{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T03:25:36Z","timestamp":1792553136607,"version":"4.5.0"},"reference-count":75,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"Xiongss Shusheng","award":["2024C01229"],"award-info":[{"award-number":["2024C01229"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-026-51217-3","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T23:02:09Z","timestamp":1787698929000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Real-time PEM fuel cell fault classification in smart manufacturing plant by using uncertainty aware federated deep learning"],"prefix":"10.1038","volume":"16","author":[{"given":"Muhammad","family":"Aurangzeb","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiong","family":"Shusheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheeraz","family":"Iqbal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Md","family":"Shafiullah","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hasan Saeed","family":"Qazi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmed Mohmed","family":"Dafalla","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhang","family":"Fuguang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lee","family":"Zhuoyu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Xinwei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sajjad","family":"Nazir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,26]]},"reference":[{"key":"51217_CR1","doi-asserted-by":"publisher","unstructured":"Quan, R., Zhang, J. & Feng, Z. Remote fault diagnosis for the powertrain system of fuel cell vehicles based on random forest optimized with a genetic algorithm. Sensors. 24(4), 1138. https:\/\/doi.org\/10.3390\/s24041138 (2024).","DOI":"10.3390\/s24041138"},{"key":"51217_CR2","doi-asserted-by":"publisher","unstructured":"Xiong, S., Wu, Z. & Cheng, J. Design of a fuel cell test system with fault identification. Electronics. 12(15), 3365. https:\/\/doi.org\/10.3390\/electronics12153365 (2023).","DOI":"10.3390\/electronics12153365"},{"key":"51217_CR3","doi-asserted-by":"publisher","unstructured":"B\u00e4umler, A., Meng, J., Benterki, A., Azib, T. & Boukhnifer, M. A system-level modeling of PEMFC considering degradation aspect towards a diagnosis process. Energies. 16(14), 5310. https:\/\/doi.org\/10.3390\/en16145310 (2023).","DOI":"10.3390\/en16145310"},{"key":"51217_CR4","doi-asserted-by":"publisher","unstructured":"Huo, W., Li, W., Sun, C., Ren, Q. & Gong, G. Research on fuel cell fault diagnosis based on genetic algorithm optimization of support vector machine. Energies. 15(6), 2294. https:\/\/doi.org\/10.3390\/en15062294 (2022).","DOI":"10.3390\/en15062294"},{"key":"51217_CR5","doi-asserted-by":"publisher","unstructured":"Xie, J., Wang, C., Zhu, W. & Yuan, H. A multi-stage fault diagnosis method for proton exchange membrane fuel cell based on support vector machine with binary tree. Energies. 14(20), 6526. https:\/\/doi.org\/10.3390\/en14206526 (2021).","DOI":"10.3390\/en14206526"},{"key":"51217_CR6","doi-asserted-by":"publisher","unstructured":"Najafi, B., Bonomi, P., Casalegno, A., Rinaldi, F. & Baricci, A. Rapid fault diagnosis of PEM fuel cells through optimal electrochemical impedance spectroscopy tests. Energies. 13(14), 3643. https:\/\/doi.org\/10.3390\/en13143643 (2020).","DOI":"10.3390\/en13143643"},{"key":"51217_CR7","doi-asserted-by":"publisher","unstructured":"Bharath, K. V. S., Blaabjerg, F., Haque, A. & Khan, M. A. Model-based data driven approach for fault identification in proton exchange membrane fuel cell, Energies. 13(12), 3144. https:\/\/doi.org\/10.3390\/en13123144 (2020).","DOI":"10.3390\/en13123144"},{"key":"51217_CR8","doi-asserted-by":"publisher","unstructured":"Mao, L. & Jackson, L. Effect of sensor set size on polymer electrolyte membrane fuel cell fault diagnosis, Sensors. 18(9), 2777. https:\/\/doi.org\/10.3390\/s18092777 (2018).","DOI":"10.3390\/s18092777"},{"key":"51217_CR9","doi-asserted-by":"publisher","unstructured":"Costamagna, P. et al. Fault diagnosis strategies for SOFC-based power generation plants, Sensors. 