{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T03:51:25Z","timestamp":1774237885857,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006579","name":"Ministry of Industry and Information Technology","doi-asserted-by":"publisher","award":["J2019-II-0013-0033"],"award-info":[{"award-number":["J2019-II-0013-0033"]}],"id":[{"id":"10.13039\/501100006579","id-type":"DOI","asserted-by":"publisher"}]},{"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":"Ministry of Education","award":["Fundamental Research Fund for the Central Universities"],"award-info":[{"award-number":["Fundamental Research Fund for the Central Universities"]}]},{"DOI":"10.13039\/501100002412","name":"Xi'an Jiaotong University","doi-asserted-by":"publisher","award":["Independent Innovation Capability Improvement"],"award-info":[{"award-number":["Independent Innovation Capability Improvement"]}],"id":[{"id":"10.13039\/501100002412","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014883","name":"China National Nuclear Corporation","doi-asserted-by":"publisher","award":["Innovative Scientific Program"],"award-info":[{"award-number":["Innovative Scientific Program"]}],"id":[{"id":"10.13039\/501100014883","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>For the sound field reconstruction of large conical surfaces, current statistical optimal near-field acoustic holography (SONAH) methods have relatively poor applicability and low accuracy. To overcome this problem, conical SONAH based on cylindrical SONAH is proposed in this paper. Firstly, elementary cylindrical waves are transformed into those suitable for the radiated sound field of the conical surface through cylinder-cone coordinates transformation, which forms the matrix of characteristic elementary waves in the conical spatial domain. Secondly, the sound pressure is expressed as the superposition of those characteristic elementary waves, and the superposition coefficients are solved according to the principle of superposition of wave field. Finally, the reconstructed conical pressure is expressed as a linear superposition of the holographic conical pressure. Furthermore, to overcome ill-posed problems, a regularization method combining truncated singular value decomposition (TSVD) and Tikhonov regularization is proposed. Large singular values before the truncation point of TSVD are not processed and remaining small singular values representing high-frequency noise are modified by Tikhonov regularization. Numerical and experimental case studies are carried out to validate the effectiveness of the proposed conical SONAH and the combined regularization method, which can provide reliable evidence for noise monitoring and control of mechanical systems.<\/jats:p>","DOI":"10.3390\/s21217150","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:52:35Z","timestamp":1635465155000},"page":"7150","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2032-7815","authenticated-orcid":false,"given":"Wei","family":"Cheng","sequence":"first","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Jinglei","family":"Ni","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6867-2589","authenticated-orcid":false,"given":"Chao","family":"Song","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2973-6404","authenticated-orcid":false,"given":"Muhammad Mubashir","family":"Ahsan","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Xuefeng","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4760-3581","authenticated-orcid":false,"given":"Zelin","family":"Nie","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Yilong","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1121\/1.384602","article-title":"Sound source reconstructions using a microphone array","volume":"68","author":"Williams","year":"1980","journal-title":"J. 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