{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T11:13:57Z","timestamp":1788347637581,"version":"build-2803163510"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T00:00:00Z","timestamp":1704326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11972144"],"award-info":[{"award-number":["11972144"]}]},{"name":"National Natural Science Foundation of China","award":["12072098"],"award-info":[{"award-number":["12072098"]}]},{"name":"China Scholarship Council","award":["11972144"],"award-info":[{"award-number":["11972144"]}]},{"name":"China Scholarship Council","award":["12072098"],"award-info":[{"award-number":["12072098"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>To improve the identification accuracy of pressure fluctuation signals in the draft tube of hydraulic turbines, this study proposes an improved manta ray foraging optimization (ITMRFO) algorithm to optimize the identification method of a probabilistic neural network (PNN). Specifically, first, discrete wavelet transform was used to extract features from vibration signals, and then, fuzzy c-means algorithm (FCM) clustering was used to automatically classify the collected information. In order to solve the local optimization problem of the manta ray foraging optimization (MRFO) algorithm, four optimization strategies were proposed. These included optimizing the initial population of the MRFO algorithm based on the elite opposition learning algorithm and using adaptive t distribution to replace its chain factor to optimize individual update strategies and other improvement strategies. The ITMRFO algorithm was compared with three algorithms on 23 test functions to verify its superiority. In order to improve the classification accuracy of the probabilistic neural network (PNN) affected by smoothing factors, an improved manta ray foraging optimization (ITMRFO) algorithm was used to optimize them. An ITMRFO-PNN model was established and compared with the PNN and MRFO-PNN models to evaluate their performance in identifying pressure fluctuation signals in turbine draft tubes. The evaluation indicators include confusion matrix, accuracy, precision, recall rate, F1-score, and accuracy and error rate. The experimental results confirm the correctness and effectiveness of the ITMRFO-PNN model, providing a solid theoretical foundation for identifying pressure fluctuation signals in hydraulic turbine draft tubes.<\/jats:p>","DOI":"10.3390\/biomimetics9010032","type":"journal-article","created":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T09:47:32Z","timestamp":1704361652000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimizing the Probabilistic Neural Network Model with the Improved Manta Ray Foraging Optimization Algorithm to Identify Pressure Fluctuation Signal Features"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4522-6308","authenticated-orcid":false,"given":"Xiyuan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6899-3289","authenticated-orcid":false,"given":"Liying","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"},{"name":"Hebei Key Laboratory of Intelligent Water Conservancy, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyan","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"},{"name":"Hebei Key Laboratory of Intelligent Water Conservancy, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingjiao","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"},{"name":"Hebei Key Laboratory of Intelligent Water Conservancy, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luyao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4069-2422","authenticated-orcid":false,"given":"Weiguo","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China"},{"name":"Hebei Key Laboratory of Intelligent Water Conservancy, Hebei University of Engineering, Handan 056038, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, B., Bo, Z., Yawu, Z., Xi, Z., and Yalan, J. 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