{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T16:33:58Z","timestamp":1770741238471,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T00:00:00Z","timestamp":1542758400000},"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":["51608136"],"award-info":[{"award-number":["51608136"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"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"}]},{"name":"Guangdong Provincial Highway Administration Bureau","award":["2017-1"],"award-info":[{"award-number":["2017-1"]}]},{"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>Deflection is one of the key indexes for the safety evaluation of bridge structures. In reality, due to the changing operational and environmental conditions, the deflection signals measured by structural health monitoring systems are greatly affected. These ambient changes in the system often cover subtle changes in the vibration signals caused by damage to the system. The deflection signals of prestressed concrete (PC) bridges are regarded as the superposition of different effects, including concrete shrinkage, creep, prestress loss, material deterioration, temperature effects, and live load effects. According to multiscale analysis theory of the long-term deflection signal, in this paper, an integrated machine learning algorithm that combines a Butterworth filter, ensemble empirical mode decomposition (EEMD), principle component analysis (PCA), and fast independent component analysis (FastICA) is proposed for separating the individual deflection components from a measured single channel deflection signal. The proposed algorithm consists of four stages: (1) the live load effect, which is a high-frequency signal, is separated from the raw signal by a Butterworth filter; (2) the EEMD algorithm is used to extract the intrinsic mode function (IMF) components; (3) these IMFs are utilized as input in the PCA model and some uncorrelated and dominant basis components are extracted; and (4) FastICA is applied to derive the independent deflection component. The simulated results show that each individual deflection component can be successfully separated when the noise level is under 10%. Verified by a practical application, the algorithm is feasible for extracting the structural deflection (including concrete shrinkage, creep, and prestress loss) only caused by structural damage or material deterioration.<\/jats:p>","DOI":"10.3390\/s18114070","type":"journal-article","created":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T09:18:25Z","timestamp":1542878305000},"page":"4070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["An Integrated Machine Learning Algorithm for Separating the Long-Term Deflection Data of Prestressed Concrete Bridges"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7946-1245","authenticated-orcid":false,"given":"Xijun","family":"Ye","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueshuai","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaxiong","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangchao","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Guangzhou University, Guangzhou 510006, 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"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, W.F., and Lian, D. (2014). Bridge Engineering Handbook: Construction and Maintenance, CRC Press.","DOI":"10.1201\/b16467"},{"key":"ref_2","first-page":"55","article-title":"Box girder bridge deflections: Why is the initial trend deceptive?","volume":"28","author":"Zich","year":"2006","journal-title":"ACI Concr. Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"04013027","DOI":"10.1061\/(ASCE)BE.1943-5592.0000564","article-title":"Deflection control of prestressed box girder bridges","volume":"19","author":"Elbadry","year":"2014","journal-title":"J. Bridge Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.engstruct.2013.02.003","article-title":"Construction assessment and long-term prediction of prestressed concrete bridges based on monitoring data","volume":"52","author":"Sousa","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1061\/(ASCE)ST.1943-541X.0000487","article-title":"Excessive Long-Time Deflections of Prestressed Box Girders I: Record-Span Bridge in Palau and Other Paradigms","volume":"138","author":"Yu","year":"2012","journal-title":"J. Struct. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1061\/(ASCE)ST.1943-541X.0000375","article-title":"Excessive long-time deflections of prestressed box girders. II: Numerical analysis and lessons learned","volume":"138","author":"Yu","year":"2012","journal-title":"J. Struct. Eng."},{"key":"ref_7","unstructured":"Leondes, C.T. (1993). Multiscale signal processing: From QMF To wavelet. International Series on Advances in Control and Dynamic Systems, Academic Press."},{"key":"ref_8","unstructured":"Pirner, M., and Fischer, O. (1997). Monitoring stresses in GRP extension of the Prague TV tower. DAMAS 97: Structural Damage Assessment Using Advanced signal Processing Procedures, University of Sheffield."