{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T03:04:45Z","timestamp":1768791885819,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The green conversion of proton exchange membrane fuel cells (PEMFCs) has received particular attention in both stationary and transportation applications. However, the poor durability of PEMFC represents a major problem that hampers its commercial application since dynamic operating conditions, including physical deterioration, have a serious impact on the cell performance. Under these circumstances, prognosis and health management (PHM) plays an important role in prolonging durability and preventing damage propagation via the accurate planning of a condition-based maintenance (CBM) schedule. In this specific topic, health deterioration modeling with deep learning (DL) is the widely studied representation learning tool due to its adaptation ability to rapid changes in data complexity and drift. In this context, the present paper proposes an investigation of further deeper representations by exposing DL models themselves to recurrent expansion with multiple repeats. Such a recurrent expansion of DL (REDL) allows new, more meaningful representations to be explored by repeatedly using generated feature maps and responses to create new robust models. The proposed REDL, which is designed to be an adaptive learning algorithm, is tested on a PEMFC deterioration dataset and compared to its deep learning baseline version under time series analysis. Using multiple numeric and visual metrics, the results support the REDL learning scheme by showing promising performances.<\/jats:p>","DOI":"10.3390\/e24071009","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T10:36:56Z","timestamp":1658399816000},"page":"1009","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Exposing Deep Representations to a Recurrent Expansion with Multiple Repeats for Fuel Cells Time Series Prognosis"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4877-4200","authenticated-orcid":false,"given":"Tarek","family":"Berghout","sequence":"first","affiliation":[{"name":"Laboratory of Automation and Manufacturing Engineering, University of Batna 2, Batna 05000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4844-508X","authenticated-orcid":false,"given":"Mohamed","family":"Benbouzid","sequence":"additional","affiliation":[{"name":"Institut de Recherche Dupuy de L\u00f4me (UMR CNRS 6027), University of Brest, 29238 Brest, France"},{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toufik","family":"Bentrcia","sequence":"additional","affiliation":[{"name":"Laboratory of Automation and Manufacturing Engineering, University of Batna 2, Batna 05000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2031-4088","authenticated-orcid":false,"given":"Yassine","family":"Amirat","sequence":"additional","affiliation":[{"name":"ISEN Yncr\u00e9a Ouest, L@bISEN, 29200 Brest, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Le\u00efla-Hayet","family":"Mouss","sequence":"additional","affiliation":[{"name":"Laboratory of Automation and Manufacturing Engineering, University of Batna 2, Batna 05000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"231256","DOI":"10.1016\/j.jpowsour.2022.231256","article-title":"A review on lifetime prediction of proton exchange membrane fuel cells system","volume":"529","author":"Hua","year":"2022","journal-title":"J. Power Sources"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1002\/fuce.201600075","article-title":"PHM-oriented Degradation Indicators for Batteries and Fuel Cells","volume":"17","author":"Zhang","year":"2017","journal-title":"Fuel Cells"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.rser.2016.11.009","article-title":"A review on prognostics and health monitoring of proton exchange membrane fuel cell","volume":"75","author":"Sutharssan","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1049\/iet-est.2020.0045","article-title":"Prognostic methods for proton exchange membrane fuel cell under automotive load cycling: A review","volume":"10","author":"Jacome","year":"2020","journal-title":"IET Electr. Syst. Transp."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Berghout, T., and Benbouzid, M. (2022). A Systematic Guide for Predicting Remaining Useful Life with Machine Learning. Electronics, 11.","DOI":"10.3390\/electronics11071125"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Berghout, T., Mouss, L., Kadri, O., Sa\u00efdi, L., and Benbouzid, M. (2020). Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine. Appl. Sci., 10.","DOI":"10.3390\/app10031062"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103936","DOI":"10.1016\/j.engappai.2020.103936","article-title":"Aircraft engines Remaining Useful Life prediction with an adaptive denoising online sequential Extreme Learning Machine","volume":"96","author":"Berghout","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"117841","DOI":"10.1016\/j.apenergy.2021.117841","article-title":"A short- and long-term prognostic associating with remaining useful life estimation for proton exchange membrane fuel cell","volume":"304","author":"Zhang","year":"2021","journal-title":"Appl. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5488","DOI":"10.1016\/j.ijhydene.2018.09.085","article-title":"Review on hydrogen fuel cell condition monitoring and prediction methods","volume":"44","author":"Lin","year":"2019","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pan, M., Hu, P., Gao, R., and Liang, K. (2022). Multistep prediction of remaining useful life of proton exchange membrane fuel cell based on temporal convolutional network. Int. J. Green Energy, 1\u201315.","DOI":"10.1080\/15435075.2022.2050377"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10976","DOI":"10.1016\/j.ijhydene.2022.01.145","article-title":"Real-time data-driven fault diagnosis of proton exchange membrane fuel cell system based on binary encoding convolutional neural network","volume":"47","author":"Zhou","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"30828","DOI":"10.1016\/j.ijhydene.2021.05.137","article-title":"Fault diagnosis of proton exchange membrane fuel cell system of tram based on information fusion and deep learning","volume":"46","author":"Zhang","year":"2021","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"118835","DOI":"10.1016\/j.apenergy.2022.118835","article-title":"A data-driven method for multi-step-ahead prediction and long-term prognostics of proton exchange membrane fuel cell","volume":"313","author":"Benaggoune","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10395","DOI":"10.1016\/j.ijhydene.2022.01.121","article-title":"A novel long short-term memory networks-based data-driven prognostic strategy for proton exchange membrane fuel cells","volume":"47","author":"Wang","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.isatra.2020.06.005","article-title":"Degradation prognosis for proton exchange membrane fuel cell based on hybrid transfer learning and intercell differences","volume":"113","author":"Ma","year":"2021","journal-title":"ISA Trans."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ma, T., Xu, J., Li, R., Yao, N., and Yang, Y. (2021). Online Short-Term Remaining Useful Life Prediction of Fuel Cell Vehicles Based on Cloud System. Energies, 14.","DOI":"10.3390\/en14102806"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"228154","DOI":"10.1016\/j.jpowsour.2020.228154","article-title":"Performance prediction and power density maximization of a proton exchange membrane fuel cell based on deep belief network","volume":"461","author":"Li","year":"2020","journal-title":"J. Power Sources"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2555","DOI":"10.1016\/j.ijhydene.2020.10.108","article-title":"A data-driven digital-twin prognostics method for proton exchange membrane fuel cell remaining useful life prediction","volume":"46","author":"Meraghni","year":"2021","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Long, B., Wu, K., Li, P., and Li, M. (2022). A Novel Remaining Useful Life Prediction Method for Hydrogen Fuel Cells Based on the Gated Recurrent Unit Neural Network. Appl. Sci., 12.","DOI":"10.3390\/app12010432"},{"key":"ref_20","unstructured":"Fabien, H. (2021). IEEE PHM Data Challenge 2014. Fuel Cell Lab UAR 2200."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/1009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:55:46Z","timestamp":1760140546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/1009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,21]]},"references-count":20,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["e24071009"],"URL":"https:\/\/doi.org\/10.3390\/e24071009","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,21]]}}}