{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T21:55:53Z","timestamp":1777931753640,"version":"3.51.4"},"reference-count":50,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:00:00Z","timestamp":1584576000000},"content-version":"vor","delay-in-days":47,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"name":"University of Danang - University of Science and Technology","award":["T2019-02-62"],"award-info":[{"award-number":["T2019-02-62"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Prediction of deflections of reinforced concrete (RC) flexural structures is vital to evaluate the workability and safety of structures during its life cycle. Empirical methods are limited to predict a long-term deflection of RC structures because they are difficult to consider all influencing factors. This study presents data-driven machine learning (ML) models to early predict the long-term deflections in RC structures. An experimental dataset was used to build and evaluate single and ensemble ML models. The models were trained and tested using the stratified 10-fold cross-validation algorithm. Analytical results revealed that the ML model is effective in predicting the deflection of RC structures with good accuracy of 0.972 in correlation coefficient (R), 8.190 mm in root mean square error (RMSE), 4.597 mm in mean absolute error (MAE), and 16.749% in mean absolute percentage error (MAPE). In performance comparison against with empirical methods, the prediction accuracy of the ML model improved significantly up to 66.41% in the RMSE and up to 82.04% in the MAE. As a contribution, this study proposed the effective ML model to facilitate designers in early forecasting long-term deflections in RC structures and evaluating their long-term serviceability and safety.<\/jats:p>","DOI":"10.1093\/jcde\/qwaa010","type":"journal-article","created":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T21:16:43Z","timestamp":1580246203000},"page":"95-106","source":"Crossref","is-referenced-by-count":27,"title":["Machine learning for predicting long-term deflections in reinforce concrete flexural structures"],"prefix":"10.1093","volume":"7","author":[{"given":"Anh-Duc","family":"Pham","sequence":"first","affiliation":[{"name":"Faculty of Project Management, The University of Danang \u2013 University of Science and Technology, 54 Nguyen Luong Bang, Danang 550000, Vietnam"}]},{"given":"Ngoc-Tri","family":"Ngo","sequence":"first","affiliation":[{"name":"Faculty of Project Management, The University of Danang \u2013 University of Science and Technology, 54 Nguyen Luong Bang, Danang 550000, Vietnam"}]},{"given":"Thi-Kha","family":"Nguyen","sequence":"first","affiliation":[{"name":"Division of Civil Engineering, Faculty of Engineering and Agriculture, The University of Danang \u2013 Campus in Kontum, 704 Phan \u0110inh Phung, Kontum, Vietnam"}]}],"member":"286","published-online":{"date-parts":[[2020,3,19]]},"reference":[{"issue":"6","key":"2020042408254877900_bib2","first-page":"637","article-title":"Deflections of reinforced concrete flexural members","volume":"63","author":"ACI","year":"1966","journal-title":"Journal Proceedings"},{"key":"2020042408254877900_bib3","first-page":"168","article-title":"Long-term deflection of RC beams under constant loads","volume":"21","author":"Alwis","year":"1999","journal-title":"Engineering Structures"},{"key":"2020042408254877900_bib4","first-page":"49","article-title":"Improvement of the ACI method for calculation of deflections of reinforced concrete beams","volume":"7","author":"Ara\u00fajo","year":"2005","journal-title":"Teoria e Pr\u00e1tica na Engenharia Civil"},{"issue":"34","key":"2020042408254877900_bib5","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1680\/macr.1982.34.121.203","article-title":"Long term deflections of reinforced concrete beams","volume":"121","author":"Bakoss","year":"1982","journal-title":"Magazine of Concrete Research"},{"key":"2020042408254877900_bib6","author":"Beton","year":"1993","journal-title":"CEB-FIP model code 1990"},{"key":"2020042408254877900_bib7","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.jobe.2018.07.021","article-title":"Parametric analysis of external and internal factors influence on building energy performance using non-linear multivariate regression models","volume":"20","author":"Bilous","year":"2018","journal-title":"Journal of Building Engineering"},{"key":"2020042408254877900_bib8","author":"Branson","year":"1977","journal-title":"Deformation of concrete structures"},{"issue":"2","key":"2020042408254877900_bib9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF00058655","article-title":"Bagging predictors","volume":"24","author":"Breiman","year":"1996","journal-title":"Machine Learning"},{"issue":"4","key":"2020042408254877900_bib10","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.jcde.2016.06.002","article-title":"Data-mining modeling for the prediction of wear on forming-taps in the threading of steel components","volume":"3","author":"Bustillo","year":"2016","journal-title":"Journal of Computational Design and Engineering"},{"key":"2020042408254877900_bib11","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.autcon.2012.07.004","article-title":"High-performance concrete compressive strength prediction using time-weighted evolutionary fuzzy support vector machines inference model","volume":"28","author":"Cheng","year":"2012","journal-title":"Automation in Construction"},{"key":"2020042408254877900_bib12","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.enbuild.2019.04.017","article-title":"Continuous-time Bayesian calibration of energy models using BIM and energy data","volume":"194","author":"Chong","year":"2019","journal-title":"Energy and Buildings"},{"key":"2020042408254877900_bib13","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.engappai.2016.09.008","article-title":"The use of artificial