{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T06:39:37Z","timestamp":1768459177019,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T00:00:00Z","timestamp":1716422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"CDTI, dependent on the Spanish Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["CER-20190001"],"award-info":[{"award-number":["CER-20190001"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The techniques that allow one to estimate measurements at the unsensed points of a system are known as virtual sensing. These techniques are useful for the implementation of condition monitoring systems in industrial equipment subjected to high cyclic loads that can cause fatigue damage, such as industrial presses. In this article, three different virtual sensing algorithms for strain estimation are tested using real measurement data obtained from a scaled bed press prototype: two deterministic algorithms (Direct Strain Observer and Least-Squares Strain Estimation) and one stochastic algorithm (Static Strain Kalman Filter). The prototype is subjected to cyclic loads using a hydraulic fatigue testing machine and is sensorized with strain gauges. Results show that sufficiently accurate strain estimations can be obtained using virtual sensing algorithms and a reduced number of strain gauges as input sensors when the monitored structure is subjected to static and quasi-static loads. Results also show that is possible to estimate the initiation of fatigue cracks at critical points of a structural component using virtual strain sensors.<\/jats:p>","DOI":"10.3390\/s24113354","type":"journal-article","created":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T11:37:13Z","timestamp":1716464233000},"page":"3354","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Strain Virtual Sensing Applied to Industrial Presses for Fatigue Monitoring"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2174-5103","authenticated-orcid":false,"given":"Bartomeu","family":"Mora","sequence":"first","affiliation":[{"name":"Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA), 20500 Arrasate-Mondragon, Spain"},{"name":"Faculty of Engineering in Bilbao, University of the Basque Country UPV-EHU, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jon","family":"Basurko","sequence":"additional","affiliation":[{"name":"Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA), 20500 Arrasate-Mondragon, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4913-6438","authenticated-orcid":false,"given":"Urko","family":"Leturiondo","sequence":"additional","affiliation":[{"name":"Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA), 20500 Arrasate-Mondragon, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4516-694X","authenticated-orcid":false,"given":"Joseba","family":"Albizuri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering in Bilbao, University of the Basque Country UPV-EHU, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,23]]},"reference":[{"key":"ref_1","unstructured":"Liu, L., Kuo, S.M., and Zhou, M.C. 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