{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T21:23:26Z","timestamp":1769635406342,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T00:00:00Z","timestamp":1609718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development plan of China under Grant 2018YFB1306103","award":["2018YFB1306103"],"award-info":[{"award-number":["2018YFB1306103"]}]},{"name":"Science and Technology Major Project of Yunnan Province","award":["202002AC080001"],"award-info":[{"award-number":["202002AC080001"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51875272"],"award-info":[{"award-number":["51875272"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The identification and separation of sources are the prerequisite of industrial noise control. Industrial machinery usually contains multiple noise sources sharing same-frequency components. There are usually multiple noise sources in mechanical equipment, and there are few effective methods available to separate the spectrum intensity of each sound source. This study tries to solve the problem by the radiation relationship between three-dimensional sound intensity vectors and the power of the sources. When the positions of the probe and the sound source are determined, the sound power of the sound source at each frequency can be solved by the particle swarm optimization algorithm. The solution results at each frequency are combined to obtain the sound power spectrum of each sound source. The proposed method is first verified by a simulation on two point sources. The experiment is carried out on a fault simulation test bed in an ordinary laboratory; we used three three-dimensional sound intensity probes to form a line array and conducted spectrum separation of the nine main noise sources. The sound intensity on the main frequency band of each sound source was close to the result of the near-field measurement of the one-dimensional sound intensity probe. The proposed spectral separation method of the sound power of multiple sound sources provides a new method for accurate noise identification in industrial environments.<\/jats:p>","DOI":"10.3390\/s21010279","type":"journal-article","created":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T03:00:51Z","timestamp":1609729251000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Separation of the Sound Power Spectrum of Multiple Sources by Three-Dimensional Sound Intensity Decomposition"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6421-3847","authenticated-orcid":false,"given":"Shiyi","family":"Chai","sequence":"first","affiliation":[{"name":"School of Key Laboratory of Vibration and Noise under Ministry of Education of Yunnan Province, Kunming University of Science and Technology, Kunming 650500, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4244-7308","authenticated-orcid":false,"given":"Xiaoqin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Key Laboratory of Vibration and Noise under Ministry of Education of Yunnan Province, Kunming University of Science and Technology, Kunming 650500, China"}]},{"given":"Xing","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Key Laboratory of Vibration and Noise under Ministry of Education of Yunnan Province, Kunming University of Science and Technology, Kunming 650500, China"},{"name":"Yunnan Vocational College of Mechanical and Electrical Technology, Kunming 650203, China"}]},{"given":"Yanjiao","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Key Laboratory of Vibration and Noise under Ministry of Education of Yunnan Province, Kunming University of Science and Technology, Kunming 650500, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ymssp.2017.04.018","article-title":"Fault detection in rotating machines with beamforming: Spatial visualization of diagnosis features","volume":"97","author":"Leclere","year":"2017","journal-title":"Mech. 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