16(8), 1336. https:\/\/doi.org\/10.3390\/s16081336 (2016).","DOI":"10.3390\/s16081336"},{"key":"51217_CR10","doi-asserted-by":"publisher","unstructured":"Xiong, Y., Yin, T., Peng, F., Tong, Z. & Ping, C. The research of fault processing strategy for fuel cell vehicle based on classification principle, World Electr. Veh. J. 4(2), 287\u2013294. https:\/\/doi.org\/10.3390\/wevj4020287 (2010).","DOI":"10.3390\/wevj4020287"},{"issue":"4","key":"51217_CR11","doi-asserted-by":"publisher","first-page":"5151","DOI":"10.1109\/TTE.2022.3222970","volume":"9","author":"S Li","year":"2023","unstructured":"Li, S. et al. Net power optimization based on extremum search and model-free adaptive control of PEMFC power generation system for high altitude. IEEE Trans. Transp. Electrific. 9 (4), 5151\u20135164 (2023).","journal-title":"IEEE Trans. Transp. Electrific"},{"issue":"1","key":"51217_CR12","doi-asserted-by":"publisher","first-page":"2707","DOI":"10.1109\/TTE.2024.3427401","volume":"11","author":"Q Li","year":"2025","unstructured":"Li, Q. et al. Online diagnosis method of water management faults based on hybrid-frequency electrochemical impedance spectroscopy for PEMFC. IEEE Trans. Transp. Electrific. 11 (1), 2707\u20132716 (2025).","journal-title":"IEEE Trans. Transp. Electrific"},{"issue":"1","key":"51217_CR13","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1109\/TTE.2023.3253060","volume":"10","author":"J Li","year":"2024","unstructured":"Li, J., Cui, H., Jiang, W. & Yu, H. A large-scale multi-agent deep reinforcement learning method for cooperative output voltage control of PEMFCs. IEEE Trans. Transp. Electrific. 10 (1), 78\u201394 (2024).","journal-title":"IEEE Trans. Transp. Electrific"},{"issue":"7","key":"51217_CR14","doi-asserted-by":"publisher","first-page":"7544","DOI":"10.1109\/TIE.2024.3522469","volume":"72","author":"H Xu","year":"2025","unstructured":"Xu, H., Wang, L., Liu, Z., Su, H. & Ortega, R. Online identification of PEMFC polarization curves with nonlinear concentration loss. IEEE Trans. Ind. Electron. 72 (7), 7544\u20137552 (2025).","journal-title":"IEEE Trans. Ind. Electron."},{"key":"51217_CR15","doi-asserted-by":"publisher","first-page":"1559","DOI":"10.1109\/OJPEL.2025.3609524","volume":"6","author":"I Kong","year":"2025","unstructured":"Kong, I., Kim, W. & Chae, S. A grid-forming control method for PEMFC power conversion systems with power ramp rate limitation to prevent fuel starvation. IEEE Open. J. Power Electron. 6, 1559\u20131570 (2025).","journal-title":"IEEE Open. J. Power Electron."},{"issue":"9","key":"51217_CR16","doi-asserted-by":"publisher","first-page":"13821","DOI":"10.1109\/TVT.2025.3565459","volume":"74","author":"J Li","year":"2025","unstructured":"Li, J. & Zhou, T. Deep meta-reinforcement learning for the flow-pressure coordination of a vehicle PEMFC system considering multivariable constraints. IEEE Trans. Veh. Technol. 74 (9), 13821\u201313833 (2025).","journal-title":"IEEE Trans. Veh. Technol."},{"key":"51217_CR17","doi-asserted-by":"publisher","first-page":"13476","DOI":"10.1109\/TTE.2025.3601894","volume":"early access","author":"C Chen","year":"2025","unstructured":"Chen, C. et al. Net power optimization based on pressure ratio for PEMFC UAV air supply system in high-altitude environment. IEEE Trans. Transp. Electrific. early access, 13476\u201313489 (2025).","journal-title":"IEEE Trans. Transp. Electrific"},{"key":"51217_CR18","doi-asserted-by":"crossref","unstructured":"Zhang, X. et al. Model-based investigation of PEMFC catalyst layer degradation behavior under dynamic conditions considering the evolution of transfer coefficient. IEEE Trans. Transp. Electrific, 11(1), 3182\u20133193 (2025).","DOI":"10.1109\/TTE.2024.3435753"},{"key":"51217_CR19","doi-asserted-by":"publisher","first-page":"8039","DOI":"10.1109\/TIE.2024.3525115","volume":"72","author":"Z Guo","year":"2025","unstructured":"Guo, Z. et al. An online fault diagnosis method for PEMFC based on outputvoltage and transfer convolutional neural network. IEEE Trans. Ind. Electron. 