{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T22:29:37Z","timestamp":1773786577245,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,6,6]],"date-time":"2022-06-06T00:00:00Z","timestamp":1654473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Natural Science Foundation of China","award":["51976193"],"award-info":[{"award-number":["51976193"]}]},{"name":"The National Natural Science Foundation of China","award":["62022073"],"award-info":[{"award-number":["62022073"]}]},{"name":"The National Natural Science Foundation of China","award":["LGG22E060011"],"award-info":[{"award-number":["LGG22E060011"]}]},{"name":"Zhejiang Provincial National Science Foundation of China","award":["51976193"],"award-info":[{"award-number":["51976193"]}]},{"name":"Zhejiang Provincial National Science Foundation of China","award":["62022073"],"award-info":[{"award-number":["62022073"]}]},{"name":"Zhejiang Provincial National Science Foundation of China","award":["LGG22E060011"],"award-info":[{"award-number":["LGG22E060011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurately predict the efficiency of centrifugal pumps at different rotational speeds is important but still intractable in practice. To enhance the prediction performance, this work proposes a hybrid modeling method by combining both the process data and knowledge of centrifugal pumps. First, according to the process knowledge of centrifugal pumps, the efficiency curve is divided into two stages. Then, the affinity law of pumps and a Gaussian process regression (GPR) model are explored and utilized to predict the efficiency at their suitable flow stages, respectively. Furthermore, a probability index is established through the prediction variance of a GPR model and Bayesian inference to select a suitable training set to improve the prediction accuracy. Experimental results show the superiority of the hybrid modeling method, compared with only using mechanism or data-driven models.<\/jats:p>","DOI":"10.3390\/s22114300","type":"journal-article","created":{"date-parts":[[2022,6,7]],"date-time":"2022-06-07T00:10:33Z","timestamp":1654560633000},"page":"4300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Two-Stage Hybrid Model for Efficiency Prediction of Centrifugal Pump"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4066-689X","authenticated-orcid":false,"given":"Yi","family":"Liu","sequence":"first","affiliation":[{"name":"Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"given":"Zhaoshun","family":"Xia","sequence":"additional","affiliation":[{"name":"Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"given":"Hongying","family":"Deng","sequence":"additional","affiliation":[{"name":"Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7112-2940","authenticated-orcid":false,"given":"Shuihua","family":"Zheng","sequence":"additional","affiliation":[{"name":"Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"119005","DOI":"10.1016\/j.energy.2020.119005","article-title":"Energy performance prediction of the centrifugal pumps by using a hybrid neural network","volume":"213","author":"Huang","year":"2020","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3041","DOI":"10.1016\/j.egyr.2022.02.072","article-title":"Application of Bayesian regularization back propagation neural network in sensorless measurement of pump operational state","volume":"8","author":"Wu","year":"2022","journal-title":"Energy Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.enconman.2019.06.004","article-title":"Optimal operation of novel hybrid district heating system driven by central and distributed variable speed pumps","volume":"196","author":"Gong","year":"2019","journal-title":"Energy Convers. 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