{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T18:53:59Z","timestamp":1763664839162,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52177007","11927801","2019YFE03130003"],"award-info":[{"award-number":["52177007","11927801","2019YFE03130003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013282","name":"National Magnetic Confinement Fusion Program of China","doi-asserted-by":"publisher","award":["52177007","11927801","2019YFE03130003"],"award-info":[{"award-number":["52177007","11927801","2019YFE03130003"]}],"id":[{"id":"10.13039\/501100013282","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Interlaminar corrosion (ILC) poses a severe threat to stratified conductors which are broadly employed in engineering fields including aerospace, energy, etc. Therefore, for the pressing concern regarding the safety and integrity of stratified conductors, it is imperative to non-intrusively and quantitatively interrogate ILC via non-destructive evaluation techniques. In this paper, pulse-modulation eddy current (PMEC) for imaging and assessment of ILC is intensively investigated through theoretical simulations and experiments. A semi-analytical model of PMEC evaluation of ILC occurring at the interlayer of two conductor layers is established based on the extended truncated region eigenfunction expansion (ETREE) along with the efficient algorithm for the numerical computation of eigenvalues for reflection coefficients of the stratified conductor under inspection. Based on theoretical investigation, PMEC evaluation of ILC in testing samples are further scrutinized by using the PMEC imaging system built up for the experimental study. The theoretical and experimental results have revealed the feasibility of PMEC for imaging and evaluation of ILC in stratified conductors.<\/jats:p>","DOI":"10.3390\/s22093458","type":"journal-article","created":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T08:26:35Z","timestamp":1651566395000},"page":"3458","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Pulse-Modulation Eddy Current Evaluation of Interlaminar Corrosion in Stratified Conductors: Semi-Analytical Modeling and Experiments"],"prefix":"10.3390","volume":"22","author":[{"given":"Zhengshuai","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Centre of NDT and Structural Integrity Evaluation, School of Aerospace Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4257-2771","authenticated-orcid":false,"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Centre of NDT and Structural Integrity Evaluation, School of Aerospace Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuting","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Centre of NDT and Structural Integrity Evaluation, School of Aerospace Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanzhao","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Centre of NDT and Structural Integrity Evaluation, School of Aerospace Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilham Mukriz Zainal","family":"Abidin","sequence":"additional","affiliation":[{"name":"Leading Edge NDT Technology (LENDT) Group, Malaysian Nuclear Agency, Bangi 43000, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenmao","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Centre of NDT and Structural Integrity Evaluation, School of Aerospace Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Geng, Q., and North, W. (1998, January 31). The detection of inter laminar corrosion in rivetted thin aluminum skins. Proceedings of the Nondestructive Evaluation of Aging Aircraft, Airports, and Aerospace Hardware II, San Antonio, TX, USA.","DOI":"10.1117\/12.305060"},{"key":"ref_2","first-page":"104201A","article-title":"Study on Detection System of Precision Casting Cracks Based on Image Processing","volume":"10420","author":"Yang","year":"2017","journal-title":"Proc. Spie."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.ultras.2013.08.007","article-title":"Quantitative evaluation of ultrasonic C-scan image in acoustically homogeneous and layered anisotropic materials using three dimensional ray tracing method","volume":"54","author":"Kolkoori","year":"2014","journal-title":"Ultrasonics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2525","DOI":"10.3390\/s110302525","article-title":"Non-Destructive Techniques Based on Eddy Current Testing","volume":"11","year":"2011","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Alvarenga, T.A., Carvalho, A.L., Honorio, L.M., Cerqueira, A.S., Luciano, M.A., and Nobrega, R.A. (2021). Detection and Classification System for Rail Surface Defects Based on Eddy Current. Sensors, 21.","DOI":"10.3390\/s21237937"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1134\/S106378502011022X","article-title":"Defect Characterization in Layered Composites Using a Pulsed Eddy-Current Technique","volume":"46","author":"Kokurov","year":"2020","journal-title":"Tech. Phys. