MODELLING OF SUSPENDED SEDIMENT

In Nile River using ANN

Abdelazim M. Negm

Water and Water Structures Eng. Dept., Faculty of Eng., Zagazig University, Zagazig, Egypt & Acting Vice Dean of FCI

M. M. Elfiky, T. M. Owais, M. H. Nassar

Department of Water and Water Structures Eng., Faculty of Eng., Zagazig University, Zagazig, Egypt

Keywords: Sediment transport, Suspension sediment, Artificial neural networks, numerical modeling, River hydraulics,

Nile River, Hydrodynamic modeling

Abstract: Artificial neural network (ANN) prediction models can be considered as an efficient tool in predictions once

they are trained from examples or patterns. These types of ANN models need large amount of data which

should be at hand before thinking to develop such models. In this paper, the capability of ANN model to

predict suspended sediment in 2-D flow field is investigated. The data used for training the network are

generated from a pre-verified 2-D hydrodynamic and a 2-D suspended sediment models which were

recently developed by the authors. About two-thirds of the data are used for training the network while the

rest of the data are used for validating and testing the developed ANN model. Field data measured by

hydraulic research Institute are used to compare the results of the ANN model. The conjugate gradient

learning algorithm is adopted. The results of the developed ANN model proved that the technique is reliable

in such field compared to both the results of the previously developed models and the field data provided

that the trained network is used to generate prediction within the range of training data.

1 INTRODUCTION

The subject of sediment transport in alluvial streams

gains its importance with the increasing of water

resources utilization. Extensive researches had been

done in this field. Generally, laboratory

investigations to predict sediment transport are time-

consuming, costly and even not possible for many

practical engineering problems. Therefore,

mathematical models for predicting sediment

transport were developed using different techniques.

Several one dimensional models were developed,

see for example (Thomas and Prasuhn,

1977),

(Bhallamudi and Chaudhry,

1991)

and (Guo and Jin,

1999). Examples of 2-D models include those

developed by (Lin and Shen, 1984), (Van Rijn,

1986), (Celik and Rodi, 1988), (Van Rijn et al.,

1990) and (Elfiky et al., 2003). Instead of

mathematical model, a relatively new computational

tool, ANN, can be used to predict the suspended

sediment load.

Although many applications in the field of

Hydraulic Engineering are available such as

(Karunanith et al., 1994) and (Dibike et al., 1999)

very few applications in the field of sediment

transport were published. (Nagy, 1999) used ANN to

estimate the natural sediment discharge in rivers in

terms of sediment concentration. (Jain, 2001) used

the ANN approach to establish an integrated stage-

discharge-sediment concentration relation. Also,

ANN approach can successfully model the

hysteresis effect that is associated with unsteady

flow in open channels. (Nagy et al., 2002) used the

ANN approach to estimate the natural sediment

discharge in rivers in terms of sediment

concentration.

In the present paper, ANN, is used to predict the

suspended sediment load in terms of the flow depth,

the velocities components in x and y directions and

the sediment carrying capacity. Since, the method

learns from examples, a large set of data should be

available. Practically, field data of different rivers

should be used to train and validate the ANN but it

is not available at the time being at the author hands

209

M. Negm A., M. Elﬁky M., M. Owais T. and H. Nassar M. (2007).

MODELLING OF SUSPENDED SEDIMENT - In Nile River using ANN.

In Proceedings of the Second International Conference on Software and Data Technologies - Volume ISDM/WsEHST/DC, pages 209-214

DOI: 10.5220/0001346202090214

 SciTePress

Therefore, the developed SED-2 numerical model by

(Elfiky et al., 2003)

is used to generate the required

data for training and verification of the ANN to test

and prove its capability to predict the suspended

sediment concentration once it gets trained.

2 OVERVIEW OF ANN

Artificial Neural Network (ANN), is a structure

composed of a number of interconnected units

(artificial neurons) Each neuron has an input/output

characteristics and implements a local computations

or function, (Schalkoff, 2002). Hence, the overall

ANN of interconnected neurons displays a

corresponding functionality. A neural system should

be capable of storing information through training.

Thus the objective of training the ANN is to develop

an internal structure enabling the ANN to correctly

identify or classify new similar patterns. Thus,

neural network is a dynamic system, its state

changes over time in response to external inputs or

an initial unstable state. Various types of ANN are in

use and could be reviewed from (Schalkoff, 2002).

