{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:53:25Z","timestamp":1769756005417,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T00:00:00Z","timestamp":1554508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["No.LY18E050002"],"award-info":[{"award-number":["No.LY18E050002"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004835","name":"Zhejiang University","doi-asserted-by":"publisher","award":["No.2018QNA4001"],"award-info":[{"award-number":["No.2018QNA4001"]}],"id":[{"id":"10.13039\/501100004835","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A preliminary backscattered signal model of carbon-fiber-reinforced plastic (CFRP) laminate was established. The backscattered signal model was composed of three sub models, which were concerned with structural signal, scattering signal, and non-acoustic noise. Resonance in structural signal and echoes excited by defects (porosity and rich-resin) were studied. The results showed that: resonance would occur when there was sufficient bandwidth; when the CFRP laminate contained voids, the center frequency of the backscattered signal decreased; and the localized defects, including rich-resin and localized porosity, tended to generate apparent echoes where they located. A simplified backscattered signal model was subsequently put forward, showing certain potential in revealing time-frequency properties of backscattered signals. The newly proposed variational mode decomposition was used for defect modes extraction, successfully avoiding the mode mixing and false modes which easily exist in empirical mode decomposition. Subsequently, the generalized Stockwell transform was adopted for the defects localization. The simulation and experiment denoted the coincidence between the backscattered signal model and the experimental signal, and showed the effectiveness of variational mode decomposition and generalized Stockwell transform in localized defects detection.<\/jats:p>","DOI":"10.3390\/s19071654","type":"journal-article","created":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T11:54:52Z","timestamp":1554724492000},"page":"1654","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Ultrasonic Inspection of Localized Defects in Low-Porosity CFRP"],"prefix":"10.3390","volume":"19","author":[{"given":"Wei","family":"Feng","sequence":"first","affiliation":[{"name":"State Key Lab of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Xiaojun","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Lab of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Xiang","family":"Zeng","sequence":"additional","affiliation":[{"name":"CRRC Zhuzhou Institute Co. Ltd., Zhuzhou 412001, China"}]},{"given":"Chenlong","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Lab of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3368","DOI":"10.1063\/1.324176","article-title":"Ultrasonic wave-propagation in fiber-reinforced solids containing voids","volume":"48","author":"Martin","year":"1977","journal-title":"J. Appl. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF00566584","article-title":"Porosity estimation using the frequency dependence of the ultrasonic attenuation","volume":"8","author":"Nair","year":"1989","journal-title":"J. Nondestruct. Eval."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0041-624X(95)00023-V","article-title":"Experimental analysis of porosity-induced ultrasonic attenuation and velocity change in carbon composites","volume":"33","author":"Jeong","year":"1995","journal-title":"Ultrasonics"},{"key":"ref_4","first-page":"105","article-title":"Ultrasonic determination of carbon fiber composite porosity using acoustic impedance","volume":"26","author":"Lin","year":"2009","journal-title":"Acta Mater. Compos. Sin."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1109\/58.660140","article-title":"Statistical moments of backscattered ultrasound in porous fiber reinforced composites","volume":"45","author":"Grolemund","year":"1998","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.ndteint.2013.01.014","article-title":"Estimation of porosity content of composite materials by applying discrete wavelet transform to ultrasonic backscattered signal","volume":"56","author":"Kim","year":"2013","journal-title":"NDT Int."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10921-013-0184-x","article-title":"Nondestructive porosity assessment of CFRP composites with spectral analysis of backscattered laser-induced ultrasonic pulses","volume":"32","author":"Karabutov","year":"2013","journal-title":"J. Nondestruct. Eval."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/s11595-016-1348-1","article-title":"CFRP voids 3D identification and location method based on the process of backscattered signal","volume":"31","author":"Chen","year":"2016","journal-title":"J. Wuhan Univ. Technol. Mater. Sci. Ed."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.compscitech.2013.09.006","article-title":"A mesoscale ultrasonic attenuation finite element model of composites with random-distributed voids","volume":"89","author":"Yu","year":"2013","journal-title":"Compos. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.ultras.2004.03.002","article-title":"Analysis of ultrasonic attenuation in particle-reinforced plastics by a differential scheme","volume":"43","author":"Biwa","year":"2004","journal-title":"Ultrasonics"},{"key":"ref_11","unstructured":"Chimenti, D.E., and Bond, L.J. (2014, January 20\u201325). Simulation of ultrasonic inspection of curved composites using a hybrid semi-analytical\/numerical code. Proceedings of the 41st Annual Review of Progress in Quantitative Nondestructive Evalution, Boise, ID, USA."},{"key":"ref_12","unstructured":"Chimenti, D.E., and Bond, L.J. (2015, January 26\u201331). Acoustic characterization of void distributions across carbon-fiber composite layers. Proceedings of the 42nd Annual Review of Progress in Quantitative Nondestructive Evalution: Incorporating the 6th European-American Workshop on Reliability of NDE, Minneapolis, MN, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1121\/1.381491","article-title":"Ultrasonic spectrum analysis for nondestructive testing of layered composite materials","volume":"62","author":"Scott","year":"1977","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Sig. Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/78.492555","article-title":"Localization of the complex spectrum: The S transform","volume":"44","author":"Stockwell","year":"1996","journal-title":"IEEE Trans. Sig. Process."},{"key":"ref_16","first-page":"1","article-title":"Evaluation of the modified S-transform for time-frequency synchrony analysis and source localization","volume":"49","author":"Assous","year":"2012","journal-title":"EURASIP"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1109\/TUFFC.2009.1233","article-title":"Model-based estimation of thin multi-layered media using ultrasonic measurements","volume":"56","author":"Hagglund","year":"2009","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1063\/1.1722545","article-title":"Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid","volume":"27","author":"Ying","year":"1956","journal-title":"J. Appl. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1016\/j.jfranklin.2013.09.028","article-title":"Asymmetric Gaussian chirplet model and parameter estimation for generalized echo representation","volume":"351","author":"Demirli","year":"2014","journal-title":"J. Frankl. Inst. Eng. Appl. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/S0041-624X(96)00084-4","article-title":"Studies of split spectrum processing, optimal detection, and maximum likelihood amplitude estimation using a simple clutter model","volume":"35","author":"Gustafsson","year":"1997","journal-title":"Ultrasonics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1109\/TSP.2007.906771","article-title":"One or two frequencies? The empirical mode decomposition answers","volume":"56","author":"Rilling","year":"2008","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1654\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:43:26Z","timestamp":1760186606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1654"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,6]]},"references-count":21,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19071654"],"URL":"https:\/\/doi.org\/10.3390\/s19071654","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,6]]}}}