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1098\/rsta.2006.1935","article-title":"Effects of Environmental and Operational Variability on Structural Health Monitoring","volume":"365","author":"Sohn","year":"2007","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1820","DOI":"10.1016\/j.engstruct.2005.05.013","article-title":"Prediction of vertical deflections for a long-span prestressed concrete bridge structure","volume":"27","author":"Robertson","year":"2005","journal-title":"Eng. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1061\/(ASCE)BE.1943-5592.0000233","article-title":"Numerical Evaluation of the Long-Term Behavior of Precast Continuous Bridge Decks","volume":"17","author":"Sousa","year":"2012","journal-title":"J. Bridge Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"05014002","DOI":"10.1061\/(ASCE)BE.1943-5592.0000604","article-title":"Assessment and Management of Concrete Bridges Supported by Monitoring Data-Based Finite-Element Modeling","volume":"19","author":"Sousa","year":"2014","journal-title":"J. Bridge Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.engstruct.2016.09.004","article-title":"Long-term performance of prestressed concrete bridges under the intertwined effects of concrete damage, static creep and traffic-induced cyclic creep","volume":"127","author":"Tong","year":"2016","journal-title":"Eng. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"04016053","DOI":"10.1061\/(ASCE)CF.1943-5509.0000909","article-title":"Deflection control of long-span PSC boxgirder bridge based on field monitoring and probabilistic FEA","volume":"30","author":"Guo","year":"2016","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"04018002","DOI":"10.1061\/(ASCE)BE.1943-5592.0001210","article-title":"Modeling for Assessment of Long-Term Behavior of Prestressed Concrete Box-Girder Bridges","volume":"23","author":"Huang","year":"2018","journal-title":"J. Bridge Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1139\/l00-050","article-title":"Two-year deflections of the Confederation Bridge","volume":"27","author":"Ghali","year":"2000","journal-title":"Can. J. Civ. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.ymssp.2012.08.026","article-title":"Long-term monitoring and data analysis of the Tamar Bridge","volume":"35","author":"Cross","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1080\/15732479.2014.951857","article-title":"Operational deformations in long-span bridges","volume":"11","author":"Brownjohn","year":"2015","journal-title":"Struct. Infrastruct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.engstruct.2005.09.001","article-title":"Long term vibration monitoring of an RC slab: Temperature and humidity effect","volume":"28","author":"Xia","year":"2006","journal-title":"Eng. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1016\/j.engstruct.2006.07.024","article-title":"Vibration-based damage monitoring in model plate-girder bridges under uncertain temperature conditions","volume":"29","author":"Kim","year":"2007","journal-title":"Eng. Struct."},{"key":"ref_21","unstructured":"Xia, H.W., Ni, Y.Q., Ko, J.M., and Wong, K.Y. (2010, January 10\u201312). Wavelet-based multi-resolution decomposition of long-term monitoring signal of in-service strain. Proceedings of the 2nd International Postgraduate Conference on Infrastructure and Environment, Hong Kong, China."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.compstruc.2012.05.003","article-title":"Reliability-based condition assessment of in-service bridges using mixture distribution models","volume":"106\u2013107","author":"Xia","year":"2012","journal-title":"Comput. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"491","DOI":"10.3390\/s18020491","article-title":"Statistical Analysis of Stress Signals from Bridge Monitoring by FBG System","volume":"18","author":"Ye","year":"2018","journal-title":"Sensors"},{"key":"ref_24","unstructured":"Smarsly, K., Dragos, K., and Wiggenbrock, J. (2016, January 5\u20138). Machine learning techniques for structural health monitoring. Proceedings of the 8th European Workshop on Structural Health Monitoring (EWSHM 2016), Bilbao, Spain."},{"key":"ref_25","first-page":"11","article-title":"Separation study of bridge deflection based on singular value decomposition","volume":"52","author":"Liu","year":"2013","journal-title":"Acta Sci. Nat. Univ. Sunyatseni"},{"key":"ref_26","first-page":"55","article-title":"A new method to separate temperature effect from long-term structural health monitoring data","volume":"27","author":"Liu","year":"2010","journal-title":"Eng. Mech."},{"key":"ref_27","first-page":"91","article-title":"Study on separation of bridge deflection temperature effect based on LS-SVM","volume":"34","author":"Yang","year":"2012","journal-title":"J. Chin. Railway Soc."