{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T09:42:55Z","timestamp":1772271775030,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T00:00:00Z","timestamp":1772064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Key R&amp;D Program of Shandong Province","award":["2024CXGC010706"],"award-info":[{"award-number":["2024CXGC010706"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Platinum (Pt)\u2013Rhodium (Rh) thermocouples are widely used in industrial processes such as chemical and nuclear power production, serving as one of the most common temperature measuring instruments and playing a vital role in real-time condition monitoring. However, the measurement accuracy can be affected by harsh high-temperature operating environments, which may cause measurement drift or even functional failure. To address this challenge, and considering the very slow drift of Pt\u2013Rh thermocouples over long time scales, a back-propagation neural network (BPNN) is introduced to compensate for the nonlinear error introduced by the linearization step of the extended Kalman filter (EKF). This combined algorithm enhances the accuracy of remaining useful life (RUL) prediction for Pt\u2013Rh thermocouples. First, based on the Seebeck effect and vapor-transport theory, a degradation model for Pt\u2013Rh thermocouples operating at high temperatures was developed. The simulation results of the degradation model align with laboratory degradation test data, confirming the validity of the model. Subsequently, the improved RUL prediction algorithm was compared with other methods. The results show that the EKF\u2013BPNN hybrid approach provides better prediction accuracy for objects with slow degradation and weak nonlinearity, with MAE 0.0016%, RMSE 0.0019%, MAPE 0.039%, R2 0.9833, respectively. Algorithms with strong nonlinear estimation capability introduce larger errors and are not suited for RUL prediction of Pt\u2013Rh thermocouples. Therefore, the proposed hybrid EKF\u2013BPNN algorithm is optimal for RUL prediction of Pt\u2013Rh thermocouples degrading under high temperature conditions.<\/jats:p>","DOI":"10.3390\/s26051483","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T16:57:13Z","timestamp":1772125033000},"page":"1483","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Remaining Useful Life Prediction for Pt\u2013Rh Thermocouples Using an Extended Kalman Filter"],"prefix":"10.3390","volume":"26","author":[{"given":"Na","family":"Li","sequence":"first","affiliation":[{"name":"State Key Laboratory of Chemical Safety, College of Mechanical and Electrical Engineering, China University of Petroleum (East China), Qingdao 266580, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7114-621X","authenticated-orcid":false,"given":"Siyang","family":"Dai","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Chemical Safety, SINOPEC Research Institute of Safety Engineering Co., Ltd., Qingdao 266000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Chemical Safety, College of Chemistry and Chemical Engineering, China University of Petroleum (East China), Qingdao 266580, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunlong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Institute of Nuclear and New Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6155-9612","authenticated-orcid":false,"given":"Jitao","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Nuclear and New Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaojin","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute of Nuclear and New Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0029-5493(02)00191-7","article-title":"Thermal hydraulic instrumentation system of the HTR-10","volume":"218","author":"Zhong","year":"2002","journal-title":"Nucl. 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