{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T08:26:58Z","timestamp":1778833618369,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"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":["51805373"],"award-info":[{"award-number":["51805373"]}],"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":["202106260138"],"award-info":[{"award-number":["202106260138"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["51805373"],"award-info":[{"award-number":["51805373"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202106260138"],"award-info":[{"award-number":["202106260138"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Track irregularities directly affect the quality and safety of railway vehicle operations. Quantitative detection and real-time monitoring of track irregularities are of great importance. However, due to the frequent variable vehicle speed, vehicle operation is a typical non-stationary process. The traditional signal analysis methods are unsuitable for non-stationary processes, making the quantitative detection of the wavelength and amplitude of track irregularities difficult. To solve the above problems, this paper proposes a quantitative detection method of track irregularities under non-stationary conditions with variable vehicle speed by order tracking analysis for the first time. Firstly, a simplified wheel\u2013rail dynamic model is established to derive the quantitative relationship between the axle-box vertical vibration and the track vertical irregularities. Secondly, the Simpson double integration method is proposed to calculate the axle-box vertical displacement based on the axle-box vertical acceleration, and the process error is optimized. Thirdly, based on the order tracking analysis theory, the angular domain resampling is performed on the axle-box vertical displacement time-domain signal in combination with the wheel rotation speed signals, and the quantitative detection of the track irregularities is achieved. Finally, the proposed method is validated based on simulation and field test analysis cases. We provide theoretical support and method reference for the quantitative detection method of track irregularities.<\/jats:p>","DOI":"10.3390\/s24123804","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T08:45:50Z","timestamp":1718181950000},"page":"3804","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Quantitative Detection of Vertical Track Irregularities under Non-Stationary Conditions with Variable Vehicle Speed"],"prefix":"10.3390","volume":"24","author":[{"given":"Qiushi","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Military Traffic Injury Prevention and Control, Daping Hospital, Army Medical University, Chongqing 400042, China"},{"name":"Institute of Rail Transit, Tongji University, Shanghai 201804, China"},{"name":"School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Military Traffic Injury Prevention and Control, Daping Hospital, Army Medical University, Chongqing 400042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dao","family":"Gong","sequence":"additional","affiliation":[{"name":"Institute of Rail Transit, Tongji University, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinsong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Institute of Rail Transit, Tongji University, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongmin","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1080\/00423114.2014.907923","article-title":"Wheel\u2013rail contact: Experimental study of the creep forces\u2013creepage relationships","volume":"52","author":"Alonso","year":"2014","journal-title":"Veh. 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