{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T03:49:55Z","timestamp":1784346595546,"version":"3.55.0"},"reference-count":29,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,18]],"date-time":"2022-12-18T00:00:00Z","timestamp":1671321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of Industry Foresight and Key Core Technologies","award":["BE2021021"],"award-info":[{"award-number":["BE2021021"]}]},{"name":"Project of Industry Foresight and Key Core Technologies","award":["BA2022009"],"award-info":[{"award-number":["BA2022009"]}]},{"name":"Special Project on Transformation of Scientific and Technological Achievements in Jiangsu Province","award":["BE2021021"],"award-info":[{"award-number":["BE2021021"]}]},{"name":"Special Project on Transformation of Scientific and Technological Achievements in Jiangsu Province","award":["BA2022009"],"award-info":[{"award-number":["BA2022009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Estimation and monitoring of cable tension is of great significance in the structural assessment of cable-supported bridges. For short cables, the traditional cable tension identification method via frequency measurement has large errors due to the influence of complex boundaries, which affect the accuracy of estimation. A new cable tension estimation method based on mode shape identification with a multiple sensor arrangement on the cable can take the influence of boundary conditions into account and its accuracy has been verified. However, it requires more sensors compared to the traditional frequency-based method, which will significantly increase the cost of long-term monitoring in practice. Therefore, a novel approach for cable tension monitoring considering both cost and accuracy is further proposed in this study. The approach adopts multiple sensors to measure the influence of boundary conditions. Then, only a single sensor is required for long-term monitoring of the cable. In this paper, an analytical model of the cable is firstly established. The influence of boundary conditions is calculated, which ensures the accuracy of mode shape identification. Furthermore, a field experiment is carried out to verify the effectiveness of the new approach. The results have demonstrated the effectiveness and accurateness of the proposed method in long-term short cable tension monitoring.<\/jats:p>","DOI":"10.3390\/s22249975","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T09:31:01Z","timestamp":1671442261000},"page":"9975","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A Novel Approach for Cable Tension Monitoring Based on Mode Shape Identification"],"prefix":"10.3390","volume":"22","author":[{"given":"Yichao","family":"Xu","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Southeast University, Nanjing 210096, China"},{"name":"Jiangsu Transportation Institute Group, Nanjing 211112, China"},{"name":"State Key Laboratory of Safefy and Health for In-Service Long Span Bridges, Nanjing 211112, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9129-255X","authenticated-orcid":false,"given":"Jian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Southeast University, Nanjing 210096, China"},{"name":"Jiangsu Key Laboratory of Engineering Mechanics, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Jiangsu Transportation Institute Group, Nanjing 211112, China"},{"name":"State Key Laboratory of Safefy and Health for In-Service Long Span Bridges, Nanjing 211112, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changzhao","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Transportation Institute Group, Nanjing 211112, China"},{"name":"State Key Laboratory of Safefy and Health for In-Service Long Span Bridges, Nanjing 211112, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, D., Ye, J., Wang, B., and Wahab, M.A. (2021). Review on the service safety assessment of main cable of long span multi-tower suspension bridge. Appl. Sci., 11.","DOI":"10.3390\/app11135920"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, H., Mao, J., Wang, H., Zhu, X., Zhang, Y., Gao, H., Ni, Y., and Hai, Z. (Int. J. Struct. Stab. Dyn., 2022). A novel acceleration-based approach for monitoring the long-term displacement of bridge cables, Int. J. Struct. Stab. Dyn., accepted.","DOI":"10.1142\/S0219455423500530"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s13349-018-0301-8","article-title":"Cable force monitoring and prediction for cable group of long-span cable-supported bridges","volume":"8","author":"Dong","year":"2018","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.4028\/www.scientific.net\/AMR.295-297.1230","article-title":"Measuring methods of cable tension in cable-stayed bridges","volume":"295","author":"Sun","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s13349-015-0115-x","article-title":"The state of the art in structural health monitoring of cable-stayed bridges","volume":"6","author":"Li","year":"2016","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103687","DOI":"10.1016\/j.autcon.2021.103687","article-title":"Measurement of cable forces for automated monitoring of engineering structures using fiber optic sensors: A review","volume":"126","author":"Yao","year":"2021","journal-title":"Autom. Constr."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hu, D., Guo, Y., Chen, X., and Zhang, C. (2017). Cable force health monitoring of Tongwamen bridge based on fiber Bragg grating. Appl. Sci., 7.","DOI":"10.3390\/app7040384"},{"key":"ref_9","unstructured":"Caetano, E. (2011, January 22\u201323). On the identification of cable force from vibration measurements. Proceedings of the IABSE-IASS Symposium, London, UK."