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Metaheuristic optimization of Levenberg–Marquardt-based artificial neural network using particle swarm optimization for prediction of foamed concrete compressive strength

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Abstract

Foamed concrete (FC) shows advantageous applications in civil engineering, such as reduction in dead loads, contribution to energy conservation, or decrease the construction phase labor cost. Compressive Strength is considered the most important factor in terms of FC mechanical properties. In recent years, Artificial Neural Network (ANN) is one of popular and effective machine learning models, which can be used to accurately predict the FCCS. However, ANN’s structure and parameters are normally chosen by experience. In this study, therefore, the objective is to use particle swarm optimization (PSO) metaheuristic optimization (one of the effective soft computing techniques) to optimize the parameters and structure of a Levenberg–Marquardt-based Artificial Neural Network (LMA-ANN) for accurate and quick prediction of the FCCS. A total of 375 data of experiments on FC gathered from the available literature were used to generate the training and testing datasets. Various validation criteria such as mean absolute error, root mean square error, and correlation coefficient (R) were used for the validation of the models. The results showed that the PSO-LMA-ANN algorithm is a highly efficient predictor of the FCCS, achieving the highest value of R up to 0.959 with the optimized [5-7-6-1] structure. An interpretation of the mixture components and the FCCS using Partial Dependence Plots was also performed to understand the effect of each input on the FCCS. The dry density was the most important parameter for the prediction of FCCS, followed by the water/cement ratio, foam volume, sand/cement ratio, and the testing age. The results of the present work might help in accurate and quick prediction of the FCCS and the design optimization process of the FC.

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  1. University of Transport Technology, Hanoi, 100000, Vietnam

    Hai-Bang Ly, May Huu Nguyen & Binh Thai Pham

  2. Civil and Environmental Engineering Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

    May Huu Nguyen

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Appendix 

Appendix 

See Figs. 17 , 18 and 19.

Fig. 17
figure 17

Results of parametric studies in terms of indicator Slope: a average Slope of training part, b standard deviation slope of training part; c average Slope of testing part, d standard deviation slope of testing part

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Fig. 18
figure 18

PDP curves of input variables using the LMA-ANN model

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Fig. 19
figure 19

Ratio of reduction in fluctuation using LMA-ANN-PSO compared to ANN. (for instance, for density variable, LMA-ANN-PSO has reduced two times the fluctuation in PDP curve compared to single ANN)

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Ly, HB., Nguyen, M.H. & Pham, B.T. Metaheuristic optimization of Levenberg–Marquardt-based artificial neural network using particle swarm optimization for prediction of foamed concrete compressive strength. Neural Comput & Applic 33, 17331–17351 (2021). https://doi.org/10.1007/s00521-021-06321-y

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