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Modeling of local scour depth downstream hydraulic structures in trapezoidal channel using GEP and ANNs

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A mathematical model between is generated by Gene expression programming (GEP) for the purpose of predicting local scour depth downstream stilling basin through trapezoidal channel. The stilling basin is provided with current deflector placed at different relative positions to control the local scour depth. In addition, an artificial neural network (ANN) and multiple linear regression (MLR) models are implemented to predict the scour depth downstream the hydraulic structures.

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Articolo Ain Shams Engineering Journal, 2013

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da Alessia De Giosa




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CIVIL ENGINEERING Modeling of local scour depth downstream
hydraulic structures in trapezoidal channel
using GEP and ANNs Yasser Abdallah Mohamed Moussa * Water Engineering Department, Faculty of Engineering, Zagazig University, Egypt Received 19 November 2012; revised 21 February 2013; accepted 16 April 2013
Available online 5 June 2013 KEYWORDS Local scour;
GEP;
ANN;
Current de'ector;
Trapezoidal channel Abstract Local scour downstream stilling basins is so complex that it makes it difficult to establish a general empirical model to provide accurate estimation for scour depth. Lack estimation of local
scour can endanger to stability of hydraulic structure and can cause risk of failure. This paper pre-
sents Gene expression program (GEP) and artificial neural network (ANNs), to simulate local scour
depth downstream hydraulic structures. The experimental data is collected from the literature for
the scour depth downstream the stilling basin through a trapezoidal channel. Using GEP approach
gives satisfactory results compared with artificial neural network (ANN) and multiple linear regres-
sion (MLR) modeling in predicting the scour depth downstream of hydraulic structures.  2013 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved. 1. Introduction Scour is a natural phenomenon caused due to the erosive
action of 'owing stream on alluvial beds which removes the
sediment around or near structures located in 'owing water.
In addition, when a hydraulic structure such as dam, regulator,
spillway, or bridge, is placed in a hydraulic/marine environ-
ment, the presence of the structure will change the 'ow pattern in its immediate neighborhood, resulting in these changes
usually cause an increase in the local sediment transport capac-
ity and thus lead to scour. Scour can induce failure of hydrau-
lic and marine structures [1]. So, local scour modeling is an
important issue in environmental/water resources engineering
in order to prevent degradation of river bed and safe the stabil-
ity of grade control structures [2,3]. The river bed in the vicin-
ity of a hydraulic structure is generally protected against
current, waves, and eddies [4''6,1,7]. The effect of baf'es on
scour depth over stilling basis was investigated by many
researchers [8''16]. ANN was used to investigate its possibility
as a modeling tool for simulation of tidal 'ow in two-dimen-
sional 'ow field [17]. An ANN has been employed to predict
scour at a culvert outlet [18,19]. The scour depth downstream
hydraulic structures were predicted using artificial neural net-
work [20]. In addition, it was employed to predict 'ow charac-
teristics in irregular open channel [21] and sediment load [22]. * Tel.: +20 01111890996.
E-mail addresses: Yasser_eng1997@yahoo.com, Yasser_eng1997@
zu.edu.eg. Peer review under responsibility of Ain Shams University. Production and hosting by Elsevier Ain Shams Engineering Journal (2013) 4, 717''722 Ain Shams University Ain Shams Engineering Journal www.elsevier.com/locate/asej www.sciencedirect.com 2090-4479  2013 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asej.2013.04.005 Moreover, the local scour depth downstream spillway and
ski-jump, was predicted [23,24], respectively. Gene expression
programming, GEP, is used by many researchers, to develop
combined run off [25], prediction of surface roughness [26],
investigate the hydraulic jump characteristics [27]. In addition,
this technique is used as a new algorithm for solving problems
[28]. GEP is used to predict the local scour depth for different
types of hydraulic structures [29''33]. This paper presents the
modeling of local scour depth though the trapezoidal channel
using artificial techniques; ANNs and GEP. The stilling basin
is provided with current de'ector at different positions from
the sluice gate, to control and minimize the local scour depth
downstream hydraulic structure. 2. Overviews of ANNs and GEP 2.1. The artificial neural networks ANNs as a technique of prediction could be used to predict the
local scour depth by building a multilayer feed forward net-
work. Such type of ANN consists of several layers (Fig. 1);
each has one or more units (neurons). Each unit of the first
layer (input layer) receives the input data of an independent
factor (variable), multiplies each input by the connection
weight, and transmits the result to the corresponding unit in
the hidden layer where the activation function is applied.
The results from the hidden layer are transferred to the output
layer by multiplying the output of each neuron in the hidden
layer by the corresponding connection weight between hidden
and output neurons. The output layer produces the network
output for further processing of the data. At this stage, the net-
work output is compared to the desired (target) output to com-
pute the error. If the error is acceptable, then the output is
assumed to be correct otherwise the weights of the connection
