{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,22]],"date-time":"2026-02-22T03:36:29Z","timestamp":1771731389896,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EPSRC EP\/R511687\/1"],"award-info":[{"award-number":["EPSRC EP\/R511687\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00297\/2020"],"award-info":[{"award-number":["UIDB\/00297\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>The degradation of lithium-ion cells with respect to increases of internal resistance (IR) has negative implications for rapid charging protocols, thermal management and power output of cells. Despite this, IR receives much less attention than capacity degradation in Li-ion cell research. Building on recent developments on \u2018knee\u2019 identification for capacity degradation curves, we propose the new concepts of \u2018elbow-point\u2019 and \u2018elbow-onset\u2019 for IR rise curves, and a robust identification algorithm for those variables. We report on the relations between capacity\u2019s knees, IR\u2019s elbows and end of life for the large dataset of the study. We enhance our discussion with two applications. We use neural network techniques to build independent state of health capacity and IR predictor models achieving a mean absolute percentage error (MAPE) of 0.4% and 1.6%, respectively, and an overall root mean squared error below 0.0061. A relevance vector machine, using the first 50 cycles of life data, is employed for the early prediction of elbow-points and elbow-onsets achieving a MAPE of 11.5% and 14.0%, respectively.<\/jats:p>","DOI":"10.3390\/en14041206","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T12:40:16Z","timestamp":1614084016000},"page":"1206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Elbows of Internal Resistance Rise Curves in Li-Ion Cells"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8930-5315","authenticated-orcid":false,"given":"Calum","family":"Strange","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1536-4195","authenticated-orcid":false,"given":"Shawn","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1606-2607","authenticated-orcid":false,"given":"Richard","family":"Gilchrist","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4993-2672","authenticated-orcid":false,"given":"Gon\u00e7alo","family":"dos Reis","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK"},{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA), FCT, UNL, Quinta da Torre, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"A389","DOI":"10.1149\/2.1111702jes","article-title":"Transition metal dissolution, ion migration, electrocatalytic reduction and capacity loss in lithium-ion full cells","volume":"164","author":"Gilbert","year":"2017","journal-title":"J. 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