent nitrogen-vacancy color centers. Quantum state tomography is then used to simultaneously measure the zero-field splitting frequency shifts of multiple color centers. This correlated measurement cancels out local thermal fluctuation noise, enabling single-point temperature measurement accuracy to surpass classical limits.

[0106] The unsteady-state heat conduction equation is discretized into a quantum Hamiltonian form, and the eigenstates are solved using a quantum phase estimation algorithm, which is then mapped to a temperature field distribution. Quantum parallel computing reduces the complexity of the traditional finite element method, achieving a thousand-fold acceleration on a quantum simulator, and outputting a two-dimensional temperature field with submicron resolution in real time.

[0107] The quantum temperature measurement results are fused with the infrared thermal imager data, and the systematic error introduced by the thermal expansion of the diamond substrate is eliminated through Kalman filtering.

[0108] Example 3

[0109] See also Figure 5 As shown, the eddy current sensor for high temperature environment described in this embodiment includes:

[0110] Data acquisition module: synchronously collects the working current and working voltage of the eddy current sensor that reaches the preset temperature and processes them to obtain impedance spectrum data; collects the surface position and corresponding temperature data of the eddy current sensor and splices them to obtain two-dimensional temperature field data; collects standard displacement signals and the original output voltage of the sensor;

[0111] Model equivalent module: Constructs an equivalent circuit model of the oxide layer based on impedance spectrum data and two-dimensional temperature field data. Optimizes the oxide layer equivalent circuit model based on the objective function established by the nature-inspired optimization algorithm to obtain the oxide layer thickness distribution.

[0112] Time-varying analysis module: Based on the oxide layer thickness distribution and two-dimensional temperature field data, an oxide layer thickness growth model is built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models between the time-varying oxide layer thickness and conductivity, and between the time-varying oxide layer thickness and dielectric constant are established to calculate the time-varying impedance.

[0113] Calibration analysis module: The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the time-varying impedance and the standard displacement signal are combined to design a segmented calibration function. The sensitivity coefficient function, critical time and segmented calibration function are combined to obtain the calibration parameter set.

[0114] Sensor calibration module: Dynamically compensates the original output voltage of the sensor in combination with the calibration parameter set to obtain the calibrated displacement.

[0115] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

[0116] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calibrating an eddy current sensor for a high temperature environment, characterized in that: The steps include: Synchronously collect and process the working current and working voltage of the eddy current sensor that has reached the preset temperature to obtain impedance spectrum data; collect the surface position and corresponding temperature data of the eddy current sensor and splice them to obtain two-dimensional temperature field data; collect the standard displacement signal and the original output voltage of the sensor; An equivalent circuit model of the oxide layer is constructed based on impedance spectrum data and two-dimensional temperature field data. The oxide layer equivalent circuit model is optimized based on the objective function constructed using the nature-inspired optimization algorithm to obtain the oxide layer thickness distribution. Based on the oxide layer thickness distribution and two-dimensional temperature field data, a thickness growth model of the oxide layer was built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models of the time-varying oxide layer thickness and conductivity, and the time-varying oxide layer thickness and dielectric constant were established respectively to calculate the time-varying impedance. The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the time-varying impedance and the standard displacement signal are combined to design a segmented calibration function. The sensitivity coefficient function, critical time and segmented calibration function are spliced together to obtain a calibration parameter set. The original output voltage of the sensor is dynamically compensated in combination with the calibration parameter set to obtain the calibrated displacement.

2. The eddy current sensor calibration method for a high temperature environment according to claim 1, characterized in that: Methods for constructing an oxide layer equivalent circuit model include: Obtaining first material data of the base metal and the oxide layer from a preset material database, the first material data including electrical conductivity, length, and cross-sectional area, calculating the base metal resistance and the oxide layer resistance based on the first material data in combination with the two-dimensional temperature field data, obtaining second material data of the base metal and the oxide layer, the second material data including dielectric constant, plate area, and plate spacing, calculating the base metal capacitance and the oxide layer capacitance based on the second material data in combination with the two-dimensional temperature field data; The diffusion coefficient is obtained from the preset material database and combined with the two-dimensional temperature field data to calculate the Warburg diffusion impedance; An equivalent circuit model of the oxide layer is constructed based on the base metal resistance, oxide layer resistance, base metal capacitance, oxide layer capacitance and Warburg diffusion impedance.

