{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T03:55:39Z","timestamp":1778903739269,"version":"3.51.4"},"reference-count":148,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,1,23]],"date-time":"2019-01-23T00:00:00Z","timestamp":1548201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2018YFF0214705"],"award-info":[{"award-number":["2018YFF0214705"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The detection of damage in bridges subjected to moving loads has attracted increasing attention in the field of structural health monitoring. Processing the dynamic responses induced by moving loads to characterize damage is the key to identifying damage in bridges. On this topic, various methods of processing dynamic responses to moving loads have been developed in recent decades, with respective strengths and weaknesses. These methods appear in different applications and literatures and their features have not been comprehensively surveyed to form a profile of this special area. To address this issue, this study presents a comprehensive survey of methods for identifying damage by processing dynamic responses of cracked bridges subjected to moving loads. First, methods utilizing the Fourier transform to process dynamic responses to moving loads for damage detection in bridges are examined. Second, methods using wavelet transform to process the dynamic responses to moving loads for damage characterization are examined. Third, methods of employing the Hilbert-Huang transform to process the dynamic responses to moving loads for damage identification are examined. Fourth, methods of dynamic response-driven heuristic interrogation of damage in bridges subjected to moving loads are examined. Finally, we recommend future research directions for advancing the development of damage identification relying on processing dynamic responses to moving loads. This study provides a profile of the state-of-the-art and state-of-the-use of damage identification in bridges based on dynamic responses to moving loads, with the primary aim of helping researchers find crucial points for further exploration of theories, methods, and technologies for damage detection in bridges subjected to moving loads.<\/jats:p>","DOI":"10.3390\/s19030463","type":"journal-article","created":{"date-parts":[[2019,1,24]],"date-time":"2019-01-24T11:12:48Z","timestamp":1548328368000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["Damage Identification in Bridges by Processing Dynamic Responses to Moving Loads: Features and Evaluation"],"prefix":"10.3390","volume":"19","author":[{"given":"Xiang","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Engineering Mechanics, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maosen","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Engineering Mechanics, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wieslaw","family":"Ostachowicz","sequence":"additional","affiliation":[{"name":"Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 14 Fiszera St., 80-231 Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3268-3646","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Engineering Mechanics, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1061\/(ASCE)0733-9399(1997)123:9(897)","article-title":"Structural control: Past, present, and future","volume":"123","author":"Housner","year":"1997","journal-title":"J. Eng. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1177\/1045389X05050106","article-title":"Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural health monitoring","volume":"16","author":"Giurgiutiu","year":"2005","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1088\/0964-1726\/15\/3\/009","article-title":"A carbon nanotube strain sensor for structural health monitoring","volume":"15","author":"Kang","year":"2006","journal-title":"Smart Mater. Struct."},{"key":"ref_4","first-page":"303","article-title":"An introduction to structural health monitoring","volume":"365","author":"Farrar","year":"2007","journal-title":"Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"ref_5","unstructured":"Sinou, J.J. (2009). A review of damage detection and health monitoring of mechanical systems from changes in the measurement of linear and non-linear vibrations. Mechanical Vibrations: Measurement, Effects and Control, Nova Science."