{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T19:44:18Z","timestamp":1773085458576,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"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":["12202103"],"award-info":[{"award-number":["12202103"]}],"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":["2021B1515120090"],"award-info":[{"award-number":["2021B1515120090"]}],"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":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2021B1515120090"],"award-info":[{"award-number":["2021B1515120090"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Ultrasonic guided wave (UGW) inspection is an emerging non-destructive testing(NDT) technique for rail flaw detection, where weak UGW signals under strong noise backgrounds are difficult to detect. In this study, a UGW signal identification model based on a chaotic oscillator is established. The approach integrates the UGW response into the critical state of the Duffing system to serve as a disturbance control variable. By evaluating the system\u2019s motion state before and after introducing the UGW response, identification of UGW signals can be realized. Thus, the parameters defining the critical state of Duffing oscillators are determined by Ke. Moreover, an electromagnetic transducer was specifically devised to enable unidirectional excitation for UGWs targeted at both the rail base and rail head. Experimental studies showed that the proposed methodology effectively detected and located a 0.46 mm notch at the rail base and a 1.78 mm notch at the rail head. Furthermore, Ke was directly proportional to the notch size, which could be used as a quantitative index to characterize the rail flaw.<\/jats:p>","DOI":"10.3390\/s24092730","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T05:26:13Z","timestamp":1714022773000},"page":"2730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Rail Flaw Detection via Kolmogorov Entropy of Chaotic Oscillator Based on Ultrasonic Guided Waves"],"prefix":"10.3390","volume":"24","author":[{"given":"Ziyan","family":"Zeng","sequence":"first","affiliation":[{"name":"School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, China"}]},{"given":"Jing","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dongguan University of Technology, Dongguan 523808, China"}]},{"given":"Mingfang","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China"}]},{"given":"Hongwei","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dongguan University of Technology, Dongguan 523808, China"},{"name":"School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China"},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering, Dongguan 523808, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rose, J.L. (2014). Ultrasonic Guided Waves in Solid Media, Cambridge University Press.","DOI":"10.1017\/CBO9781107273610"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.sigpro.2013.05.025","article-title":"Structure damage localization with ultrasonic guided waves based on a time\u2013frequency method","volume":"96","author":"Dai","year":"2014","journal-title":"Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3056","DOI":"10.1177\/1475921720979283","article-title":"A novel time\u2013frequency transform for broadband Lamb waves dispersion characteristics analysis","volume":"20","author":"Luo","year":"2021","journal-title":"Struct. Health Monit."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, G., Zhang, J., Cheng, J., Wang, K., Yang, D., and Yuan, Y. (2023). Multi-Order Mode Excitation and Separation of Ultrasonic Guided Waves in Rod Structures Using 2D-FFT. Sensors, 23.","DOI":"10.3390\/s23208483"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"04021051","DOI":"10.1061\/(ASCE)PS.1949-1204.0000600","article-title":"Damage identification of pipeline based on ultrasonic guided wave and wavelet denoising","volume":"12","author":"Xu","year":"2021","journal-title":"J. Pipeline Syst. Eng. Pract."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105948","DOI":"10.1016\/j.ultras.2019.105948","article-title":"Automatic mode extraction of ultrasonic guided waves using synchrosqueezed wavelet transform","volume":"99","author":"Liu","year":"2019","journal-title":"Ultrasonics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jappgeo.2018.02.001","article-title":"Non-destructive testing of full-length bonded rock bolts based on HHT signal analysis","volume":"151","author":"Shi","year":"2018","journal-title":"J. Appl. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00339-016-9753-z","article-title":"Detection and localization of damage using empirical mode decomposition and multilevel support vector machine","volume":"122","author":"Dushyanth","year":"2016","journal-title":"Appl. Phys. