{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:07:41Z","timestamp":1760242061092,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,16]],"date-time":"2018-12-16T00:00:00Z","timestamp":1544918400000},"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":["51708359"],"award-info":[{"award-number":["51708359"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010877","name":"Shenzhen Science and Technology Innovation Commission","doi-asserted-by":"publisher","award":["JCYJ20170817102125407"],"award-info":[{"award-number":["JCYJ20170817102125407"]}],"id":[{"id":"10.13039\/501100010877","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Shenzhen University","award":["2016067"],"award-info":[{"award-number":["2016067"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cables are the main load-bearing structural components of long-span bridges, such as suspension bridges and cable-stayed bridges. When relative slip occurs among the wires in a cable, the local bending stiffness of the cable will significantly decrease, and the cable enters a local interlayer slip damage state. The decrease in the local bending stiffness caused by the local interlayer slip damage to the cable is symmetric or approximately symmetric for multiple elements at both the fixed end and the external load position. An eigenpair sensitivity identification method is introduced in this study to identify the interlayer slip damage to the cable. First, an eigenparameter sensitivity calculation formula is deduced. Second, the cable is discretized as a mass-spring-damping structural system considering stiffness and damping, and the magnitude of the cable interlayer slip damage is simulated based on the degree of stiffness reduction. The Tikhonov regularization method is introduced to solve the damage identification equation of the inverse problem, and artificial white noise is introduced to evaluate the robustness of the method to noise. Numerical examples of stayed cables are investigated to illustrate the efficiency and accuracy of the method proposed in this study.<\/jats:p>","DOI":"10.3390\/s18124456","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T02:15:59Z","timestamp":1545099359000},"page":"4456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cable Interlayer Slip Damage Identification Based on the Derivatives of Eigenparameters"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8950-0073","authenticated-orcid":false,"given":"Jintu","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quansheng","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5198-6506","authenticated-orcid":false,"given":"Liu","family":"Mei","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7946-1245","authenticated-orcid":false,"given":"Xijun","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1069-9372","authenticated-orcid":false,"given":"Jie","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"541","DOI":"10.4028\/www.scientific.net\/AMM.50-51.541","article-title":"Normal Stress between Steel Wires in the Stay-Cable","volume":"50","author":"Zheng","year":"2011","journal-title":"Appl. Mech. Mater."},{"key":"ref_2","first-page":"104","article-title":"Layered Slippage of stay cables shearing and its influence on bending stress","volume":"3","author":"Lin","year":"2009","journal-title":"Technol. Highw. Transp."},{"key":"ref_3","first-page":"185","article-title":"Influence of Slip Effect to the Bending Character of Frictional Laminated Beams","volume":"33","author":"Zhen","year":"2016","journal-title":"Eng. Mech."},{"key":"ref_4","first-page":"41","article-title":"Model Experiment on Bending Stiffness of Main Cable of Long-span Suspension Bridge","volume":"27","author":"Yan","year":"2010","journal-title":"J. Arch. Civ. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.ijsolstr.2012.10.032","article-title":"Analytical solutions of two-layer beams with interlayer slip and bi-linear interface law","volume":"50","author":"Campi","year":"2013","journal-title":"Int. J. Solids Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/j.compstruct.2014.09.003","article-title":"Analytical solutions of three-layer beams with interlayer slip and step-wise linear interface law","volume":"120","author":"Monetto","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cao, M.P., and Qiao, P. (2008, January 27). Damage detection of laminated composite beams with progressive wavelet transforms. Proceedings of the SPIE\u2014The International Society for Optical Engineering, San Diego, CA, USA.","DOI":"10.1117\/12.775606"},{"key":"ref_8","first-page":"363","article-title":"Damage detection in laminated composite beam by using vibration data","volume":"11","author":"Rucevskis","year":"2009","journal-title":"J. Vibroeng."},{"key":"ref_9","first-page":"60","article-title":"Damage detection of composite laminated beam based on strain model method","volume":"42","author":"Zhang","year":"2015","journal-title":"J. Hunan Univ."},{"key":"ref_10","first-page":"127","article-title":"Damage detection of a composite laminated structure using inner product vector under white noise excitation","volume":"28","author":"Le","year":"2009","journal-title":"J. Vib. Shock."