},{"key":"ref_10","unstructured":"Irvine, H.M. (1981). Cable Structures, The MIT Press. [1st ed.]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.jsv.2007.03.012","article-title":"Estimation of cable tension force using the frequency-based system identification method","volume":"304","author":"Kim","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_12","first-page":"575","article-title":"Cable vibration control with internal and external dampers: Theoretical analysis and field test validation","volume":"26","author":"Di","year":"2020","journal-title":"Smart Struct. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1061\/(ASCE)0733-9445(1996)122:6(651)","article-title":"Practical formulas for estimation of cable tension by vibration method","volume":"122","author":"Zui","year":"1996","journal-title":"J. Struct. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"363","DOI":"10.12989\/sem.2005.20.3.363","article-title":"Empirical formulas to estimate cable tension by cable fundamental frequency","volume":"20","author":"Ren","year":"2005","journal-title":"Struct. Eng. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1061\/(ASCE)BE.1943-5592.0000200","article-title":"Practical formula for cable tension estimation by vibration method","volume":"17","author":"Fang","year":"2012","journal-title":"J. Bridge Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1260\/1369-4332.18.3.405","article-title":"Unified practical formulas for vibration-based method of cable tension estimation","volume":"18","author":"Huang","year":"2015","journal-title":"Adv. Struct. Eng."},{"key":"ref_17","first-page":"8640674","article-title":"A laser-based noncontact vibration technique for health monitoring of structural cables: Background, success, and new developments","volume":"2018","author":"Mehrabi","year":"2018","journal-title":"Adv. Acoust. Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1111\/mice.12567","article-title":"Noncontact cable force estimation with unmanned aerial vehicle and computer vision","volume":"36","author":"Tian","year":"2021","journal-title":"Comput. Aided Civ. Infrastruct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yan, B., Li, D., Chen, W., Deng, L., and Jiang, X. (2020). Mode shape\u2013aided cable force determination using digital image correlation. Struct. Health Monit., 1475921720952163.","DOI":"10.1177\/1475921720952163"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.measurement.2016.12.020","article-title":"Cable tension force estimate using novel noncontact vision-based sensor","volume":"99","author":"Feng","year":"2017","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e2155","DOI":"10.1002\/stc.2155","article-title":"A non-contact vision-based system for multipoint displacement monitoring in a cable-stayed footbridge","volume":"25","author":"Xu","year":"2018","journal-title":"Struct. Control. Health Monit."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"06014015","DOI":"10.1061\/(ASCE)EM.1943-7889.0000836","article-title":"Estimation of cable tension force independent of complex boundary conditions","volume":"141","author":"Yan","year":"2015","journal-title":"J. Eng. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.jsv.2018.10.018","article-title":"Mode shape-aided tension force estimation of cable with arbitrary boundary conditions","volume":"440","author":"Yan","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"111319","DOI":"10.1016\/j.measurement.2022.111319","article-title":"Tension force identification for cable of various end-restraints using equivalent effective vibration lengths of mode pairs","volume":"197","author":"Syamsi","year":"2022","journal-title":"Measurement"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.measurement.2018.03.077","article-title":"Tension determination for suspenders of arch bridge based on multiple vibration measurements concentrated at one end","volume":"123","author":"Wu","year":"2018","journal-title":"Measurement"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.engstruct.2018.03.070","article-title":"A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions","volume":"166","author":"Chen","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.compstruc.2018.07.010","article-title":"Extension of dynamic stiffness method to complicated damped structures","volume":"208","author":"Han","year":"2018","journal-title":"Comput. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1093\/qjmam\/24.3.263","article-title":"A general algorithm for computing natural frequencies of elastic structures","volume":"24","author":"Wittrick","year":"1971","journal-title":"Q. J. Mech. Appl. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.compstruct.2018.07.108","article-title":"An improved Wittrick-Williams algorithm for beam-type structures","volume":"204","author":"Han","year":"2018","journal-title":"Compos. Struct."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9975\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:31Z","timestamp":1760147011000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9975"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,18]]},"references-count":29,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22249975"],"URL":"https:\/\/doi.org\/10.3390\/s22249975","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,18]]}}}