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
Copyright
c
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
j
is The input to the neuron j of the hidden
layer and given by
=
+=
m
1j
jijij
bwxIh
(2)
where x
i
is the input of the neuron i in the input
layer with m is the number of neurons in the input
layer and b
j
is the bias of the unit. The w
ij
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
k
, using a linear combine function defined
by Eq. (3).
=
+=
n
j
kjkjk
bCOhOo
1
(3)
in which C
jk
is weight of the connection between
neuron j of the hidden layer and neuron k of the
output layer and b
k
is the bias to the neuron k.
Input Layer Hidden Layer
Output Layer
Input Variables
Output Variable
U
V
H
C*
1.0
. . . .
2
3
Bias
1
1
0
1
.0
1
2
3
4
Bias
1
S. S
Figure 1: Typical three layers Feed-Forward ANN.
Training the network involves the determination
of the weight vectors w
ij
and C
jk
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,
is
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
R
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
R
No. of hidden neurons
A
(
B
)
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
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
g
the network out
p
u
t
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
g
of networ
k
out
p
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
In
p
ut data includin
g
data s
p
ecification
C
o
ll
ect
i
n
g
o
f
tra
i
n
i
n
g
d
ata
P
re-
p
rocess
i
ng o
f
d
ata
S
e
l
ect
i
on o
f
re
l
evant var
i
a
bl
es
1
2
3
4
5
Check
stability of
the
tk
Sto
p
N
o.
N
o.
Yes
Yes
0
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.
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