Early estimation of the long-term deflection of reinforced concrete beams using surrogate models

Ngoc Mai Nguyen, Wei Chih Wang, Minh-Tu Cao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper describes the development and testing of a novel artificial intelligence-based inference model for the early prediction of long-term deflection in RC beams, which is a critical but onerous task for civil engineers. This model, called WFR-FBI-LSSVR, integrates wrapper-based feature refinement (WFR) with the forensic-based investigation (FBI) algorithm and the least squares support vector regression (LSSVR) technique. In this model, the FBI algorithm performs the optimization process to gradually fine-tune LSSVR's hyper-parameter values and wrapper-refined features, while LSSVR uses the received potential hyper-parameter values (γ and C) and sets of features to build comparative inference models, which are used to generate prediction values that are then used to calculate the objective function values of FBI. A comprehensive survey of the literature collected data on a wide range of settings to improve the construction of WFR-FBI-LSSVR and verify its performance. The statistical results of 10-fold cross-validation confirmed WFR-FBI-LSSVR as significantly more accurate than several widely used AI models and mathematical approaches, achieving the best values in terms of root mean square error (RMSE = 7.86 mm), mean absolute percentage error (MAPE = 15.21 %), and coefficient of determination (R2 = 0.908). The calculated prediction-to-actual value ratio further validated the robustness of WFR-FBI-LSSVR with an average ratio value of 1.01, which was the closest value to 1 achieved among the models and approaches compared in this study. In summary, this paper contributes a novel free-formulae prediction model for researchers and civil engineers to accurately predict long-term deflection in RC beams.

Original languageEnglish
Article number130670
JournalConstruction and Building Materials
StatePublished - 17 Mar 2023


  • Forensic-based investigation
  • Least square support vector regression
  • Long-term deflection
  • Reinforced concrete beams
  • Wrapper feature refinement


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