72, 8 (2025).","journal-title":"IEEE Trans. Ind. Electron."},{"key":"51217_CR20","doi-asserted-by":"crossref","unstructured":"Sheng, C. et al. Water management fault diagnosis for open-cathode PEMFC systems based on electrochemical impedance spectroscopy. IEEE Trans. Power Electron. early access., 2674\u20132684 (2025).","DOI":"10.1109\/TPEL.2025.3618083"},{"issue":"1","key":"51217_CR21","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1109\/TIA.2023.3313134","volume":"60","author":"Y Shi","year":"2024","unstructured":"Shi, Y. et al. PEMFC fault diagnosis based on an equivalent circuit and OS-ELM framework. IEEE Trans. Ind. Appl. 60 (1), 1277\u20131287 (2024).","journal-title":"IEEE Trans. Ind. Appl."},{"issue":"3","key":"51217_CR22","doi-asserted-by":"publisher","first-page":"7720","DOI":"10.1109\/TTE.2025.3530572","volume":"11","author":"X Zhang","year":"2025","unstructured":"Zhang, X. et al. A novel approach to PEMFCs degradation prediction: an enhanced refinement of the gray Verhulst model. IEEE Trans. Transp. Electrific. 11 (3), 7720\u20137731 (2025).","journal-title":"IEEE Trans. Transp. Electrific"},{"key":"51217_CR23","doi-asserted-by":"publisher","first-page":"116924","DOI":"10.1109\/ACCESS.2025.3580704","volume":"13","author":"AAZ Diab","year":"2025","unstructured":"Diab, A. A. Z., Ali, A. H., Sultan, H. M., Ismeil, M. A. & Abdelsattar, M. Novel mathematical modeling parameters of PEMFC based on Newton\u2013Raphson iterative method. IEEE Access. 13, 116924\u2013116933 (2025).","journal-title":"IEEE Access."},{"key":"51217_CR24","doi-asserted-by":"crossref","unstructured":"Song, K. et al. Data-driven health state estimation and remaining useful life prediction of fuel cells. Appl Energy, 332, Art. 120486 (2024).","DOI":"10.1016\/j.renene.2024.120491"},{"key":"51217_CR25","doi-asserted-by":"crossref","unstructured":"Park, Y. et al. Severity-based fault diagnostic method for polymer electrolyte membrane fuel cell systems. Appl. Energy. 332, Art. 120486 (2023).","DOI":"10.1016\/j.apenergy.2022.120486"},{"key":"51217_CR26","doi-asserted-by":"crossref","unstructured":"Li, J., Cui, H., Jiang, W. & Yu, H. A large-scale multi-agent deep reinforcement learning method for cooperative output voltage control of PEMFCs. Appl. Energy. 305, Art. 117482 (2024).","DOI":"10.1109\/TTE.2023.3253060"},{"key":"51217_CR27","doi-asserted-by":"crossref","unstructured":"Li, D. et al. Multi-time-step and multi-parameter prediction for real-world proton exchange membrane fuel cell vehicles (PEMFCVs) toward fault prognosis and energy consumption prediction. Appl. Energy. 325, Art. 119883 (2022).","DOI":"10.1016\/j.apenergy.2022.119703"},{"key":"51217_CR28","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1016\/j.ijhydene.2025.01.079","volume":"102","author":"M Liu","year":"2025","unstructured":"Liu, M., Chen, X., Wang, R. & Mo, Z. A method for predicting long-term degradation of fuel cells: wavelet-linear enhanced neural network. Int. J. Hydrogen Energy. 102, 800\u2013815 (2025).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR29","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1016\/j.ijhydene.2024.12.512","volume":"143","author":"Y Wang","year":"2025","unstructured":"Wang, Y., Zhang, L., Chen, X. & Li, H. The long-term degradation prediction of proton exchange membrane fuel cell based on the adaptive time-scale pathformer model. Int. J. Hydrogen Energy. 143, 1120\u20131132 (2025).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR30","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.ijhydene.2025.02.005","volume":"106","author":"H Zhang","year":"2025","unstructured":"Zhang, H., Liu, Y., Wang, Z. & Chen, L. Long-term degradation prediction method for proton exchange membrane fuel cells based on hybrid transfer learning. Int. J. Hydrogen Energy. 106, 454\u2013470 (2025).