Most of the applications of ANNs in fields of water

Engineering were reviewed in (Negm, 2002). In this

paper, the multilayer feedforward network or the

multilayer perceptrons is used in modeling

suspended sediment concentration in river flow.

A typical ANN consists of three layers (4-10-1)

is shown in Figure 1. The input variables determine

the number of neurons in the input layer and the

input data vectors are applied to the input layers

from an external source. A bias neuron is normally

used with input of unity to shift or scale the

activation function. The output layer is where the

output are processed and are sent to an external

source for further analysis or extra treatments or

plotting, .etc. The layers between the input and the

output are hidden where the entire processing are not

accessible. The most common nonlinear transfer

functions are the sigmoidal functions including the

logistic and the hyperbolic tangent. The latter

function is given by Equation (2)

)exp()exp()exp()exp(

jjjjj

IhIhIhIhOh

−

+−−=

(1)

where Ih

is The input to the neuron j of the hidden

layer and given by

∑

jijij

bwxIh

(2)

where x

is the input of the neuron i in the input

layer with m is the number of neurons in the input

layer and b

is the bias of the unit. The w

is the

weights vector of the connections between the

neurons of the input layer and the neurons of the

hidden layer.

The outgoing singnal from the hidden neuron is

then combined with the weights of the connections

between the neurons of the hidden layers and those

of the output layer yielding the output of the output

layer, Oo

, using a linear combine function defined

by Eq. (3).

∑

kjkjk

bCOhOo

(3)

in which C

is weight of the connection between

neuron j of the hidden layer and neuron k of the

output layer and b

is the bias to the neuron k.

Input Layer Hidden Layer

Output Layer

Input Variables

Output Variable

1.0

. . . .

Bias

S. S

Figure 1: Typical three layers Feed-Forward ANN.

Training the network involves the determination

of the weight vectors w

and C

such that the sum of

squares of the error between the actual value of the

output and the desired value of the output is

minimal. The network weights are randomly

assumed within a particular range. Then they are

updated.

3 COLLECTION OF DATA FOR

TRAINING, VALIDATION AND

TEST

The numerical sediment transport model (SED-2)

developed by (Elfiky et al., 2003) was used to

generate the suspended sediment load ((kg/m.sec)

for a canal reach of 830 m long. The two basic

inputs of the SED-2 model (velocities) was obtained

by running the HYD-2 model by Elfiky et al., 1997).

The inputs to the SED-2 model include the velocities

in x and in y directions and the flow depth. The

output of the model is the suspended sediment

concentration. Figure 2: shows a definition sketch

ICSOFT 2007 - International Conference on Software and Data Technologies

210

for the reach where the model was applied. The

reach is confined between cross section (1) at KM

57.000 and cross section (2) at KM 57.830 on El-

Noubaria canal. Also, El-Nasser canal was included

in the simulation using SED-2. Each canal was

simulated separately using the ANN because the

change in the flow direction at the canal junction

was misunderstood by the network leading to very

poor neural network model. The effective total

number of generated data points are 963 for El-

Nubraia canal reach.

4 COLLECTION OF FIELD DATA

The collected field measurements at two cross-

sections on EL-Nubaria main canal are used to

compare the model results. The data were collected

by the Hydraulic Research Institute (HRI), National

Water Research Center NWRC), Delta Barrages,

Egypt on November, 1998, (Saad et al., 1999). The

average velocity and the suspended sediment load

were measured at two stations along both of Sec. (1)

at KM 57 and Sec. (2) at KM 57.83 on EL-Nubaria

canal, see Figure 2.

Figure 2: Definition sketch for the canal reach where the

SED-2 numerical model was applied.

5 BUILDING THE NETWORK

Many factors affect the accuracy of the network. The

most important factors will be discussed in the

following paragraphs.

Normalization of Data ensures that each input

contributes equally to the decision or the prediction

made by the network. If the input values were not

normalized, an input data, which have large

numbers, will be more significant than that which

has small numbers. Several methods could be used

for normalization. One of these methods the zero-

mean unit-standard deviation normalization method

in which the mean and the standard deviation for

each field is determined. Each field is then

normalized such that the mean value for the field

becomes zero and the values at plus and minus one

standard deviation are mapped onto plus and minus

one.

