Fuel rod oxide film thickness measurement system and method

Abstract

The application provides a fuel rod oxide film thickness measurement system and method, the system comprising: an excitation signal source for providing an excitation signal; a probe module, the probe module adopts a bridge structure, the input end of the bridge structure is connected with the excitation signal source, and the output end of the bridge structure outputs a differential signal; a processing module connected with the output end of the probe module, for processing the differential signal to obtain a base frequency demodulation signal reflecting the oxide film thickness information; and an upper computer for processing the base frequency demodulation signal to obtain the oxide film thickness of the fuel rod. The method is based on the system, the measurement results under multi-frequency excitation are processed, the influence of the differences in the fuel rod cladding tube conductivity and the metal coating thickness between different samples is reduced, and the precise measurement of the fuel rod oxide film thickness is realized.

Description

Technical Field

[0001] This application belongs to the field of nuclear power generation technology, and in particular relates to a system and method for measuring the thickness of oxide film on fuel rods. Background Technology

[0002] To generate electricity using nuclear energy, nuclear fuel is processed into small cylindrical pellets. Hundreds of these pellets are then stacked in a zirconium (Zr) alloy cladding tube and sealed to form fuel rods. Multiple fuel rods are combined to form fuel assemblies for use in the reactor. The fuel rod cladding tube is the first pressure boundary of a nuclear power plant, and its reliability is crucial for maintaining nuclear power safety. After operating in the reactor for a period of time, the cladding tube will corrode and deteriorate under the high temperature and radiation environment, accumulating an oxide film on its surface and thinning the tube wall. To prevent serious problems caused by corrosion and improve the safety and service life of nuclear fuel rods, the current main method is to coat the fuel rods with a metallic coating. This method involves spraying chromium (Cr) particles onto the Zr alloy fuel rod cladding tube to mitigate corrosion caused by environmental factors. However, the oxide film that forms during operation severely affects the thermal conductivity of the cladding tubes, increasing the thermal resistance between the cladding tube surface and the coolant, reducing the heat exchange capacity of the fuel assembly, and accelerating the corrosion and aging of the fuel rods as the oxide film thickness increases. Therefore, oxide film thickness and cladding tube wall thickness are crucial parameters for the safe operation of nuclear power plants, necessitating regular inspection to ensure the safe operation of the fuel rods. The oxide film thickness on fuel rods is typically only tens of micrometers. Measurement accuracy is paramount when measuring oxide film thickness, as even micrometer-level thickness differences are important for assessing fuel assembly safety. Zero breakage of nuclear fuel is a shared goal of fuel design, production, supply, and nuclear power plant operation. Therefore, comprehensive and accurate inspection of the fuel cladding tubes to ensure their safety and reliability is an essential step in the research, development, production, and testing of fuel assemblies.

[0003] Existing methods for measuring the thickness of the oxide film on the outer surface of cladding tubes mainly include optical detection, ultrasonic detection, and electromagnetic detection. Optical coherence tomography (OCT) can be used to detect the thickness of the oxide film formed on the surface of fuel rods, as well as the thickness of ferromagnetic material deposits caused by external corrosion. However, optical detection is difficult to detect defects in the oxide film and the deposited material. High-frequency ultrasonic probes can also be used for oxide film thickness measurement, but ultrasonic detection is limited by the need for a coupling agent, making rapid imaging difficult. Electromagnetic detection has advantages such as non-contact operation, high sensitivity, and fast detection speed. Eddy current detection is widely used for the detection of samples of non-ferromagnetic metal materials. The main principle of eddy current detection is the mutual inductance effect between the coil and the detection material. After an excitation signal is applied to the measuring coil, an induced magnetic field is generated near the coil. The alternating induced magnetic field induces a current inside the metal material. The induced current affects the magnitude of the current signal at the coil port through mutual inductance. By measuring the change in the coil output signal, parameters such as the thickness, defects, and conductivity of the metal material can be measured. For measuring the oxide film thickness of fuel rods, eddy current detection can be used. When an excitation signal is applied to the probe coil, the relationship between the change in the voltage signal output by the coil at the same frequency and the thickness of the oxide layer being measured is studied. This allows for the investigation of the impedance characteristics at different lift-off heights or excitation frequencies, thus accurately detecting the oxide film thickness of fuel rod samples. Currently, several foreign companies and institutions have developed fuel rod oxide film detection equipment based on the eddy current lift-off effect. The SICOM-COR series equipment from the Spanish nuclear fuel company ENUSA uses the eddy current lift-off effect for detection, achieving a measurement error of 6μm. The Idaho National Laboratory in the United States studied the performance of probes for measuring the oxide film thickness of nuclear fuel cladding tubes, demonstrating a strong correlation between temperature changes and the detection results of eddy current sensors; as the temperature increases, the response of the eddy current sensor decreases, resulting in a decrease in the measured oxide film thickness. Domestically, fuel rod oxide film detection technology is also under development. The China Institute of Atomic Energy has studied surface oxide film measurement technology for spent fuel elements in pressurized water reactors. Using eddy current detection technology, they conducted the first full-scale measurement study of the oxide film thickness of spent fuel rod cladding at the Qinshan Nuclear Power Plant in a hot chamber. The CGN Research Institute has studied the structure of the oxide film detection device for nuclear fuel assemblies. By drawing on the Hooke hinge mechanism, a structure for an oxide film detection device has been developed, and the oxide film on the fuel rods is measured by mounting an eddy current probe.

