{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T01:13:41Z","timestamp":1778116421521,"version":"3.51.4"},"reference-count":50,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T00:00:00Z","timestamp":1720569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2017YFB0102802"],"award-info":[{"award-number":["2017YFB0102802"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["202306260098"],"award-info":[{"award-number":["202306260098"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"State Scholarship Funding of CSC","doi-asserted-by":"publisher","award":["2017YFB0102802"],"award-info":[{"award-number":["2017YFB0102802"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"State Scholarship Funding of CSC","doi-asserted-by":"publisher","award":["202306260098"],"award-info":[{"award-number":["202306260098"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Proton-exchange membrane fuel cells (PEMFCs) play a crucial role in the transition to sustainable energy systems. Accurately estimating the state of health (SOH) of PEMFCs under dynamic operating conditions is essential for ensuring their reliability and longevity. This study designed dynamic operating conditions for fuel cells and conducted durability tests using both crack-free fuel cells and fuel cells with uniform cracks. Utilizing deep learning methods, we estimated the SOH of PEMFCs under dynamic operating conditions and investigated the performance of long short-term memory networks (LSTM), gated recurrent units (GRU), temporal convolutional networks (TCN), and transformer models for SOH estimation tasks. We also explored the impact of different sampling intervals and training set proportions on the predictive performance of these models. The results indicated that shorter sampling intervals and higher training set proportions significantly improve prediction accuracy. The study also highlighted the challenges posed by the presence of cracks. Cracks cause more frequent and intense voltage fluctuations, making it more difficult for the models to accurately capture the dynamic behavior of PEMFCs, thereby increasing prediction errors. However, under crack-free conditions, due to more stable voltage output, all models showed improved predictive performance. Finally, this study underscores the effectiveness of deep learning models in estimating the SOH of PEMFCs and provides insights into optimizing sampling and training strategies to enhance prediction accuracy. The findings make a significant contribution to the development of more reliable and efficient PEMFC systems for sustainable energy applications.<\/jats:p>","DOI":"10.3390\/s24144451","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T13:34:38Z","timestamp":1720618478000},"page":"4451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Deep Learning-Based State-of-Health Estimation of Proton-Exchange Membrane Fuel Cells under Dynamic Operation Conditions"],"prefix":"10.3390","volume":"24","author":[{"given":"Yujia","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Automotive Studies, Tongji University, Shanghai 201804, China"}]},{"given":"Xingwang","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Automotive Studies, Tongji University, Shanghai 201804, China"}]},{"given":"Sichuan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Automotive Studies, Tongji University, Shanghai 201804, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4932-7787","authenticated-orcid":false,"given":"Chuanyu","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1016\/j.ijhydene.2023.08.044","article-title":"Fueling the future: A comprehensive review of hydrogen energy systems and their challenges","volume":"54","author":"Le","year":"2024","journal-title":"Int. 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