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Frontiers of Structural and Civil Engineering

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 Authors: 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:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0600-0
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I2/374
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Reza ASHEGHI
Seyed Abbas HOSSEINI
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.
variable mean standard error standard deviation variation range
Q (ft3/s) 154.7 11.8 117.9 9.88–645.0
S (ft/ft) 0.002 0.0001 0.0011 0.0058–0.0003
V (ft/s) 2.851 0.095 0.949 0.56–5.01
d (ft) 1.428 0.049 0.490 0.34–3.13
D50 (mm) 8.852 0.929 9.38 0.40–45.50
Tab.1  Statistical description of input parameters for prediction of sediment loads
Fig.2  The proposed block procedure to find the optimum architecture topology.
ANN type training algorithm min RMSE no. of neuron corresponding topology layer activation transfer function R2 for randomized data sets
hidden output train test validate
MLP QN 0.289 9 5-5-4-1 Log HyT 0.91 0.92 0.93
GFFN MO 0. 201 9 5-4-5-1 HyT HyT 0.94 0.96 0.97
RBF LM 0.191 7 5-7-1 Log Log 0.96 0.97 0.98
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.
Target
output
network output RBF (validation data sets) calculated results
0.04–1.08 1.08–2.11 2.11–3.15 3.15–4.19 4.19–5.22 5.22–6.26 6.26–7.29 7.29–8.33 8.33–9.37 9.37–10.4 total true false CR (%)
0.04–1.08 9 0 0 0 0 0 0 0 0 0 9 9 0 100
1.08–2.11 0 4 1 0 0 0 0 0 0 0 5 3 2 75
2.11–3.15 0 0 0 0 0 0 0 0 0 0 0 0 0
3.15–4.19 0 0 0 0 0 0 0 0 0 0 0 0 0
4.19–5.22 0 0 0 0 1 0 0 0 0 0 1 1 0 100
5.22–6.26 0 0 0 0 0 0 0 0 0 0 0 0 0
6.26–7.29 0 0 0 0 0 0 0 0 0 0 0 0 0
7.29–8.33 0 0 0 0 0 0 1 1 0 0 2 1 1 50
8.33–9.37 0 0 0 0 0 0 0 0 0 0 0 0 0
9.37–10.4 0 0 0 0 0 0 0 0 1 1 2 1 1 50
note 9 3 2 0 1 0 1 1 1 1 19 16 3 84
target
output
network output RBF (test data sets) calculated results
0.01–1.89 1.89–3.77 3.77–5.65 5.65–7.53 7.53–9.41 9.41–11.29 11.29–13.17 13.17–15.05 15.05–16.93 >16.93 total true false CR (%)
0.01–1.89 12 1 0 0 0 0 0 0 0 0 13 12 1 92.3
1.89–3.77 0 4 2 0 0 0 0 0 0 0 6 4 2 66.7
3.77–5.65 0 0 1 1 0 0 0 0 0 0 2 1 1 50
5.65–7.53 0 0 0 1 1 0 0 0 0 0 2 1 1 50
7.53–9.41 0 0 0 0 1 0 0 0 0 0 1 1 0 100
9.41–11.29 0 0 0 0 0 0 0 0 0 0 0 0 0
11.29–13.17 0 0 0 0 0 0 0 0 0 0 0 0 0
13.17–15.05 0 0 0 0 0 0 0 0 0 0 0 0 0
15.05–16.93 0 0 0 0 0 0 0 0 0 0 0 0 0
>16.93 0 0 0 0 0 0 0 0 0 1 1 1 0 100
note 12 5 3 2 2 0 0 0 0 1 25 20 5 80
Tab.3  Confusion matrix of optimum RBF model
model CCR (%) CE (%)
test validate test validate
RBF 80 84 20 16
GFFN 80 79 20 21
MLP 65 68 35 32
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] ϕb= [12(θ0.05 )(θ0.5)] 0 0.11
Ackers and White [48] ϕb=[θ1.25Log(16.5θ /S)] 0 0.10
Wong and Parker [49] ϕb=3.97 (θ 0.0495) 1.5 7/19
Wilson [50] ϕb=12 (θ θc) 1.5 7/19
Paintal [51] ϕb=6.56 ×1018 θ16 0 0.14
Madsen [52] ϕb=[k(θθc)(θ0.50.7 θc0.5)] 0 0.11
Meyer-Peiter and Muler [53] ϕb=8 (fθθ c)1.5 12/19
Rottner [54] ϕb={(V (g( GS1)D 50)0.5) [0.667 (D50d) 0.67+ 0.14] 0.778 (D50d) 0.67}3 0 0.13
Van-Rijn [55] ϕb=[( 0.053 D50( g(G S1)θ 2) ( 1 3)) ( θ θc1)2.1] 12/19
Kalinske [56] qb=gdSD50 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.
Model MAPE RMSE MAD MSD VAF R2
MLP 6.98 0.289 0.93 0.127 81.56 0.93
GFFN 5.23 0.201 0.80 0.025 96.49 0.97
RBF 5.27 0.191 0.77 0.018 95.77 0.98
Nielsen [47] 18.08 7.673 1.75 0.463 26.38 0.11
Ackers and White [48] 20.82 8.517 2.09 1.05 23.16 0.10
Paintal [51] 14.07 4.291 1.73 0.365 35.22 0.14
Madsen [52] 17.20 6.424 1.73 0.533 27.06 0.11
Rottner [54] 15.92 4.348 1.72 0.517 30.88 0.13
Kalinske [56] 11.38 3.562 1.45 0.316 54.24 0.21
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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