[0004] To date, there are few reports on the application of eddy current thickness measurement to the oxide layer thickness of fuel rods, while research on the thickness of metal coatings and other metal materials is more extensive and in-depth. Sungkyunkwan University in South Korea has studied a technique for measuring coating thickness using pulsed eddy currents, achieving a resolution of approximately 20 μm. The Korea National Institute of Standards and Technology (KIST) has studied a method for measuring the thickness of chromium coatings on fuel rod surfaces. They used a swept-frequency eddy current detection method, selecting a frequency range sensitive to changes in surface coating thickness, and obtained thickness measurement results for non-uniform coatings by analyzing the impedance of the measuring coil. The University of Science and Technology of China recently studied a system for measuring the thickness of non-ferromagnetic metal thin films based on the phase difference between signals from a reference coil and an induction coil. The developed probe can measure copper film thicknesses of 3-650 μm and aluminum film thicknesses of 5-900 μm. These methods for measuring coating or metal material thickness also have important reference value for research on fuel rod oxide film cladding detection methods.

[0005] Measuring the thickness of the oxide film on fuel rods requires not only micrometer-level precision but also the resolution of other interfering factors, such as differences in the conductivity of the cladding tube and the thickness of the metal coating. The fuel rod cladding tube itself is made of Zr alloy, which reacts with water at high temperatures to form an oxide film. The resulting hydrogen ions react with Zr, affecting the conductivity of the cladding tube itself. This leads to variations in conductivity across different samples due to differences in the aging state of the cladding tube. Simultaneously, the metal coating used to prevent corrosion also varies between different samples and at different locations within the same sample. Both of these factors have been proven to affect the accuracy of oxide film thickness measurements. Summary of the Invention

[0006] The purpose of this application is to provide a fuel rod oxide film thickness measurement system and method to solve the problem of inaccurate measurement of fuel rod oxide film thickness.

[0007] In a first aspect, this application provides a fuel rod oxide film thickness measurement system, characterized in that the system comprises: an excitation signal source for providing an excitation signal; a probe module employing a bridge structure, the input end of the bridge structure being connected to the excitation signal source, and the output end of the bridge structure outputting a differential signal; a processing module connected to the output end of the probe module for processing the differential signal to obtain a fundamental frequency demodulated signal reflecting oxide film thickness information; and a host computer for processing the fundamental frequency demodulated signal to obtain the oxide film thickness of the fuel rod. The probe module in this application is designed with a bridge structure, which effectively suppresses interference from the ambient magnetic field and measurement noise and drift caused by the probe's own structure, improving measurement accuracy and thus improving the accuracy of oxide film thickness calculation.

[0008] In one implementation of the first aspect, the probe module includes a reference probe and a measuring probe. Both the reference probe and the measuring probe include a magnetic core, a first coil, and a second coil. The first coil and the second coil are respectively wound around two ends of the magnetic core. The four coils of the reference probe and the measuring probe are connected to form a bridge structure. In this implementation, the measuring probe and the reference probe each have two coils forming a bridge structure, constituting a differential measurement method. This effectively suppresses common-mode noise, eliminates measurement errors caused by variations in interference factors, and achieves accurate measurement of the oxide film.

[0009] In one implementation of the first aspect, when measuring the oxide film thickness of the fuel rod, the reference probe is attached to the fuel rod sample for eddy current detection.

[0010] In one implementation of the first aspect, the processing module includes: a differential amplifier connected to the output of the probe module and amplifying the differential signal output by the probe module; and a lock-in amplifier connected to the output of the differential amplifier and the excitation signal source, wherein the lock-in amplifier locks the differential amplified signal output by the differential amplifier with the excitation signal and outputs a fundamental frequency demodulated signal reflecting thickness information.

