{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T01:32:45Z","timestamp":1776216765666,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T00:00:00Z","timestamp":1715212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major Science and Technology Program for Hubei Province","award":["2022AAA002"],"award-info":[{"award-number":["2022AAA002"]}]},{"name":"Major Science and Technology Program for Hubei Province","award":["41721003"],"award-info":[{"award-number":["41721003"]}]},{"name":"Major Science and Technology Program for Hubei Province","award":["42004017"],"award-info":[{"award-number":["42004017"]}]},{"name":"Innovative Research Group Project of the National Natural Science Foundation of China","award":["2022AAA002"],"award-info":[{"award-number":["2022AAA002"]}]},{"name":"Innovative Research Group Project of the National Natural Science Foundation of China","award":["41721003"],"award-info":[{"award-number":["41721003"]}]},{"name":"Innovative Research Group Project of the National Natural Science Foundation of China","award":["42004017"],"award-info":[{"award-number":["42004017"]}]},{"name":"National Natural Science Foundation of China","award":["2022AAA002"],"award-info":[{"award-number":["2022AAA002"]}]},{"name":"National Natural Science Foundation of China","award":["41721003"],"award-info":[{"award-number":["41721003"]}]},{"name":"National Natural Science Foundation of China","award":["42004017"],"award-info":[{"award-number":["42004017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>High-speed railway suspension bridges (HSRSBs) have been constructed with the new advancements in technology. The deformation prediction for HSRSBs is essential to their safety and maintenance. The conventional prediction methods are developed for bridges without high-speed railway. Different factors, including temperature (TEMP), time delay compensation (TDC), train live load (TLL), are considered in these methods. However, the train side (TS) and train instantaneous position (TIP) have a significant impact on deformation for HSRSBs, and they are not used in the prediction. More importantly, the coupling issue among different factors is so significant that it cannot be neglected. In this study, we propose a deformation prediction model based on a backpropagation (BP) neural network. This model uses different factors as model input, including TEMP, TDC, TLL, TS, and TIP. The coupling issue is addressed by using the new model. The new model was evaluated using a dataset of 10-day field measurements. It achieves a mean absolute error (MAE) of 8.81 mm, a mean relative error (MRE) of 9.82%, and coefficient of determination (R2) of 0.94. The new model will provide high-precision prediction for deformation and will be used in the development of an early warning system.<\/jats:p>","DOI":"10.3390\/rs16101687","type":"journal-article","created":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T10:31:16Z","timestamp":1715250676000},"page":"1687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Deformation Analysis and Prediction of a High-Speed Railway Suspension Bridge under Multi-Load Coupling"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3960-723X","authenticated-orcid":false,"given":"Simin","family":"Liu","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3267-9682","authenticated-orcid":false,"given":"Weiping","family":"Jiang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0068-0141","authenticated-orcid":false,"given":"Qusen","family":"Chen","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6512-4803","authenticated-orcid":false,"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4919-7241","authenticated-orcid":false,"given":"Xuyan","family":"Tan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430064, China"}]},{"given":"Ruiqi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Wuhan University, Wuhan 430072, China"}]},{"given":"Zhongtao","family":"Ye","sequence":"additional","affiliation":[{"name":"China Railway Bridge Science Research Institute, Ltd., Wuhan 430034, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1016\/j.istruc.2021.03.089","article-title":"Study on live load reduction factors of train for long span mul-titrack railway suspension bridges","volume":"32","author":"Li","year":"2021","journal-title":"Structures"},{"key":"ref_2","unstructured":"Xu, G.Y. (2020). Design of Long Span Railway Suspension Bridges, Shanghai Science and Technology Press. (In Chinese)."},{"key":"ref_3","unstructured":"Li, Y.J. (2019). Current Situation and Expectation of Construction Technology for HSP Suspension Bridge with Kilometers Span. China Railw., 1\u20138. (In Chinese)."},{"key":"ref_4","first-page":"14","article-title":"Displacement Characteristics at Girder End of Long Span Railway Suspension Bridge Under Design Loads","volume":"59","author":"Guo","year":"2019","journal-title":"Railway Eng."