3. The eddy current sensor calibration method for a high temperature environment according to claim 2, characterized in that: Methods for obtaining oxide layer thickness distribution include: The equivalent impedance is calculated based on the oxide layer equivalent circuit model. Taking the minimization of the weighted residual between the real and imaginary parts of the equivalent impedance and the impedance as the objective function, an iterative optimization algorithm is used to obtain the optimized parameter set. The optimized parameter set includes the optimized base metal resistance, optimized oxide layer resistance, optimized base metal capacitance, optimized oxide layer capacitance, and optimized Warburg diffusion impedance. The surface oxide layer of the eddy current sensor is discretized into N×M grid cells, each of which corresponds to an independent oxide layer resistance and oxide layer capacitance, where N and M are the number of rows and columns of the grid cells, respectively. Based on the optimized parameter set, each grid cell is assigned a locally optimized oxide layer resistance, locally optimized oxide layer capacitance, and locally optimized Warburg diffusion impedance. According to the locally optimized oxide layer resistance, the first local oxide layer thickness is obtained by combining the oxide layer resistivity and the electrode effective area inversion; According to the locally optimized oxide layer capacitance, the second local oxide layer thickness is obtained by combining the vacuum dielectric constant and the oxide layer relative dielectric constant inversion; The thickness of the third local oxide layer is obtained based on the locally optimized Warburg diffusion impedance and the Warburg coefficient inversion. Performing weighted fusion on the first local oxide layer thickness, the second local oxide layer thickness, and the third local oxide layer thickness to obtain the local oxide layer thickness; wherein the oxide layer resistivity and the oxide layer relative dielectric constant are corrected by using the Arrhenius equation; The local oxide layer thickness of each grid cell is calculated to obtain the oxide layer thickness distribution.

4. The method for calibrating an eddy current sensor for a high temperature environment according to claim 3, wherein: Methods for obtaining time-varying impedance include: Based on a preset material database, the oxidation kinetic parameters, including the oxidation rate constant, activation energy, oxide layer limit thickness, and oxidation inhibition factor, are initialized. The N×M grid cells of the oxide layer on the surface of the eddy current sensor are obtained, and the local temperature and time-varying oxide layer thickness are extracted in each grid cell. The oxidation kinetic equation is solved for each grid cell. The oxide layer thickness distribution is used as the true value, and the oxidation kinetic parameters are optimized using the least squares method. The updated value of the time-varying oxide layer thickness is calculated based on the optimized oxidation kinetic parameters. Combined with the porosity correction factor, a relationship model between conductivity and time-varying oxide layer thickness is established. Combined with the oxide layer thickness threshold, a relationship model between dielectric constant and time-varying oxide layer thickness is established. Substituting the updated value of the time-varying oxide layer thickness into the model, the conductivity field and dielectric constant field for each grid cell are obtained. According to the conductivity field and dielectric constant field of each grid cell, the corresponding resistance component, capacitance component and Warburg impedance are calculated; based on the conductivity field and dielectric constant field of each grid cell, the time-domain Maxwell equations are constructed; the time-domain Maxwell equations are solved by the time-domain finite difference method to calculate the port time-domain voltage and current of the eddy current sensor at the current moment, and the time-varying impedance is obtained by short-time Fourier transform based on the port time-domain voltage and current of the eddy current sensor at the current moment.

5. The method for calibrating an eddy current sensor for a high temperature environment according to claim 4, wherein: Methods for obtaining time-varying oxide thickness include: The surface oxide layer of the eddy current sensor is divided into N×M grid units. A thickness growth model of the oxide layer of each grid unit is established based on the Arrhenius equation. The model parameters of the thickness growth model are obtained by fitting the oxide layer thickness distribution with the two-dimensional temperature field data through the least squares method. The obtained model parameters are substituted into the thickness growth model to obtain the time-varying oxide layer thickness. The division of the grid units is dynamically adjusted according to the growth of the oxide layer.