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"167647","DOI":"10.1016\/j.jmmm.2020.167647","article-title":"Estimation method of yield strength of ferromagnetic materials based on pulsed eddy current testing","volume":"523","author":"Li","year":"2021","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, Z.W., and Yu, Y.T. (2018). Traditional Eddy Current-Pulsed Eddy Current Fusion Diagnostic Technique for Multiple Micro-Cracks in Metals. Sensors, 18.","DOI":"10.3390\/s18092909"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102444","DOI":"10.1016\/j.ndteint.2021.102444","article-title":"Detection of circumferential cracks in heat exchanger tubes using pulsed eddy current testing","volume":"121","author":"Yu","year":"2021","journal-title":"NDT E Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/TIM.2018.2890757","article-title":"Eddy Current Testing Probe Based on Double-Coil Excitation and GMR Sensor","volume":"68","author":"Bernieri","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112450","DOI":"10.1016\/j.sna.2020.112450","article-title":"Bobbin pulsed eddy current array probe for detection and classification of defects in nonferromagnetic tubes","volume":"317","author":"Ge","year":"2021","journal-title":"Sens. Actuat. A Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, H.W., Huang, J.B., Liu, L.H., Qin, S.Q., and Fu, Z.H. (2022). A Novel Pulsed Eddy Current Criterion for Non-Ferromagnetic Metal Thickness Quantifications under Large Liftoff. Sensors, 22.","DOI":"10.3390\/s22020614"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.3233\/JAE-209428","article-title":"Thickness measurement for non-ferromagnetic metal under the large liftoff based on the last peak point of differential pulsed eddy current signals","volume":"64","author":"Song","year":"2020","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, Q., and Wu, X.J. (2021). Wall Thinning Assessment for Ferromagnetic Plate with Pulsed Eddy Current Testing Using Analytical Solution Decoupling Method. Appl. Sci., 11.","DOI":"10.3390\/app11104356"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.ndteint.2016.02.001","article-title":"Pulse-modulation eddy current inspection of subsurface corrosion in conductive structures","volume":"79","author":"Li","year":"2016","journal-title":"NDT E Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.ndteint.2017.02.009","article-title":"Pulse-modulation eddy current probes for imaging of external corrosion in nonmagnetic pipes","volume":"88","author":"Li","year":"2017","journal-title":"NDT E Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111991","DOI":"10.1016\/j.sna.2020.111991","article-title":"A funnel-shaped probe for sensitivity enhancement in pulse-modulation eddy current inspection of subsurface flaws in conductors","volume":"307","author":"Li","year":"2020","journal-title":"Sens. Actuat. A Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102404","DOI":"10.1016\/j.ndteint.2021.102404","article-title":"Pulse-modulation eddy current imaging and evaluation of subsurface corrosion via the improved small sub-domain filtering method","volume":"119","author":"Yan","year":"2021","journal-title":"NDT E Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"28087","DOI":"10.1109\/JSEN.2021.3125027","article-title":"Pulse-Modulation Eddy Current Imaging for 3D Profile Reconstruction of Subsurface Corrosion in Metallic Structures of Aviation","volume":"21","author":"Yan","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.ndteint.2008.02.001","article-title":"Fast analytical modelling for pulsed eddy current evaluation","volume":"41","author":"Li","year":"2008","journal-title":"NDT E Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/TMAG.2005.844838","article-title":"Eddy-current interaction of a long coil with a slot in a conductive plate","volume":"41","author":"Theodoulidis","year":"2005","journal-title":"IEEE T Magn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125002","DOI":"10.1088\/1361-6463\/aaaef9","article-title":"Evaluation of cracks with different hidden depths and shapes using surface magnetic field measurements based on semi-analytical modelling","volume":"51","author":"Jiang","year":"2018","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"015501","DOI":"10.1088\/1402-4896\/ab3d66","article-title":"Analytical solution for magnetic field of cylindrical defect in eddy current nondestructive testing","volume":"95","author":"Yu","year":"2020","journal-title":"Phys. Scr."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1515\/msr-2018-0002","article-title":"I-Cored Coil Probe Located above a Conductive Plate with a Surface Hole","volume":"18","author":"Tytko","year":"2018","journal-title":"Meas. Sci. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1800","DOI":"10.1108\/COMPEL-03-2019-0130","article-title":"Locating complex eigenvalues for analytical eddy-current models used to detect flaws","volume":"38","author":"Tytko","year":"2019","journal-title":"Compel"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1109\/TMAG.2009.2036724","article-title":"Interaction of an Eddy-Current Coil with a Right-Angled Conductive Wedge","volume":"46","author":"Theodoulidis","year":"2010","journal-title":"IEEE T Magn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1090\/S0025-5718-1967-0228165-4","article-title":"A numerical method for locating the zeros of an analytic function","volume":"21","author":"Delves","year":"1967","journal-title":"Math. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7004310","DOI":"10.1109\/TMAG.2016.2518993","article-title":"Computation of the Eigenvalues for Bounded Domain Eddy-Current Models with Coupled Regions","volume":"52","author":"Vasic","year":"2016","journal-title":"IEEE T Magn."},{"key":"ref_29","first-page":"286","article-title":"Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples","volume":"15","author":"Strakova","year":"2017","journal-title":"Adv. Electr. Electron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3458\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:05:31Z","timestamp":1760137531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3458"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,1]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22093458"],"URL":"https:\/\/doi.org\/10.3390\/s22093458","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,5,1]]}}}