{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T04:06:43Z","timestamp":1773288403479,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T00:00:00Z","timestamp":1638403200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fund for Distinguished Young Scientists of Jiangsu Province","award":["BK20190013"],"award-info":[{"award-number":["BK20190013"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51978154, 52008099, and 51608258"],"award-info":[{"award-number":["51978154, 52008099, and 51608258"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fund for Jiangsu Graduate Research and Practice Innovation Program","award":["Grant KYCX21_0116"],"award-info":[{"award-number":["Grant KYCX21_0116"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A cable-stayed bridge is a typical symmetrical structure, and symmetry affects the deformation characteristics of such bridges. The main girder of a cable-stayed bridge will produce obvious deflection under the inducement of temperature. The regression model of temperature-induced deflection is hoped to provide a comparison value for bridge evaluation. Based on the temperature and deflection data obtained by the health monitoring system of a bridge, establishing the correlation model between temperature and temperature-induced deflection is meaningful. It is difficult to complete a high-quality model only by the girder temperature. The temperature features based on prior knowledge from the mechanical mechanism are used as the input information in this paper. At the same time, to strengthen the nonlinear ability of the model, this paper selects an independent recurrent neural network (IndRNN) for modeling. The deep learning neural network is compared with machine learning neural networks to prove the advancement of deep learning. When only the average temperature of the main girder is input, the calculation accuracy is not high regardless of whether the deep learning network or the machine learning network is used. When the temperature information extracted by the prior knowledge is input, the average error of IndRNN model is only 2.53%, less than those of BPNN model and traditional RNN. Combining knowledge with deep learning is undoubtedly the best modeling scheme. The deep learning model can provide a comparison value of bridge deformation for bridge management.<\/jats:p>","DOI":"10.3390\/sym13122293","type":"journal-article","created":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T02:56:14Z","timestamp":1638413774000},"page":"2293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Case Study of Deep Learning Model of Temperature-Induced Deflection of a Cable-Stayed Bridge Driven by Data Knowledge"],"prefix":"10.3390","volume":"13","author":[{"given":"Zixiang","family":"Yue","sequence":"first","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}]},{"given":"Youliang","family":"Ding","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}]},{"given":"Hanwei","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 210096, China"}]},{"given":"Zhiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"Shenzhen Express Engineering Consulting Co., Ltd., Shenzhen 518000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1631\/jzus.A20CSBE1","article-title":"Technical challenges in the construction of bridge-tunnel sea-crossing projects in China","volume":"21","author":"Song","year":"2020","journal-title":"J. Zhejiang Univ. Sci. A Appl. Phys. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108343","DOI":"10.1016\/j.measurement.2020.108343","article-title":"Structural health monitoring methods of cables in cable-stayed bridge: A review","volume":"168","author":"Zhang","year":"2020","journal-title":"Measurement"},{"key":"ref_3","first-page":"587","article-title":"A Study on the intelligent bridge with an advanced monitoring system and smart control techniques","volume":"19","author":"Miyamoto","year":"2017","journal-title":"Smart Struct. Syst."},{"key":"ref_4","first-page":"7","article-title":"Design of Structural Health Monitoring System for Hutong Changjiang River Bridge","volume":"47","author":"Yan","year":"2017","journal-title":"Bridge Constr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"445","DOI":"10.4028\/www.scientific.net\/AMM.488-489.445","article-title":"Parametric Study of Cable Deflection and Gravity Stiffness of Cable-Stayed Suspension Bridge","volume":"488","author":"Xia","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_6","first-page":"129","article-title":"Life-cycle simulation method of temperature field of steel box girder for Runyang cable-stayed bridge based on field monitoring data","volume":"46","author":"Ding","year":"2013","journal-title":"China Civ. Eng. J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Xu, X., Xu, C., Zhang, Y., and Wang, H. (2021). Preliminary Study on the Loss Laws of Bearing Capacity of Tunnel Structure. Symmetry, 13.","DOI":"10.3390\/sym13101951"},{"key":"ref_8","first-page":"54","article-title":"Study on Mechanical Characteristics of Railway Cable-Stayed Bridges with High and Low Towers","volume":"40","author":"Li","year":"2019","journal-title":"China Railw. