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Data-driven models commonly employ machine learning algorithms, but they often lack the ability to adapt to changes in the system over time. This paper proposes a method that uses <jats:italic>Echo State Networks<\/jats:italic> (ESN), a simplified version of <jats:italic>Recurrent Neural Networks<\/jats:italic> (RNN), to model an industrial plant. The ESN model incorporates online adaptation to system changes and enables the visualisation of deviations or errors in the operation of the plant. This adaptive model acknowledges acceptable changes within the original system while identifying potential problems or errors. The advantage of this approach is that the same model can be applied to other systems with the same design, eliminating the need for algorithm retraining. Firstly, its successful offline application in visualising anomalies applied to the reference plant is assessed. Secondly, the model is tested for online adaptation to changes in another plant with an identical design but slight differences, while still observing the generated faults. Residual colour maps are used for the visualisation of anomalies.<\/jats:p>","DOI":"10.1007\/s12530-024-09626-0","type":"journal-article","created":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T09:01:11Z","timestamp":1737795671000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Adaptive model based on ESN for anomaly detection in industrial systems"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0401-3995","authenticated-orcid":false,"given":"Jos\u00e9 Ram\u00f3n","family":"Rodr\u00edguez-Ossorio","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2762-6949","authenticated-orcid":false,"given":"Antonio","family":"Mor\u00e1n","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9023-0341","authenticated-orcid":false,"given":"Juan J.","family":"Fuertes","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1563-1556","authenticated-orcid":false,"given":"Miguel A.","family":"Prada","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0420-2315","authenticated-orcid":false,"given":"Ignacio","family":"D\u00edaz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3921-1599","authenticated-orcid":false,"given":"Manuel","family":"Dom\u00ednguez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,25]]},"reference":[{"key":"9626_CR1","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.neunet.2016.09.009","volume":"85","author":"EA Antonelo","year":"2017","unstructured":"Antonelo EA, Camponogara E, Foss B (2017) Echo state networks for data-driven downhole pressure estimation in gas-lift oil wells. 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