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR31","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.ijhydene.2023.12.096","volume":"56","author":"Y Zhao","year":"2024","unstructured":"Zhao, Y., Luo, M., Yang, J., Chen, B. & Sui, P. Numerical analysis of PEMFC stack performance degradation using an empirical approach. Int. J. Hydrogen Energy. 56, 147\u2013163 (2024).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR32","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.ijhydene.2024.06.095","volume":"74","author":"C Tu","year":"2024","unstructured":"Tu, C., Zhou, F. & Pan, M. A model with high-precision on proton exchange membrane fuel cell performance degradation prediction based on temporal convolutional network-long short-term memory. Int. J. Hydrogen Energy. 74, 128\u2013135 (2024).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR33","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1016\/j.ijhydene.2024.09.097","volume":"95","author":"L Zhang","year":"2024","unstructured":"Zhang, L., Wang, Y., Chen, X. & Li, H. A predictive framework for PEMFC dynamic load performance degradation based on feature parameter analysis. Int. J. Hydrogen Energy. 95, 1011\u20131021 (2024).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR34","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/j.ijhydene.2023.08.258","volume":"50","author":"M Chen","year":"2024","unstructured":"Chen, M., Zhao, Z., Wang, Y. & Liu, L. Degradation prediction of 65\u00a0kW proton exchange membrane fuel cells on city buses using a hybrid approach with the advantage actor-critic method. Int. J. Hydrogen Energy. 50, 492\u2013500 (2024). Part C.","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR35","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.ijhydene.2025.06.086","volume":"145","author":"Y Liu","year":"2025","unstructured":"Liu, Y., Zhang, X., Wang, H. & Chen, Z. Catalyst degradation in proton exchange membrane fuel cells: mechanisms, investigation techniques, and predictive modelling. Int. J. Hydrogen Energy. 145, 633\u2013643 (2025).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR36","first-page":"1121","volume":"80","author":"J Wang","year":"2024","unstructured":"Wang, J., Li, H., Zhang, Y. & Chen, X. Analysis of PEMFC undershoot behavior and performance stabilization under transient loading. Int. J. Hydrogen Energy. 80, 1121\u20131135 (2024).","journal-title":"Int. J. Hydrogen Energy"},{"issue":"22","key":"51217_CR37","doi-asserted-by":"publisher","first-page":"12206","DOI":"10.1016\/j.ijhydene.2020.06.211","volume":"46","author":"X Wang","year":"2021","unstructured":"Wang, X. et al. Review on water management methods for proton exchange membrane fuel cells. Int. J. Hydrogen Energy. 46 (22), 12206\u201312229 (2021).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR38","doi-asserted-by":"crossref","unstructured":"Kim, K. et al. Pre-diagnosis of flooding and drying in proton exchange membrane fuel cells by bagging ensemble deep learning models using long short-term memory and convolutional neural networks, Energy. 266, Art. no. 126441 (2023).","DOI":"10.1016\/j.energy.2022.126441"},{"key":"51217_CR39","doi-asserted-by":"publisher","first-page":"10021","DOI":"10.1016\/j.ijhydene.2022.01.064","volume":"47","author":"M Kandidayeni","year":"2022","unstructured":"Kandidayeni, M., Trov\u00e3o, J. P., Soleymani, M. & Boulon, L. Towards health-aware energy management strategies in fuel cell hybrid electric vehicles: a review. Int. J. Hydrogen Energy. 47, 10021\u201310043 (2022).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR40","first-page":"890","volume":"76","author":"H Wang","year":"2024","unstructured":"Wang, H. et al. Machine learning-based fault diagnosis for various steady conditions of proton exchange membrane fuel cell systems. Int. J. Hydrogen Energy. 76, 890\u2013902 (2024).","journal-title":"Int. J. Hydrogen Energy"},{"key":"51217_CR41","doi-asserted-by":"crossref","unstructured":"Zhu, W., Li, C., Xu, Y., Yang, W. & Xie, C. High accuracy and adaptability of PEMFC degradation interval prediction with Informer-GPR under dynamic conditions. Energy. 