Journal of Water Resource and Protection, 2012, 4, 870-876 Published Online October 2012 (
Comparison between Multi-Layer Perceptron and Radial
Basis Function Networks for Sediment Load Estimation in
a Tr opical Watershed
Hadi Memarian1, Siva Kumar Balasundram2*
1Department of Land Management, Faculty of Agriculture, Universiti Putra Malaysia, Serdang, Malaysia
2Department of Agriculture Technology, Faculty of Agriculture, Universiti Putra Malaysia, Serdang, Malaysia
Email: *
Received August 21, 2012; revised September 20, 2012; accepted October 19, 2012
Prediction of highly non-linear behavior of suspended sediment flow in rivers has prime importance in environmental
studies and watershed management. In this study, the predictive performance of two Artificial Neural Networks (ANNs),
namely Radial Basis Function (RBF) and Multi-Layer Perceptron (MLP) were compared. Time series data of daily
suspended sediment discharge and water discharge at the Langat River, Malaysia were used for training and testing the
networks. Mean Square Error (MSE), Normalized Mean Square Error (NMSE) and correlation coefficient (r) were used
for performance evaluation of the models. Using the testing data set, both models produced a similar level of robustness
in sediment load simulation. The MLP network model showed a slightly better output than the RBF network model in
predicting suspended sediment discharge, especially in the training process. However, both ANNs showed a weak ro-
bustness in estimating large magnitudes of sediment load.
Keywords: Sediment Load; Neural Network; MLP; RBF; Hulu Langat Watershed
1. Introduction
River suspended sediment load is a principal parameter
in reservoir management and can serve as an index to
understand the status of soil erosion and ecological envi-
ronment in a watershed [1]. The rainfall-sediment yield
process is extremely complex, non-linear, dynamic, and
fragmented due to spatial variability of watershed geo-
morphologic characteristics, spatial/temporal variability
of rainfall and involvement of other physical processes
[2,3]. Therefore, predicting sediment yield process in ri-
ver basins requires a non-linear modeling approach such
as Artificial Neural Network (ANN), which can capture
complex temporal variations within time series data [4].
The ANN is a powerful soft computational technique
which has been widely used in many areas of water re-
source management and environmental sciences [5-15].
ANN comprises parallel systems that are composed of
Processing Elements (PE) or neurons, which are assem-
bled in layers and connected through several links or
weights. After feeding input data to the input layer, they
pass through and are operated on by the network until an
output is produced at the output layer. Each neuron re-
ceives numerous inputs from other neurons through some
weighted connections. These weighted inputs are then
summed and a standard threshold is added, generating
the argument for a transfer function (usually linear, lo-
gistic, or hyperbolic tangent) which in turn produces the
final output of the neuron [14].
This study was aimed at comparing the predictive
performance of the Multi-Layer Perceptron (MLP) and
the Radial Basis Function (RBF) neural networks in pre-
diction of suspended sediment discharge at the Hulu
Langat watershed using time series of daily water dis-
charge as the input data.
2. Materials and Methods
2.1. Study Area
Hydrometeorologically, the Hulu Langat watershed is
affected by two monsoon seasons, i.e. the Northeast
(November to March) and the Southwest (May to Sep-
tember). Average annual rainfall is about 2400 mm. The
wettest months are April and November with an average
monthly rainfall exceeding 250 mm, while the driest
month is June with an average monthly rainfall below
100 mm. Topographically, the Hulu Langat watershed
can be divided into three distinct areas in reference to the
Langat River, i.e. mountainous area in the upstream, un-
*Corresponding author.
opyright © 2012 SciRes. JWARP
dulating land in the center and flat flood plain in the
downstream. This watershed consists of a rich diversity
of landforms, surface features and land cover [16,17].
Descriptions about this watershed are shown in Figure 1
and Table 1.
2.2. Data Sets
Daily water discharge and sediment load data from 1997
through 2008 recorded at Sungai Langat hydrometer sta-
tion were obtained from the Department of Irrigation and
Drainage (DID) of Malaysia.
2.3. Multi-Layer Perceptron
Multi-Layer Perceptron (MLP) is a popular architecture
used in ANN. The MLP can be trained by a back-
propagation algorithm [18]. Typically, the MLP is or-
ganized as a set of interconnected layers of artificial
neurons, input, hidden and output layers. When a neural
group is provided with data through the input layer, the
neurons in this first layer propagate the weighted data
and randomly selected bias through the hidden layers.