[0011] Secondly, this application provides a method for measuring the oxide film thickness of fuel rods. The method is based on the system described in the first aspect of this application. The method includes: constructing an inversion function for retrieving oxide film thickness based on the fundamental frequency demodulated signal and an optimized solution model for the inversion function; the excitation signal source provides excitation signals of different frequencies to the probe module, and measures the fundamental frequency demodulated signals of multiple fuel rod samples at each excitation frequency to form a sample dataset; using the sample dataset to solve the optimized solution model to obtain the inversion function; the excitation signal source provides an excitation signal at a certain frequency to the probe module, and measures the fundamental frequency demodulated signal of the fuel rod under test at that excitation frequency; inputting the measured fundamental frequency demodulated signal of the fuel rod under test into the solved inversion function to calculate the oxide film thickness of the fuel rod under test. This application proposes a multi-frequency algorithm principle, which involves adding a series of excitation signals to the probe, measuring the probe's induced signal at each excitation frequency, and processing the measurement results under multi-frequency excitation to fit the inversion function, thereby enabling accurate measurement of the oxide film thickness.

[0012] In one implementation of the second aspect, the inversion function is constructed using a quadratic relation.

[0013] In one implementation of the second aspect, the inversion function is expressed as: h = f(X) = k0 + X(1)k1 + X(2)k2 + X(1)2 k3+X(2) 2 k4+X(1)X(2)k5, where h is the oxide film thickness, X is the fundamental frequency demodulated signal, f is the inversion function, X(1) is the real part of the fundamental frequency demodulated signal, X(2) is the imaginary part of the fundamental frequency demodulated signal, and k0, k1, k2, k3, k4, k5 are the coefficients of the quadratic relation.

[0014] In one implementation of the second aspect, the optimization solution model is expressed as: Where h is the oxide film thickness, X is the fundamental frequency demodulation signal, f is the inversion function, d is the thickness of the fuel rod metal coating, and σ is the conductivity of the fuel rod cladding tube.

[0015] In one implementation of the second aspect, solving the optimization model using the sample dataset to obtain the inversion function includes: assuming the number of fuel rod samples is m, the excitation signal source provides n excitation signals of different frequencies to the probe module, obtaining the oxide film thickness of the fuel rod samples and forming a vector h = [h1; h2; ... h...]. m ], h i To determine the oxide film thickness of the i-th fuel rod sample, the real and imaginary parts of the measured fundamental frequency demodulated signal are used to form matrices X(1) and X(2), where X(1) and X(2) are both m*n dimensional matrices. The element in the i-th row and j-th column of X(1) and X(2) corresponds to the real and imaginary parts of the fundamental frequency demodulated signal measured at the j-th excitation frequency for the i-th fuel rod sample, i = 1, 2, ..., m, j = 1, 2, ..., n. The coefficient vector K = [k0; k1; k2; k3; k4; k5] of the quadratic relation is constructed, where k0, k1, k2, k3, k4, and k5 are n-dimensional vectors, and k0 = [k 01 ;k 02 ;...k 0n ], k1=[k 11 ;k 12 ;...k 1n ], k2=[k 21 ;k 22 ;...k 2n ], k3=[k 31 ;k 32 ;...k 3n ], k4=[k 41 ;k 42 ;...k 4n ], k5=[k 51 ;k 52 ;...k 5n ], where k 0j k 1j k 2j k 3j k4j k 5j The coefficients of the quadratic relation of the inversion function corresponding to the j-th excitation frequency are given; the optimization solution model is transformed into:

[0016]

[0017] sth = [e (m，n) X(1) X(2) X(1) 2 X(2) 2 X(1)X(2)]*K

[0018] Among them, e (m，n) Let D be an m*n dimensional identity matrix and D be a partial differential matrix; solve the optimization model to obtain the coefficient vector K and obtain the inversion function under different excitation frequencies.

[0019] In one implementation of the second aspect, the fundamental frequency demodulated signal obtained from the measurement of the fuel rod under test is input to the solved inversion function to calculate the oxide film thickness of the fuel rod under test, which includes: selecting the inversion function at the corresponding excitation frequency according to the excitation frequency of the excitation signal applied during measurement, and using the inversion function to calculate the oxide film thickness of the fuel rod under test.

[0020] As described above, the fuel rod oxide film thickness measurement system and method of this application have the following beneficial effects:

[0021] (1) A new probe structure design for thickness measurement is proposed, which can effectively suppress the interference caused by the ambient magnetic field and the measurement noise and drift caused by the probe structure itself.

