{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:00:24Z","timestamp":1760148024593,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T00:00:00Z","timestamp":1679616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Foundation Ireland (SFI)","award":["SFI\/12\/RC\/2289","13\/RC\/2094"],"award-info":[{"award-number":["SFI\/12\/RC\/2289","13\/RC\/2094"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Autoencoders have been used widely for diagnosing devices, for example, faults in rotating machinery. However, autoencoder-based approaches lack explainability for their results and can be hard to tune. In this article, we propose an explainable method for applying autoencoders for diagnosis, where we use a metric that maximizes the diagnostics accuracy. Since an autoencoder projects the input into a reduced subspace (the code), we define a theoretically well-understood approach, the subspace principal angle, to define a metric over the possible fault labels. We show how this approach can be used for both single-device diagnostics (e.g., faults in rotating machinery) and complex (multi-device) dynamical systems. We empirically validate the theoretical claims using multiple autoencoder architectures.<\/jats:p>","DOI":"10.3390\/a16040178","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T03:50:21Z","timestamp":1679629821000},"page":"178","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Toward Explainable AutoEncoder-Based Diagnosis of Dynamical Systems"],"prefix":"10.3390","volume":"16","author":[{"given":"Gregory","family":"Provan","sequence":"first","affiliation":[{"name":"School of Computer Science and IT, University College Cork (UCC), T12 R229 Cork, Ireland"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ymssp.2018.02.016","article-title":"Artificial intelligence for fault diagnosis of rotating machinery: A review","volume":"108","author":"Liu","year":"2018","journal-title":"Mech. 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