{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T05:02:16Z","timestamp":1789621336767,"version":"build-2803163510"},"reference-count":32,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:00:00Z","timestamp":1788998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To address the limitations of traditional analytical models in characterising multi-core coupling effects and the excessive computational cost of finite element simulations, this paper presents a high-precision analytical model for a novel T-II composite-core eddy current testing (ECT) probe using the Truncated Region Eigenfunction Expansion (TREE) method. The analytical expressions of coil impedance are derived by partitioning the solution domain into ten subdomains under an axisymmetric cylindrical coordinate system, with rigorous satisfaction of electromagnetic continuity at all material interfaces. Numerical cross-validation against 2D and 3D Finite Element Method (FEM) simulations under idealised modelling assumptions across the frequency range of 100 Hz to 10 kHz shows that the proposed TREE model yields relative errors below 2% for both coil resistance and reactance. Notably, the proposed approach requires significantly less computation time than 2D and 3D FEM. Further parametric analysis confirms that the proposed T-II composite-core probe delivers superior electromagnetic performance compared to conventional single-core probes, including intensified subsurface eddy current densities and improved magnetic field redistribution. This work overcomes the inherent limitations of single-core ECT analytical models, establishes a robust theoretical paradigm to interpret the distinctive electromagnetic field advantages of composite-core probes, and provides solid support for the structural optimisation of multi-core ECT sensors.<\/jats:p>","DOI":"10.3390\/s26185756","type":"journal-article","created":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T13:04:57Z","timestamp":1789045497000},"page":"5756","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytical Impedance Model of T-II Composite-Core ECT Probe Using Truncated Region Eigenfunction Expansion"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1181-0482","authenticated-orcid":false,"given":"Siquan","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Electrical and Automation, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"key":"ref_1","first-page":"6002908","article-title":"Eddy Current Method for Inspecting Foil-to-Tab Weld Quality in Li-Ion Batteries","volume":"74","author":"Finley","year":"2025","journal-title":"IEEE Trans. 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