{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:47:50Z","timestamp":1765039670284,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T00:00:00Z","timestamp":1670198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Funds of the National Natural Science Foundation of China","award":["U2268205","2021JJ40765","TPL2109","20220812171109001"],"award-info":[{"award-number":["U2268205","2021JJ40765","TPL2109","20220812171109001"]}]},{"name":"Natural Science Foundation of Hunan Province China","award":["U2268205","2021JJ40765","TPL2109","20220812171109001"],"award-info":[{"award-number":["U2268205","2021JJ40765","TPL2109","20220812171109001"]}]},{"name":"Open Project of State Key Laboratory","award":["U2268205","2021JJ40765","TPL2109","20220812171109001"],"award-info":[{"award-number":["U2268205","2021JJ40765","TPL2109","20220812171109001"]}]},{"name":"Stable Support Plan for Colleges and Universities in Shenzhen","award":["U2268205","2021JJ40765","TPL2109","20220812171109001"],"award-info":[{"award-number":["U2268205","2021JJ40765","TPL2109","20220812171109001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Early detection of defects inside a rail is of great significance to ensure the safety of rail transit. This work investigated the ability of ultrasonic guided waves (UGWs) to detect internal defects in a rail head. First, the model of UGW propagation in rail, which has an irregular cross-section, was constructed based on the semi-analytical finite element (SAFE) method. Fundamental characteristics, such as wavenumber, phase or group velocity, and wave structure inside the rail, were then calculated. Following modal and vibration energy distribution analysis, a guided wave mode that is sensitive to transverse fissure (TF) defects was selected, and its excitation method was proposed. The effectiveness of the excitation method was confirmed by simulations performed in the ABAQUS software. According to the simulation data, the dispersion curve calculated by using the two-dimensional Fourier fast transform (2D-FFT) coincided well with that of the SAFE method. After that, the sensitivity of the selected mode to internal rail defects was validated and its ability to locate defects was also demonstrated. Finally, the effects of excitation frequency, defect size, and vertical and horizontal defect depth on the reflection waveforms were investigated.<\/jats:p>","DOI":"10.3390\/sym14122566","type":"journal-article","created":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T03:38:38Z","timestamp":1670211518000},"page":"2566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Defect Detection inside a Rail Head by Ultrasonic Guided Waves"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7280-3556","authenticated-orcid":false,"given":"Jingsong","family":"Xie","sequence":"first","affiliation":[{"name":"State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8020-4665","authenticated-orcid":false,"given":"Wenxiang","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Shenzhen Polytechnic, Shenzhen 518055, China"}]},{"given":"Wen","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0137-7881","authenticated-orcid":false,"given":"Tiantian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha 410083, China"}]},{"given":"Jinsong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"020801","DOI":"10.1115\/1.4037295","article-title":"Rail Flaw Detection Technologies for Safer, Reliable Transportation: A Review","volume":"140","author":"Alahakoon","year":"2017","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"106922","DOI":"10.1016\/j.measurement.2019.106922","article-title":"Rail Foot Flaw Detection Based on a Laser Induced Ultrasonic Guided Wave Method","volume":"148","author":"Pathak","year":"2019","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"413","DOI":"10.17148\/IJARCCE.2016.51295","article-title":"Advanced Monitoring of Rail Cracks Using LASER-EMAT System","volume":"5","author":"Vishesh","year":"2016","journal-title":"IJARCCE"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1243\/09544097JRRT209","article-title":"A Review on Non-Destructive Evaluation of Rails: State-of-the-Art and Future Development","volume":"222","author":"Papaelias","year":"2008","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1046\/j.1460-2695.2003.00693.x","article-title":"Rail Defects: An Overview","volume":"26","author":"Cannon","year":"2003","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bombarda, D., Vitetta, G.M., and Ferrante, G. (2021). Rail Diagnostics Based on Ultrasonic Guided Waves: An Overview. Appl. Sci., 11.","DOI":"10.3390\/app11031071"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1177\/09544097211025898","article-title":"On the Use of Ultrasonic Guided Waves for the Health Monitoring of Rails","volume":"236","author":"Masmoudi","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1134\/S1061830919040028","article-title":"Detectability of Rail Defects by Magnetic Flux Leakage Method","volume":"55","author":"Antipov","year":"2019","journal-title":"Russ. J. Nondestruct. Test."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1025518","DOI":"10.3389\/fmats.2022.1025518","article-title":"Ultrasonic Inspection of near Surface Defects with Additive Manufactured Metasurface Lens","volume":"9","author":"Zhu","year":"2022","journal-title":"Front. