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Since fog computing physically close to IoT devices can alleviate these issues, much attention has recently been focused on this area. Fans are nearly ubiquitous in manufacturing sites for cooling and ventilation purposes. Thereby, we built a fan system with an accelerometer installed and monitored the operating state of the fan. We analyzed time-series data transmitted from the accelerometer. We applied machine learning under streaming data analytics at the fog computing level to create a fan\u2019s cyber-physical model (CPM). This work employed the symbolic approximation algorithm to approximate the time series data as symbols of arbitrary length. We compared the performance of CPMs made with five time-series classification (TSC) algorithms to monitor the state of the fan for anomalies in real time. The CPM made with the BOSS VS algorithm, a symbol approximation algorithm, accurately determined the current state of the fan within a fog computing environment, achieving approximately 98% accuracy at a 95% confidence level. Furthermore, we conducted a posthoc analysis, running statistical rigor tests on experimental data and simulation results. The workflow proposed in this work would be expected to be utilized for various IoT devices in smart manufacturing systems.<\/jats:p>","DOI":"10.1186\/s13677-022-00337-y","type":"journal-article","created":{"date-parts":[[2022,10,5]],"date-time":"2022-10-05T05:02:38Z","timestamp":1664946158000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fog computing application of cyber-physical models of IoT devices with symbolic approximation algorithms"],"prefix":"10.1186","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3474-3430","authenticated-orcid":false,"given":"Deok-Kee","family":"Choi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,5]]},"reference":[{"key":"337_CR1","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.procir.2019.04.239","volume":"84","author":"SJ Oks","year":"2019","unstructured":"Oks SJ, Jalowski M, Fritzsche A, M\u00f6slein KM (2019) Cyber-physical modeling and simulation: A reference architecture for designing demonstrators for industrial cyber-physical systems. 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