307, Art. no. 132556 (2024).","DOI":"10.1016\/j.energy.2024.132781"},{"key":"51217_CR42","doi-asserted-by":"crossref","unstructured":"Fan, Y., Liu, L., Luo, X. & Chan, S. H. Performance degradation prediction method of PEM fuel cells using bidirectional long short-term memory neural network based on Bayesian optimization. Energy. 285, Art. no. 128691 (2024).","DOI":"10.1016\/j.energy.2023.129469"},{"key":"51217_CR43","doi-asserted-by":"crossref","unstructured":"Luo, Z. et al. Dynamic response characteristics and water-gas-heat synergistic transport mechanism of proton exchange membrane fuel cell during transient loading. Energy. 302, Art. no. 131487 (2024).","DOI":"10.1016\/j.energy.2024.131852"},{"key":"51217_CR44","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.energy.2019.04.074","volume":"179","author":"OS Ijaodola","year":"2019","unstructured":"Ijaodola, O. S. et al. Energy efficiency improvements by investigating the water flooding management on proton exchange membrane fuel cell (PEMFC). Energy 179, 246\u2013267 (2019).","journal-title":"Energy"},{"key":"51217_CR45","doi-asserted-by":"crossref","unstructured":"Pettorossi, C., Morvillier, R., Heiries, V., Rosini, S. & Gerard, M. Physics-guided fault diagnosis method for proton exchange membrane fuel cells based on LSTM neural network. J. Power Sources. 626, Art. 235696 (2025).","DOI":"10.1016\/j.jpowsour.2024.235696"},{"key":"51217_CR46","doi-asserted-by":"crossref","unstructured":"Van Der Linden, F., Pahon, E., Morando, S. & Bouquain, D. A review on the Proton-Exchange Membrane Fuel Cell break-in physical principles, activation procedures, and characterization methods. J. Power Sources, 575, Art. 233168 (2023).","DOI":"10.1016\/j.jpowsour.2023.233168"},{"key":"51217_CR47","doi-asserted-by":"crossref","unstructured":"Choi, H. et al. Real-time detection of flooding in polymer electrolyte membrane fuel cells using high-frequency electrochemical impedance. J. Power Sources. 580, Art. 233311 (2023).","DOI":"10.1016\/j.jpowsour.2023.233311"},{"issue":"1","key":"51217_CR48","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.jpowsour.2003.12.035","volume":"130","author":"A Taniguchi","year":"2004","unstructured":"Taniguchi, A., Akita, T., Yasuda, K. & Miyazaki, Y. Analysis of electrocatalyst degradation in PEMFC caused by cell reversal during fuel starvation. J. Power Sources. 130 (1), 42\u201349 (2004).","journal-title":"J. Power Sources"},{"key":"51217_CR49","doi-asserted-by":"crossref","unstructured":"Lv, J., Shen, X., Gao, Y., Liu, J. & Sun, G. The seasonal-trend disentangle based prognostic framework for PEM fuel cells. Renew. Energy, 228, Art. 120654 (2024).","DOI":"10.1016\/j.renene.2024.120648"},{"key":"51217_CR50","doi-asserted-by":"crossref","unstructured":"Yang, Y. et al. Degradation prediction of proton exchange membrane fuel cells with model uncertainty quantification. Renew. Energy, 219, Art. 119525 (2023).","DOI":"10.1016\/j.renene.2023.119525"},{"key":"51217_CR51","doi-asserted-by":"crossref","unstructured":"Yang, J. et al. Remaining useful life prediction for vehicle-oriented PEMFC systems based on IGWO-BP neural network under real-world traffic conditions. Energy. 291, Art. no. 130359 (2024).","DOI":"10.1016\/j.energy.2024.130334"},{"key":"51217_CR52","doi-asserted-by":"crossref","unstructured":"Garc\u00eda-V\u00e1zquez, M. A., Fern\u00e1ndez-Ram\u00edrez, L. M., Jurado, F. & Aleem, H. Square root unscented Kalman filter-based multiple-model fault diagnosis of PEM fuel cells. Sensors. 25(1), Art. no. 29 (2025).","DOI":"10.3390\/s25010029"},{"key":"51217_CR53","doi-asserted-by":"crossref","unstructured":"Ariza, E., Correcher, A. & Vargas-Salgado, C. PEMFCs model-based fault diagnosis: a proposal based on virtual and real sensors data fusion. Sensors. 23(17), Art. no. 7383 (2023).","DOI":"10.3390\/s23177383"},{"key":"51217_CR54","doi-asserted-by":"crossref","unstructured":"Mao, L. & Jackson, L. Effect of sensor set size on polymer electrolyte membrane fuel cell fault diagnosis. Sensors. 