},{"key":"ref_5","first-page":"58","article-title":"Influence of Track Profile Setting on Dynamic Behavior of High-Speed Railway Suspension Bridge with Kilometer Span","volume":"42","author":"Tan","year":"2021","journal-title":"China Railw. Sci."},{"key":"ref_6","first-page":"58","article-title":"Analysis of the Train Running Safety of Multi\u2014Line Railway Cable\u2014Stayed Bridge","volume":"35","author":"Luo","year":"2018","journal-title":"J. Railw. Eng. Soc."},{"key":"ref_7","first-page":"1262","article-title":"Antiseismic performance of the world\u2019s first high-speed railway suspension bridge","volume":"42","author":"Zhao","year":"2021","journal-title":"J. Harbin Eng. Univ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"112393","DOI":"10.1016\/j.engstruct.2021.112393","article-title":"Effect of the main cable bending stiffness on flexural and torsional vibrations of suspension bridges: Analytical approach","volume":"240","author":"Zhang","year":"2021","journal-title":"Eng. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"045029","DOI":"10.1088\/1361-665X\/ab79b3","article-title":"Anomaly detection for large span bridges during operational phase using structural health monitoring data","volume":"29","author":"Xu","year":"2020","journal-title":"Smart Mater. Struct."},{"key":"ref_10","first-page":"13","article-title":"Feasibility Analysis of Applying of Suspension Bridge Type to Railway Bridges","volume":"47","author":"Tang","year":"2017","journal-title":"Bridge Constr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"04022055","DOI":"10.1061\/(ASCE)BE.1943-5592.0001892","article-title":"An Analytical Algorithm for Estimating the Deck\u2019s Maximum Deflection and Deck-End Rotation Angle of a Suspension Bridge under Live Load","volume":"27","author":"Zhang","year":"2022","journal-title":"J. Bridge Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"05017011","DOI":"10.1061\/(ASCE)BE.1943-5592.0001143","article-title":"Early Warning of Abnormal Train-Induced Vibrations for a Steel-Truss Arch Railway Bridge: Case Study","volume":"22","author":"Ding","year":"2017","journal-title":"J. Bridge Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"04020123","DOI":"10.1061\/(ASCE)CF.1943-5509.0001537","article-title":"Real-Time Dynamic Warning on Deflection Abnormity of Cable-Stayed Bridges Considering Operational Environment Variations","volume":"35","author":"Fan","year":"2020","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104168","DOI":"10.1016\/j.autcon.2022.104168","article-title":"Integrated structural health monitoring in bridge engineering","volume":"136","author":"He","year":"2022","journal-title":"Autom. Constr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"115261","DOI":"10.1016\/j.engstruct.2022.115261","article-title":"Prediction and early warning of wind-induced girder and tower vibration in cable-stayed bridges with machine learning-based approach","volume":"275","author":"Ye","year":"2023","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1177\/14759217211063424","article-title":"Sensor data-based probabilistic monitoring of time-history deflections of railway bridges induced by high-speed trains","volume":"21","author":"Lee","year":"2022","journal-title":"Struct. Health Monit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.ymssp.2019.01.026","article-title":"A comprehensive study of the thermal response of a long-span cable-stayed bridge: From monitoring phenomena to underlying mechanisms","volume":"124","author":"Zhou","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"04018075","DOI":"10.1061\/(ASCE)BE.1943-5592.0001279","article-title":"Fine temperature effect analysis-based time-varying dynamic properties evaluation of long-span suspension bridges in natural environments","volume":"23","author":"Meng","year":"2018","journal-title":"J. Bridge Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yang, K., Ding, Y., Sun, P., Zhao, H., and Geng, F. (2019). Modeling of temperature time-lag effect for concrete box-girder bridges. Appl. Sci., 9.","DOI":"10.3390\/app9163255"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109279","DOI":"10.1016\/j.measurement.2021.109279","article-title":"Modeling relationships for field strain data under thermal effects using functional data analysis","volume":"177","author":"Jiang","year":"2021","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"05018013","DOI":"10.1061\/(ASCE)BE.1943-5592.0001327","article-title":"Behavior Analysis and Early Warning of Girder Deflections of a Steel-Truss Arch Railway Bridge under the Effects of Temperature and Trains: Case Study","volume":"24","author":"Zhao","year":"2019","journal-title":"J. Bridge Eng."},{"key":"ref_22","first-page":"23","article-title":"Analysis of Global Static and Dynamic Property of Long-Span Steel Truss Girder Rail-cum-Road Suspension Bridge","volume":"50","author":"Liu","year":"2020","journal-title":"Bridge Constr."