Neural network prediction of bed material load transport

Figures & data

Fig. 1 Estimated value of bed shear stress and critical shear stress.

Fig. 2 Neural network architecture.

Table 1  Descriptive statistics of the observations used in the analysis. Bed forms considered in the present analysis are: plane bed near or before initiation of motion (1), ripples (2), dunes (3), transition (4), plane bed (5), standing waves (6) and antidunes (7)

	Q (m^3/s)	b (m)	y (m)	Sf	d (m)	τ b (N/m^2)	τ c (N/m^2)	σ	Gs	ν (m^2/s)	C ppm by mass
Training data set
Mean	16.12	8.67	0.315	0.0045	0.0012	4.48	0.82	1.40	2.65	1.09E-06	3398.36
Standard deviation	67.227	29.26	0.629	0.0048	0.0024	5.06	1.90	0.39	0.03	1.24E-07	6257.11
Minimum	0.00059	0.131	0.0079	0.000045	0.00019	0.26	0.12	1	2.25	6.47E-07	3.71
Maximum	486.82	162.43	4.29	0.027	0.027	51.09	21.79	3.85	2.68	1.57E-06	52238
Count	1200	1200	1200	1200	1200	1200	1200	1200	1200	1200	1200
Testing data set
Mean	15.80	7.51	0.314	0.0044	0.0014	4.53	1.00	1.40	2.64	1.01E-06	3044.88
Standard deviation	70.04	26.52	0.667	0.0048	0.0028	5.66	2.32	0.42	0.03	1.21E-07	5385.15
Minimum	0.00091	0.134	0.013	0.000058	0.00019	0.29	0.14	1	2.25	6.89E-07	4.2
Maximum	451.39	140.22	4.24	0.0258	0.026	47.54	20.98	3.78	2.68	1.59E-06	36100
Count	567	567	567	567	567	567	567	567	567	567	567
Q: channel discharge; b: width of the channel; y: flow depth; S f : friction/energy slope; d: mean size of sediment; τb: bed shear stress; τc: critical shear stress or Shields' shear stress; σ. gradation coefficient of the sediment particles; G s : specific gravity; ν. viscosity; and C: bed material load transport (equation (1)(1)).

Fig. 3 ANN model results: (a) for training sets, (b) for test sets, and (c) for entire sets.

Fig. 4 Performance analyses of bed material load formulas.

Table 2  Statistical performance of bed material load transport formulas

Methods	R ^2	E		σ a
ANN model—training	0.977	0.807	0.103	0.298
ANN model—testing	0.957	0.754	0.129	0.316
ANN model—overall	0.969	0.723	0.134	0.326
Engelund and Hansen (1967)	0.659	0.597	0.268	0.756
Acaroglu (1968)	0.684	0.289	0.584	0.823
Graf (1971)	0.685	0.288	0.568	0.821
Shen and Hung (1972)	0.681	0.094	0.874	0.704
Ackers and White (1973)	0.772	0.669	0.156	0.627
Brownlie (1981)	0.78	0.689	0.442	0.814
Karim and Kennedy (1981)	0.44	0.324	0.831	0.752
Yang (1996)	0.543	0.161	0.341	0.652
Yang (2005)	0.6	0.236	0.543	0.614

Table 3  Input significance test of the variables

Variables	Connection weights	Garson's algorithm	Partial derivative	Ranking
Q	3.188	16.95	0.270	1
y	3.105	16.5	0.166	2
d	2.703	14.4	0.112	3
τ b	2.214	11.8	0.105	4
τ c	2.095	11.1	0.082	5
Sf	1.957	10.4	0.080	6
BF	1.191	6.3	0.058	7
B	0.946	5	0.058	8
V	0.729	3.9	0.033	9
Gs	0.469	2.5	0.025	10
σ	0.210	1.1	0.011	11