},{"key":"ref_6","first-page":"37","article-title":"Vibration based inspection of civil engineering structure","volume":"29","author":"Rytter","year":"1993","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_7","unstructured":"Xiang, H.F. (2000, January 11\u201313). China major bridge projects facing 21st century. Proceedings of the International Conference on Engineering and Technological Science, Beijing, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ge, Y.J., and Xiang, H.F. (2007, January 19\u201321). Great Demand and Great Challenge-Chinese Major Bridges under Construction for Improving Traffic Infrastructure Nationwide. Proceedings of the Improving Infrastructure Worldwide of the Conference, IABSE Symposium, Weimar, Germany.","DOI":"10.2749\/222137807796119528"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.soildyn.2010.11.002","article-title":"Dynamic effects of moving loads on road pavements: A review","volume":"31","author":"Beskou","year":"2011","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_10","first-page":"1","article-title":"Damage detection by a moving mass on beam structure","volume":"89","author":"Ahn","year":"2015","journal-title":"Adv. Sci. Technol. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1016\/j.ymssp.2010.12.010","article-title":"Moving-load dynamic problems: A tutorial (with a brief overview)","volume":"25","author":"Ouyang","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","first-page":"514","article-title":"Dynamic response of a floating bridge to a moving light rail train","volume":"2013","author":"Sedarat","year":"2013","journal-title":"Struct. Congr."},{"key":"ref_13","first-page":"763810","article-title":"Recent research and applications of numerical simulation for dynamic response of long-span bridges subjected to multiple loads","volume":"2014","author":"Chen","year":"2014","journal-title":"Sci. World J."},{"key":"ref_14","unstructured":"Lin, H.P. (2007, January 9\u201312). Vibration analysis of a cracked beam subjected to a traveling vehicle. Proceedings of the 14th International Congress on Sound and Vibration, Cairns, Australia."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/S0141-0296(96)00149-6","article-title":"Detection of structural damage through changes in frequency: A review","volume":"19","author":"Salawu","year":"1997","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1002\/stc.1749","article-title":"Bridge damage detection using ambient traffic and moving force identification","volume":"22","author":"Obrien","year":"2015","journal-title":"Struct. Control Health Monit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.jsv.2003.01.001","article-title":"Vibration of damaged beams under a moving mass: Theory and experimental validation","volume":"274","author":"Bilello","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1016\/j.ijmecsci.2006.06.014","article-title":"Forced responses of cracked cantilever beams subjected to a concentrated moving load","volume":"48","author":"Lin","year":"2006","journal-title":"Int. J. Mech. Sci."},{"key":"ref_19","unstructured":"Zhu, X.Q., and Hao, H. (2007). Damage Detection of Bridge Beam Structures under Moving Loads, School of Civil and Resource Engineering, the University of Western Australia. Research Program Report."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.4028\/www.scientific.net\/AMM.578-579.1096","article-title":"Damage identification of the arch bridge based on the difference of deflection with moving load","volume":"578\u2013579","author":"Zhao","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_21","first-page":"8454567","article-title":"A damage detection algorithm utilizing dynamic displacement of bridge under moving vehicle","volume":"2016","author":"Sun","year":"2016","journal-title":"Shock Vib."},{"key":"ref_22","first-page":"788","article-title":"Dynamic analysis of beam under the moving mass for damage assessment","volume":"4","author":"Chatterjee","year":"2015","journal-title":"Int. J. Eng. Res. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1177\/1077546315580470","article-title":"Dynamic response of cracked Timoshenko beams on elastic foundations under moving harmonic loads","volume":"23","author":"Attar","year":"2017","journal-title":"J. Vib. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF01213564","article-title":"Dynamic response of a cracked beam subject to a moving load","volume":"106","author":"Lee","year":"1994","journal-title":"Acta Mech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1002\/stc.1841","article-title":"A mode shape-based damage detection approach using laser measurement from a vehicle crossing a simply supported bridge","volume":"23","author":"Obrien","year":"2016","journal-title":"Struct. Control Health Monit."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1006\/jsvi.2001.4213","article-title":"Dynamic response of a beam with a crack subject to a moving mass","volume":"256","author":"Mahmoud","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1260\/1369-4332.16.9.1621","article-title":"Calculation of dynamic response sensitivity to substructural damage identification under moving load","volume":"16","author":"Zhu","year":"2013","journal-title":"Adv. Struct. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3201","DOI":"10.1016\/j.jsv.2013.01.024","article-title":"An investigation into the acceleration response of a damaged beam-type structure to a moving force","volume":"332","author":"Hester","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/15732479.2014.890631","article-title":"A bridge-monitoring tool based on bridge and vehicle accelerations","volume":"11","author":"Hester","year":"2015","journal-title":"Struct. Infrastruct. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"917","DOI":"10.12989\/sss.2014.14.5.917","article-title":"An integrated approach for structural health monitoring using an in-house built fiber optic system and non-parametric data analysis","volume":"14","author":"Malekzadeh","year":"2014","journal-title":"Smart Struct. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.ymssp.2013.02.019","article-title":"Damage detection using data-driven methods applied to moving-load responses","volume":"39","author":"Cavadas","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","unstructured":"Li, R., and Xiong, X. (2015, January 18\u201319). Damage detection of bridge beam subjected to moving loads based on energy ratio from vibration response. Proceedings of the Sixth International Conference on Intelligent Systems Design and Engineering Applications, Guiyang, China."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1007\/s00158-010-0528-4","article-title":"Simultaneous identification of moving masses and structural damage","volume":"42","author":"Zhang","year":"2010","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"261","DOI":"10.12989\/sem.2015.53.2.261","article-title":"Structural damage and force identification under moving load","volume":"53","author":"Zhu","year":"2015","journal-title":"Struct. Eng. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"012064","DOI":"10.1088\/1742-6596\/628\/1\/012064","article-title":"Footprint caused by a vehicle configuration on the dynamic amplification of the bridge response","volume":"628","author":"Mohammed","year":"2015","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s11802-007-0199-y","article-title":"New damage-locating method for bridges subjected to a moving load","volume":"6","author":"Liu","year":"2007","journal-title":"J. Ocean Univ. China"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"04016059","DOI":"10.1061\/(ASCE)BE.1943-5592.0000933","article-title":"Strain-based damage-assessment method for bridges under moving vehicular loads using long-gauge strain sensing","volume":"21","author":"Hong","year":"2016","journal-title":"J. Bridge Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/S0022-460X(02)01555-9","article-title":"A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source","volume":"268","author":"Majumder","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_39","unstructured":"Bracewell, R.N. (1986). The Fourier Transform and Its Applications, McGraw-Hill."},{"key":"ref_40","first-page":"15","article-title":"Fourier transforms and the fast Fourier transform (FFT) Algorithm","volume":"2","author":"Heckbert","year":"1995","journal-title":"Comput. Graph."},{"key":"ref_41","unstructured":"Bhatt, P. (2010). Maximum Marks Maximum Knowledge in Physics, Allied Publishers."},{"key":"ref_42","first-page":"159","article-title":"FFT-based spectral element analysis for the linear continuum dynamic systems subjected to arbitrary initial conditions by using the pseudo-force method","volume":"74","author":"Usik","year":"2010","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_43","first-page":"1","article-title":"Comparison of natural frequency vibration analysis for a bridge using accelerometers and a piezoelectric cable vibration sensor","volume":"4","author":"Shimoi","year":"2015","journal-title":"Int. J. Instrum. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.jsv.2007.10.034","article-title":"Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load","volume":"312","author":"Yang","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.proeng.2016.05.003","article-title":"Conditions of visibility of bridge natural frequency in vehicle vertical acceleration","volume":"144","author":"Lalthlamuana","year":"2016","journal-title":"Procedia Eng."},{"key":"ref_46","unstructured":"Keenahan, J., McGetrick, P., O\u2019Brien, E.J., and Gonzalez, A. (2012, January 22\u201327). Using instrumented vehicles to detect damage in bridges. Proceedings of the 15th International Conference on Experimental Mechanics, Porto, Portugal. Paper No. 2934."},{"key":"ref_47","unstructured":"Malekjafarian, A., and O\u2019Brien, E.J. (2014, January 28\u201329). Application of output-only modal method in monitoring of bridges using an instrumented vehicle. Proceedings of the Civil Engineering Research in Ireland, Belfast, UK."