According to the Neural Connection software,

the normalized input data, which are provided to the

neural network, are classified into three sets, i.e.

training, validation and test data sets. The training

data is used to train the proposed ANN and is taken

as 70% of the total records (2/3 of the data may be

enough for large set of data). Validation data is used

to monitor neural network performance during

training phase and it represents 15% of total input

data. Test data is used to test the performance of a

trained ANN in generating the required prediction.

The test data set is unseen data to the ANN model

and represents 15% of the total utilized records by

the present application.

The choice of the connections weights have a

large effect on the performance of the network. The

best initial values of the connections weight are

found by trial and errors by conducting many

computer experiments and the correlation

coefficient, R, between the target and the output of

the proposed network is computed for each

experiment. Also, the root mean square error, rmse,

computed. The values of the weights that

generate output with maximum R and minimum

rmse are chosen. In the present application, the best

initial weights was assumed to be in the range

12.2.6.

Generally, increasing the number of neurons in

the hidden layer improves the performance of

network on the training data, but not necessarily on

the validation data. If so many hidden neurons are

used in a network, the network will have enough

weights to exactly represent all the training patterns.

Such network will be poor network because it will

be able to generalize the solution. This means that

the network is overtrained. As the total number of

hidden units is increased from one, the network

performance on the validation data increases rapidly.

This is because each new hidden unit starts to

represent one of the underlying features in the data

set. As more units are added, performance levels off.

At that point, the training should stop. However,

adding further units may then cause a decrease in

performance because the power of generalization is

lost and the network begins to learn the noise present

in the data. It is always better to use as few neurons

as possible to achieve the desired result. Generally,

the number of neurons depends on the complexity of

the data and on both the number of input and output

variables. From experience, a rough initial

Flo

MODELLING OF SUSPENDED SEDIMENT - In Nile River using ANN

211

estimation to the number of neurons in the hidden

layer may be the geometric mean of the neurons in

both input and output layers. The procedure is

achieved by conducting many computer

experiments. In the present application, the best

number of neurons in the hidden layer is 10. The

results of the conducted experiments are presented in

Figure 2 in terms of R and rmse. The best value of R

and the minimum value of rmse are when the

network has a size of 4-10-1. It should be noted a

similar figure to figure 3 is prepared to select the

optimal value of each of the important factors

affecting the ANN performance but not presented

here to avoid repetition.

Figure 3: Typical performance of the proposed network in

terms of (a) R and (b) rmse.

In most of the application one hidden layer will

produce enough accuracy. However, more than one

hidden layers can be used based on the complexity

of the data structures. This can be achieved by

conducting several computer

experiments using

single and multiple hidden layers and then a decision

is taken based on the performance of the network. In

this application, one hidden layer is found to be

enough.

The type of activation functions used in the

hidden layer is chosen by trials. In this application

the tansh activation function is found to be the best

one compared to the linear or the sigmoid.

The learning algorithm affects highly the

performance of the networks. In the present

application, the conjugate gradient is used to prevent

the network from being trapped in a local minima.

Unlike back-propagation, the conjugate gradient

method does not proceed along the direction of the

error gradient, but in a direction orthogonal to the

one in the previous step. This prevents future steps

from influencing the minimization achieved during

the current step. In addition to the above factors, the

maximum number of updates is important which is

fixed when the validation error reaches to each

minimum during training process. Keeping in mind

the above discussed factors, building the network for

the present application is well represented, see

Figure 4.