Table A1  Weight matrices

W 1											W 2
Q	ν	y	τb	BF	d	σ	Gs	b	Sf	τ c
−0.1558	−0.2773	1.0477	0.0129	0.2011	−0.2158	0.1744	−0.8004	−0.0097	−0.0665	−0.1336	−0.8695
0.0911	0.1230	−0.3697	0.0684	1.8339	0.1861	−0.2698	−0.0685	0.4674	−0.1077	−0.2067	0.2221
−0.2325	0.2858	−0.4104	0.4163	0.1193	−0.2689	−0.8905	−0.0381	−0.7755	0.7752	−0.1155	0.2097
−1.2946	0.4959	0.5904	0.5939	0.3196	−0.6002	−0.0756	−1.7632	−0.2341	−1.3411	0.8841	−0.2477
−1.1393	0.3146	0.0506	0.5158	1.1465	1.1357	0.0151	−0.2895	0.2894	1.3928	−0.2864	0.0997
−0.9666	−0.0274	−1.0328	0.5945	−0.9163	0.7381	−0.2802	−1.4654	0.0735	0.4512	−0.2167	0.0000
−0.3283	0.0803	5.6167	3.0315	1.4699	1.8563	−1.4297	−0.7516	0.8443	0.0298	0.2088	0.0815
−0.8896	0.3008	0.5761	−2.0237	0.0446	−0.3332	0.9142	0.2024	0.9183	0.2331	−1.0951	−0.0829
−0.3328	0.3336	−0.2417	−1.1195	0.1102	−0.0197	−1.7063	0.4604	0.6857	−1.0897	1.3110	−1.1683
0.8940	−0.0132	1.0262	−0.1982	−0.2299	−0.1648	−0.4126	0.1082	0.4695	−0.0200	2.2779	0.3138
0.0437	−0.1040	−4.2744	−0.1417	−0.7450	−0.2747	−1.0096	−0.1128	0.8009	0.0191	−1.7323	−0.3956
−0.1216	−0.7499	−0.7576	−0.3355	−0.3592	0.3934	−0.3788	−0.1462	0.5131	0.2008	−1.3517	−0.0991
0.1190	−0.0819	0.1587	−0.1738	0.3811	−0.9379	−1.1022	0.0056	0.9724	−0.0415	−1.8211	0.9032
0.5689	1.4315	−0.2085	−0.3312	0.4113	0.1756	−1.5672	−0.0903	−0.2907	−0.0169	−1.6850	−0.4707
−3.0459	1.0170	−0.4964	0.1447	0.3097	0.0264	−0.4860	−0.0642	−1.0142	0.8469	0.3909	−0.0211
0.7778	0.5366	0.4451	0.1627	0.1752	1.0257	−0.4383	−0.0475	0.3107	0.0392	1.0492	2.9038

Engelund , F.A. and Hansen , E. 1967 . A monograph on sediment transport in alluvial streams , Copenhagen : Tech. Forlag .

 Google Scholar

Acaroglu , E.R. 1968 . “ Sediment transport in convenyance system ” . In Thesis (PhD), Cornell University, Ithaca , USA : New York .

 Google Scholar

Graf , W.H. 1971 . Hydraulics of sediment transport , New York : McGraw-Hill .

 Google Scholar

Shen , H.W. and Hung , C.S. 1972 . “ An engineering approach to total bed material load by regression analysis ” . In Proceedings of Sedimentation Symposium 14-1 – 14-17 . Berkley, Calfornia

 Google Scholar

Ackers , P. and White , W.R. 1973 . Sediment transport: new approach and analysis . Journal of the Hydraulic Division, American Society of Civil Engineers , 99 ( 11 ) : 2041 – 2060 .

 Google Scholar

Brownlie , W.R. 1981 . Compilation of alluvial channel data: laboratory and field , California Institute of Technology, Report no. KH-R-43B .

 Google Scholar

Karim , M.F. and Kennedy , J.F. 1981 . “ Computer based predictions for sediment discharge and friction factors of alluvial streams ” . In Proceedings of the second international symposium on river sedimentation Nanjing , , China

 Google Scholar

Yang , C.T. 1996 . Sediment transport: theory and practice , New York : McGraw-Hill .

 Google Scholar

Yang , S-Q. 2005 . Prediction of total bed material discharge . Journal of Hydraulic Research , 43 ( 1 ) : 12 – 22 .

 Web of Science ®Google Scholar