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"04018070","DOI":"10.1061\/(ASCE)CF.1943-5509.0001212","article-title":"Correlation-Based Estimation Method for Cable-Stayed Bridge Girder Deflection Variability under Thermal Action","volume":"32","author":"Yang","year":"2018","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"111012","DOI":"10.1016\/j.engstruct.2020.111012","article-title":"General formulas for estimating temperature-induced mid-span vertical displacement of cable-stayed bridges","volume":"221","author":"Zhou","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pedraza, A., Deniz, O., and Bueno, G. (2021). On the Relationship between Generalization and Robustness to Adversarial Examples. Symmetry, 13.","DOI":"10.3390\/sym13050817"},{"key":"ref_12","first-page":"179","article-title":"On the performance of higher order moment neural computation","volume":"3","author":"Porter","year":"1995","journal-title":"Inf. Sci. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02312395","article-title":"A way to improve an architecture of neural network classifier for remote sensing applications","volume":"1","author":"Korczak","year":"1994","journal-title":"Neural Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ymssp.2019.05.063","article-title":"Effects of environmental and operational actions on the modal frequency variations of a sea-crossing bridge: A periodicity perspective","volume":"131","author":"Zhou","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","first-page":"109","article-title":"Deep learning-based recovery method for missing structural temperature data using LSTM network","volume":"7","author":"Liu","year":"2020","journal-title":"Struct. Monit. Maint."},{"key":"ref_16","first-page":"203","article-title":"Temperature monitoring and analysis of a long-span cable-stayed bridge during construction period","volume":"8","author":"Mei","year":"2021","journal-title":"Struct. Monit. Maint."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0924-0136(00)00498-2","article-title":"A BP-neural network predictor model for plastic injection molding process","volume":"103","author":"Sadeghi","year":"2000","journal-title":"J. Mater. Process. Technol."},{"key":"ref_18","first-page":"440","article-title":"Action potential initiation and backpropagation in neurons of the mammalian CNS","volume":"134","author":"Stuart","year":"2016","journal-title":"Trends Neurosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1162\/neco.1989.1.2.270","article-title":"A Learning Algorithm for Continually Running Fully Recurrent Neural Networks","volume":"1","author":"Williams","year":"1998","journal-title":"Neural Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2855","DOI":"10.1162\/neco_a_01134","article-title":"Applications of Recurrent Neural Networks in Environmental Factor Forecasting: A Review","volume":"30","author":"Chen","year":"2018","journal-title":"Neural Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/s12539-019-00351-w","article-title":"Plant miRNA-lncRNA Interaction Prediction with the Ensemble of CNN and IndRNN","volume":"12","author":"Zhang","year":"2020","journal-title":"Interdiscip. Sci. Comput. Life Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.patcog.2018.03.005","article-title":"Revisiting Batch Normalization for Practical Domain Adaptation","volume":"80","author":"Li","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"108341","DOI":"10.1016\/j.ymssp.2021.108341","article-title":"An ensemble classifier for vibration-based quality monitoring","volume":"165","author":"Yaghoubi","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_24","unstructured":"Yaghoubi, V., Liangliang, C., Wim, V.P., and Mathias, K. (2020). A novel multi-classifier information fusion based on Dempster\u2013Shafer theory: Application to vibration-based fault detection. Struct. Health Monit., 14759217211007130."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ymssp.2017.03.051","article-title":"Fault diagnosis for rotary machinery with selective ensemble neural networks","volume":"113","author":"Wang","year":"2018","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2293\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:38:40Z","timestamp":1760168320000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,2]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122293"],"URL":"https:\/\/doi.org\/10.3390\/sym13122293","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,2]]}}}