Once the net sum at a hidden node is determined, an
output response is provided at the node using a transfer
function [19,20].
Two important characteristics of the MLP are its non-
linear processing elements which have a non-linear acti-
vation function that must be smooth (the logistic function
and the hyperbolic tangent are the most widely used) and
its massive interconnectivity (i.e. any element of a given
layer feeds all the elements of the next layer). The two
main activation functions used in this study were sigmoid,
and are described as follows:
 
tanhand1 i
ii i
yw ye
in which the former function is a hyperbolic tangent
ranging from –1 to 1, and the latter is a logistic function
similar in shape but ranges from 0 to 1. Here, yi is the
output of the ith node (neuron) and wi is the weighted
sum of the input synapses [15,21,22].
The MLP network is trained with error correction
learning, which means that the desired response for the
system must be known. Error correction learning works
in the following way: From the system response at PEi at
iteration n, yi(n) and the desired response di(n) for a
given input pattern, an instantaneous error ei(n) is de-
fined by:
endn yn (2)
Using the theory of gradient descent learning [21,
23-25], each weight in the network can be adapted by
correcting the present value of the weight with a term
that is proportional to the present input and error at the
weight, such that:
Figure 1. Location of study area.
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Table 1. General information of the Hulu Langat water-
Main River Langat
Geographic Coordinate 3˚00' - 3˚17'N and
101˚44' - 101˚58'E
Drainage Area (km2) 390.26
Watershed Length (km) 34.5
Average Slope (%) 29.5
Max. Altitude (m) 1480
Min. Altitude (m) 36
Ave. Altitude (m) 278
Reference Hydrometer Station Sungai Langat
Annual Water Discharge (*106 m3) 289.64
Annual Sediment Load (*103 ton) 146.6
Annual Runoff (mm·km2) 742.16
Annual Sediment Yield (ton·km2) 375.65
Reference Rainfall Station UPM Serdang, Kampung Lui,
Ladang Dominion
Precipitation (mm) 2453
Land Cover*
Forest (54.6%), Cultivated Rub
(15.6%), Orchard (2%), Ur
Area (15%), Horticulture and Crops,
Oil Palm, Lake and Mining Land
*Based on the 2006 land use map.
ijiji jij
wnwnnxn w
 
 1
n wn 
The local error i can be directly computed from
i at the output PE or can be computed as a
weighted sum of errors at the internal PEs. The constant
η is known as the step size and α is known as the mo-
mentum. This procedure is referred to as the back-
propagation algorithm imposed into the momentum
learning. Back-propagation computes the sensitivity of a
cost function with respect to each weight in the network,
and updates each weight proportional to the sensitivity
2.4. Radial Basis Function
The Radial Basis Function (RBF) is another popular ar-
chitecture used in ANN. The RBF, which is multilayer
and feed-forward, is often used for strict interpolation in
multi-dimensional space. The term “feed-forward” means
that the neurons are organized as layers in a layered neu-
ral network [26]. The basic architecture of a three-lay-
ered neural network is shown in Figure 2.
The RBF network comprises three layers, i.e. input,
hidden and output. The input layer is composed of input
data. The hidden layer transforms the data from the input
space to the hidden space using a non-linear function.
The output layer, which is linear, yields the response of
the network. The argument of the activation function of
each hidden unit in an RBF network computes the Eu-
clidean distance between the input vector and the center
of that unit. In the structure of RBF network, the input
data, x, is a p-dimensional vector, which is transmitted to
each hidden unit. The activation function of hidden units
is symmetric in the input space, and the output of each
hidden unit depends only on the radial distance between
the input vector, x, and the center for the hidden unit [26].