[0022] (2) A multi-frequency measurement algorithm is proposed, which adds a series of excitation signals to the probe module and measures the probe's induced signal at each excitation frequency. By processing the measurement results under multi-frequency excitation, the influence of differences in the conductivity of fuel rod cladding tubes and the thickness of metal coatings between different samples is reduced, and the thickness of the oxide film on the fuel rod is accurately measured. Attached Figure Description

[0023] Figure 1 The diagram shown is a schematic representation of the fuel rod oxide film thickness measurement system described in an embodiment of this application.

[0024] Figure 2 The diagram shows a sample measurement performed using the measuring probe described in an embodiment of this application.

[0025] Figure 3A The figure shows the simulation results of the effect of the difference in conductivity of the cladding tube material on the measurement of oxide film thickness when the excitation frequency is 1MHz.

[0026] Figure 3B The figure shows the simulation results of the effect of the difference in conductivity of the cladding tube material on the oxide film thickness measurement when the excitation frequency is 2.17MHz.

[0027] Figure 3C The figure shows the simulation results of the effect of the difference in conductivity of the cladding tube material on the oxide film thickness measurement when the excitation frequency is 4.75MHz.

[0028] Figure 4A The figure shows the simulation results of the effect of the difference in metal coating thickness on the measurement of oxide film thickness when the excitation frequency is 1MHz.

[0029] Figure 4B The figure shows the simulation results of the effect of the difference in metal coating thickness on the measurement of oxide film thickness when the excitation frequency is 2.17MHz.

[0030] Figure 4C The figure shows the simulation results of the effect of the difference in metal coating thickness on the measurement of oxide film thickness when the excitation frequency is 4.75MHz.

[0031] Figure 5 The flowchart shown is a method for measuring the oxide film thickness of fuel rods according to an embodiment of this application.

[0032] Component designation explanation

[0033] 11-Excitation signal source

[0034] 12-Reference Probe

[0035] 13-Measuring probe

[0036] 14-Differential Amplifier

[0037] 15-Lock-in Amplifier

[0038] 16-Host computer

[0039] 21-Oxide film

[0040] 22-Metallic Coating

[0041] 23-Fuel rod cladding tube Detailed Implementation

[0042] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0043] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. Therefore, the drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0044] Measuring the thickness of the oxide film on fuel rods requires not only micrometer-level accuracy but also the resolution of interference from various factors, such as differences in the conductivity of the cladding tube and the thickness of the metal coating. The fuel rod cladding tube itself is made of Zr alloy, which reacts with water at high temperatures to form an oxide film. The resulting hydrogen ions react with Zr, affecting the conductivity of the cladding tube itself. This leads to variations in conductivity across different samples due to differences in the aging state of the cladding tube. Furthermore, the metal coating used to prevent corrosion also varies between different samples and at different locations within the same sample. Both of these factors have been proven to affect the accuracy of oxide film thickness measurements. Therefore, this application proposes a fuel rod oxide film thickness measurement system and method. It employs a probe structure with strong anti-interference capabilities and low noise to achieve accurate oxide film thickness measurement. Simultaneously, it provides a multi-frequency algorithm to eliminate interference from differences in the conductivity of the cladding tube and the thickness of the metal coating, thus achieving accurate measurement of the fuel rod oxide film thickness.

[0045] The technical solutions in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0046] like Figure 1 As shown, this embodiment provides a fuel rod oxide film thickness measurement system. The system includes: an excitation signal source 11 for providing an excitation signal; a probe module, which adopts a bridge structure, with the input end of the bridge structure connected to the excitation signal source and the output end of the bridge structure outputting a differential signal; a processing module, which is connected to the output end of the probe module, for processing the differential signal to obtain a fundamental frequency demodulated signal reflecting oxide film thickness information; and a host computer 16, which processes the fundamental frequency demodulated signal to obtain the oxide film thickness of the fuel rod.

[0047] Preferably, the probe module includes a reference probe 12 and a measuring probe 13. Both the reference probe 13 and the measuring probe 13 include a magnetic core, a first coil, and a second coil. The first coil and the second coil are respectively wound around the two ends of the magnetic core. The four coils of the reference probe 12 and the measuring probe 13 are connected to form a bridge structure. Figure 1In the diagram, the four coils are L1 to L4. L1 and L2 together form the reference probe 12, and L3 and L4 together form the measuring probe 13.

[0048] The processing module includes: a differential amplifier 14, which is connected to the output of the probe module and amplifies the differential signal output by the probe module; and a lock-in amplifier 15, which is connected to the output of the differential amplifier 14 and the excitation signal source 11. The lock-in amplifier 15 locks the differential amplified signal output by the differential amplifier 14 with the excitation signal and outputs a fundamental frequency demodulated signal reflecting thickness information.

