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| A Multiple-Frequency Eddy Current Testing Method for of Multi-Layer Heterogeneous Membrane Stacks Measurement in Nuclear Fuel Cladding Tube |
| Huang Pu1, Han Zheng2, Peng Lisha2, Wen Yinghong1, Huang Songling2 |
1. School of Automation and Intelligence Beijing Jiaotong University Beijing 100044 China;
2. Department of Electrical Engineering Tsinghua University Beijing 100084 China |
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Abstract Within the extreme operational environment of a nuclear reactor, the fuel assembly functions as the cornerstone of nuclear safety, acting as the first physical barrier against radioactive release. The zirconium alloy cladding tube, serving as the pressure boundary, must maintain impeccable structural integrity to effectively contain fission products, prevent the leakage of radioactive materials, and provide long-term mechanical support for the fuel pellets. However, prolonged exposure to high-temperature, high-pressure coolant flow induces persistent thermo-chemical interactions. These interactions lead to oxidation reactions that consume the metallic matrix, resulting in the formation of a heterogeneous oxide film on the outer cladding surface. This corrosion phenomenon not only reduces the effective load-bearing wall thickness but also severely compromises the mechanical properties—particularly the strength and toughness—of the fuel assembly, thereby elevating the risk of functional failure. Consequently, the accurate assessment of the cladding’s structural state necessitates the high-precision, non-destructive measurement of multiple coupled parameters, specifically the oxide film thickness, the wall thickness, and the electromagnetic properties induced by irradiation and corrosion. Traditional single-frequency eddy current testing (ECT) methods are fundamentally limited in this context, as the lift-off, thickness, and conductivity are highly intertwined, creating a complex inverse problem that hinders decoupled measurement.
To surmount these limitations, this paper proposes a novel multi-layer heterogeneous film characterization methodology utilizing a stacked-array multiple-frequency eddy current testing technique. The core innovation lies in the synergistic integration of a bespoke sensor architecture and an advanced inversion algorithm. First, a specialized stacked-array eddy current sensor was designed and fabricated, comprising three coaxial coils arranged in a compact, layered configuration. This unique geometry optimizes the spatial sensitivity distribution, enabling the simultaneous acquisition of electromagnetic responses at varying penetration depths. Correspondingly, an analytical forward model was established based on the electromagnetic theory of a two-layer composite medium, representing the conductive metallic cladding substrate and the relatively non-conductive oxide film layer. By solving Maxwell’s equations under quasi-static conditions, the mutual inductance expressions governing the interactions between the excitation and pickup coils were rigorously derived. These formulations establish the complex mathematical relationship between the measured coil impedance and the target material parameters—namely, oxide thickness, cladding thickness, and electrical conductivity—across a broad spectrum of excitation frequencies.
Subsequently, a multi-parameter stepwise decoupling inversion method was developed to resolve the ambiguities inherent in the coupled signals. This strategy strategically exploits the frequency-dependent skin effect: high-frequency eddy currents are confined primarily to the surface region, rendering them highly sensitive to the oxide film but insensitive to the substrate, whereas low-frequency currents penetrate deeper, carrying information about the metallic matrix. Specifically, the high-frequency response signals are first utilized to invert the thickness of the surface oxide film layer, effectively isolating surface effects from the underlying substrate. Once the oxide thickness is accurately determined, the low-frequency response signals are processed in conjunction with the spatial sensitivity characteristics of the coil array. This allows for the subsequent decoupled reconstruction of the cladding thickness and the conductivity. This stepwise approach transforms a traditionally ill-posed multi-variable optimization problem into a sequence of stable, single-variable estimations, significantly enhancing the robustness of the inversion process.
Finally, the proposed method is validated through finite element numerical simulations and experiments. Parametric FEM simulations are conducted to analyze the sensitivity coefficients of various frequencies to the target parameters, confirming the theoretical basis for frequency selection. Furthermore, experimental tests are performed on zirconium alloy cladding tube specimens with artificially prepared oxide layers with varying thicknesses. The results demonstrate that accurate estimation of all three heterogeneous film parameters can be achieved by analyzing the differential multi-frequency responses based on the eddy current skin effect in stacked arrays. Quantitative analysis indicates that the average relative error for the oxide film thickness, cladding thickness, and electrical conductivity was maintained below 3.5%. This level of precision effectively proves the feasibility and accuracy of the proposed method, offering a robust technical solution for the in-situ, high-precision evaluation of fuel cladding degradation and contributing significantly to the predictive maintenance and safety assessment of nuclear power plants.