Each node in the hidden layer is a p-multivariate Gaus-
sian function, given as follows:
where: xi is the mean (center) and i
is the variance
(width). These functions are referred to as radial basis
functions. Finally, a linear weight is applied to the output
of the hidden nodes to obtain:
The problem with this solution is that it may lead to a
very large hidden layer. Thus, the solution should be ap-
proximated to reduce the number of PEs in the hidden
layer and cleverly position them over the input space
regions. This entails the need to estimate the position of
each radial basis function and its variance, as well as to
compute the linear weights, wi [21,26]. An unsupervised
technique, known as the k-nearest neighbor rule, is used
to estimate the mean and the variance. The input space is
first discretized into k clusters and the size of each clus-
ter is obtained from the structure of the input data. The
centers of the clusters give the centers of the RBFs, while
the distance between the clusters provides the width of
the Gaussians. NeuroSolutions, an ANN computer pro-
gram, uses competitive learning to compute the centers
and the widths. It sets each width proportional to the dis-
tance between the center and its nearest neighbor. The
output weights are obtained through supervised learning.
Therefore, the error correction learning described earlier
in the MLP section is employed [21,27].
Figure 2. Basic RBF architecture.
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2.5. Performance Metrics
The metrics used for network training and validation
were Mean Square Error (MSE), Normalized Mean Square
Error (NMSE) and correlation coefficient (r). Meanwhile,
Akaike’s Information Criterion (AIC) and Minimum
Description Length (MDL) measurements were used by
NeuroSolutions to produce a network with the best gen-
eralization. The AIC is used to measure the tradeoff be-
tween training performance and network size. The MDL
is similar to the AIC in that it tries to combine the
model’s error with the number of degrees of freedom to
determine the level of generalization [21,24]. The com-
putations of MSE, NMSE and r are given below:
ij ij
MSE  (6)
dd 2
where: P is the number of output processing elements, N
is the number of exemplars in the data set, yij is network
output for the exemplar i at the processing element j, and
dij is desired output for the exemplar i at the processing
element j [21,24].
2.6. Application of MLP
Data randomization was performed before the training
process. In the training process, 54% and 14% of the
total data were utilized for training and cross validation,
respectively. Network testing was conducted using 32%
of the total data. Data normalization was performed using
NeuroSolutions. In this process, data sets were scaled in
the range of 0.05 - 0.95. The number of neurons in the
first and second hidden layers, and learning rates were
determined based on several trials. The optimum proper-
ties of the MLP network are shown in Table 2.
2.7. Application of RBF
Network training and testing were performed using the
same data sets applied in the MLP network. With regard
to the form of activation function, applied in the hidden
layer (i.e. hyperbolic tangent), data sets were normalized
in the scale of –0.9 - 0.9. The number of neurons in the
hidden layer, the number of clusters and learning rates
were determined based on several trials. The optimum
properties of the RBF network are shown in Table 2.
3. Results and Discussion
3.1. Error Analysis during the Training Process
Minimum MSE and final MSE obtained during the train-
ing process of the RBF network were significantly larger
than those in the MLP network (Table 3 and Figure 3).
Comparatively, the MLP network is able to produce a
more fitted output to cross validation data set in com-
parison to the RBF network. As indicated in recent lit-
erature [4,28], the RBF network gives a higher perform-
ance than the MLP network when the input data is multi
dimensional. In this work, only water discharge was used
as the input data. Thus, higher performance of the MLP
network as compared to the RBF network is justifiable,
especially during the training process.
3.2. Error Analysis during the Testing Process
Based on Table 4, both ANNs show similar strength in
sediment load simulation during the testing process.
However, application of the MLP network using the
testing data set resulted in lesser MSE and NMSE, as
compared to the RBF network. Difference in the r value
between both networks is negligible.
Table 2. Optimum properties of the ANNs.
Network properties MLP RBF
Number of hidden layers 2 1
Number of neurons in the first hidden layer 20 20
Number of neurons in the second hidden
layer 10 -
Momentum rate & step size in the first hidden
layer 0.7 & 1.0 0.7 & 1.0
Momentum rate & step size in the second
hidden layer 0.7 & 0.1 -
Momentum rate & step size in the outpu
layer 0.7 & 0.010.7 & 0.1
Activation function in the first hidden layer Logistic Hyperbolic
Activation function in the second hidden
layer Logistic -
Activation function in the output layer Linear
logistic Bias
Number of cluster centers in the input layer - 5
Number of epochs for supervised learning 1200 1000
Number of epochs for unsupervised learning - 100
Number of exemplars for training 1795 1795
Number of exemplars for cross validation 450 450
Number of exemplars for testing 1058 1058
Table 3. Error analysis during the training process.