[0049] Figure 2 This is a schematic diagram of a measurement probe performing sample measurement. The measurement probe 13 consists of a measurement coil L4, a reference coil L3, and a magnetic core. The measurement probe 13 is attached to the sample for eddy current detection. The sample mainly consists of three layers: an oxide film 21, a metal coating 22, and a fuel rod cladding tube 23. During measurement, an alternating current of a specific frequency is passed through coil L4 to generate an excitation magnetic field. Simultaneously, L4 senses and detects changes in the magnetic field generated by eddy currents in the sample. The function of coil L3 is to suppress common-mode interference and improve the probe's anti-interference capability. The four coils of the measurement probe and the reference probe are connected in accordance with... Figure 1 The bridge connection is implemented using a specific method. The output differential signal eliminates common-mode noise and drift. The amplitude and phase of this differential signal vary depending on the material of the sample being measured and the thickness of the oxide film and metal coating. The differential signal output from the measuring probe is amplified by a differential amplifier and then fed into a lock-in amplifier. It is phase-locked with a reference signal to extract the fundamental frequency demodulated signal reflecting the thickness information, which is then transmitted to the host computer for processing. The reference signal is the excitation signal output from the excitation signal source. The basic principle of thickness measurement is based on the lift-off effect of induced eddy currents. The measuring probe and the reference probe each have two coils, forming a bridge structure to constitute a differential measurement method. This effectively suppresses common-mode noise, eliminates measurement errors caused by variations in interference factors, and achieves accurate measurement of the oxide film.

[0050] Figure 3A , Figure 3B as well as Figure 3C The simulation results shown demonstrate the influence of differences in the conductivity of the cladding material on the oxide film thickness measurement. The cladding conductivity was 1.43 MS / m and 0.805 MS / m, the excitation frequencies were 1 MHz, 2.17 MHz, and 4.75 MHz, the metal coating thickness was 15 μm, and the oxide film thickness ranged from 3 μm to 9 μm. The results show that the coil output voltage changes with the cladding conductivity, and the output voltage varies with frequency at different excitation frequencies.

[0051] Figure 4A , Figure 4B as well as Figure 4C The simulation results shown demonstrate the effect of variations in metal coating thickness on the measurement of oxide film thickness. The conductivity of the cladding tube was fixed at 1.43 MS / m, and the oxide film thicknesses were 3 μm and 7 μm, with the metal coating thickness varying from 12 μm to 20 μm. The results show that the coil output voltage changes with increasing metal coating thickness.

[0052] To eliminate measurement errors caused by variations in the two factors mentioned above and achieve accurate measurement of the oxide film, this application proposes a method for measuring the oxide film thickness of fuel rods. This method is a multi-frequency measurement algorithm that applies a series of excitation signals to the probe and measures the probe's induced signal at each excitation frequency. By processing the measurement results under multi-frequency excitation, the influence of differences in the conductivity of the fuel rod cladding tube and the thickness of the metal coating between different samples is reduced, enabling precise measurement of the oxide film thickness of the fuel rods.

[0053] like Figure 5 As shown, this application provides a method for measuring the oxide film thickness of a fuel rod. The method is based on the system described above and includes steps S1 to S5.

[0054] Step S1: Construct an inversion function for retrieving oxide film thickness based on the fundamental frequency demodulation signal and an optimized solution model for the inversion function.

[0055] Preferably, the inversion function is constructed using a quadratic relation, and the inversion function is expressed as:

[0056] h=f(X)=k0+X(1)k1+X(2)k2+X(1) 2 k3+X(2) 2 k4+X(1)X(2)k5

[0057] Where h is the oxide film thickness, X is the fundamental frequency demodulated signal, f is the inversion function, X(1) is the real part of the fundamental frequency demodulated signal, X(2) is the imaginary part of the fundamental frequency demodulated signal, and k0, k1, k2, k3, k4, and k5 are the coefficients of the quadratic relation.

[0058] The optimization solution model is expressed as follows:

[0059]

[0060] Where h is the oxide film thickness, X is the fundamental frequency demodulation signal, f is the inversion function, d is the thickness of the fuel rod metal coating, and σ is the conductivity of the fuel rod cladding tube.

[0061] Step S2: The excitation signal source provides excitation signals of different frequencies to the probe module, and measures the fundamental frequency demodulation signals of multiple fuel rod samples at each excitation frequency to form a sample dataset.