},{"key":"ref_28","first-page":"71","article-title":"Separation of bridge temperature deflection effect based on M-LS-SVM","volume":"33","author":"Yang","year":"2014","journal-title":"J. Vib. Shock"},{"key":"ref_29","first-page":"1672","article-title":"Time series analysis and support vector machine for landslide displacement prediction","volume":"47","author":"Peng","year":"2013","journal-title":"J. Zhejiang Univ. Eng. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/j.ymssp.2004.12.002","article-title":"Structural damage diagnosis under varying environmental conditions-Part I: A linear analysis","volume":"19","author":"Yan","year":"2005","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1106\/104538902030904","article-title":"Statistical damage classification under changing environmental and operational conditions","volume":"13","author":"Sohn","year":"2003","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"15","DOI":"10.4018\/IJHCR.2016100102","article-title":"Butterworth Filter Application for Structural Health Monitoring","volume":"7","author":"Abdelgawad","year":"2016","journal-title":"Int. J. Handheld Comput. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/LSP.2003.821662","article-title":"Empirical mode decomposition as a filter bank","volume":"11","author":"Flandrin","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.jsv.2004.10.005","article-title":"An improved Hilbert Huang transform and its application in vibration signal analysis","volume":"286","author":"Peng","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2059","DOI":"10.1016\/j.ymssp.2009.04.002","article-title":"Analytical basics of the EMD: Two harmonics decomposition","volume":"23","author":"Feldman","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/14786440109462720","article-title":"On Lines and Planes of Closest Fit to Systems of Points in Space","volume":"2","author":"Pearson","year":"1901","journal-title":"Philos. Mag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1037\/h0071325","article-title":"Analysis of a complex of statistical variables into principal components","volume":"24","author":"Hotelling","year":"1933","journal-title":"J. Educ. Psychol."},{"key":"ref_40","first-page":"648097","article-title":"A bioinspired methodology based on an artiicial immune system for damage detection in structural health monitoring","volume":"501","author":"Anaya","year":"2015","journal-title":"Shock Vib."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1002\/stc.1540","article-title":"Damage classification in structural health monitoring using principal component analysis and self organizing maps","volume":"20","author":"Tibaduiza","year":"2012","journal-title":"Struct. Control Health Monit."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","article-title":"Independent component analysis: A new concept?","volume":"36","author":"Comon","year":"1994","journal-title":"Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0893-6080(00)00026-5","article-title":"Independent Component Analysis: Algorithms and applications","volume":"13","author":"Hyvarinen","year":"2000","journal-title":"Neural Netw."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1162\/neco.1997.9.7.1483","article-title":"A Fast Fixed-Point Algorithm for Independent Component Analysis","volume":"9","author":"Oja","year":"1997","journal-title":"Neural Comput."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ye, X.J., and Chen, B.C. Condition assessment of bridge structures based on a liquid level sensing system: Theory, verification and application. Arabian J. Sci. Eng., 2018.","DOI":"10.1007\/s13369-018-3425-6"},{"key":"ref_46","unstructured":"Ministry of Transport of the People\u2019s Republic of China (2015). General Specifications for Design of Highway Bridges and Culverts."},{"key":"ref_47","first-page":"94","article-title":"Study on the model of the fatigue-loaded vehicles in Guangzhou trestle bridges","volume":"32","author":"Wang","year":"2004","journal-title":"J. South China Univ. Technol. (Nat. Sci. Ed.)"},{"key":"ref_48","first-page":"209","article-title":"Design of concrete bridges for temperature gradients","volume":"75","author":"Priestley","year":"1978","journal-title":"ACI J."},{"key":"ref_49","unstructured":"Ministry of Transport of the People\u2019s Republic of China (2018). Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts."},{"key":"ref_50","first-page":"116","article-title":"Measured sustained deflection analysis of long-span prestressed concrete beam bridges","volume":"6","author":"Niu","year":"2008","journal-title":"Eng. Mech."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4070\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:31:10Z","timestamp":1760196670000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,21]]},"references-count":50,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["s18114070"],"URL":"https:\/\/doi.org\/10.3390\/s18114070","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,21]]}}}