Prediction of bed load sediments using different artificial neural network models

doi:10.1007/s11709-019-0600-0

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (2) : 374-386 https://doi.org/10.1007/s11709-019-0600-0

RESEARCH ARTICLE

Prediction of bed load sediments using different artificial neural network models

Reza ASHEGHI, Seyed Abbas HOSSEINI(

)

Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

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Abstract

Modeling and prediction of bed loads is an important but difficult issue in river engineering. The introduced empirical equations due to restricted applicability even in similar conditions provide different accuracies with each other and measured data. In this paper, three different artificial neural networks (ANNs) including multilayer percepterons, radial based function (RBF), and generalized feed forward neural network using five dominant parameters of bed load transport formulas for the Main Fork Red River in Idaho-USA were developed. The optimum models were found through 102 data sets of flow discharge, flow velocity, water surface slopes, flow depth, and mean grain size. The deficiency of empirical equations for this river by conducted comparison between measured and predicted values was approved where the ANN models presented more consistence and closer estimation to observed data. The coefficient of determination between measured and predicted values for empirical equations varied from 0.10 to 0.21 against the 0.93 to 0.98 in ANN models. The accuracy performance of all models was evaluated and interpreted using different statistical error criteria, analytical graphs and confusion matrixes. Although the ANN models predicted compatible outputs but the RBF with 79% correct classification rate corresponding to 0.191 network error was outperform than others.

Keywords bed load prediction artificial neural network modeling empirical equations

Corresponding Author(s): Seyed Abbas HOSSEINI

Just Accepted Date: 17 January 2020 Online First Date: 18 March 2020 Issue Date: 08 May 2020

Cite this article:

Reza ASHEGHI,Seyed Abbas HOSSEINI. Prediction of bed load sediments using different artificial neural network models[J]. Front. Struct. Civ. Eng., 2020, 14(2): 374-386.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-019-0600-0
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I2/374

Fig.1 Digital elevation map (DEM) of (a) studied area and (b) variation of cross section of river using USDA information for 3 years interval of the measurements.

Tab.1 Statistical description of input parameters for prediction of sediment loads

Fig.2 The proposed block procedure to find the optimum architecture topology.

Tab.2 Results of implemented training algorithms to assess the optimized ANN based model

Fig.3 Variation of calculated network RMSE for different training algorithms based on the number of neurons (the range of neurons for minimum observed error as well as used activation functions are given in rectangles and parentheses, respectively). (a) GFFN; (b) RBF; (c) MLP; (d) example of some tested structure to find the optimum GFFN model subjected to MO training algorithm and HyT activation function; (e) performance of optimized models corresponding to used learning rule in training stage in GFFN, (f) Performance of optimized models corresponding to used learning rule in training stage in RBF; (g) performance of optimized models corresponding to used learning rule in training stage in MLP.

Tab.3 Confusion matrix of optimum RBF model

Tab.4 Comparison of CCR and classification error of optimized models for validation and test data sets

researcher(s)	equation	misestimated data	R²
Nielsen [⁴⁷]	$ϕ b = [12 (θ − 0.05) (θ 0.5)]$	0	0.11
Ackers and White [⁴⁸]	$ϕ b = [θ 1.25 L o g (16.5 θ / S)]$	0	0.10
Wong and Parker [⁴⁹]	$ϕ b = 3.97 (θ − 0.0495) 1.5$	7/19	–
Wilson [⁵⁰]	$ϕ b = 12 (θ − θ c) 1.5$	7/19	–
Paintal [⁵¹]	$ϕ b = 6.56 × 1018 θ 16$	0	0.14
Madsen [⁵²]	$ϕ b = [k (θ − θ c) (θ 0.5 − 0.7 θ c 0.5)]$	0	0.11
Meyer-Peiter and Muler [⁵³]	$ϕ b = 8 (f θ − θ c) 1.5$	12/19	–
Rottner [⁵⁴]	$ϕ b = {(V (g (G S − 1) D 50) 0.5) [0.667 (D 50 d) 0.67 + 0.14] − 0.778 (D 50 d) 0.67} 3$	0	0.13
Van-Rijn [⁵⁵]	$ϕ b = [(0.053 D 50 (g (G S − 1) θ 2) (13)) (θ θ c − 1) 2.1]$	12/19	–
Kalinske [⁵⁶]	$q b = g d S D 50 f (τ C τ)$	0	0.21

Tab.5 Some of the tested bed load empirical equations in this study

Fig.4 (a) Comparing the predicted bed load values using ANN and empirical models; (b) scattering of predicted bed loads using ANN models regarding 1:1 line; (c) predicted bed loads using empirical equations.

Tab.6 Results of statistical criteria to evaluate the performance of used models

Fig.5 (a) Comparison of CR for ANN and empirical models; (b) comparison of AE for ANN and empirical models; (c) variation of CR values based on the used data sets in ANN models; (d) variation of AE values based on the used data sets in ANN models (The used colors are similar to those defined in Fig. 4).

Fig.6 Sensitivity analysis of ANN models to identify the contribution of input parameters on predicted bed loads (the used colors are similar to Fig. 4).

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