{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T06:01:10Z","timestamp":1778047270463,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["2019YFB1600702"],"award-info":[{"award-number":["2019YFB1600702"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["CJGJZD20210408092601005"],"award-info":[{"award-number":["CJGJZD20210408092601005"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["51978154"],"award-info":[{"award-number":["51978154"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shenzhen Technology Research Project","award":["2019YFB1600702"],"award-info":[{"award-number":["2019YFB1600702"]}]},{"name":"Shenzhen Technology Research Project","award":["CJGJZD20210408092601005"],"award-info":[{"award-number":["CJGJZD20210408092601005"]}]},{"name":"Shenzhen Technology Research Project","award":["51978154"],"award-info":[{"award-number":["51978154"]}]},{"name":"Program of the National Natural Science Foundation of China","award":["2019YFB1600702"],"award-info":[{"award-number":["2019YFB1600702"]}]},{"name":"Program of the National Natural Science Foundation of China","award":["CJGJZD20210408092601005"],"award-info":[{"award-number":["CJGJZD20210408092601005"]}]},{"name":"Program of the National Natural Science Foundation of China","award":["51978154"],"award-info":[{"award-number":["51978154"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Changes in the deflection of cable-stayed bridges due to thermal effects may adversely affect the bridge structure and reflect the degradation of bridge performance. Therefore, complete deflection field data are important for bridge health monitoring. A strong linear correlation has been found between temperature-induced deflections in different positions of the same span of a cable-stayed bridge in many studies, which make the deflection data matrix\/tensor have a low-rank structure. Therefore, it is appropriate to use a low-rank matrix\/tensor learning to model the temperature\u2013deflection field of a cable-stayed bridge. Moreover, to avoid disturbing the recovery results via abnormal data (e.g., baseline shift and outliers), a Bayesian robust tensor learning method is proposed to extract the spatio-temporal characteristics of the bridge temperature\u2013deflection field. The missing data recovery and abnormal data cleaning are achieved simultaneously in the process of reconstructing the temperature-induced field via tensor learning. The performance of the method is verified with actual continuous monitoring data from a cable-stayed bridge. The experimental results show that low-order tensor (i.e., matrix) learning has a good recovery and cleaning performance. The extension to higher-order tensor learning is proposed to extract the spatial symmetry of the sensor locations, which is experimentally proven to have better missing recovery and abnormal data cleaning performance.<\/jats:p>","DOI":"10.3390\/sym15061234","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T08:37:33Z","timestamp":1686299853000},"page":"1234","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The Temperature-Induced Deflection Data Missing Recovery of a Cable-Stayed Bridge Based on Bayesian Robust Tensor Learning"],"prefix":"10.3390","volume":"15","author":[{"given":"Shouwang","family":"Sun","sequence":"first","affiliation":[{"name":"YunJi Intelligent Engineering Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"YunJi Intelligent Engineering Co., Ltd., Shenzhen 518000, China"},{"name":"Key Laboratory of Concrete and Pre-Stressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zili","family":"Xia","sequence":"additional","affiliation":[{"name":"Hong Kong-Zhuhai-Macao Bridge Authority, Zhuhai 519060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Letian","family":"Yi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Pre-Stressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zixiang","family":"Yue","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Pre-Stressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youliang","family":"Ding","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Pre-Stressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108343","DOI":"10.1016\/j.measurement.2020.108343","article-title":"Structural health monitoring methods of cables in cable-stayed bridge: A review","volume":"168","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.eng.2017.11.001","article-title":"Developments and Prospects of Long-Span High-Speed Railway Bridge Technologies in China","volume":"3","author":"Qin","year":"2017","journal-title":"Engineering"},{"key":"ref_3","first-page":"34","article-title":"Inspection and repair of Lake Maracaibo Bridge suspension cables","volume":"40","author":"Contreras","year":"2001","journal-title":"Mater. 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