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Brincker, R., Zhang, L., and Andersen, P. (2000, January 7\u201310). Modal identification from ambient responses using frequency domain decomposition. Proceedings of the 18th International Modal Analysis Conference, San Antonio, TX, USA.","DOI":"10.1088\/0964-1726\/10\/3\/303"},{"key":"ref_49","unstructured":"Zhang, L., and Brincker, R. (2005, January 26\u201327). An overview of operational modal analysis: Major development and issues. Proceedings of the 1st International Operational Modal Analysis Conference, Copenhagen, Denmark."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1006\/mssp.2000.1356","article-title":"The transmissibility concept in multi-degree-of-freedom systems","volume":"15","author":"Maia","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"15","DOI":"10.12989\/sss.2015.15.1.015","article-title":"Structural damage identification with power spectral density transmissibility: Numerical and experimental studies","volume":"15","author":"Li","year":"2015","journal-title":"Smart Struct. Syst."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1111\/j.1467-8667.2011.00735.x","article-title":"Operational modal parameter identification from power spectrum density transmissibility","volume":"27","author":"Yan","year":"2012","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"04014102","DOI":"10.1061\/(ASCE)EM.1943-7889.0000821","article-title":"Damage detection based on transmissibility of a vehicle and bridge coupled system","volume":"141","author":"Kong","year":"2015","journal-title":"J. Eng. Mech."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1061\/(ASCE)0733-9399(2000)126:7(677)","article-title":"Wavelet-based approach for structural damage detection","volume":"126","author":"Hou","year":"2000","journal-title":"J. Eng. Mech."},{"key":"ref_55","first-page":"339","article-title":"Wavelet-based damage detection method for beam-like structures","volume":"23","year":"2010","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.engstruct.2003.10.008","article-title":"Damage detection of structures by wavelet analysis","volume":"26","author":"Kim","year":"2004","journal-title":"Eng. Struct."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0888-3270(03)00075-X","article-title":"Application of the wavelet transform in machine condition monitoring and fault diagnostics: A review with bibliography","volume":"18","author":"Peng","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2899","DOI":"10.1016\/S0020-7403(01)00064-9","article-title":"Sensitivity analysis of crack detection in beams by wavelet technique","volume":"43","author":"Quek","year":"2001","journal-title":"Int. J. Mech. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.jsv.2006.04.015","article-title":"Application of continuous wavelet transform in vibration based damage detection method for beams and plates","volume":"297","author":"Rucka","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1061\/(ASCE)0733-9399(1998)124:2(152)","article-title":"Application of wavelet theory for crack identification in structures","volume":"124","author":"Liew","year":"1998","journal-title":"J. Eng. Mech."},{"key":"ref_61","first-page":"1141","article-title":"Crack detection of a beam using the wavelet transform","volume":"2251","author":"Surace","year":"1994","journal-title":"SPIE Int. Soc. Opt. Eng."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1061\/(ASCE)0733-9445(2002)128:10(1354)","article-title":"Structural damage assessment based on wavelet packet transform","volume":"128","author":"Sun","year":"2002","journal-title":"J. Struct. Eng."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"3557","DOI":"10.1016\/S0020-7683(03)00147-1","article-title":"Crack identification in beams using wavelet analysis","volume":"40","author":"Douka","year":"2003","journal-title":"Int. J. Solids Struct."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/stc.366","article-title":"Crack detection in simply supported beams using stationary wavelet transform of modal data","volume":"18","author":"Zhong","year":"2011","journal-title":"Struct. Control Health Monit."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.jsv.2003.09.035","article-title":"Crack identification in double-cracked beams using wavelet analysis","volume":"277","author":"Loutridis","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_66","unstructured":"Mallat, S. (2008). A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1177\/1475921709352147","article-title":"A bridge-vehicle interaction based experimental investigation of damage evolution","volume":"9","author":"Pakrashi","year":"2010","journal-title":"Struct. Health Monit."