{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T14:46:01Z","timestamp":1767192361233,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"],"award-info":[{"award-number":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"]}]},{"name":"National Natural Science Foundation of China","award":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"],"award-info":[{"award-number":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"]}]},{"name":"Project of Hunan Provincial Department of Education, China","award":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"],"award-info":[{"award-number":["2021YFF0501101","62173137","52172403","62303178","23A0426","22B0577"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>The wheel\u2013rail contact force is a crucial indicator for ensuring the secure operation of a heavy-load train. However, obtaining the real-time wheel\u2013rail contact force of a heavy-load train is a challenging task as, due to safety considerations, it is not possible to install instrumented wheelsets on heavy-load trains. This work presents a novel approach to quantify the wheel\u2013rail contact force of a heavy-load train, utilizing a cooperative calibration methodology. First, a ground measurement platform for the wheel\u2013rail contact force of a heavy-load train is constructed on a selected rail section. The railway inspection car\u2019s wheel\u2013rail contact force measurement system is fine-tuned using a multilayer perceptron calibration approach, and the ground platform then uses the results to fine-tune the railway inspection car\u2019s examined wheelset. Second, based on actual measured data on the wheel\u2013rail contact force of a heavy-load train, and using the golden jackal optimization algorithm, the multilayer perceptron correction approach is employed to create a data relationship mapping model. This model correlates the corrected data on the wheel\u2013rail contact force obtained from the railway inspection car with the wheel\u2013rail contact force of a heavy-haul train with an axle load of 25 tons, and the precision of the mapping is guaranteed. Finally, by combining the wheel\u2013rail contact force correction method for the railway inspection car and the contact force mapping model between the railway inspection car and the heavy-load train, collaborative calibration of the wheel\u2013rail contact force of the heavy-load train is realized. The experimental results under two working conditions show that this method can realize high-precision, real-time measurement of the wheel\u2013rail contact force of a heavy-load train. For the working condition of a straight-line section, the calibration error was within 1.593 kN, and the MAPE was 0.105%; for the working condition of a curved-line section, the calibration error was 2.344 kN, and the RMSE was 184.72 N.<\/jats:p>","DOI":"10.3390\/info15090535","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T12:54:42Z","timestamp":1725281682000},"page":"535","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Wheel\u2013Rail Contact Force for a Heavy-Load Train Can Be Measured Using a Collaborative Calibration Algorithm"],"prefix":"10.3390","volume":"15","author":[{"given":"Tianning","family":"Wen","sequence":"first","affiliation":[{"name":"College of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3650-3270","authenticated-orcid":false,"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"College of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7439-1775","authenticated-orcid":false,"given":"Changfan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia","family":"He","sequence":"additional","affiliation":[{"name":"China Energy Baoshen Railway Group, Baotou 014010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"ref_1","first-page":"131","article-title":"China\u2019s railway train speed, density and weight in developing","volume":"1","author":"Jiang","year":"2022","journal-title":"Railw. 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