{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T01:47:00Z","timestamp":1768787220157,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,30]],"date-time":"2023-05-30T00:00:00Z","timestamp":1685404800000},"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":["52275077"],"award-info":[{"award-number":["52275077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021J012"],"award-info":[{"award-number":["2021J012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["KJS2136"],"award-info":[{"award-number":["KJS2136"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Ningbo Natural Science Foundation","doi-asserted-by":"publisher","award":["52275077"],"award-info":[{"award-number":["52275077"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Ningbo Natural Science Foundation","doi-asserted-by":"publisher","award":["2021J012"],"award-info":[{"award-number":["2021J012"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Ningbo Natural Science Foundation","doi-asserted-by":"publisher","award":["KJS2136"],"award-info":[{"award-number":["KJS2136"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Lab of Modern Optical Technologies of Jiangsu Province, Soochow University","award":["52275077"],"award-info":[{"award-number":["52275077"]}]},{"name":"Key Lab of Modern Optical Technologies of Jiangsu Province, Soochow University","award":["2021J012"],"award-info":[{"award-number":["2021J012"]}]},{"name":"Key Lab of Modern Optical Technologies of Jiangsu Province, Soochow University","award":["KJS2136"],"award-info":[{"award-number":["KJS2136"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Traditional Lamb wave inspection and imaging methods heavily rely on prior knowledge of dispersion curves and baseline recordings, which may not be feasible in the majority of real cases due to production uncertainties and environmental variations. In order to solve this problem, a two-step Lamb wave strategy utilizing adaptive multiple signal classification (MUSIC) and sparse reconstruction of dispersion reconstruction is proposed. The multimodal Lamb waves are initially reconstructed in the f-k domain using random measurements, allowing for the identification and characterization of multimodal Lamb waves. Then, using local polynomial expansion and derivation, the phase and group velocities for each Lamb wave mode could be computed. Thus, the steering vectors of all potential scattering Lamb waves for each grid in the scanning area can be established, thereby allowing for the formulation of the MUSIC algorithm. To increase the precision and adaptability of the MUSIC method, the local wave components resulting from potential scatters are extracted with an adaptive window, which is governed by the group velocities and distances of Lamb wave propagation. As a result, the reconstructed dispersion relations and windowed wave components can be used to highlight the scattering features. For the method investigation, both a simulation and experiment are carried out, and both the dispersion curves and damage locations can be detected. The results demonstrate that damage localization is possible without theoretical dispersion data and baseline recordings while exhibiting a considerable accuracy and resolution.<\/jats:p>","DOI":"10.3390\/sym15061171","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T02:01:15Z","timestamp":1685498475000},"page":"1171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Two-Step Model-Based Reconstruction and Imaging Method for Baseline-Free Lamb Wave Inspection"],"prefix":"10.3390","volume":"15","author":[{"given":"Hang","family":"Fan","sequence":"first","affiliation":[{"name":"Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu 610213, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100191, China"},{"name":"Advanced Manufacturing Center, Ningbo Institute of Technology, Beihang University, Ningbo 315100, China"},{"name":"Key Lab of Modern Optical Technologies of Jiangsu Province, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenhao","family":"Li","sequence":"additional","affiliation":[{"name":"Advanced Manufacturing Center, Ningbo Institute of Technology, Beihang University, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu 610213, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106114","DOI":"10.1016\/j.ultras.2020.106114","article-title":"Environmental and operational conditions effects on Lamb wave based structural health monitoring systems: A review","volume":"105","author":"Gorgin","year":"2020","journal-title":"Ultrasonics"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yang, T., Zhou, W., and Yu, L. (2023). Guided Wave-Based Damage Detection of Square Steel Tubes Utilizing Structure Symmetry. Symmetry, 15.","DOI":"10.3390\/sym15040805"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"053001","DOI":"10.1088\/0964-1726\/25\/5\/053001","article-title":"Guided wave based structural health monitoring: A review","volume":"25","author":"Mitra","year":"2016","journal-title":"Smart Mater. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1088\/0964-1726\/16\/2\/003","article-title":"Lamb wave propagation modelling for damage detection: I. Two-dimensional analysis","volume":"16","author":"Lee","year":"2007","journal-title":"Smart Mater. