Improved Levenberg–Marquardt backpropagation neural network by particle swarm and whale optimization algorithms to predict the deflection of RC beams


The aim of this study is to develop a novel computer-aided method for the prediction of the deflection of reinforced concrete beams (DRCB) under concentrated loads. To this end, in the present work, a Levenberg–Marquardt-based backpropagation novel neural network model, optimized by the whale optimization algorithm (WOA), called WOA-LMBPNN, has been developed. Specifically, a neural network, using the Levenberg–Marquardt backpropagation training algorithm with multiple hidden layers, was optimized by the WOA, aiming to obtain higher accuracy in predicting DRCB. For the training of the models, 120 experiments with the geometrical and mechanical properties of concrete beams were compiled using were used as the input parameters. Seven datasets with different number of input variables were investigated to evaluate the effect of the input variables on DRCB. For comparison purposes, another swarm optimization algorithm (i.e., particle swarm optimization—PSO) was also used to optimize the LMBPNN model (i.e., PSO-LMBPNN model). The results obtained by the PSO-LMBPNN and WOA-LMBPNN models are then compared based on the different datasets. Finally, the results revealed the effective role of the WOA, as well as the efficiency and robustness of the new hybrid WOA-LMBPNN model in predicting DRCB.

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Project supported by the Research Foundation of Education Bureau of Hunan Province(Grant No. 18A295).

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Zhao, J., Nguyen, H., Nguyen-Thoi, T. et al. Improved Levenberg–Marquardt backpropagation neural network by particle swarm and whale optimization algorithms to predict the deflection of RC beams. Engineering with Computers (2021).

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  • Reinforced concrete beam
  • Evolutionary computing
  • Artificial intelligence
  • Smart structures
  • Neural network computing
  • Computer-aided method