{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T04:51:08Z","timestamp":1773636668617,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:00:00Z","timestamp":1650412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Founding of Key Laboratory of Building Collapse Mechanism and Disaster Prevention, China Earthquake Administration","award":["FZ211111"],"award-info":[{"award-number":["FZ211111"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52078104"],"award-info":[{"award-number":["52078104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Dalian High Level Talent Innovation Support Program","award":["2019RD01"],"award-info":[{"award-number":["2019RD01"]}]},{"name":"Dalian High Level Talent Innovation Support Program","award":["2020RQ056"],"award-info":[{"award-number":["2020RQ056"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["DUT21JC07"],"award-info":[{"award-number":["DUT21JC07"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Dynamic displacement plays an essential role in structural health monitoring. To overcome the shortcomings of displacement measured directly, such as installation difficulty of monitoring devices, this paper proposes a smart reconstruction method, which can realize real-time intelligent online reconstruction of structural displacement. Unlike the existing approaches, the proposed algorithm combines the improved mode superposition methods that is suitable for complex beam structures with the Kalman filtering approach using acceleration and strain data. The effectiveness of the proposed multi-rate data fusion method for dynamic displacement reconstruction is demonstrated by both numerical simulation and model vibration experiment. Parametric analysis shows that the reconstruction error is only 5% when the noise signal to noise ratio is 5 dB, illustrating that the proposed algorithm has excellent anti-noise performance. The results also indicate that both the high-frequency and low-frequency components of the dynamic displacements can be accurately reconstructed through the proposed method, which has good robustness.<\/jats:p>","DOI":"10.3390\/s22093167","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T03:46:11Z","timestamp":1650512771000},"page":"3167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Smart Multi-Rate Data Fusion Method for Displacement Reconstruction of Beam Structures"],"prefix":"10.3390","volume":"22","author":[{"given":"Qing","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4431-3872","authenticated-orcid":false,"given":"Xing","family":"Fu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiguo","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Building Collapse Mechanism and Disaster Prevention, China Earthquake Administration, Langfang 065201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2705-4669","authenticated-orcid":false,"given":"Liang","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1061\/(ASCE)0733-9445(1995)121:3(488)","article-title":"Dynamic Assessment of Bridge Load-Carrying Capacities. II","volume":"121","author":"Law","year":"1995","journal-title":"J. Struct. Eng.-ASCE"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"309","DOI":"10.12989\/was.2005.8.5.309","article-title":"Experimental evaluation of aerodynamic damping of square super high-rise buildings","volume":"8","author":"Quan","year":"2005","journal-title":"Wind Struct. Int. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1002\/tal.393","article-title":"Across-wind dynamic response of high-rise building under wind action with interference effects from one and two tall buildings","volume":"18","author":"Xie","year":"2009","journal-title":"Struct. Des. Tall Spec. Build."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e2000","DOI":"10.1002\/stc.2000","article-title":"Color and depth data fusion using an RGB-D sensor for inexpensive and contactless dynamic displacement-field measurement","volume":"24","author":"Chen","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_5","first-page":"2578","article-title":"Damage localization method for building structures based on the interrelation of dynamic displacement measurements using convolutional neural network","volume":"27","author":"Oh","year":"2020","journal-title":"Struct. Control Health Monit."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1977","DOI":"10.1002\/stc.1977","article-title":"Eulerian-based virtual visual sensors to measure dynamic displacements of structures","volume":"24","author":"Shariati","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.3390\/s7071028","article-title":"Development of a Fully Automated, GPS Based Monitoring System for Disaster Prevention and Emergency Preparedness: PPMS + RT","volume":"7","author":"Bond","year":"2007","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"04019089","DOI":"10.1061\/(ASCE)BE.1943-5592.0001472","article-title":"Noncontact Dynamic Displacement Measurement of Structures Using a Moving Laser Doppler Vibrometer","volume":"24","author":"Garg","year":"2019","journal-title":"J. Bridge Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0141-0296(93)90054-8","article-title":"Measurements of static and dynamic displacement from visual monitoring of the Humber Bridge","volume":"15","author":"Stephen","year":"1993","journal-title":"Eng. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/0022-460X(84)90429-2","article-title":"Determination of displacement by double integration of accelerometer signals","volume":"93","author":"Croker","year":"1984","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e2209","DOI":"10.1002\/stc.2209","article-title":"Reference-free structural dynamic displacement estimation method","volume":"25","author":"Gomez","year":"2018","journal-title":"Struct. Control Health Monit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e2122","DOI":"10.1002\/stc.2122","article-title":"Visual-inertial displacement sensing using data fusion of vision-based displacement with acceleration","volume":"25","author":"Park","year":"2018","journal-title":"Struct. Control Health Monit."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.engstruct.2014.02.009","article-title":"Deformation monitoring of a super-tall structure using real-time strain data","volume":"67","author":"Xia","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.jsv.2007.04.037","article-title":"Estimation of dynamic structural displacements using fiber Bragg grating strain sensors","volume":"305","author":"Kang","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1061\/(ASCE)1084-0702(2005)10:5(564)","article-title":"Using Inclinometers to Measure Bridge Deflection","volume":"10","author":"Hou","year":"2005","journal-title":"J. Bridge Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"229","DOI":"10.12989\/sem.2012.42.2.229","article-title":"Estimation of bridge displacement responses using FBG sensors and theoretical mode shapes","volume":"42","author":"Shin","year":"2012","journal-title":"Struct. Eng. Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1088\/0964-1726\/5\/6\/005","article-title":"Shape and vibration mode sensing using a fiber optic Bragg grating array","volume":"5","author":"Davis","year":"1996","journal-title":"Smart Mater. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.conbuildmat.2006.08.007","article-title":"Deflection estimation of a full scale prestressed concrete girder using long-gauge fiber optic sensors","volume":"22","author":"Chung","year":"2008","journal-title":"Constr. Build. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ymssp.2016.05.027","article-title":"Dynamic displacement estimation by fusing LDV and LiDAR measurements via smoothing based Kalman filtering","volume":"82","author":"Kim","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.ymssp.2013.09.014","article-title":"Autonomous dynamic displacement estimation from data fusion of acceleration and intermittent displacement measurements","volume":"42","author":"Kim","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.measurement.2018.08.057","article-title":"Data fusion based multi-rate Kalman filtering with unknown input for on-line estimation of dynamic displacements","volume":"131","author":"Zheng","year":"2019","journal-title":"Measurement"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.engstruct.2017.06.018","article-title":"Long-span bridges: Enhanced data fusion of GPS displacement and deck accelerations","volume":"147","author":"Xu","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1177\/1369433219898103","article-title":"Field measurements of typhoon effects on a transmission tower and its modal parameter identification","volume":"23","author":"Li","year":"2020","journal-title":"Adv. Struct. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"110947","DOI":"10.1016\/j.engstruct.2020.110947","article-title":"Modal parameters of a transmission tower considering the coupling effects between the tower and lines","volume":"220","author":"Zhang","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"04020107","DOI":"10.1061\/(ASCE)EM.1943-7889.0001847","article-title":"Modal Identification of High-Speed Railway Bridges through Free-Vibration Detection","volume":"146","author":"Yang","year":"2020","journal-title":"J. Eng. Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.ymssp.2008.05.003","article-title":"Online automatic identification of the modal parameters of a long span arch bridge","volume":"23","author":"Cunha","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.marstruc.2018.09.012","article-title":"Modal analysis for the global flexural response of ships","volume":"63","author":"Hageman","year":"2019","journal-title":"Mar. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"125045","DOI":"10.1088\/0964-1726\/23\/12\/125045","article-title":"Strain modes based dynamic displacement estimation of beam structures with strain sensors","volume":"23","author":"Wang","year":"2014","journal-title":"Smart Mater. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1177\/1475921719857043","article-title":"Multi-rate data fusion for dynamic displacement measurement of beam-like supertall structures using acceleration and strain sensors","volume":"19","author":"Zhu","year":"2019","journal-title":"Struct. Health Monit.-Int. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:57:47Z","timestamp":1760137067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,20]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22093167"],"URL":"https:\/\/doi.org\/10.3390\/s22093167","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,20]]}}}