{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T05:34:46Z","timestamp":1780637686701,"version":"3.54.1"},"reference-count":42,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2023,12,11]],"date-time":"2023-12-11T00:00:00Z","timestamp":1702252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52209114"],"award-info":[{"award-number":["52209114"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["BX20220243"],"award-info":[{"award-number":["BX20220243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021M702527"],"award-info":[{"award-number":["2021M702527"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"scientific research foundation of China Postdoctoral Innovation Talents Support Program","award":["52209114"],"award-info":[{"award-number":["52209114"]}]},{"name":"scientific research foundation of China Postdoctoral Innovation Talents Support Program","award":["BX20220243"],"award-info":[{"award-number":["BX20220243"]}]},{"name":"scientific research foundation of China Postdoctoral Innovation Talents Support Program","award":["2021M702527"],"award-info":[{"award-number":["2021M702527"]}]},{"name":"China Postdoctoral Science Foundation","award":["52209114"],"award-info":[{"award-number":["52209114"]}]},{"name":"China Postdoctoral Science Foundation","award":["BX20220243"],"award-info":[{"award-number":["BX20220243"]}]},{"name":"China Postdoctoral Science Foundation","award":["2021M702527"],"award-info":[{"award-number":["2021M702527"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurately predicting the changes in turbine vibration trends is a key part of the operational condition maintenance of hydropower units, which is of great significance for improving both the operational condition and operational efficiency of hydropower plants. In this paper, we propose a multistep prediction model for the vibration trend of a hydropower unit. This model is based on the theoretical principles of signal processing and machine learning, incorporating variational mode decomposition (VMD), stochastic configuration networks (SCNs), and the recursive strategy. Firstly, in view of the severe fluctuations of the vibration signal of the unit, this paper decomposes the unit vibration data into intrinsic mode function (IMF) components of different frequencies by VMD, which effectively alleviates the instability of the vibration trend. Secondly, an SCN model is used to predict different IMF components. Then, the predicted values of all the IMF components are superimposed to form the prediction results. Finally, according to the recursive strategy, a multistep prediction model of the HGU\u2019s vibration trends is constructed by adding new input variables to the prediction results. This model is applied to the prediction of vibration data from different components of a unit, and the experimental results show that the proposed multistep prediction model can accurately predict the vibration trend of the unit. The proposed multistep prediction model of the vibration trends of hydropower units is of great significance in guiding power plants to adjust their control strategies to reach optimal operating efficiency.<\/jats:p>","DOI":"10.3390\/s23249762","type":"journal-article","created":{"date-parts":[[2023,12,11]],"date-time":"2023-12-11T14:12:51Z","timestamp":1702303971000},"page":"9762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Multistep Prediction Model for the Vibration Trends of Hydroelectric Generator Units Based on Variational Mode Decomposition and Stochastic Configuration Networks"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-9362-2940","authenticated-orcid":false,"given":"Shaokai","family":"Yan","sequence":"first","affiliation":[{"name":"State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiandong","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1531-489X","authenticated-orcid":false,"given":"Zhigao","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"233343","DOI":"10.1016\/j.jpowsour.2023.233343","article-title":"Overcoming the challenges of integrating variable renewable energy to the grid: A comprehensive review of electrochemical battery storage systems","volume":"580","author":"Deguenon","year":"2023","journal-title":"J. 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