{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T12:15:54Z","timestamp":1768652154445,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T00:00:00Z","timestamp":1581292800000},"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":["61973306"],"award-info":[{"award-number":["61973306"]}],"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":["61802107"],"award-info":[{"award-number":["61802107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["E2017402115"],"award-info":[{"award-number":["E2017402115"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Project Foundation of State Key Laboratory of Synthetical Automation for Process Industries","award":["PAL-N201706"],"award-info":[{"award-number":["PAL-N201706"]}]},{"name":"Collaborative Innovation Center of Steel Technology Open Subject","award":["2015001"],"award-info":[{"award-number":["2015001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The floating height of the strip in an air cushion furnace is a key parameter for the quality and efficiency of production. However, the high temperature and high pressure of the working environment prevents the floating height from being directly measured. Furthermore, the strip has multiple floating states in the whole operation process. It is thus difficult to employ a single model to accurately describe the floating height in different states. This paper presents a multi-model soft sensor to estimate the height based on state identification and the soft transition. First, floating states were divided using a partition method that combined adaptive k-nearest neighbors and principal component analysis theories. Based on the identified results, a hybrid model for the stable state, involving a double-random forest model for the vibration state and a soft-transition model, was created to predict the strip floating height. In the hybrid model for the stable state, a mechanistic model combined thick jet theory and the equilibrium equation of force to cope with the lower floating height. In addition, a novel soft-transition model based on data gravitation that further reflects the intrinsic process characteristic was developed for the transition state. The effectiveness of the proposed approach was validated using a self-developed air cushion furnace experimental platform. This study has important value for the process prediction and control of air cushion furnaces.<\/jats:p>","DOI":"10.3390\/s20030926","type":"journal-article","created":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T09:25:21Z","timestamp":1581413121000},"page":"926","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Multi-Model- and Soft-Transition-Based Height Soft Sensor for an Air Cushion Furnace"],"prefix":"10.3390","volume":"20","author":[{"given":"Shuai","family":"Hou","sequence":"first","affiliation":[{"name":"School of Information and Electrical Engineering, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Electrical Engineering, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolin","family":"Han","sequence":"additional","affiliation":[{"name":"School of Information and Electrical Engineering, Hebei University of Engineering, Handan 056038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuan","family":"Hua","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.jclepro.2017.06.174","article-title":"Designing a new sustainable approach to the change for lightweight materials in structural components used in truck industry","volume":"164","author":"Santos","year":"2017","journal-title":"J. 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