{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T09:49:22Z","timestamp":1779270562134,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T00:00:00Z","timestamp":1709596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2022JM-337"],"award-info":[{"award-number":["2022JM-337"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study introduces a novel nonlinear dynamic analysis method, known as beluga whale optimization\u2013slope entropy (BWO-SlEn), to address the challenge of recognizing sea state signals (SSSs) in complex marine environments. A method of underwater acoustic signal recognition based on BWO-SlEn and one-dimensional convolutional neural network (1D-CNN) is proposed. Firstly, particle swarm optimization\u2013slope entropy (PSO-SlEn), BWO-SlEn, and Harris hawk optimization\u2013slope entropy (HHO-SlEn) were used for feature extraction of noise signal and SSS. After 1D-CNN classification, BWO-SlEn were found to have the best recognition effect. Secondly, fuzzy entropy (FE), sample entropy (SE), permutation entropy (PE), and dispersion entropy (DE) were used to extract the signal features. After 1D-CNN classification, BWO-SlEn and 1D-CNN were found to have the highest recognition rate compared with them. Finally, compared with the other six recognition methods, the recognition rates of BWO-SlEn and 1D-CNN for the noise signal and SSS are at least 6% and 4.75% higher, respectively. Therefore, the BWO-SlEn and 1D-CNN recognition methods proposed in this paper are more effective in the application of SSS recognition.<\/jats:p>","DOI":"10.3390\/s24051680","type":"journal-article","created":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T05:31:19Z","timestamp":1709616679000},"page":"1680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Research on Sea State Signal Recognition Based on Beluga Whale Optimization\u2013Slope Entropy and One Dimensional\u2013Convolutional Neural Network"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5035-223X","authenticated-orcid":false,"given":"Yuxing","family":"Li","sequence":"first","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoyu","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiumei","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1121\/10.0019937","article-title":"Self-supervised learning\u2013based underwater acoustical signal classification via mask modeling","volume":"154","author":"Xu","year":"2023","journal-title":"J. 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