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"095601","DOI":"10.1088\/1361-6501\/abef3c","article-title":"An advanced Wigner\u2013Ville time\u2013frequency analysis of Lamb wave signals based upon an autoregressive model for efficient damage inspection","volume":"32","author":"Rizvi","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"112403","DOI":"10.1016\/j.compstruct.2020.112403","article-title":"Detection and classification of matrix cracking in laminated composites using guided wave propagation and artificial neural networks","volume":"246","author":"Mardanshahi","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1177\/1475921709341012","article-title":"A linear mapping technique for dispersion removal of Lamb waves","volume":"9","author":"Liu","year":"2010","journal-title":"Struct. Health Monit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106767","DOI":"10.1016\/j.ultras.2022.106767","article-title":"An efficient Lamb wave-based virtual refined time-reversal method for damage localization in plates using broadband measurements","volume":"124","author":"Kannusamy","year":"2022","journal-title":"Ultrasonics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/TCST.2019.2897946","article-title":"Robust monitoring and fault isolation of nonlinear industrial processes using denoising autoencoder and elastic net","volume":"28","author":"Yu","year":"2019","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"12752","DOI":"10.1109\/TIE.2023.3239861","article-title":"A robust dissimilarity distribution analytics with Laplace distribution for incipient fault detection","volume":"70","author":"Yu","year":"2023","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8340","DOI":"10.1109\/TCYB.2021.3050398","article-title":"MoniNet with concurrent analytics of temporal and spatial information for fault detection in industrial processes","volume":"52","author":"Yu","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic nonperiodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"key":"ref_17","first-page":"8781","article-title":"Exact solution to duffing equation and the pendulum equation","volume":"8","author":"Salas","year":"2014","journal-title":"Appl. Math. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4028\/www.scientific.net\/AMM.430.3","article-title":"On the Van der Pol oscillator: An overview","volume":"430","author":"Cveticanin","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/S0007-8506(07)60606-4","article-title":"Decision making in logistics: A chaos theory based analysis","volume":"52","author":"Kumara","year":"2003","journal-title":"CIRP Ann."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/S0960-0779(01)00052-2","article-title":"Control of chaos in Lorenz system","volume":"13","author":"Yang","year":"2002","journal-title":"Chaos Solitons Fractals"},{"key":"ref_21","first-page":"1","article-title":"The application of Duffing oscillator in weak signal detection","volume":"9","author":"Jalilvand","year":"2011","journal-title":"ECTI Trans. Electr. Eng. Electron. Commun."},{"key":"ref_22","first-page":"359","article-title":"Periodic Solutions of the Duffing Equation with the Square Wave External Force","volume":"60","author":"NOHARA","year":"2012","journal-title":"Theor. Appl. Mech. Japan"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.chaos.2007.07.090","article-title":"Effect of nonsinusoidal periodic forces in Duffing oscillator: Numerical and analog simulation studies","volume":"40","author":"Srinivasan","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s13349-022-00668-z","article-title":"Application of chaotic information entropy for ultrasonic guided wave detection in pipe","volume":"14","author":"Cheng","year":"2024","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/j.measurement.2017.06.033","article-title":"Detection of minor damage in structures with guided wave signals and nonlinear oscillator","volume":"122","author":"Zhang","year":"2018","journal-title":"Measurement"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.jsv.2017.05.044","article-title":"Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system","volume":"405","author":"Liu","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.ymssp.2017.07.048","article-title":"Location identification of closed crack based on Duffing oscillator transient transition","volume":"100","author":"Liu","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.ymssp.2016.05.012","article-title":"Defect detection of pipes using Lyapunov dimension of Duffing oscillator based on ultrasonic guided waves","volume":"82","author":"Wu","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"107111","DOI":"10.1016\/j.optlaseng.2022.107111","article-title":"A novel laser-based duffing oscillator system to identify weak ultrasonic guided wave signals related to rail defects","volume":"157","author":"Ng","year":"2022","journal-title":"Opt. Lasers Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"110196","DOI":"10.1016\/j.ymssp.2023.110196","article-title":"Analysis and application of weak guided wave signal detection based on double Duffing oscillators","volume":"191","author":"Cheng","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Karmakar, C., Udhayakumar, R., and Palaniswami, M. (2020). Entropy profiling: A reduced\u2014Parametric measure of kolmogorov\u2014sinai entropy from short-term HRV signal. Entropy, 22.","DOI":"10.3390\/e22121396"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kiss, G., and Bakucz, P. (2024). Using Kolmogorov Entropy to Verify the Description Completeness of Traffic Dynamics of Highly Autonomous Driving. Appl. Sci., 14.","DOI":"10.3390\/app14062261"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2730\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:33:50Z","timestamp":1760106830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,25]]},"references-count":32,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["s24092730"],"URL":"https:\/\/doi.org\/10.3390\/s24092730","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,25]]}}}