[0062] Step S3: Use the sample dataset to solve the optimization model to obtain the inversion function.

[0063] Preferably, step S3 includes:

[0064] First, assuming the number of fuel rod samples is m, the excitation signal source provides n excitation signals of different frequencies to the probe module to obtain the oxide film thickness of the fuel rod samples and form a vector h = [h1; h2; ... h...]. m ], h i Let X(1) be the oxide film thickness of the i-th fuel rod sample. The real and imaginary parts of the measured fundamental frequency demodulation signal are used to form matrices X(1) and X(2). X(1) and X(2) are both m*n dimensional matrices. The element in the i-th row and j-th column of X(1) and X(2) corresponds to the real and imaginary parts of the fundamental frequency demodulation signal of the i-th fuel rod sample measured at the j-th excitation frequency, i = 1, 2, ..., m, j = 1, 2, ..., n.

[0065] Then, construct the coefficient vector K = [k0; k1; k2; k3; k4; k5] of the quadratic relation, where k0, k1, k2, k3, k4, and k5 are n-dimensional vectors, and k0 = [k 01 ;k 02 ;...k 0n ], k1=[k 11 ;k 12 ;...k 1n ], k2=[k 21 ;k 22 ;...k 2n ], k3=[k 31 ;k 32 ;...k 3n ], k4=[k 41 ;k 42 ;...k 4n ], k5=[k 51 ;k 52 ;……k5n],where k 0j k 1j k 2j k 3j k 4j k 5j These are the coefficients of the quadratic relation of the inversion function corresponding to the j-th excitation frequency;

[0066] Next, the optimization solution model is transformed into:

[0067]

[0068] sth = [e (m，n) x(1) X(2) X(1) 2 X(2) 2 X(1)X(2)]*K

[0069] Among them, e (m，n) Let D be an m*n dimensional identity matrix, and D be a partial differential matrix;

[0070] Finally, the optimization model is solved to obtain the coefficient vector K, and the inversion function under different excitation frequencies is obtained.

[0071] Step S4: The excitation signal source provides an excitation signal at a certain frequency to the probe module, and measures the fundamental frequency demodulated signal of the fuel rod under test at that excitation frequency. The excitation frequency in this step can be any excitation frequency applied during the inversion function optimization solution described above.

[0072] Step S5: Input the fundamental frequency demodulated signal obtained from the measurement of the fuel rod under test into the solved inversion function to calculate the oxide film thickness of the fuel rod under test. In this step, the inversion function corresponding to the excitation frequency of the excitation signal applied during measurement is selected, and the oxide film thickness of the fuel rod under test is calculated using the inversion function.

[0073] To more clearly explain the principle of the measurement method of this application, the following detailed explanation is provided.

[0074] The method first measures the fundamental frequency demodulated signal output by the above system at n different frequencies. The fundamental frequency demodulated signal at each frequency includes the real part and the imaginary part of the signal. Therefore, the output data X of the n measurements is an n×2 matrix. Next, the functional relationship shown in Equation (1) is constructed to invert the oxide film thickness h from the measurement data X.

[0075] h=f(X) (1)

[0076] Considering that X is also affected by the thickness (d) of the metal coating and the conductivity (σ) of the cladding tube, in order to ensure that the oxide film thickness calculation result is not affected by d and σ, the inversion function f should satisfy formula (2), that is, the partial derivative of f with respect to the thickness d of the metal coating and the conductivity σ of the cladding tube is equal to 0. Based on this consideration, this application adopts the optimization idea shown in formula (3) to determine the inversion function f.

[0077]

[0078]

[0079] This application uses a quadratic polynomial to fit the inversion function f. Let the number of test samples be m, and the number of detection frequencies used for each sample be n. Then h can be expressed as a matrix h0. (m，1) That is, h = [h1; h2; ... h m X is expressed as matrix X (m ，n，2) X consists of two parts, X(1) and X(2), both of which are m*n dimensional matrices. The element in the i-th row and j-th column of X(1) and X(2) corresponds to the real and imaginary parts of the fundamental frequency demodulated signal measured at the j-th excitation frequency for the i-th fuel rod sample, i = 1, 2, ..., m, j = 1, 2, ..., n. Let the coefficient matrix of the functional relationship be K. (6*n，1) Its expression is formula (4). Then, formula (1) can be written in the form of (5).