6 RESULTS OF THE

DEVELOPED NETWORK

Results of the developed network are presented in

three figures. Figure 5 presents the comparison

between the ANN estimation and the values

predicted from the previously developed numerical

model (SED-2) for training data set. The correlation

coefficient, R is 0.9993. Clearly, perfect agreement

is obtained for this set and this expected because the

generated data from the numerical model was used

to train the network. The very few data points which

seem to deviate from the line of perfect agreement

are those points where the velocities are affected by

the entering flow to the El-Nasser canal and hence

the suspended sediment is also affected because a

remarkable portion of suspended sediment flow to

El-Naser canal. It should be noted that El-Nasser

canal was not included in the simulation using the

neural network, in spite of its inclusion in the

numerical model, because its inclusion interrupts the

performance of the network. Figure 6 presents the

ANN results for validation and test data versus those

of the numerical model. The correlation coefficient

is (R=0.9993) for validation data and equals

(R=0.9992) for test data. The correlation coefficient

for all data set is 0.9993. Figure 7 represents the

variation of the residuals for all the three data sets

versus the network predictions. The residuals seem

to be distributed around the line of zero error,

uncorrelated with the ANN outputs (estimated and

predicted) and of very small values. The correlation

coefficient of the residuals with the network

prediction is very small and equals -0.0272. In this

figure, the high values of the residuals are for the

points that affected by El-Nasser canal where the

0.9900

0.9920

0.9940

0.9960

0.9980

1.0000

(4-1-1) (4-3-1) (4-5-1) (4-7-1) (4-10-1) (4-20-1) (4-30-1 )

Training data

Validation data

Test data

No. of hi dden neurons

0.0000

0.0004

0.0008

0.0012

0.0016

0.0020

(4-1-1) (4-3-1) (4-5-1) (4-7-1) (4-10-1) (4-20-1) (4-30-1)

Training data

Validation data

Test d ata

No. of hidden neurons

(

)

(

)

ICSOFT 2007 - International Conference on Software and Data Technologies

212

velocity component in x direction is suddenly

affected (because it changes its direction and

becomes in y direction as the flow enters El-Nasser

canal) and the suspended sediment load is in turn

reduced compared to the upstream sections.

Figure 4: Flowchart showing the basic steps of building a

neural network for an application.

Figure 5: Comparison between predictions of ANN and

those of SED-2 numerical model.

Figure 6: Comparison between predictions of ANN and

those of SED-2 numerical model.

Figure 7: Variations of the residuals of all ANN data with

the estimated values.

7 COMPARISONS

The collected field data at the two cross sections, 1

and 2 are compared to both the predicted values

using the numerical model and the neural network

model in Figures 8 and 9 for sections (2) and (1).

Clearly, good matching is observed between the

field data and the models results at section (2). At

Sec. (1), there are a great agreement at the left and

right stations while a gab is noticed between the

models results and the field data in the middle

station, perhaps due to the inflow boundary effect,

Elfiky et al.8). Comparisons between results of ANN

model and the numerical model at other sections as

(3) and (4) indicate very great agreement (not

presented here to reserve space).

Figure 8: Comparison between predictions of ANN, SED-

2 numerical model and field data.

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0.0005

0.001

0.0015

0.002

0.0025

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Estimated and Predicted

Residuals

Test

Validation

Train

Savin

the network out

1- Iterations to find the best weights

2- Iterations to find best activation function

3- Iterations to find no. of hidden neurons

4- Iterations to find the number of hidden layers

5- Iterations to find max number of updates

Processin

of networ

out

uts

Check

if R is max.

and rmse is

min.value

Save the output of the best networks as i.e.

training, validation and test data sets

Calculation of the R and rmse

Post processing of output and further analysis

Set initial values of the network parameters as weights, hidden

layers, neurons, activation function, max updates and convergence

ut data includin

data s

ecification

ect

tra

ata

re-

rocess

ng o

ata

ect

on o

evant var

Check

stability of

the

Sto

Yes

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 0.010.020.030.040.050.060.07

Calculated using numerical model

Predicted using ANN

Test da ta s e t

Validation data set

validation and test data sets

30% of whole data

MODELLING OF SUSPENDED SEDIMENT - In Nile River using ANN

213

Comparisons between results of ANN model and

those of numerical model at the longitudinal sections

as L.S.1, L.S.2 and L.S.3 show also very close

agreement between both results. Indicated in Fig. 10.

Figure 9: Comparison between predictions of ANN, SED-

2 numerical model and field data.

Figure 10: Comparison between prediction of ANN and

those of SED-2 numerical model at L.S.1.

8 CONCLUSION

A multilayer feedforward artificial neural network

(4-10-1) is used to estimate the suspended sediment

concentration efficiently based on four inputs

including the depth of flow, the components of flow

velocities in x and y directions and the sediment

carrying capacity. Since, the field data are very

limited, a 2-D numerical model (SED-2) was used to

generate the required training and validation data for

the developed neural network. The present paper

proved that the ANNs are a powerful computational

tool for computing the suspended sediment

concentration in rivers provided that the trained and

verified network should be used to predict values

within the training range otherwise, poor predictions

are obtained.