intelligence combiners for modeling steel pitting risk and corrosion rate","volume":"65","author":"Chou","year":"2016","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"2020042408254877900_bib14","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.engappai.2016.09.008","article-title":"The use of artificial intelligence combiners for modeling steel pitting risk and corrosion rate","volume":"65","author":"Chou","year":"2017","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"2020042408254877900_bib15","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.conbuildmat.2013.08.078","article-title":"Enhanced artificial intelligence for ensemble approach to predicting high performance concrete compressive strength","volume":"49","author":"Chou","year":"2013","journal-title":"Construction and Building Materials"},{"key":"2020042408254877900_bib16","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/j.conbuildmat.2014.09.054","article-title":"Machine learning in concrete strength simulations: Multi-nation data analytics","volume":"73","author":"Chou","year":"2014","journal-title":"Construction and Building Materials"},{"key":"2020042408254877900_bib17","first-page":"(pp. 1","author":"Dietterich","year":"2000","journal-title":"Proceedings of the First International Workshop on Ensemble Methods in Machine Learning, Multiple Classifier Systems. MCS 2000, Cagliari, Italy, 21\u201323 June 2000"},{"key":"2020042408254877900_bib18","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.jhydrol.2012.11.015","article-title":"Advancing monthly streamflow prediction accuracy of CART models using ensemble learning paradigms","volume":"477","author":"Erdal","year":"2013","journal-title":"Journal of Hydrology"},{"issue":"1","key":"2020042408254877900_bib19","first-page":"88","article-title":"Long-term sustained loading tests on reinforced concrete beams: A selected data base","volume":"88","author":"Espion","year":"1988","journal-title":"Bulletin du Service G\u00e9nie Civil"},{"key":"2020042408254877900_bib20","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.strusafe.2017.03.003","article-title":"Bootstrapped Artificial Neural Networks for the seismic analysis of structural systems","volume":"67","author":"Ferrario","year":"2017","journal-title":"Structural Safety"},{"issue":"1","key":"2020042408254877900_bib21","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s12205-016-1078-0","article-title":"Multiple crack identification in Euler beams using extreme learning machine","volume":"21","author":"Ghadimi","year":"2017","journal-title":"KSCE Journal of Civil Engineering"},{"key":"2020042408254877900_bib22","author":"Ghali","year":"1986","journal-title":"Concrete structure: Stress and deformation"},{"issue":"6","key":"2020042408254877900_bib23","first-page":"1027","article-title":"Deflection calculation for reinforced concrete structures\u2014why we sometimes get it wrong","volume":"96","author":"Gilbert","year":"1999","journal-title":"American Concrete Institute"},{"issue":"3","key":"2020042408254877900_bib24","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s11043-012-9184-y","article-title":"Long-term deflections of reinforced concrete elements: Accuracy analysis of predictions by different methods","volume":"17","author":"Gribniak","year":"2013","journal-title":"Mechanics of Time-Dependent Materials"},{"key":"2020042408254877900_bib25","doi-asserted-by":"crossref","first-page":"2175","DOI":"10.1016\/j.engstruct.2013.08.045","article-title":"Deflection prediction of reinforced concrete beams by design codes and computer simulation","volume":"56","author":"Gribniak","year":"2013","journal-title":"Engineering Structures"},{"issue":"1","key":"2020042408254877900_bib26","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1145\/1656274.1656278","article-title":"The WEKA data mining software: An update","volume":"11","author":"Hall","year":"2009","journal-title":"SIGKDD Explorations Newsletter"},{"key":"2020042408254877900_bib27","article-title":"The advantages of machine learning","author":"Innofactor","year":"2018"},{"issue":"4","key":"2020042408254877900_bib28","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.jcde.2017.04.003","article-title":"Self-organizing and error driven (SOED) artificial neural network for smarter classifications","volume":"4","author":"Jafari-Marandi","year":"2017","journal-title":"Journal of Computational Design and Engineering"},{"issue":"8","key":"2020042408254877900_bib29","first-page":"262","article-title":"Data analysis based on data mining algorithms using Weka workbench","volume":"5","author":"Jamil","year":"2016","journal-title":"International Journal of Engineering Sciences & Research Technology"},{"key":"2020042408254877900_bib30","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.jobe.2018.11.012","article-title":"Prediction of optimum heating timing based on artificial neural network by utilizing BEMS data","volume":"22","author":"Jang","year":"2019","journal-title":"Journal of Building Engineering"},{"key":"2020042408254877900_bib31","author":"John","year":"1998","journal-title":"Sequential minimal optimization: A fast algorithm for training support vector machines"},{"issue":"9","key":"2020042408254877900_bib32","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.advengsoft.2009.02.002","article-title":"Prediction of deflection of reinforced concrete shear walls","volume":"40","author":"Kara","year":"2009","journal-title":"Advances in Engineering Software"},{"issue":"3","key":"2020042408254877900_bib33","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/34.667881","article-title":"On combining classifiers","volume":"20","author":"Kittler","year":"1998","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"4","key":"2020042408254877900_bib34","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.jcde.2018.03.002","article-title":"Applying novelty detection to