[0080] K=[k0;k1;k2;k3;k4;k5] (4)

[0081] Where k0, k1, k2, k3, k4, and k5 are n-dimensional vectors, and k0 = [k 01 ;k 02 ;...k 0n ], k1=[k 11 ;k 12 ;...k 1n ], k2=[k 21 ;k 22 ;...k 2n ], k3=[k 31 ;k 32 ;...k 3n ], k4=[k 41 ;k 42 ;...k 4n ], k5=[k 51 ;k 52 ;...k 5n ], where k 0j k 1j k 2j k 3j k 4j k 5j The coefficients of the quadratic relation of the inversion function corresponding to the j-th excitation frequency are given.

[0082] h = e (m，n) k0+X(1)k1+v(2)k2+v(1) 2 k3+X(2) 2 k4+X(1)v(2)k5=[e (m，n) X(1) X(2) X(1) 2 X(2)2 X(1)X(2)]*K (5)

[0083] Among them, e (m，n) Let be an m-row, n-column identity matrix. The partial derivatives of equation (5) with respect to the metal coating thickness d and the cladding tube conductivity σ are shown in equations (6) and (7), respectively.

[0084]

[0085]

[0086] By solving the partial differential equations described above, equation (3) can be rewritten as (8). Optimizing the solution to equation (8) yields the coefficient matrix K. (6 *n，1) The quadratic relationship between h and X is obtained, and then the fitted quadratic relationship is used for multi-frequency excitation measurement data of other samples to accurately solve the oxide film thickness of the samples.

[0087]

[0088] sth = [e (m，n) X(1) X(2) X(1) 2 X(2) 2 X(1)X(2)]*K (8)

[0089] D is a partial differential matrix, which can be obtained through calculation.

[0090] This application embodiment simultaneously conducted simulation experiments and actual thickness test experiments on the multi-frequency algorithm. The starting frequency was 0.4MHz, the ending frequency was 8MHz, and a total of 24 frequencies were selected, namely (0.40, 0.46, 0.52, 0.59, 0.67, 0.77, 0.87, 1.00, 1.13, 1.29, 1.47, 1.68, 1.91, 2.17, 2.48, 2.82, 3.21, 3.66, 4.17, 4.75, 5.41, 6.17, 7.02, 8.00)MHz.

[0091] Thickness measurement experiments were conducted on the sample, and data processing was performed on the host computer. The thickness results calculated based on the obtained coefficient matrix K are shown in Table 1.

[0092] Table 1: Measured oxide film thickness at a conductivity of 1.25 MS / m

[0093]

[0094] Table 1 shows that when the conductivity of the fuel rod cladding tube is 1.25 MS / m and the thickness d of the metal coating is 12 μm, 15 μm, 18 μm, and 20 μm, respectively, the oxide film thickness of fuel rod samples with oxide film thickness of 3 μm, 5 μm, 7 μm, and 9 μm was measured using the method of this application. The measured values ​​show that the method of this application has high measurement accuracy.

[0095] In summary, given the high temperatures, strong radiation, and electromagnetic interference present in the field measurement environment, another issue that needs to be addressed is how to obtain high-precision measurement results under complex field measurement conditions. This application proposes a novel probe structure design for thickness measurement, which can effectively suppress interference from the ambient magnetic field as well as measurement noise and drift caused by the probe's own structure.

[0096] To address the impact of differences in the conductivity of the fuel rod cladding tube and the thickness of the metal coating among different samples in a three-layer structure of fuel rod cladding tube, metal coating, and oxide film, this application proposes a multi-frequency algorithm. A series of excitation signals are applied to the probe, and the probe's induced signal is measured at each excitation frequency. The measurement results under multi-frequency excitation are processed to accurately measure the oxide film thickness.

[0097] In the embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, or methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of modules / units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or units may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection of apparatuses or modules or units may be electrical, mechanical, or other forms.

[0098] The modules / units described as separate components may or may not be physically separate. The components shown as modules / units may or may not be physical modules; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules / units can be selected to achieve the objectives of the embodiments of this application, depending on actual needs. For example, the functional modules / units in the various embodiments of this application may be integrated into one processing module, or each module / unit may exist physically separately, or two or more modules / units may be integrated into one module / unit.

[0099] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0100] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0101] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.

