{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T15:25:09Z","timestamp":1780500309931,"version":"3.54.1"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T00:00:00Z","timestamp":1693785600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technology","award":["MOST 111-2221-E-006-170"],"award-info":[{"award-number":["MOST 111-2221-E-006-170"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Digital twins can reflect the dynamical behavior of the identified system, enabling self-diagnosis and prediction in the digital world to optimize the intelligent manufacturing process. One of the key benefits of digital twins is the ability to provide real-time data analysis during operation, which can monitor the condition of the system and prognose the failure. This allows manufacturers to resolve the problem before it happens. However, most digital twins are constructed using discrete-time models, which are not able to describe the dynamics of the system across different sampling frequencies. In addition, the high computational complexity due to significant memory storage and large model sizes makes digital twins challenging for online diagnosis. To overcome these issues, this paper proposes a novel structure for creating the digital twins of cooling fan systems by combining with neural ordinary differential equations and physical dynamical differential equations. Evaluated using the simulation data, the proposed structure not only shows accurate modeling results compared to other digital twins methods but also requires fewer parameters and smaller model sizes. The proposed approach has also been demonstrated using experimental data and is robust in terms of measurement noise, and it has proven to be an effective solution for online diagnosis in the intelligent manufacturing process.<\/jats:p>","DOI":"10.3390\/fi15090302","type":"journal-article","created":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T10:14:11Z","timestamp":1693822451000},"page":"302","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Hybrid Neural Ordinary Differential Equation Based Digital Twin Modeling and Online Diagnosis for an Industrial Cooling Fan"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4068-0632","authenticated-orcid":false,"given":"Chao-Chung","family":"Peng","sequence":"first","affiliation":[{"name":"Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6635-3819","authenticated-orcid":false,"given":"Yi-Ho","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103540","DOI":"10.1016\/j.pnucene.2020.103540","article-title":"A RELAP5-3D\/LSTM model for the analysis of drywell cooling fan failure","volume":"130","author":"Guillen","year":"2020","journal-title":"Prog. 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