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.ymssp.2011.06.007","article-title":"A wavelet-based damage detection algorithm based on bridge acceleration response to a vehicle","volume":"28","author":"Hester","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/18.119727","article-title":"Singularity detection and processing with wavelets","volume":"38","author":"Mallat","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1117\/1.482718","article-title":"Wavelet transforms: Introduction to theory and applications","volume":"8","author":"Rao","year":"1998","journal-title":"J. Electron. Imaging"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"055014","DOI":"10.1088\/0964-1726\/17\/5\/055014","article-title":"Integrated wavelet transform and its application to vibration mode shapes for the damage detection of beam-type structures","volume":"17","author":"Cao","year":"2008","journal-title":"Smart Mater. Struct."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1016\/j.ymssp.2011.11.011","article-title":"A multi-scale pseudo-force model in wavelet domain for identification of damage in structural components","volume":"28","author":"Cao","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s40032-015-0208-7","article-title":"Wavelet analysis of acceleration response of beam under the moving mass for damage assessment","volume":"97","author":"Vaidya","year":"2016","journal-title":"J. Inst. Eng. (India) Ser. C"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1051\/meca\/2012036","article-title":"Wavelets-based damage localization on beams under the influence of moving loads","volume":"14","author":"Manuel","year":"2013","journal-title":"Mech. Ind."},{"key":"ref_75","unstructured":"Machorro-L\u00f3pez, J.M., Bellino, A., Marchesiello, S., and Garibaldi, L. (2012, January 4\u20137). Damage detection for beams subject to moving loads based on wavelet transforms. Proceedings of the 11th International Conference on Computational Structures Technology, Dubrovnik, Croatia. Paper 79."},{"key":"ref_76","unstructured":"Gonz\u00e1lez, A., and Hester, D. (July, January 30). The use of wavelets on the response of a beam to a calibrated vehicle for damage detection. Proceedings of the 7th International Symposium on Non-destructive Testing in Civil Engineering, Nantes, France."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2299","DOI":"10.1016\/j.ijsolstr.2005.07.024","article-title":"Wavelet-based crack identification of bridge beam from operational deflection time history","volume":"43","author":"Zhu","year":"2006","journal-title":"Int. J. Solids Struct."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"1550003","DOI":"10.1142\/S0219455415500030","article-title":"Bridge damage identification from moving load induced deflection based on wavelet transform and Lipschitz exponent","volume":"16","author":"Yu","year":"2016","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"321","DOI":"10.12989\/imm.2010.3.4.321","article-title":"Identification of beam crack using the dynamic response of a moving spring-mass unit","volume":"3","author":"An","year":"2010","journal-title":"Interact. Multiscale Mech."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.euromechsol.2012.12.012","article-title":"Multiple cracks detection in a beam subjected to a moving load using wavelet analysis combined with factorial design","volume":"40","author":"Khorram","year":"2013","journal-title":"Eur. J. Mech. A Solids"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.ijengsci.2011.10.001","article-title":"Comparison studies between two wavelet based crack detection methods of a beam subjected to a moving load","volume":"51","author":"Khorram","year":"2012","journal-title":"Int. J. Eng. Sci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"854","DOI":"10.4028\/www.scientific.net\/KEM.569-570.854","article-title":"Numerical studies on wavelet-based crack detection based on velocity response of a beam subjecting to moving load","volume":"569\u2013570","author":"Zhang","year":"2013","journal-title":"Key Eng. Mater."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"4455","DOI":"10.1016\/j.jsv.2010.05.005","article-title":"Multi-cracks detection of a beam-like structure based on the on-vehicle vibration signal and wavelet analysis","volume":"329","author":"Nguyen","year":"2010","journal-title":"J. Sound Vib."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.engstruct.2003.08.009","article-title":"Applications of wavelet transforms to damage detection in frame structures","volume":"26","author":"Ovanesova","year":"2004","journal-title":"Eng. Struct."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.ymssp.2012.02.002","article-title":"Damage identification of a target substructure with moving load excitation","volume":"30","author":"Li","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"3601","DOI":"10.1177\/1077546314564587","article-title":"Moving load-induced response of damaged beam and its application in damage localization","volume":"22","author":"He","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"81","DOI":"10.12989\/sem.2011.38.1.081","article-title":"Wavelet-based damage detection method for a beam-type structure carrying moving mass","volume":"38","year":"2011","journal-title":"Struct. Eng. Mech."