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Applications of soft computing techniques for prediction of energy dissipation on stepped spillways

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Abstract

In this study, numbers type of soft computing including artificial neural network (ANN), support vector machine (SVM), multivariate adaptive regression splines (MARS), and group method of data handling (GMDH) were applied to model and predict energy dissipation of flow over stepped spillways. Results of ANN indicated that this model including hyperbolic tangent sigmoid as transfer function obtained coefficient of determination (R 2 = 0.917) and root-mean-square error (RMSE = 6.927) in testing stage. Results of development of SVM showed that developed model consists of radial basis function as kernel function achieved R 2 = 0.98 and RMSE = 2.61 in validation stage. Developed MARS model with R 2 = 0.99 and RMSE = 0.65 has suitable performance for predicating the energy dissipation. Results of developed GMDH model show with R 2 = 0.95 and RMSE = 5.4 has suitable performance for modeling energy dispersion. Reviewing of results of prepared models showed that all of them have suitable performance to predict the energy dissipation. However, MARS and SVM are more accurate than the others. Attention to structures of GMDH and MARS models declared that Froude number, drop number, and ratio of critical depth to height of step are the most important parameters for modeling energy dissipation. The best radial basis function was found that as best kernel function in developing the SVM.

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Abbreviations

ANN:

Artificial neural network

SVM:

Support vector machine

GMDH:

Group method of data handling

MARS:

Multivariate adaptive regression splines

DN:

Drop number

Fr:

Froude number

y c/h :

Ratio of critical depth to height of steps

ANFIS:

Adaptive neuro-fuzzy inference system

GEP:

Genetic expression programming

GA:

Genetic algorithm

PSO:

Particle swarm optimization

GP:

Genetic programming

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Authors and Affiliations

  1. Hydro-Structure Engineering, Water Engineering Department, Lorestan University, Khorramabad, Iran

    Abbas Parsaie

  2. Water Engineering Department, Lorestan University, Khorramabad, Iran

    Amir Hamzeh Haghiabi & Hasan Torabi

  3. Soil Conservation and Watershed Management Institute, Tehran, Iran

    Mojtaba Saneie

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  1. Abbas Parsaie
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  2. Amir Hamzeh Haghiabi
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  3. Mojtaba Saneie
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  4. Hasan Torabi
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Correspondence to Amir Hamzeh Haghiabi.

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Parsaie, A., Haghiabi, A.H., Saneie, M. et al. Applications of soft computing techniques for prediction of energy dissipation on stepped spillways. Neural Comput & Applic 29, 1393–1409 (2018). https://doi.org/10.1007/s00521-016-2667-z

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