Networks Training Cross
Validation Training Cross
Epoch#1200 820 999 584
MSE 0.001598738 0.001605163 0.0061319280.006382225
MSE 0.001598738 0.001613058 0.0061319280.006416793
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The MLP network is comparatively more capable of
tracing fluctuations in daily sediment load than the RBF
network (Figures 4 and 5). As highlighted in Figures 4
and 5, the points corresponding to sediment load with an
observed large magnitude are mostly situated at the bot-
tom quad of the 1:1 line. Clearly, both ANNs showed
weak robustness in estimating sediment load with a large
magnitude, especially for records higher than 4000 ton/
day. Such limitation in the application of neural networks
has also been reported in the works of Hsu et al. (1995)
[29], Morid et al. (2002) [30] and Talebizadeh et al.
(2010) [14], commonly attributable to scarcity of large
observed values in the training data set. In other words,
inefficiency of the ANN model in estimating large mag-
nitudes of sediment load can be attributed to different
non-linear relationships governing the process of sedi-
ment detachment and final sediment load generated from
a watershed. For example, the mechanism of sediment
load generation induced by a low flow event is obviously
different from the sediment load produced by a storm
event in which a significant amount of wash load enters
the watershed drainage network and passes the outlet.
Therefore, due to different mechanisms, a single ANN
which may produce satisfactory results for the simulation
of medium and low loads may not simulate large sediment
load events with the same accuracy. In this data set, there
was inadequate data corresponding to high sediment load
events to train a separate ANN model for simulating these
high values, as suggested by Cigizoglu and Kisi (2006)
[31] and confirmed by Talebizadeh et al. (2010) [14].
(a) MLP
(b) RBF
Figure 3. MSE versus epoch for (a) MLP and (b) RBF.
Table 4. Performance metrics computed based on the test-
ing data set.
Performance MLP RBF
MSE 274088.998 281938.375
NMSE 0.420 0.432
MAE 131.454 130.925
Min Abs Error 0.069 0.186
Max Abs Error 6823.613 6838.253
r 0.812 0.814
Besides the above reason, in recent decades, the Hulu
Langat watershed has experienced an extensive rate of
urban development. Infrastructure constructions such as
roads, tunnels, and bridges, and landslide occurrences
can result in large amounts of sediment load for a num-
ber of years which can affect water quantity and quality.
Wastewater discharges into water streams from industrial
or residential areas and water treatment plants are mostly
Figure 4. Observed sediment load ve r sus simulate d se dime nt load by the MLP network.
Figure 5. Observed sediment load versus simulated sediment load by the RBF network.
unknown in the Hulu Langat watershed. These sources of
sediment load are not describable only by water dis-
charge and can produce a large amount of uncertainty in
ANN simulation [32,33]. Therefore, using more input
data (e.g. rainfall, temperature and reservoir level) would
assist us in obtaining a higher level of accuracy for sedi-
ment load simulation by ANN.
4. Conclusion
The minimum MSE obtained during the training process
of the RBF network was significantly larger than that in
the MLP network. Thus, the MLP network produced a
more fitted output to the cross validation data set than the
RBF network. Network testing showed that both ANNs
had similar strength in sediment load simulation. How-
ever, the application of the MLP network using the test-
ing data set resulted in lesser amounts of the MSE and
NMSE, i.e. 274,089 and 0.42, respectively, as compared
to the RBF network. In addition, the MLP network was
more capable in tracing fluctuations in daily sediment
load than the RBF network. Both ANNs showed a weak
robustness in estimating large magnitudes of sediment
load, especially for records higher than 4000 ton/day.
This was attributable to scarcity of large observed values
in the training data set and different non-linear relation-
ships governing the process of sediment detachment and
final sediment load by a high storm event, as compared
to those by low or medium storm events. Additionally,
infrastructure constructions, landslide occurrences and
wastewater discharges in the study area resulted in large
amounts of sediment load over several years, which af-
fected water quantity and quality. These sources of sedi-
ment load may have contributed to a level of uncertainty
in ANN simulation.
5. Acknowledgements
Necessary hydrological data for this study was provided
by the Department of Irrigation and Drainage, Malaysia.
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