18(9), Art. no. 2777 (2018).","DOI":"10.3390\/s18092777"},{"key":"51217_CR55","doi-asserted-by":"crossref","unstructured":"Chen, Y., Zhang, X., Wang, H. & Liu, L. Deep learning-based state-of-health estimation of proton-exchange membrane fuel cells under dynamic operation conditions. Sensors. 24(14), Art. no. 4451 (2024).","DOI":"10.3390\/s24144451"},{"key":"51217_CR56","doi-asserted-by":"crossref","unstructured":"Tian, Y., Zou, Q. & Han, J. Data-driven fault diagnosis for automotive PEMFC systems based on the steady-state identification, Energies. 14(7), Art. no. 1918 (2021).","DOI":"10.3390\/en14071918"},{"key":"51217_CR57","doi-asserted-by":"crossref","unstructured":"Zhang, L., Wang, X., Chen, Y. & Li, H. State estimation of membrane water content of PEMFC based on GA-BP neural network. Sustainability. 15(11), Art. no. 9094 (2023).","DOI":"10.3390\/su15119094"},{"key":"51217_CR58","doi-asserted-by":"crossref","unstructured":"Xu, L., Chen, J., Zhang, H., Wang, Y. & Liu, Z. Diagnosing improper membrane water content in proton exchange membrane fuel cell using two-dimensional convolutional neural network, Energies. 15(12), Art. no. 4247 (2022).","DOI":"10.3390\/en15124247"},{"key":"51217_CR59","doi-asserted-by":"crossref","unstructured":"B\u00e4umler, A., Meng, J., Benterki, A., Azib, T. & Boukhnifer, M. A system-level modeling of PEMFC considering degradation aspect towards a diagnosis process, Energies. 16(14), Art. no. 5310 (2023).","DOI":"10.3390\/en16145310"},{"key":"51217_CR60","doi-asserted-by":"crossref","unstructured":"Arama, F. Z. et al. Efficient water-related failure detection in PEM fuel cells: Combining a PEMFCs fractional order impedance model with FFT-PWM techniques and artificial neural network classification, Heliyon. 10(7), Art. no. e29084 (2024).","DOI":"10.1016\/j.heliyon.2024.e29084"},{"key":"51217_CR61","doi-asserted-by":"crossref","unstructured":"Melo, E., Barzola-Monteses, J., Noriega, H. H. & Espinoza-Andaluz, M. Enhanced fault detection in polymer electrolyte fuel cells via integral analysis and machine learning, Energy Informatics, vol. 7, Art. no. 10. (2024).","DOI":"10.1186\/s42162-024-00318-2"},{"key":"51217_CR62","doi-asserted-by":"crossref","unstructured":"Zhang, L. et al. Water management fault diagnosis of polymer electrolyte membrane fuel cells based on complementary ensemble empirical mode decomposition and sensitivity analysis. J Energy Eng, 151, 3, Art. 04025008 (2025).","DOI":"10.1061\/JLEED9.EYENG-5508"},{"issue":"3","key":"51217_CR63","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1002\/fuce.201900085","volume":"20","author":"B Chen","year":"2020","unstructured":"Chen, B. et al. Proton exchange membrane fuel cell prognostics using genetic algorithm and extreme learning machine. Fuel Cells. 20 (3), 263\u2013271 (2020).","journal-title":"Fuel Cells"},{"issue":"8","key":"51217_CR64","first-page":"2245","volume":"19","author":"Y \u00c7elikdemir","year":"2025","unstructured":"\u00c7elikdemir, Y., Yilmaz, M. & Kilic, H. A novel approach to flooding fault detection and risk assessment in PEM fuel cells using data-driven models. IET Renew. Power Gener. 19 (8), 2245\u20132258 (2025).","journal-title":"IET Renew. Power Gener."},{"key":"51217_CR65","doi-asserted-by":"crossref","unstructured":"Zhang, H., Liu, Y., Chen, X. & Wang, Z. A review of portability of fault diagnosis methods from PEM fuel cells to PEM water electrolyzers. Discover Appl. Sci, 7, Art. 318 (2025).","DOI":"10.1007\/s42452-025-07318-1"},{"issue":"1","key":"51217_CR66","first-page":"456","volume":"11","author":"Q Li","year":"2025","unstructured":"Li, Q. et al. Online diagnosis method of water management faults based on hybrid-frequency electrochemical impedance spectroscopy for PEMFC. IEEE Trans. Transp. Electrific. 