Claims

1. A fuel rod oxide film thickness measurement system, characterized in that, The system includes: Excitation signal source, used to provide excitation signals; The probe module adopts a bridge structure. The input terminal of the bridge structure is connected to the excitation signal source, and the output terminal of the bridge structure outputs a differential signal. The probe module includes a reference probe and a measuring probe. Both the reference probe and the measuring probe include a magnetic core, a first coil, and a second coil. The first coil and the second coil are respectively wound around the two ends of the magnetic core. The four coils of the reference probe and the measuring probe are connected to form a bridge structure. A processing module, connected to the output of the probe module, is used to process the differential signal to obtain a fundamental frequency demodulated signal reflecting oxide film thickness information. The processing module includes: a differential amplifier connected to the output of the probe module and amplifying the differential signal output by the probe module; and a lock-in amplifier connected to the output of the differential amplifier and the excitation signal source, which locks the amplified differential signal output by the differential amplifier with the excitation signal and outputs a fundamental frequency demodulated signal reflecting thickness information. The host computer processes the fundamental frequency demodulated signal to obtain the oxide film thickness of the fuel rod. The processing of the fundamental frequency demodulated signal includes: constructing an inversion function based on the fundamental frequency demodulated signal to retrieve the oxide film thickness and an optimized solution model for the inversion function. The optimized solution model is an inversion function that makes the partial derivative of the inversion function with respect to the changes in the conductivity of the fuel rod cladding tube and the thickness of the metal coating equal to zero.

2. The fuel rod oxide film thickness measurement system according to claim 1, characterized in that, When measuring the oxide film thickness of fuel rods, the reference probe is attached to the fuel rod sample for eddy current detection.

3. A method for measuring the thickness of an oxide film on a fuel rod, characterized in that, The method is based on the system of claim 1 or 2, and the method includes: An inversion function for retrieving oxide film thickness based on the fundamental frequency demodulated signal and an optimized solution model for the inversion function are constructed. The optimized solution model is an inversion function that makes the partial derivatives of the inversion function with respect to the changes in the conductivity of the fuel rod cladding tube and the thickness of the metal coating equal to zero. The excitation signal source provides excitation signals of different frequencies to the probe module, and the fundamental frequency demodulated signals of multiple fuel rod samples at each excitation frequency are measured to form a sample dataset. The inversion function is obtained by solving the optimization model using the sample dataset. The excitation signal source provides an excitation signal at a certain frequency to the probe module, and measures the fundamental frequency demodulated signal of the fuel rod under test at that excitation frequency. The fundamental frequency demodulated signal obtained from the measurement of the fuel rod under test is input into the inversion function obtained by solving, and the oxide film thickness of the fuel rod under test is calculated.

4. The method for measuring the oxide film thickness of fuel rods according to claim 3, characterized in that, The inversion function is constructed using a quadratic relation.

5. The method for measuring the oxide film thickness of fuel rods according to claim 4, characterized in that, The inversion function is expressed as: in, For oxide film thickness, The signal is a fundamental frequency demodulated signal, and f is the inversion function. This represents the real part of the fundamental frequency demodulated signal. This represents the imaginary part of the fundamental frequency demodulated signal. , , , , , is the coefficient of the quadratic relation.

6. The method for measuring the oxide film thickness of fuel rods according to claim 5, characterized in that, The optimization solution model is expressed as follows: in, For oxide film thickness, The signal is a fundamental frequency demodulated signal, and f is the inversion function. The thickness of the metal coating on the fuel rod. The conductivity of the fuel rod cladding tube.

7. The method for measuring the oxide film thickness of fuel rods according to claim 6, characterized in that, The inversion function obtained by solving the optimization model using the sample dataset includes: Assuming the number of fuel rod samples is m, the excitation signal source provides n excitation signals of different frequencies to the probe module to obtain the oxide film thickness of the fuel rod samples and form a vector. , For the oxide film thickness of the i-th fuel rod sample, the real and imaginary parts of the measured fundamental frequency demodulated signal are used to construct a matrix. , , , All are m*n dimensional matrices. , The element in the i-th row and j-th column corresponds to the real and imaginary parts of the fundamental frequency demodulated signal measured at the j-th excitation frequency for the i-th fuel rod sample, i=1,2,……,m,j=1,2,……,n; Constructing the coefficient vector of the quadratic relation ,in , , , , , They are n-dimensional vectors, , , , , , ,in, , , , , , These are the coefficients of the quadratic relation of the inversion function corresponding to the j-th excitation frequency; The optimization solution model is transformed into: in, It is an m*n dimensional identity matrix. It is a partial differential matrix; Solve the optimization model to obtain the coefficient vector K, and obtain the inversion function under different excitation frequencies.

8. The method for measuring the oxide film thickness of fuel rods according to claim 7, characterized in that, The fundamental frequency demodulated signal obtained from the measurement of the fuel rod under test is input into the inversion function obtained by solving, and the oxide film thickness of the fuel rod under test is calculated by: selecting the inversion function at the corresponding excitation frequency according to the excitation frequency of the excitation signal applied during measurement, and using the inversion function to calculate the oxide film thickness of the fuel rod under test.

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