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106554","DOI":"10.1016\/j.ultras.2021.106554","article-title":"Two-dimensional scattering features of the mixed second harmonic A0 mode Lamb waves for incipient damage localization","volume":"119","author":"Shan","year":"2022","journal-title":"Ultrasonics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"110364","DOI":"10.1016\/j.measurement.2021.110364","article-title":"Surface damage detection of steel plate with different depths based on Lamb wave","volume":"187","author":"Hu","year":"2022","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102466","DOI":"10.1016\/j.ndteint.2021.102466","article-title":"Experimental investigation of the surface corrosion damage in plates based on nonlinear Lamb wave methods","volume":"121","author":"Ding","year":"2021","journal-title":"NDT E Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"115029","DOI":"10.1088\/1361-665X\/ab47e1","article-title":"Determination of Lamb wave phase velocity dispersion using time\u2013frequency analysis","volume":"28","author":"Ding","year":"2019","journal-title":"Smart Mater. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ndteint.2018.08.004","article-title":"A new method to detect delamination in composites using chirp-excited Lamb wave and wavelet analysis","volume":"100","author":"Feng","year":"2018","journal-title":"NDT E Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.sna.2014.10.037","article-title":"Linearly dispersive signal construction of Lamb waves with measured relative wavenumber curves","volume":"221","author":"Cai","year":"2015","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.ultras.2018.05.003","article-title":"Extraction of guided wave dispersion curve in isotropic and anisotropic materials by Matrix Pencil method","volume":"89","author":"Chang","year":"2018","journal-title":"Ultrasonics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107712","DOI":"10.1016\/j.ymssp.2021.107712","article-title":"Mean local frequency-wavenumber estimation through synthetic time-reversal of diffuse Lamb waves","volume":"156","author":"Spytek","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"110973","DOI":"10.1016\/j.compstruct.2019.110973","article-title":"Lamb wave inspection for composite laminates using a combined method of sparse reconstruction and delay-and-sum","volume":"223","author":"Xu","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1177\/1045389X14544140","article-title":"Damage location by ultrasonic Lamb waves and piezoelectric rosettes","volume":"26","author":"Kijanka","year":"2015","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e1919","DOI":"10.1002\/stc.1919","article-title":"Delamination detection in composite plates by synthesizing time-reversed Lamb waves and a modified damage imaging algorithm based on RAPID","volume":"24","author":"Liu","year":"2017","journal-title":"Struct. Control. Health Monit."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1177\/1475921710379512","article-title":"Direction of arrival estimation of Lamb waves using circular arrays","volume":"10","author":"Engholm","year":"2011","journal-title":"Struct. Health Monit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106592","DOI":"10.1016\/j.ultras.2021.106592","article-title":"Damage characterization using CNN and SAE of broadband Lamb waves","volume":"119","author":"Gao","year":"2022","journal-title":"Ultrasonics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.ultras.2018.07.007","article-title":"Damage localization method for plates based on the time reversal of the mode-converted Lamb waves","volume":"91","author":"Mori","year":"2019","journal-title":"Ultrasonics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"085012","DOI":"10.1088\/0964-1726\/23\/8\/085012","article-title":"Lamb wave based automatic damage detection using matching pursuit and machine learning","volume":"23","author":"Agarwal","year":"2014","journal-title":"Smart Mater. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Xu, B., Giurgiutiu, V., and Yu, L. (2009, January 9\u201312). Lamb waves decomposition and mode identification using matching pursuit method. Proceedings of the Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2009, San Diego, CA, USA.","DOI":"10.1117\/12.816087"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xie, J., Ding, W., Zou, W., Wang, T., and Yang, J. (2022). Defect Detection inside a Rail Head by Ultrasonic Guided Waves. Symmetry, 14.","DOI":"10.21203\/rs.3.rs-1817243\/v1"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ymssp.2017.09.020","article-title":"Impact induced damage assessment by means of Lamb wave image processing","volume":"102","author":"Kudela","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","unstructured":"Zhongqing, S. (2009). Identification of Damage Using Lamb Waves, Identification of Damage Using Lamb Waves, Springer."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1121\/1.4974063","article-title":"Reconstruction of Lamb wave dispersion curves by sparse representation with continuity constraints","volume":"141","author":"Zhao","year":"2017","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1177\/1475921715623359","article-title":"Lamb wave-based subwavelength damage imaging using the DORT-MUSIC technique in metallic plates","volume":"15","author":"He","year":"2016","journal-title":"Struct. Health Monit."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"025033","DOI":"10.1088\/1361-665X\/ac4874","article-title":"Dispersive MUSIC algorithm for Lamb wave phased array","volume":"31","author":"Xu","year":"2022","journal-title":"Smart Mater. Struct."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:45:00Z","timestamp":1760125500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,30]]},"references-count":27,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["sym15061171"],"URL":"https:\/\/doi.org\/10.3390\/sym15061171","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,30]]}}}