{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:50:48Z","timestamp":1765356648085,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:00:00Z","timestamp":1578614400000},"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 of China","doi-asserted-by":"publisher","award":["2018YFC0705604"],"award-info":[{"award-number":["2018YFC0705604"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["51878118"],"award-info":[{"award-number":["51878118"]}]},{"name":"Liaoning Provincial Natural Science Foundation of China","award":["20180551205"],"award-info":[{"award-number":["20180551205"]}]},{"DOI":"10.13039\/501100004442","name":"National Science Centre, Poland","doi-asserted-by":"publisher","award":["DEC- 2017\/25\/B\/ST8\/01800"],"award-info":[{"award-number":["DEC- 2017\/25\/B\/ST8\/01800"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Structural damage identification plays an important role in providing effective evidence for the health monitoring of bridges in service. Due to the limitations of measurement points and lack of valid structural response data, the accurate identification of structural damage, especially for large-scale structures, remains difficult. Based on additional virtual mass, this paper presents a damage identification method for bridges using a vehicle bump as the excitation. First, general equations of virtual modifications, including virtual mass, stiffness, and damping, are derived. A theoretical method for damage identification, which is based on additional virtual mass, is formulated. The vehicle bump is analyzed, and the bump-induced excitation is estimated via a detailed analysis in four periods: separation, free-fall, contact, and coupled vibrations. The precise estimation of bump-induced excitation is then applied to a bridge. This allows the additional virtual mass method to be used, which requires knowledge of the excitations and acceleration responses in order to construct the frequency responses of a virtual structure with an additional virtual mass. Via this method, a virtual mass with substantially more weight than a typical vehicle is added to the bridge, which provides a sufficient amount of modal information for accurate damage identification while avoiding the bridge overloading problem. A numerical example of a two-span continuous beam is used to verify the proposed method, where the damage can be identified even with 15% Gaussian random noise pollution using a 1-degree of freedom (DOF) car model and 4-DOF model.<\/jats:p>","DOI":"10.3390\/s20020394","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:20:29Z","timestamp":1578651629000},"page":"394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Bridge Damage Identification Using Vehicle Bump Based on Additional Virtual Masses"],"prefix":"10.3390","volume":"20","author":[{"given":"Qingxia","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Dalian Minzu University, Dalian 116600, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3554-7036","authenticated-orcid":false,"given":"Jilin","family":"Hou","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering &amp; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9773-0688","authenticated-orcid":false,"given":"\u0141ukasz","family":"Jankowski","sequence":"additional","affiliation":[{"name":"Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/15732479.2010.498282","article-title":"Bridge monitoring in Japan: The needs and strategies","volume":"7","author":"Fujino","year":"2011","journal-title":"Struct. Infrastruct. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Abdollah, M., McGetrick, P.J., and OBrien, E.J. (2015). A review of indirect bridge monitoring using passing vehicles. Shock Vib., 286139.","DOI":"10.1155\/2015\/286139"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1177\/1475921716653278","article-title":"Applications of structural health monitoring technology in Asia","volume":"16","author":"Annamdas","year":"2017","journal-title":"Struct. Health Monit."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Agis, D., and Pozo, F. (2019). A Frequency-Based Approach for the Detection and Classification of Structural Changes Using t-SNE+. Sensors, 19.","DOI":"10.3390\/s19235097"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Jiang, T.Y., Zhang, Y.W., Wang, L., Zhang, L., and Song, G.B. (2018). Monitoring fatigue damage of modular bridge expansion joints using piezoceramic transducers. Sensors, 18.","DOI":"10.3390\/s18113973"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ymssp.2007.07.004","article-title":"Vibration-based structural health monitoring using output-only measurements under changing environment","volume":"22","author":"Deraemaeker","year":"2018","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"117101","DOI":"10.1016\/j.conbuildmat.2019.117101","article-title":"Long-term monitoring for the condition-based structural maintenance of the Milan Cathedral","volume":"228","author":"Gentile","year":"2019","journal-title":"Const. Build. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1080\/15583058.2019.1605552","article-title":"Continuous Dynamic Monitoring to Enhance the Knowledge of a Historic Bell-Tower","volume":"3","author":"Gentile","year":"2019","journal-title":"Int. J. Archit. Herit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1260\/1369-4332.16.7.1187","article-title":"Review of benchmark studies and guidelines for structural health monitoring","volume":"16","author":"Zhou","year":"2013","journal-title":"Adv. Struct. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1080\/15732479.2017.1406959","article-title":"Dynamic identification and continuous dynamic monitoring of bridges: Different applications along bridges life cycle","volume":"14","author":"Cunha","year":"2018","journal-title":"Struct. Infrastruct. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"366","DOI":"10.24084\/repqj17.313","article-title":"Damage diagnosis for offshore fixed wind turbines","volume":"17","author":"Agis","year":"2019","journal-title":"Renew. Energy Power Qual. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Weng, S., Zhu, H., Xia, Y., Li, J., and Tian, W. (2019). A review on dynamic substructuring methods for model updating and damage detection of large-scale structures. Adv. Struct. Eng.","DOI":"10.1177\/1369433219872429"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.ymssp.2012.06.018","article-title":"Simultaneous identification of excitation time histories and parametrized structural damages","volume":"33","author":"Zhang","year":"2012","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/j.ymssp.2015.01.019","article-title":"Development and validation of an automated operational modal analysis algorithm for vibration-based monitoring and tensile load estimation","volume":"60","author":"Rainieri","year":"2015","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s11831-012-9069-x","article-title":"System Identification Methods for (Operational) Modal Analysis: Review and Comparison","volume":"19","author":"Reynders","year":"2012","journal-title":"Arch. Comput. Meth. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, S., Long, X., Luo, H., and Zhu, H. (2018). Damage Identification for Underground Structure Based on Frequency Response Function. Sensors, 18.","DOI":"10.3390\/s18093033"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"117287","DOI":"10.1016\/j.conbuildmat.2019.117287","article-title":"Behavior of circular ice-filled self-luminous FRP tubular stub columns under axial compression","volume":"232","author":"Wang","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"04019085","DOI":"10.1061\/(ASCE)ST.1943-541X.0002373","article-title":"Behavior of circular fiber-reinforced polymer-steel-confined concrete columns subjected to reversed cyclic loads: Experimental studies and finite-element analysis","volume":"145","author":"Wang","year":"2019","journal-title":"J. Struct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Noori, M., Altabey, W.A., Ghiasi, R., and Wu, Z.S. (2018). Deep learning-based damage, load and support identification for a composite pipeline by extracting modal macro strains from dynamic excitations. Appl. Sci., 8.","DOI":"10.3390\/app8122564"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.jsv.2018.04.030","article-title":"Extraction of bridge fundamental frequency from estimated vehicle excitation through a particle filter approach","volume":"428","author":"Wang","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.jweia.2011.03.016","article-title":"Estimating aeroelastic effects from full bridge responses by operational modal analysis","volume":"99","author":"Ubertini","year":"2011","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"04016025","DOI":"10.1061\/(ASCE)EM.1943-7889.0001033","article-title":"Numerically extracting bridge modal properties from dynamic responses of moving vehicles","volume":"142","author":"Kong","year":"2016","journal-title":"J. Eng. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Qin, S.Q., Zhang, Y.Z., Zhou, Y.L., and Kang, J.T. (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_24","doi-asserted-by":"crossref","first-page":"431","DOI":"10.12989\/sss.2016.17.3.431","article-title":"Automated identification of the modal parameters of a cable-stayed bridge: Influence of the wind conditions","volume":"17","author":"Magalhaes","year":"2016","journal-title":"Smart Struct. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.ymssp.2018.03.027","article-title":"Bayesian operational modal analysis of Jiangyin Yangtze River Bridge","volume":"110","author":"Brownjohn","year":"2018","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1450028","DOI":"10.1142\/S021945541450028X","article-title":"Structural multi-damage identification based on modal strain energy equivalence index method","volume":"14","author":"Guo","year":"2014","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.measurement.2018.05.004","article-title":"A damage detection method based on strain modes for structures under ambient excitation","volume":"125","author":"Cui","year":"2018","journal-title":"Measurement"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1260\/1369-4332.18.1.137","article-title":"Frequency-Domain Substructure Isolation for Local Damage Identification","volume":"18","author":"Hou","year":"2015","journal-title":"Adv. Struct. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.measurement.2018.04.034","article-title":"Frequency Co-integration-based damage detection for bridges under the influence of environmental temperature variation","volume":"125","author":"Liang","year":"2018","journal-title":"Measurement"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.engstruct.2012.03.035","article-title":"Substructure damage identification based on response reconstruction in frequency domain and model updating","volume":"41","author":"Li","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1177\/1369433216660018","article-title":"Damage identification using structural modes based on substructure virtual distortion method","volume":"20","author":"Zhang","year":"2017","journal-title":"Adv. Struct. Eng."},{"key":"ref_32","first-page":"157","article-title":"A mass or stiffness addition technique for structural parameter updating","volume":"7","author":"Nalitolela","year":"1992","journal-title":"Int. J. Anal. Exp. Modal Anal."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1006\/mssp.1993.1005","article-title":"Updating model parameters by adding an imagined stiffness to the structure","volume":"7","author":"Nalitolela","year":"1993","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1002\/nme.136","article-title":"Model updating by adding known masses","volume":"50","author":"Cha","year":"2001","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1016\/j.compstruc.2010.07.005","article-title":"Damage identification using modal, static and thermographic analysis with additional control parameters","volume":"88","author":"Dems","year":"2010","journal-title":"Comput. Struct."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1002\/stc.444","article-title":"Structural parameter identification by use of additional known masses and its experimental application","volume":"19","author":"Dinh","year":"2012","journal-title":"Struct. Control Health Monit."},{"key":"ref_37","first-page":"295","article-title":"Influencing factors of beam structure damage identification based on additional mass","volume":"18","author":"Lu","year":"2017","journal-title":"J. PLA Univ. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"025013","DOI":"10.1088\/1361-665X\/aaa46f","article-title":"Improving substructure identification accuracy of shear structures using virtual control system","volume":"27","author":"Zhang","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.ymssp.2018.11.025","article-title":"Adaptive Substructure Identification for Shear Structures with Virtual Control System","volume":"121","author":"Zhang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s00158-012-0879-0","article-title":"Structural damage identification by adding virtual masses","volume":"48","author":"Hou","year":"2013","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00158-007-0158-7","article-title":"The virtual distortion method\u2014A versatile reanalysis tool for structures and systems","volume":"36","author":"Wiklo","year":"2008","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"04018097","DOI":"10.1061\/(ASCE)EM.1943-7889.0001523","article-title":"Structural damage localization and quantification based on additional virtual masses and Bayesian theory","volume":"144","author":"Hou","year":"2018","journal-title":"J. Eng. Mech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.ymssp.2019.01.017","article-title":"Estimation of dynamic tire force by measurement of vehicle body responses with numerical and experimental validation","volume":"123","author":"Wang","year":"2019","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_44","unstructured":"Tan, G.J., Liu, Z.Y., and Jiao, Y.B. (2016, January 7\u20138). Determination of limit vehicle bump height in dynamic detection of simply supported bridge. Proceedings of the 24th International Conference on Vibroengineering, Shanghai, China."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3737","DOI":"10.21595\/jve.2017.18198","article-title":"Determination method of limit vehicle bump height in dynamic load test of simply supported bridge","volume":"19","author":"Tan","year":"2017","journal-title":"J. Vibroeng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1687814019843758","DOI":"10.1177\/1687814019843758","article-title":"Analysis method of dynamic response in the whole process of the vehicle bump test of simply supported bridge","volume":"11","author":"Tan","year":"2019","journal-title":"Adv. Mech. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Hou, J., Wang, S., Zhang, Q., and Jankowski, \u0141. (2019). An Improved Objective Function for Modal-Based Damage Identification Using Substructural Virtual Distortion Method. Appl. Sci., 9.","DOI":"10.3390\/app9050971"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/2\/394\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:19:24Z","timestamp":1760361564000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/2\/394"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":47,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["s20020394"],"URL":"https:\/\/doi.org\/10.3390\/s20020394","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,1,10]]}}}