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Received: 02 June 2026
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[1] Sun Ling, Xiao Yuchen, Huang Weijiu, et al.Review on the preparation and high-temperature oxidation resistance of metal coating for fuel cladding zirconium alloys[J]. Nuclear Science and Engineering, 2024, 198(4): 755-770.
[2] Ni Yezhou, Topham R, Skippon T, et al.Detection of zirconium hydrides in transmission electron micrographs using deep neural networks[J]. Engineering Applications of Artificial Intelligence, 2023, 117: 105573.
[3] 黄璞, 韩正, 彭丽莎, 等. 基于叠阵涡流的核燃料包壳管电导率和壁厚同时测量方法[J]. 仪器仪表学报, 2025, 46(12): 274-283.
Huang Pu, Han Zheng, Peng Lisha, et al.Simultaneous measurement method for conductivity and wall thickness of nuclear fuel cladding tubes based on stacked array eddy current testing[J]. Chinese Journal of Scientific Instrument, 2025, 46(12): 274-283.
[4] Huang Pu, Han Zheng, Peng Lisha, et al.A novel wall thickness measurement of metallic tube using stacked array eddy current sensor[J]. IEEE Sensors Journal, 2025, 25(15): 28974-28983.
[5] Yasuda R, Matsubayashi M, Nakata M, et al.Application of neutron radiography for estimating concentration and distribution of hydrogen in Zircaloy cladding tubes[J]. Journal of Nuclear Materials, 2002, 302(2/3): 156-164.
[6] Huang Songhua, Wang Tao, Tang Bo, et al.Application of multi-channel ultrasonic and machine learning for defect detection in nuclear fuel assemblies[J]. Nondestructive Testing and Evaluation, 2025: 1-22.
[7] Yuan Zheng, Feng Song, Wang Yongliang, et al.An inductive sensor with a biased magnetic field to distinguish wear debris by magnetism and conductivity[J]. IEEE/ASME Transactions on Mechatronics, 2025, 30(1): 727-738.
[8] 段志荣, 解社娟, 李丽娟, 等. 基于磁力传动式阵列涡流探头的管道缺陷检测[J]. 电工技术学报, 2020, 35(22): 4627-4635.
Duan Zhirong, Xie Shejuan, Li Lijuan, et al.Detection of defects in pipeline structures based on magnetic transmission eddy current array probe[J]. Transactions of China Electrotechnical Society, 2020, 35(22): 4627-4635.
[9] 张宇翔, 何为, 孔晓涵,等. 基于硅钢片均一化的超低场磁共振抗涡流Z梯度线圈设计方法[J]. 电工技术学报, 2025, 40(4): 987-996.
Zhang Yuxiang, He Wei, Kong Xiaohan, et al.A design method for eddy current-resistant Z-gradient coil in ultra-low field magnetic resonance imaging systems based on homogeneous of silicon steel sheets[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 987-996.
[10] Huang Pu, Pu Hang, Li Jiyao, et al.A novel eddy current method for defect detection immune to lift-off[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 6005913.
[11] Beck F R, Lind R P, Smith J A.Temperature sensitivity study of eddy current and digital gauge probes for oxide measurement[J]. Research in Nondestructive Evaluation, 2019, 30(6): 334-349.
[12] Zhang Na, Li Yifan, Ye Chaofeng, et al.Measurement of oxide film thickness for coated fuel rod cladding using swept-frequency ECT and parameters separation[J]. NDT & E International, 2025, 154: 103377.
[13] Zhu Shuang, Huang Ruochen, Salas Avila J R, et al. Simultaneous measurements of wire diameter and conductivity using a combined inductive and capacitive sensor[J]. IEEE Sensors Journal, 2020, 20(19): 11617-11624.
[14] Ye Chaofeng, Wang Yang, Wang Meiling, et al.Frequency domain analysis of magnetic field images obtained using TMR array sensors for subsurface defect detection and quantification[J]. NDT & E International, 2020, 116: 102284.
[15] Ye Chaofeng, Zhang Na, Peng Lei, et al.Flexible array probe with in-plane differential multichannels for inspection of microdefects on curved surface[J]. IEEE Transactions on Industrial Electronics, 2022, 69(1): 900-910.
[16] Lu Mingyang, Meng Xiaobai, Huang Ruochen, et al.Thickness measurement of circular metallic film using single-frequency eddy current sensor[J]. NDT & E International, 2021, 119: 102420.
