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Extreme learning machine assessment for estimating sediment transport in open channels

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Abstract

The minimum velocity required to prevent sediment deposition in open channels is examined in this study. The parameters affecting transport are first determined and then categorized into different dimensionless groups, including “movement,” “transport,” “sediment,” “transport mode,” and “flow resistance.” Six different models are presented to identify the effect of each of these parameters. The feed-forward neural network (FFNN) is used to predict the densimetric Froude number (Fr) and the extreme learning machine (ELM) algorithm is utilized to train it. The results of this algorithm are compared with back propagation (BP), genetic programming (GP) and existing sediment transport equations. The results indicate that FFNN-ELM produced better results than FNN-BP, GP and existing sediment transport methods in both training (RMSE = 0.26 and MARE = 0.052) and testing (RMSE = 0.121 and MARE = 0.023). Moreover, the performance of FFNN-ELM is examined for different pipe diameters.

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Abbreviations

A :

Cross-sectional area of the flow

a i :

Learning factors of the hidden nodes (Eq. 6)

B j :

Bias of the jth neuron of the hidden layer (Eq. 8)

b i :

Learning factors of the hidden nodes (Eq. 6)

C V :

Volumetric sediment concentration

d :

Median diameter of particle size

D :

Pipe diameter

D gr :

Dimensionless particle number

Fr :

Densimetric Froude number

G(a i , b i , x):

Is the output of the ith hidden node for input x (Eq. 6)

g :

Gravitational acceleration

g(.):

Nonlinear activation piecewise continuous function (Eq. 8)

H ik :

Activation matrix of the jth neuron of the hidden layer for the kth training case (Eq. 8)

H’:

is the Moore-Penrose inverse of Matrix H (Eq. 14)

R :

Hydraulic radius

s :

Specific gravity of sediment (=ρ s /ρ)

S 0 :

Pipe slope

T :

Axis representing the target values for the training cases (Eqs. 9, 14)

V :

Flow velocity

V t :

Velocity required for the sediment’s incipient motion (Eq. 2)

W ji :

Weight of the ith input neuron and the jth neuron of the hidden layer (Eq. 8)

X ik :

Input of the input neuron for the kth training case (Eq. 8)

y :

Flow depth

β :

Indicates the weight between the output layer neurons and hidden layer neurons (Eqs. 9, 14)

β i :

Weight between the ith hidden node and the output node (Eq. 6)

λ c :

Clear water friction factor

λ s :

Overall friction factor with sediment

ρ :

Density of water

ρ s :

Density of sediment

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Authors and Affiliations

  1. Department of Civil Engineering, Razi University, Kermanshah, Iran

    Isa Ebtehaj & Hossein Bonakdari

  2. Department of Computer Science, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia

    Shahaboddin Shamshirband

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  1. Isa Ebtehaj
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Correspondence to Hossein Bonakdari.

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Ebtehaj, I., Bonakdari, H. & Shamshirband, S. Extreme learning machine assessment for estimating sediment transport in open channels. Engineering with Computers 32, 691–704 (2016). https://doi.org/10.1007/s00366-016-0446-1

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