identify model element to IFC class misclassifications on architectural and infrastructure Building Information Models","volume":"5","author":"Koo","year":"2018","journal-title":"Journal of Computational Design and Engineering"},{"issue":"1","key":"2020042408254877900_bib35","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jcde.2018.04.002","article-title":"On the learning machine with compensatory aggregation based neurons in quaternionic domain","volume":"6","author":"Kumar","year":"2019","journal-title":"Journal of Computational Design and Engineering"},{"key":"2020042408254877900_bib36","doi-asserted-by":"crossref","DOI":"10.1002\/9781118914564","author":"Kuncheva","year":"2014","journal-title":"Combining pattern classifiers: Methods and algorithms"},{"issue":"4","key":"2020042408254877900_bib37","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1016\/j.jmva.2008.08.003","article-title":"Improved estimation in multiple linear regression models with measurement error and general constraint","volume":"100","author":"Liang","year":"2009","journal-title":"Journal of Multivariate Analysis"},{"issue":"3","key":"2020042408254877900_bib38","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.engstruct.2009.12.009","article-title":"Long-term deflections in cracked reinforced concrete flexural members","volume":"32","author":"Mar\u00ed","year":"2010","journal-title":"Engineering Structures"},{"issue":"2","key":"2020042408254877900_bib39","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/00401706.1991.10484804","article-title":"Factorial sampling plans for preliminary computational experiments","volume":"33","author":"Morris","year":"1991","journal-title":"Technometrics"},{"key":"2020042408254877900_bib40","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.jobe.2018.01.007","article-title":"Compressive strength prediction of environmentally friendly concrete using artificial neural networks","volume":"16","author":"Naderpour","year":"2018","journal-title":"Journal of Building Engineering"},{"key":"2020042408254877900_bib41","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.enbuild.2018.10.004","article-title":"Early predicting cooling loads for energy-efficient design in office buildings by machine learning","volume":"182","author":"Ngo","year":"2019","journal-title":"Energy and Buildings"},{"issue":"3","key":"2020042408254877900_bib42","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1007\/s12205-018-1290-1","article-title":"A bayesian learning method for structural damage assessment of Phase I IASC-ASCE benchmark problem","volume":"22","author":"Oh","year":"2018","journal-title":"KSCE Journal of Civil Engineering"},{"issue":"7","key":"2020042408254877900_bib1","doi-asserted-by":"crossref","first-page":"2220","DOI":"10.1061\/(ASCE)0733-9445(1994)120:7(2220)","article-title":"Long-term deflection of RC beams","volume":"120","author":"Olorunniwo","year":"1994","journal-title":"Journal of Structural and Construction Engineering"},{"key":"2020042408254877900_bib43","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.strusafe.2017.04.006","article-title":"An efficient reliability method combining adaptive Support Vector Machine and Monte Carlo simulation","volume":"67","author":"Pan","year":"2017","journal-title":"Structural Safety"},{"key":"2020042408254877900_bib44","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.proeng.2014.12.044","article-title":"The methodology for calculating deflections of reinforced concrete beams exposed to short duration uniform loading (based on nonlinear deformation model)","volume":"91","author":"Panfilov","year":"2014","journal-title":"Procedia Engineering"},{"issue":"4","key":"2020042408254877900_bib45","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1061\/(ASCE)0733-9445(2007)133:4(495)","article-title":"Short- and long-term deflections in reinforced, prestressed, and composite concrete beams","volume":"133","author":"Rodriguez-Gutierrez","year":"2007","journal-title":"Journal of Structural Engineering"},{"key":"2020042408254877900_bib46","author":"Rosenblatt","year":"1961","journal-title":"Principles of neurodynamics: Perceptrons and the theory of brain mechanisms"},{"issue":"3","key":"2020042408254877900_bib47","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","article-title":"A tutorial on support vector regression","volume":"14","author":"Smola","year":"2004","journal-title":"Statistics and Computing"},{"issue":"2","key":"2020042408254877900_bib48","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.jcde.2015.06.010","article-title":"E-quality control: A support vector machines approach","volume":"3","author":"Tseng","year":"2016","journal-title":"Journal of Computational Design and Engineering"},{"issue":"2","key":"2020042408254877900_bib49","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0893-6080(05)80023-1","article-title":"Stacked generalization","volume":"5","author":"Wolpert","year":"1992","journal-title":"Neural Networks"},{"key":"2020042408254877900_bib50","first-page":"212","article-title":"Predictions of concrete effects using age adjusted effective modulus method","volume":"69","author":"ZP","year":"1972","journal-title":"Journal of the American Concrete Institute"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/7\/1\/95\/33123058\/qwaa010.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/7\/1\/95\/33123058\/qwaa010.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T20:50:28Z","timestamp":1695675028000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/7\/1\/95\/5809436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,1]]},"references-count":50,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,3,19]]},"published-print":{"date-parts":[[2020,2,1]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwaa010","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,2]]},"published":{"date-parts":[[2020,2,1]]}}}