[17] Yin Wuliang, Xu Kai.A novel triple-coil electromagnetic sensor for thickness measurement immune to lift-off variations[J]. IEEE Transactions on Instrumentation and Measurement, 2016, 65(1): 164-169.
[18] Xie Yuedong, Huang Pu, Ding Yiqing, et al.A novel conductivity measurement method for non-magnetic materials based on sweep-frequency eddy current method[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 6004212.
[19] Huang Pu, Ding Yiqing, Li Jiyao, et al.Conductivity estimation of non-magnetic materials using eddy current method[J]. Nondestructive Testing and Evaluation, 2023, 38(1): 130-146.
[20] Lu Mingyang, Yin Liyuan, Peyton A J, et al.A novel compensation algorithm for thickness measurement immune to lift-off variations using eddy current method[J]. IEEE Transactions on Instrumentation and Measurement, 2016, 65(12): 2773-2779.
[21] 李威, 段淑玉, 宋韵, 等. 基于Laplace小波特征频率的不锈钢钢板脉冲涡流测厚方法[J]. 仪器仪表学报, 2020, 41(12): 166-172.
Li Wei, Duan Shuyu, Song Yun, et al.A pulse eddy current thickness measurement method of stainless steel plate based on Laplace wavelet’s characteristic frequency[J]. Chinese Journal of Scientific Instrument, 2020, 41(12): 166-172.
[22] 苏冰洁,李勇,王艺融,等. 脉冲调制涡流检测涂层系统减薄缺陷的检出概率分析[J/OL]. 中国机械工程, 1-10[2026-07-08]. https://link.cnki.net/urlid/42.1294.TH.20251021.1420.0152025.
Su Binjie,Li Yong,Wang Yirong,et al. Analysis of POD for pulse-modulation eddy current testing of the thickness reduction in coating systems[J/OL]. China Mechanical Engineering, 1-10[2026-07-08]. https://link.cnki.net/urlid/42.1294.TH.20251021.1420.0152025.
[23] 李超, 范孟豹, 曹丙花, 等. 热障涂层电涡流检测新变压器模型与信号解耦方法研究[J]. 机械工程学报, 2025, 61(12): 12-25.
Li Chao, Fan Mengbao, Cao Binghua, et al.Study on novel transformer model of eddy current testing and signal decoupling of thermal barrier coating[J]. Journal of Mechanical Engineering, 2025, 61(12): 12-25.
[24] Huang Pu, Pu Hang, Li Jiyao, et al.An eddy current testing method for thickness and conductivity measurement of non-magnetic material[J]. IEEE Sensors Journal, 2023, 23(5): 4445-4454.
[25] Xu Jin, Wang Dongli, Xin Wei.Coupling relationship and decoupling method for thickness and conductivity measurement of ultra-thin metallic coating using swept-frequency eddy-current technique[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 6004809.
[26] Bouhlal A, Nait-Said N, Louai F Z, et al.Inverse problem approach for electrical conductivity measurement using eddy current NDE and artificial neural networks: modeling and experimental validation[J]. Engineering, Technology & Applied Science Research, 2025, 15(3): 23479-23485.
[27] 范文茹, 昌勇. 热障涂层厚度的脉冲涡流检测反演方法[J]. 计量学报, 2024, 45(6): 819-826.
Fan Wenru, Chang Yong.Inversion method of pulsed eddy current detection for thermal barrier coatings thickness[J]. Acta MetrologicaSinica, 2024, 45(6): 819-826.
[28] Huang Pu, Bao Zhenyu, Huang Ruochen, et al.Decoupling permeability, conductivity, thickness, lift-off for eddy current testing using machine learning[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 6007510.
[29] Xia Zihan, Meng Tian, Huang Ruochen, et al.Physics-guided deep learning for plate permeability estimation with single to multiple frequency transformation of eddy-current testing[J]. IEEE Transactions on Industrial Informatics, 2024, 20(4): 6109-6118.
[30] Dodd C V, Deeds W E.Analytical solutions to eddy-current probe-coil problems[J]. Journal of Applied Physics, 1968, 39(6): 2829-2838.
[31] Yin Wuliang, Peyton A J.Thickness measurement of metallic plates with an electromagnetic sensor using phase signature analysis[J]. IEEE Transactions on Instrumentation and Measurement, 2008, 57(8): 1803-1807. |
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2026, Vol. 41 
