Prediction of long-term deflections of reinforced-concrete members using a novel swarm optimized extreme gradient boosting machine

Hieu Nguyen, Ngoc Mai Nguyen, Minh Tu Cao, Nhat Duc Hoang, Xuan Linh Tran*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


During the life cycle of buildings and infrastructure systems, the deflection of reinforced-concrete members generally increases due to both internal and external factors. Accurate forecasting of long-term deflection of these members can significantly enhance the effectiveness of structural maintenance processes. This research develops a hybrid data-driven method which employs the extreme gradient boosting machine and the particle swarm optimization metaheuristic for predicting long-term deflections of reinforced-concrete members. The former, a machine learning technique, generalizes a non-linear mapping function that helps to infer long-term deflection results from the input data. The later, a swarm-based metaheuristic, aims at optimizing the machine learning model by fine-tuning its hyper-parameters. The proposed hybridization of machine learning and swarm intelligence is constructed and verified by a dataset consisting of 217 experiments. The experiment results, supported by statistical tests, point out that the hybrid framework is able to attain good predictive performances with average root-mean-square error of 11.38 (a reduction of 17.4%), and average coefficient of determination of 0.88 (an increase of 6.0%) compared to the non-hybrid model. These results also outperform those obtained by other popular techniques, including Backpropagation Neural Networks and Regression Tree in several popular benchmarks, such as root-mean-square error, mean absolute percentage error, and the coefficient of determination R2. This is backed up by statistical tests with the level of significance α= 0.05. Therefore, the newly developed model can be a promising tool to assist civil engineers in forecasting deflections of reinforced-concrete members.

Original languageEnglish
Pages (from-to)1255-1267
Number of pages13
JournalEngineering with Computers
StatePublished - Jun 2022


  • Concrete members
  • Extreme gradient boosting
  • Long-term deflection
  • Machine learning
  • Swarm optimization


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