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Daubechies, I. (1992). Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611970104"},{"key":"ref_89","unstructured":"Gao, R.X., and Yan, R.Q. (2011). Wavelets\u2014Theory and Applications for Manufacturing, Springer Science & Business Media."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Cao, M.S., Ding, Y.J., Ren, W.X., Wang, Q., Ragulskis, M., and Ding, Z.C. (2017). Hierarchical wavelet-aided neural intelligent identification of structural damage in noisy conditions. Appl. Sci., 7.","DOI":"10.3390\/app7040391"},{"key":"ref_91","first-page":"2693","article-title":"Study on parameters for identification of wavelet packet energy spectrum for structural damage alarming","volume":"163\u2013167","author":"Sun","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1002\/cjg2.708","article-title":"A method of detecting seismic singularities using combined wavelet with fractal","volume":"48","author":"Cao","year":"2005","journal-title":"Chin. J. Geophys."},{"key":"ref_93","first-page":"43","article-title":"Damage detection optimization using wavelet multiresolution analysis and genetic algorithm","volume":"2","author":"Ravanfar","year":"2016","journal-title":"Dyn. Civ. Struct."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.4028\/www.scientific.net\/AMR.594-597.1105","article-title":"Application of wavelet packet transform and neural network to detect damage of elastic thin plate","volume":"594\u2013597","author":"Xie","year":"2012","journal-title":"Adv. Mater. Res."},{"key":"ref_95","first-page":"1537","article-title":"Damage detection in beam-like structure based on wavelet packet","volume":"6","author":"Koohdaragh","year":"2011","journal-title":"Sci. Res. Essays"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"065021","DOI":"10.1088\/0964-1726\/19\/6\/065021","article-title":"Smart aggregate based damage detection of circular RC columns under cyclic combined loading","volume":"19","author":"Moslehy","year":"2010","journal-title":"Smart Mater. Struct."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/978-3-642-03718-4_7","article-title":"Structural damage localization of steel arch bridge based on wavelet packet transform","volume":"114","author":"Guo","year":"2012","journal-title":"Softw. Eng. Knowl. Eng. Theory Pract."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"285","DOI":"10.4028\/www.scientific.net\/KEM.413-414.285","article-title":"Studies on wavelet packet-based crack detection for a beam under the moving load","volume":"413\u2013414","author":"Zhang","year":"2009","journal-title":"Key Eng. Mater."},{"key":"ref_99","first-page":"1671","article-title":"Damage identification for bridge based on local sample entropy of wavelet packet frequency band","volume":"15","author":"Sun","year":"2015","journal-title":"Sci. Technol. Eng."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.ymssp.2006.03.013","article-title":"Vibration-based damage detection in composite wingbox structures by HHT","volume":"21","author":"Chen","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/asmb.501","article-title":"Applications of Hilbert-Huang transform to non-stationary financial time series analysis","volume":"19","author":"Huang","year":"2003","journal-title":"Appl. Stoch. Models Bus. Ind."},{"key":"ref_103","unstructured":"Quek, S.T., Tua, P.S., and Wang, Q. (2005). Comparison of Hilbert-Huang, wavelet, and Fourier transforms for selected applications. The Hilbert\u2013Huang Transform in Engineering, CRC Press."},{"key":"ref_104","first-page":"317954","article-title":"Application of Hilbert-Huang transform in structural health monitoring: A state-of-the-art review","volume":"2014","author":"Chen","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"141","DOI":"10.12989\/sss.2006.2.2.141","article-title":"HHT method for system identification and damage detection: An experimental study","volume":"2","author":"Zhou","year":"2006","journal-title":"Smart Struct. Syst."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1088\/0964-1726\/12\/3\/316","article-title":"Detecting anomalies in beams and plate based on the Hilbert-Huang transform of real signals","volume":"12","author":"Quek","year":"2003","journal-title":"Smart Mater. Struct."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s12206-008-1110-5","article-title":"Hilbert-Huang transform and marginal spectrum for detection and diagnosis of localized defects in roller bearings","volume":"23","author":"Li","year":"2009","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1061\/(ASCE)0733-9399(2004)130:1(85)","article-title":"Hilbert-Huang based approach for structural damage detection","volume":"130","author":"Yang","year":"2004","journal-title":"J. Eng. Mech."