11 (1), 456\u2013468 (2025).","journal-title":"IEEE Trans. Transp. Electrific"},{"issue":"4","key":"51217_CR67","doi-asserted-by":"publisher","first-page":"5234","DOI":"10.1109\/TTE.2022.3222970","volume":"9","author":"S Li","year":"2023","unstructured":"Li, S. et al. Net power optimization based on extremum search and model-free adaptive control of PEMFC power generation system for high altitude. IEEE Trans. Transp. Electrific. 9 (4), 5234\u20135246 (2023).","journal-title":"IEEE Trans. Transp. Electrific"},{"issue":"8","key":"51217_CR68","doi-asserted-by":"publisher","first-page":"8956","DOI":"10.1109\/TIE.2024.3525115","volume":"72","author":"Z Guo","year":"2025","unstructured":"Guo, Z. et al. An online fault diagnosis method for PEMFC based on output voltage and transfer convolutional neural network. IEEE Trans. Ind. Electron. 72 (8), 8956\u20138967 (2025).","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"7","key":"51217_CR69","doi-asserted-by":"publisher","first-page":"7234","DOI":"10.1109\/TIE.2024.3522469","volume":"72","author":"H Xu","year":"2025","unstructured":"Xu, H., Wang, L., Liu, Z., Su, H. & Ortega, R. Online identification of PEMFC polarization curves with nonlinear concentration loss. IEEE Trans. Ind. Electron. 72 (7), 7234\u20137244 (2025).","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"1","key":"51217_CR70","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1109\/TIA.2023.3313134","volume":"60","author":"Y Shi","year":"2024","unstructured":"Shi, Y. et al. PEMFC fault diagnosis based on an equivalent circuit and OS-ELM framework. IEEE Trans. Ind. Appl. 60 (1), 892\u2013903 (2024).","journal-title":"IEEE Trans. Ind. Appl."},{"issue":"9","key":"51217_CR71","doi-asserted-by":"publisher","first-page":"12456","DOI":"10.1109\/TVT.2025.3565459","volume":"74","author":"J Li","year":"2025","unstructured":"Li, J. & Zhou, T. Deep meta-reinforcement learning for the flow-pressure coordination of a vehicle PEMFC system considering multivariable constraints. IEEE Trans. Veh. Technol. 74 (9), 12456\u201312468 (2025).","journal-title":"IEEE Trans. Veh. Technol."},{"key":"51217_CR72","first-page":"12340","volume":"13","author":"AAZ Diab","year":"2025","unstructured":"Diab, A. A. Z., Ali, A. H., Sultan, H. M., Ismeil, M. A. & Abdelsattar, M. Novel mathematical modeling parameters of PEMFC based on Newton-Raphson iterative method. IEEE Access. 13, 12340\u201312351 (2025).","journal-title":"IEEE Access."},{"key":"51217_CR73","doi-asserted-by":"crossref","unstructured":"Zhu, S., Wang, Y., Xiong, Q., Geng, J. & Chen, H. Fault diagnosis of proton exchange membrane fuel cells based on deep learning and transfer learning. SAE Tech. (2025). Paper 2025\u201301\u20137076, 122524. (2025).","DOI":"10.4271\/2025-01-7076"},{"key":"51217_CR74","doi-asserted-by":"crossref","unstructured":"Ochella, S., Dinmohammadi, F. & Shafiee, M. Bayesian neural networks for uncertainty quantification in remaining useful life prediction of systems with sensor monitoring. Reliab Eng. Syst. Saf, 246, Art. 110064 (2024).","DOI":"10.1177\/16878132241239802"},{"key":"51217_CR75","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1007\/s10462-023-10562-9","volume":"56","author":"J Gawlikowski","year":"2023","unstructured":"Gawlikowski, J. et al. A survey of uncertainty in deep neural networks. Artif. Intell. Rev. 56, 1513\u20131589 (2023).","journal-title":"Artif. Intell. Rev."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51217-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51217-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51217-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T11:03:40Z","timestamp":1787742220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-51217-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,26]]},"references-count":75,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["51217"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-51217-3","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,26]]},"assertion":[{"value":"12 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"<b>Declarations<\/b>"}}],"article-number":"26722"}}