},{"key":"ref_23","first-page":"11","article-title":"Design Techniques and Exploration of High-Speed Railway Bridges in China","volume":"48","author":"Zhou","year":"2018","journal-title":"Bridge Constr."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"566","DOI":"10.4028\/www.scientific.net\/AMM.80-81.566","article-title":"Numerical Seismic Analysis of Simply-Supported Girder Railway Bridge under High-Speed Train Load","volume":"80\u201381","author":"Wang","year":"2011","journal-title":"Appl. Mech. Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1177\/14759217221116637","article-title":"Displacement response estimation of a cable-stayed bridge subjected to various loading conditions with one-dimensional residual convolutional autoencoder method","volume":"22","author":"Lei","year":"2023","journal-title":"Struct. Health Monit."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.eng.2017.11.001","article-title":"Developments and prospects of long-span high-speed railway bridge technologies in China","volume":"3","author":"Qin","year":"2017","journal-title":"Engineering"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1515\/jag-2019-0057","article-title":"Predicting displacement of bridge based on CEEMDAN-KELM model using GNSS monitoring data","volume":"14","author":"Fan","year":"2020","journal-title":"J. Appl. Geod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107888","DOI":"10.1016\/j.oceaneng.2020.107888","article-title":"Efficient prediction of wind and wave induced long-term extreme load effects of floating suspension bridges using artificial neural networks and support vector machines","volume":"217","author":"Xu","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.engstruct.2018.11.065","article-title":"Structural health monitoring of concrete dams using long-term air temperature for thermal effect simulation","volume":"180","author":"Kang","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Gu, C.S., Wu, B.Q., and Chen, Y.J. (2023). A High-robust displacement prediction model for super-high arch dams integrating wavelet de-noising and improved random forest. Water, 15.","DOI":"10.3390\/w15071271"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, Q., Jiang, W., Meng, X., Jiang, P., Wang, K., Xie, Y., and Ye, J. (2018). Vertical deformation monitoring of the suspension bridge tower using GNSS: A case study of the Forth Road Bridge in the UK. Remote Sens., 10.","DOI":"10.3390\/rs10030364"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"104504","DOI":"10.1016\/j.tust.2022.104504","article-title":"Prediction for the future mechanical behavior of underwater shield tunnel fusing deep learning algorithm on SHM data","volume":"125","author":"Tan","year":"2022","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1177\/1475921721996238","article-title":"Investigation on the data augmentation using machine learning algorithms in structural health monitoring information","volume":"20","author":"Tan","year":"2021","journal-title":"Struct. Health Monit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1016\/j.jrmge.2022.06.015","article-title":"Real-time prediction of mechanical behaviors of underwater shield tunnel structure using machine learning method based on structural health monitoring data","volume":"15","author":"Tan","year":"2023","journal-title":"J. Rock Mech. Geotech. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1007\/s11771-022-5124-4","article-title":"Parametric analysis on buffeting performance of a long-span high-speed railway suspension bridge","volume":"29","author":"Zhao","year":"2022","journal-title":"J. Cent. South Univ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"04019028","DOI":"10.1061\/(ASCE)BE.1943-5592.0001387","article-title":"Modeling and separation of thermal effects from cable-stayed bridge response","volume":"24","author":"Xu","year":"2019","journal-title":"J. Bridge Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1177\/1475921718773954","article-title":"Insights into temperature effects on structural deformation of a cable-stayed bridge based on structural health monitoring","volume":"18","author":"Zhou","year":"2018","journal-title":"Struct. Health Monit."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"106568","DOI":"10.1016\/j.ymssp.2019.106568","article-title":"Analytical solution to temperature-induced deformation of suspension bridges","volume":"139","author":"Zhou","year":"2020","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/10\/1687\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:42:53Z","timestamp":1760107373000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/10\/1687"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,9]]},"references-count":38,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["rs16101687"],"URL":"https:\/\/doi.org\/10.3390\/rs16101687","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,9]]}}}