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1177\/1475921716680849","article-title":"Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure","volume":"16","author":"Zhou","year":"2016","journal-title":"Struct. Health Monit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.engstruct.2006.05.019","article-title":"Eigen-parameter decomposition of element matrices for structural damage detection","volume":"29","author":"Di","year":"2007","journal-title":"Eng. Struct."},{"key":"ref_13","first-page":"264","article-title":"Structure Damage Detection Based on Improved Eigen Value Sensitivity","volume":"36","author":"Qiu","year":"2016","journal-title":"J. Vib. Meas. Diagn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1016\/j.jsv.2005.02.020","article-title":"Damage detection in discrete vibrating systems","volume":"289","author":"Dilena","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Qin, S., Zhang, Y., Zhou, Y.-L., and Kang, J. (2018). Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes. Sensors, 18.","DOI":"10.3390\/s18061879"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"85","DOI":"10.12989\/sem.2017.62.1.085","article-title":"Form-finding analysis of suspension bridges using an explicit Iterative approach","volume":"62","author":"Cao","year":"2017","journal-title":"Struct. Eng. Mech."},{"key":"ref_17","unstructured":"Zhou, Z. (2016). Mechanism and Mechanical Behavior of Delamination and Slippage between Wires or Strands of Cables for Large-Span Bridges, South China University of Technology."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1016\/j.jsv.2012.11.017","article-title":"A new method for calculating derivatives of eigenvalues and eigenvectors for discrete structural systems","volume":"332","author":"Liu","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Friswell, M., and Mottershead, J.E. (1995). Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-8508-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1088\/0266-5611\/19\/3\/311","article-title":"Direct analytic model of the L-curve for Tikhonov regularization parameter selection","volume":"19","author":"Carthy","year":"2003","journal-title":"Inverse Probl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1137\/0914086","article-title":"The use of the L-curve in the regularization of discrete ill-posed problems","volume":"14","author":"Hansen","year":"1991","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"687","DOI":"10.12989\/sem.2015.55.4.687","article-title":"Simultaneous identification of stiffness and damping based on derivatives of eigen-parameters","volume":"55","author":"Li","year":"2015","journal-title":"Struct. Eng. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1061\/(ASCE)0733-9445(1993)119:6(1961)","article-title":"Estimation Curve for Modal Damping in Stay Cables with Viscous Damper","volume":"119","author":"Pacheco","year":"1993","journal-title":"J. Struct. Eng."},{"key":"ref_24","first-page":"35","article-title":"Experimental study on damping characteristics of stay cables","volume":"4","author":"Zheng","year":"2002","journal-title":"Technol. Highw. Transp."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5122","DOI":"10.1016\/j.ijsolstr.2006.12.024","article-title":"Nonlinear FE-based investigation of flexural damping of slacking wire cables","volume":"44","author":"Zhu","year":"2007","journal-title":"Int. J. Solids Struct."},{"key":"ref_26","first-page":"211","article-title":"Theoretical analysis and experimental test on damping characteristics of CFRP stay cables","volume":"205","author":"Xu","year":"2010","journal-title":"Eng. Mech."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1016\/j.compstruct.2010.10.018","article-title":"Modal damping evaluation of hybrid FRP cable with smart dampers for long-span cable-stayed bridges","volume":"93","author":"Wang","year":"2011","journal-title":"Compos. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.engstruct.2017.11.014","article-title":"Multi-level damage identification of a bridge structure: A combined numerical and experimental investigation","volume":"156","author":"Xu","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_29","first-page":"157","article-title":"Modal identification and cable tension estimation oflong span cable-stayed bridge based on ambient excitation","volume":"31","author":"Xijun","year":"2012","journal-title":"J. Vib. Shock"},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.engstruct.2017.11.018","article-title":"Computer vision for SHM of civil infrastructure: From dynamic response measurement to damage detection\u2014A review","volume":"156","author":"Feng","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ndteint.2013.05.002","article-title":"Dynamic characteristics of suspension bridge hanger cables using digital image processing","volume":"59","author":"Kim","year":"2013","journal-title":"NDT E Int."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1016\/j.jsv.2010.10.036","article-title":"Finite element model updating from full-field vibration measurement using digital image correlation","volume":"330","author":"Wang","year":"2011","journal-title":"J. Sound Vib."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4456\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:34:21Z","timestamp":1760196861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4456"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,16]]},"references-count":33,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["s18124456"],"URL":"https:\/\/doi.org\/10.3390\/s18124456","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,12,16]]}}}