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1006\/jsvi.1997.1182","article-title":"Non-linear free vibration identification via the Hilbert transform","volume":"208","author":"Feldman","year":"1997","journal-title":"J. Sound Vib."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1155\/2012\/804590","article-title":"Empirical Mode Decomposition of the acceleration response of a prismatic beam subject to a moving load to identify multiple damage locations","volume":"19","author":"Meredith","year":"2012","journal-title":"Shock Vib."},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Bradley, M., Gonz\u00e1lez, A., and Hester, D. (2010). Analysis of the structural response to a moving load using empirical mode decomposition. Bridge Maintenance, Safety, Management and Life-Cycle Optimization, Proceedings of the 5th International IABMAS Conference, Philadelphia, PA, USA, 11\u201315 July 2010, Taylor & Francis Group. Paper 117.","DOI":"10.1201\/b10430-49"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.ymssp.2015.05.027","article-title":"Identification of sudden stiffness changes in the acceleration response of a bridge to moving loads using ensemble empirical mode decomposition","volume":"66\u201367","author":"Aied","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"984","DOI":"10.4028\/www.scientific.net\/AMM.166-169.984","article-title":"Damage detection of simply supported beam under effect of moving load by Hilbert-Huang transform","volume":"166\u2013169","author":"Liu","year":"2012","journal-title":"Appl. Mech. Mater."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.ymssp.2011.06.018","article-title":"Damage detection in structures under traveling loads by Hilbert-Huang transform","volume":"28","author":"Roveri","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijmecsci.2016.11.014","article-title":"Vibration and multi-crack identification of Timoshenko beams under moving mass using the differential quadrature method","volume":"120","author":"Chouiyakh","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.ymssp.2014.09.014","article-title":"Damage detection of shear connectors under moving loads with relative displacement measurements","volume":"60\u201361","author":"Li","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1111\/0885-9507.00151","article-title":"Convergence variability and population sizing in micro-genetic algorithms","volume":"14","author":"Benekohal","year":"1999","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1006\/jsvi.1996.0416","article-title":"An application of genetic algorithms to identify damage in elastic structures","volume":"195","author":"Mares","year":"1996","journal-title":"J. Sound Vib."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1016\/S0045-7949(01)00027-X","article-title":"Genetic algorithm in structural damage detection","volume":"79","author":"Chou","year":"2001","journal-title":"Comput. Struct."},{"key":"ref_121","first-page":"1942","article-title":"Particle swarm optimization","volume":"4","author":"Kennedy","year":"2011","journal-title":"Encycl. Mach. Learn."},{"key":"ref_122","unstructured":"Eberhart, R.C., and Kennedy, J. (1995, January 4\u20136). A new optimizer using particle swarm theory. Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1016\/j.asoc.2012.03.050","article-title":"Damage detection based on improved particle swarm optimization using vibration data","volume":"12","author":"Kang","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_124","unstructured":"Schalkoff, R.J. (1997). Artificial Neural Networks, McGraw-Hill."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/0045-7949(92)90132-J","article-title":"Use of neural networks in detection of structural damage","volume":"42","author":"Wu","year":"1992","journal-title":"Comput. Struct."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1007\/s12205-014-2161-z","article-title":"Optimal reconstruction of the damage distribution in bridge decks by measuring the noisy response induced by traffic loads","volume":"19","author":"Rus","year":"2015","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s12205-008-0391-7","article-title":"Stiffness assessment of bridge decks repaired by steel plates using an advanced system identification method","volume":"12","author":"Lee","year":"2008","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_128","doi-asserted-by":"crossref","unstructured":"Lee, S.Y., Noh, M.H., Jang, H.T., and Park, T. (2008, January 10\u201312). Nondestructive evaluation of strengthened decks using a microgenetic algorithm. Proceedings of the Asia Simulation Conference\u20147th International Conference on System Simulation and Scientific Computing, Beijing, China.","DOI":"10.1109\/ASC-ICSC.2008.4675624"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1061\/(ASCE)1084-0702(2009)14:5(355)","article-title":"Identification of a distribution of stiffness reduction in reinforced concrete slab bridges subjected to moving loads","volume":"14","author":"Park","year":"2009","journal-title":"J. Bridge Eng."