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.jsv.2006.01.021","article-title":"Modeling Wave Propagation in Damped Waveguides of Arbitrary Cross-Section","volume":"295","author":"Bartoli","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Xing, B., Yu, Z., Xu, X., Zhu, L., and Shi, H. (2019). Research on a Rail Defect Location Method Based on a Single Mode Extraction Algorithm. Appl. Sci., 9.","DOI":"10.3390\/app9061107"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.ndteint.2003.04.001","article-title":"Guided Wave Inspection Potential of Defects in Rail","volume":"37","author":"Rose","year":"2004","journal-title":"NDT & E Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.ndteint.2008.09.013","article-title":"A Guided Wave Approach to Defect Detection under Shelling in Rail","volume":"42","author":"Lee","year":"2009","journal-title":"NDT & E Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.ndteint.2004.10.008","article-title":"Modeling Guided Wave Propagation with Application to the Long-Range Defect Detection in Railroad Tracks","volume":"38","author":"Bartoli","year":"2005","journal-title":"NDT & E Int."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.ndteint.2010.09.011","article-title":"Numerical and Experimental Study of Guided Waves for Detection of Defects in the Rail Head","volume":"44","author":"Coccia","year":"2011","journal-title":"NDT & E Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ndteint.2018.02.002","article-title":"Development of an Optimal Piezoelectric Transducer to Excite Guided Waves in a Rail Web","volume":"95","author":"Ramatlo","year":"2018","journal-title":"NDT & E Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"115102","DOI":"10.1088\/1361-6501\/aadc47","article-title":"Ultrasonic Guided Wave-Based Switch Rail Monitoring Using Independent Component Analysis","volume":"29","author":"Wu","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1007\/s10921-014-0264-6","article-title":"An Intelligent Methodology for Railways Monitoring Using Ultrasonic Guided Waves","volume":"33","author":"Moustakidis","year":"2014","journal-title":"J. Nondestruct. Eval."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4756574","DOI":"10.1155\/2020\/4756574","article-title":"Guided Wave Propagation for Monitoring the Rail Base","volume":"2020","author":"Yue","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1177\/1045389X15610910","article-title":"Non-Contact Inspection of Rail Surface and Internal Defects Based on Electromagnetic Ultrasonic Transducers","volume":"27","author":"Han","year":"2015","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0041-624X(03)00097-0","article-title":"Guided Wave Dispersion Curves for a Bar with an Arbitrary Cross-Section, a Rod and Rail Example","volume":"41","author":"Hayashi","year":"2003","journal-title":"Ultrasonics"},{"key":"ref_22","unstructured":"Andhavarapu, E.V., Loveday, P., Long, C.S., and Heyns, P. (2010, January 10\u201313). Accuracy of Semi-Analytical Finite Elements for Modelling Wave Propagation in Rails. Proceedings of the Seventh South African Conference on Computational and Applied Mechanics (SACAM10), Pretoria, South Africa."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1061\/(ASCE)EM.1943-7889.0000136","article-title":"Quantitative Structural Health Monitoring by Ultrasonic Guided Waves","volume":"136","author":"Srivastava","year":"2010","journal-title":"J. Eng. Mech."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Long, C.S., and Loveday, P.W. (2015). Validation of Hybrid SAFE-FE Guided Wave Scattering Predictions in Rail. AIP Conference Proceedings, AIP Publishing LLC.","DOI":"10.1063\/1.4914671"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.ijsolstr.2019.08.015","article-title":"Global-Local Model for Guided Wave Scattering Problems with Application to Defect Characterization in Built-up Composite Structures","volume":"182\u2013183","author":"Spada","year":"2020","journal-title":"Int. J. Solids Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1121\/1.400530","article-title":"A Two-Dimensional Fourier Transform Method for the Measurement of Propagating Multimode Signals","volume":"89","author":"Alleyne","year":"1991","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2150012","DOI":"10.1142\/S1758825121500125","article-title":"Analysis of Wave Scattering in Pipes with Non-Axisymmetric and Inclined Angle Defects Using Finite Element Modeling","volume":"13","author":"Masoumi","year":"2021","journal-title":"Int. J. Appl. Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0378-3804(80)90020-0","article-title":"The Standard Rail Section, Transverse Fissures and Reformed Mill Practice, 1911\u20131955","volume":"4","author":"Duffy","year":"1980","journal-title":"J. Mech. Work. Technol."},{"key":"ref_29","unstructured":"Danbury, C. (1964). Rail Defects Manual, Sperry Rail Service."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10921-007-0027-8","article-title":"Single Mode Tuning Effects on Lamb Wave Time Reversal with Piezoelectric Wafer Active Sensors for Structural Health Monitoring","volume":"26","author":"Xu","year":"2007","journal-title":"J. Nondestruct. Eval."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1121\/1.4770238","article-title":"A Spacing Compensation Factor for the Optimization of Guided Wave Annular Array Transducers","volume":"133","author":"Borigo","year":"2013","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"60414","DOI":"10.1109\/ACCESS.2018.2875123","article-title":"An Ultrasonic Guided Wave Mode Excitation Method in Rails","volume":"6","author":"Xining","year":"2018","journal-title":"IEEE Access"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2566\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:04Z","timestamp":1760146444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,5]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["sym14122566"],"URL":"https:\/\/doi.org\/10.3390\/sym14122566","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,12,5]]}}}