{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T23:01:31Z","timestamp":1772060491607,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"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":["51775407"],"award-info":[{"award-number":["51775407"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Project supported by National Natural Science Foundation of China","award":["61633001"],"award-info":[{"award-number":["61633001"]}]},{"name":"The National Key Research and Development Program of China","award":["2017YFC0805701"],"award-info":[{"award-number":["2017YFC0805701"]}]},{"name":"The China Postdoctoral Science Foundation","award":["2014T70911"],"award-info":[{"award-number":["2014T70911"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To identify the major vibration and radiation noise, a source contribution quantitative estimation method is proposed based on underdetermined blind source separation. First, the single source points (SSPs) are identified by directly searching the identical normalized time-frequency vectors of mixed signals, which can improve the efficiency and accuracy in identifying SSPs. Then, the mixing matrix is obtained by hierarchical clustering, and source signals can also be recovered by the least square method. Second, the optimal combination coefficients between source signals and mixed signals can be calculated based on minimum redundant error energy. Therefore, mixed signals can be optimally linearly combined by source signals via the coefficients. Third, the energy elimination method is used to quantitatively estimate source contributions. Finally, the effectiveness of the proposed method is verified via numerical case studies and experiments with a cylindrical structure, and the results show that source signals can be effectively recovered, and source contributions can be quantitatively estimated by the proposed method.<\/jats:p>","DOI":"10.3390\/s19061413","type":"journal-article","created":{"date-parts":[[2019,3,25]],"date-time":"2019-03-25T06:56:52Z","timestamp":1553497012000},"page":"1413","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Novel Underdetermined Blind Source Separation Method and Its Application to Source Contribution Quantitative Estimation"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9674-165X","authenticated-orcid":false,"given":"Jiantao","family":"Lu","sequence":"first","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Cheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanyang","family":"Zi","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1109\/TIM.2013.2293236","article-title":"Kurtosis-based constrained independent component analysis and its application on source contribution quantitative estimation","volume":"63","author":"Zhang","year":"2014","journal-title":"IEEE Trans. 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