},{"key":"ref_130","unstructured":"G\u00f6kda\u011f, H. (2012, January 26\u201330). Particle swarm optimization based damage detection method for beam type structures subject to moving vehicle. Proceedings of the 2012 World Congress on Advances in Civil, Environmental, and Materials Research, Seoul, Korea."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"114","DOI":"10.3139\/120.110412","article-title":"A crack identification approach for beam-like structures under moving vehicle using particle swarm optimization","volume":"55","year":"2013","journal-title":"Mater. Test."},{"key":"ref_132","first-page":"634217","article-title":"A crack identification method for bridge type structures under vehicular load using wavelet transform and particle swarm optimization","volume":"2013","year":"2013","journal-title":"Adv. Acoust. Vib."},{"key":"ref_133","first-page":"1","article-title":"Structural damage detection for beams subject to moving load using PSO algorithms","volume":"5","year":"2013","journal-title":"Int. J. Eng. Appl. Sci."},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Parsopoulos, K.E. (2010). Particle Swarm Optimization and Intelligence: Advances and Applications, IGI Global.","DOI":"10.4018\/978-1-61520-666-7"},{"key":"ref_135","unstructured":"Shi, Y., and Eberhart, R. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, Anchorage, AK, USA."},{"key":"ref_136","unstructured":"Shi, Y., and Eberhart, R.C. (1999, January 6\u20139). Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation, Washington, DC, USA."},{"key":"ref_137","unstructured":"Zheng, Y.L., Ma, L.H., Zhang, L.Y., and Qian, J.X. (2003, January 5). On the convergence analysis and parameter selection in particle swarm optimization. Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, Xi\u2019an, China."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm-explosion, stability, and convergence in a multidimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_139","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1080\/17415977.2012.727086","article-title":"A bivariate Gaussian function approach for inverse cracks identification of forced-vibrating bridge decks","volume":"21","author":"Noh","year":"2013","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_140","first-page":"146802","article-title":"Damage detection of a continuous bridge from response of a moving vehicle","volume":"2014","author":"Li","year":"2014","journal-title":"Shock Vib."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"61","DOI":"10.4067\/S0718-50732014000100004","article-title":"Structural damage detection: Comparison between GA and PSO techniques","volume":"29","author":"Barrera","year":"2014","journal-title":"Rev. Ing. Constr."},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1080\/17415977.2010.500381","article-title":"Application of a hybrid of particle swarm and genetic algorithm for structural damage detection","volume":"18","author":"Sandesh","year":"2010","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1016\/j.proeng.2016.05.175","article-title":"Response of damaged structure to high speed mass","volume":"144","author":"Jena","year":"2016","journal-title":"Procedia Eng."},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"2198","DOI":"10.1016\/j.ymssp.2006.10.002","article-title":"Development in vibration-based structural damage detection technique","volume":"21","author":"Yan","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_145","unstructured":"Waltz, E., and Llinas, J. (1990). Multisensor Data Fusion, Artech house."},{"key":"ref_146","doi-asserted-by":"crossref","unstructured":"Hall, D.L., and Llinas, J. (2001). Multisensor Data Fusion, CRC Press.","DOI":"10.1201\/9781420038545"},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.inffus.2011.08.001","article-title":"Multisensor data fusion: A review of the state-of-the-art","volume":"14","author":"Khaleghi","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/5.554205","article-title":"An introduction to multisensor data fusion","volume":"85","author":"Hall","year":"1997","journal-title":"Proc. IEEE"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/463\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:28:14Z","timestamp":1760185694000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,23]]},"references-count":148,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["s19030463"],"URL":"https:\/\/doi.org\/10.3390\/s19030463","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,23]]}}}