REFERENCES

Thomas, W.A. and Prasuhn, A.L. (1977). "Mathematical

Modeling of Scour and Deposition." J. Hyd. Div.,

ASCE, Vol. 103, No. 8, PP.851-863.

Bhallaamudi, S.M. and Chaaudhry, M.H. (1991).

"Numerical Modeling of Aggradation and Degradation

in Alluvial Channels.", J. of Hyd. Engrg., Vol. 117,

No. 9, Sep., PP.1145-1164.

Guo, Q.-C. and Jin, Y.-C. (1999). "Modeling Sediment

Transport Using Depth Averaged and Moment

Equations.", J. Hyd. Engrg., Vol.. 125, No.12, Dec., PP.

1262-1269.

Lin, P. and Shen, H. W. (1984), “Two-D Flow with

Sediment by Characteristics Method”, J. Hyd. Engrg.,

Vol. 110, No. 5, PP.615-626.

Van Rijn, L. C. (1986) “Mathematical Modeling of

Suspended Sediment in Non-uniform Flows.” J. of

Hyd. Engrg., Vol. 112, No. 6, PP.589-600.

Celik, I. and Rodi, W. (1988). "Modeling Suspended

Sediment Transport in Nonequilibrium Situations.", J.

of Hyd. Engrg., Vol. 114, No. 10, Oct., PP.1157-1191.

Van Rijn, L. C., Rossum, H. and Thermes, P. (1990).

"Field Verification of 2-D and 3-D Suspended

Sediment Models." J. of Hyd. Engrg., Vol. 116, No.

10, PP.1270-1288.

Elfiky, MM., Negm, A.M., Owais, T.M. and Nassar, M.H.

(2003). "Development of A 2-D Sediment Transport

Model For The Nile River" Proc. Of 6

Int.

Conference on River Engineering, 28-30 Jan., Ahvaz,

Iran.

Dawdy, D.R. and Vanoni, V.A. (1986). "Modeling alluvial

Channels.", J. Water Resour. Res., Vol. 22, No. 9, PP.

71s-81s.

Schalkoff, R.J. (1997). "Artificial Neural Networks."

Computer Science Series, McGraw-Hill Co., Inc.,

New York.

Negm, A.M. (2002). "Prediction of Hydraulic Design

Parameters of Expanding Stilling Basins Using

Artificial Neural Network." Egyptian Journal for

Engineering Science and Technology (EJEST),

Faculty of Engineering, Zagazig University, Egypt,

Vol. 6, No.1, PP.1-24.

Karunanithi, N., Grenney, W.J., Whitley, D. and Bovee,

K. (1994). "Neural Networks for River Flows

Prediction." J. Computing in Civil Engineering,

ASCE, Vol.8, No.2, April, pp.201-219 and Discussion

Vol.9, No.5, P293.

Dibike, Y.B., Solomatine, D. and Abbott, M.B. (1999), On

the Encapsulation of Numerical-Hydraulic Models in

Artificial Neural Network”, J. Hyd. Res., IAHR,

Vol.37, No.2, PP.147-162.

Nagy, H. M. (1999),“ Sediment Transport Capacity in

Open Channels: Neural Network Approach.”, Alex.

Engineering Journal, Vol. 38, No. 2.

Jain, S.K. (2001). "Development of Integrated Sediment

Rating Curves Using ANNs." J. Hyd. Engrg., Vol.

127, No. 1, Jan., PP.30-37.

Nagy, H.M., Watanabe, K. and Hirano, M. (2002).

"Prediction of Sediment Load Concentration in Rivers

Using Artificial Neural Network Model.", J. Hyd.

Engrg., Vol. 128, No. 6, June, PP.588-593.

Elfiky M.M., Marmoush Y.R. and Abdel-Aal G.M.

(1997). "A 2-D Model Simulating the Flow Patterns in

Rivers." The Egyptian Journal For Engineering

Sciences and Technology (EJEST), Faculty of Eng.,

Zagazig Univ., Jan., Vol. No.1, PP. 60-67.

Saad, S.A., El-Belasy, A.M. and Amin, A.M. (1999).

"Field Studies For Silting Phenomenon at El-Nassr

Canal Intake." HRI, Delta Barrages, NWRC, Egypt.

ICSOFT 2007 - International Conference on Software and Data Technologies

214