6. The method for calibrating an eddy current sensor for a high temperature environment according to claim 5, characterized in that: Methods for obtaining a calibration parameter set include: According to the time-varying impedance and the oxide layer thickness distribution, an initial sensitivity coefficient function consisting of an initial sensitivity coefficient, an oxide layer thickness attenuation coefficient, an oxide layer thickness distribution, and the imaginary and real parts of the time-varying impedance is constructed. The parameters to be determined in the initial sensitivity coefficient function are obtained by a regression analysis method, including the initial sensitivity coefficient and the oxide layer thickness attenuation coefficient. The sensitivity coefficient function is updated according to the parameters to be determined in the obtained initial sensitivity coefficient function. According to the oxidation rate equation, the critical time corresponding to half the maximum oxide layer thickness is obtained, a segmented calibration function is constructed, and the parameters to be measured in the segmented calibration function are fitted according to the critical time by the least squares method. The segmented calibration function is then constructed based on the obtained parameters to be measured; The sensitivity coefficient function, segmented calibration function and critical time are spliced together to obtain the calibration parameter set.

7. The method for calibrating an eddy current sensor for a high temperature environment according to claim 1, wherein: Methods for obtaining calibrated displacements include: Obtain the real-time impedance and corresponding time of the eddy current sensor, and calculate the real-time effective impedance based on the real-time impedance; The real-time effective oxide layer thickness is calculated through the real-time effective impedance; the critical time is calculated according to the real-time effective oxide layer thickness, the real-time effective displacement signal is obtained according to the real-time effective impedance calculation through the preset conversion function of the eddy current sensor, and the real-time effective displacement signal is calibrated through the segmented calibration function to obtain the calibrated displacement.

8. The method for calibrating an eddy current sensor for a high temperature environment according to claim 1, wherein: Methods for obtaining impedance spectroscopy data include: The impedance is obtained by calculating the ratio of the working voltage to the working current, the amplitude and phase difference of the working voltage and the working current are measured synchronously, the complex impedance is calculated, and the impedance and the complex impedance are added to obtain the impedance spectrum data.

9. The method for calibrating an eddy current sensor for a high temperature environment according to claim 1, wherein: Methods for obtaining two-dimensional temperature field data include: Use Kriging interpolation or finite element thermal simulation method to convert discrete temperature measurement points into a continuous two-dimensional temperature field to obtain two-dimensional temperature field data.

10. An eddy current sensor for use in a high temperature environment, applied to the eddy current sensor calibration method for use in a high temperature environment according to any one of claims 1 to 9, characterized in that: include: Data acquisition module: synchronously collects the working current and working voltage of the eddy current sensor that reaches the preset temperature and processes them to obtain impedance spectrum data; Collect the surface position and corresponding temperature data of the eddy current sensor, and splice them to obtain two-dimensional temperature field data; collect standard displacement signals and sensor original output voltage; Model equivalent module: Constructs an equivalent circuit model of the oxide layer based on impedance spectrum data and two-dimensional temperature field data. Optimizes the oxide layer equivalent circuit model based on the objective function established by the nature-inspired optimization algorithm to obtain the oxide layer thickness distribution. Time-varying analysis module: Based on the oxide layer thickness distribution and two-dimensional temperature field data, an oxide layer thickness growth model is built to obtain the time-varying oxide layer thickness. Based on the thickness growth model, relationship models between the time-varying oxide layer thickness and conductivity, and between the time-varying oxide layer thickness and dielectric constant are established to calculate the time-varying impedance. Calibration analysis module: The sensitivity coefficient function is obtained based on the time-varying impedance calculation. According to the predefined critical time, the time-varying impedance and the standard displacement signal are combined to design a segmented calibration function. The sensitivity coefficient function, critical time and segmented calibration function are combined to obtain the calibration parameter set. Sensor calibration module: Dynamically compensates the original output voltage of the sensor in combination with the calibration parameter set to obtain the calibrated displacement.

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