are adjusted starting from the output layer and propagating
backward. Once the weights are updates, a new iteration be-
gins and so on until training is completed. The training is
stopped when the error level is reached or when the number
of iterations is finished. The basics of the ANNs were intro-
duced by many authors, e.g. [34,17,35]. 2.2. Gene expression programming GEP is considered as an extension of Genetic programming
(GP). Gene expression programming is a full-'edged geno-
type/phenotype system, with the genotype totally separated from the phenotype, where in GP, genotype and phenotype
are mixed together in a simple replicator system. GEP com-
puter program is encoded in linear chromosomes composed
of genes structurally organized in a head and a tail. The
chromosomes function as a genome and are subjected to mod-
ification by means of mutation, transposition, root transposi-
tion, gene transposition, gene recombination, and one- and
two-point recombination. The chromosomes encode expres-
sion trees which are object of selection. The creation of these
separates entities (genome and expression tree) with distinct
functions allows the algorithm to perform with the high
efficiency that greatly surpasses existing adaptive techniques
[28]. The interplay of chromosomes and expression trees in
GEP implies an unequivocal translation system for translating
the language of chromosomes into the language of expression
trees (ETs). The genetic code of Gene expression programming
is very simple: a one-to-one relationship between the symbols
of chromosome and the nodes they represent in the trees.
The rules are also very simple. They determine the spatial
organization of nodes in the expression trees and the type of
interaction between sub-ETs. Therefore, there are two
languages in GEP, the language of genes and the language
of expression trees. This unequivocal bilingual notation is
called karva language. Expression trees and Karva Language
are explained in details by [36,28]. The steps for GEP are
shown in Fig. 2. The process begins with random generation
of chromosome of the initial population. Then, the chromo-
somes are expressed, and fitness of each individual is evalu-
ated. The individuals are then selected according to fitness to Figure 1 Structure shape of ANN. Create Chromosome of Initial Population Express Chromosome Execute Each Program Evaluate Fitness Iterate or
Terminate Keep Best Program Select Program Reproduction steps Prepare New Programs of Next Generation End Iterate Figure 2 Flow chart of a gene expression algorithm, Ferreira 2001. 718 Y.A.M. Moussa reproduce with modification, leaving progeny with new traits.
The individuals of this new generation are, in their turn, sub-
jected to the same developmental process: expression of the
genomes, confrontation of the selection environment, and
reproduction with modification. The process is repeated for a
certain number of generations or the required accuracy is
achieved [28]. In GEP system, the operators used for the genet-
ic modification of chromosomes are explained [36]. 3. Theoretical background Fig. 3 shows a definition sketch of the experimental model [37].
Using the principles of the dimensional analysis, the following
relationship is obtained; Ds=y1 ¼ fðLg=Lb; F1' ð1' In which, Ds is the local scour depth downstream stilling basin,
y1 is the super critical 'ow depth, Lg is the length from gate to
the beginning of Current de'ector, Lb is the basin length, and
F1 is the initial Froude number at the depth of y1. The exper-
imental data are collected from [37]. The ranges of various
parameters included in the present study are summarized in
Table 1. Figure 3 Definition sketch for the experimental model Shaheen [37]. Table 1 Ranges of data employed to train and test the GEP, ANN, and MLR. Parameter Range Froude number F1 1.45''8.45 Grain size 1.77 mm Channel side slope 1 (Horizontal): 4 (Vertical) Current de'ector
configurations Lg /Lb = 0.00''0.74, Height = 2.5 cm, With angle = 10.2  Table 2 Parameters of the GEP models. Function set +, , ·, /, S qrt, Exp, Ln, Sin,
Cos, Atan Mutation rate 0.044 Number of gene 23 IS transportation rate 0.1 Head size 7 RIS transportation rate 0.1 Linking function + Gene transportation rate 0.1 Number of
generation 1000 One-point recombination
rate 0.3 Number of
population 100 Two-point recombination
rate 0.3 Number of best
individuals cloning 10 Gene recombination rate 0.1 Figure 4 Experimental data versus the output of GEP model for train data set. Figure 5 Experimental data versus the output of GEP model for test data set. Figure 6 Experimental data versus the output of ANN model for train data set. Modeling of local scour depth downstream hydraulic structures in trapezoidal channel 719 4. Modeling of local scour depth using ANNs, GEP and MLR 4.1. ANNs model The experimental data are divided into 70% of the data for the
training of the network and the remaining 30% of the data for
testing the network prediction. The Neural Connection Soft-
ware 1998 is used to train the network [38]. All the data are
normalized using the zero-mean-unit-standard deviation. Sev-
eral trials are conducted to have the best structure of the arti-
ficial neural network. The best values of the initial weights
(±0.01), the transfer functions (Sigmoid), the number of hid-
den neurons and the best number of iterations are 4, and
2000 respectively, See Fig. 1. 4.2. GEP model Automatic Problem Solver  '' APS 3.0 '' (www.gepsoft.com), GEP a powerful soft computing software package, is used in
modeling the local scour depth downstream stilling basin
through a trapezoidal channel. The previous 70% of data set
is used to build GEP model and the rest of observations for
check the test data set. The parameters used in the GEP mod-
els are given in Table 2. Froude number (F1), and relative po-
sition of current de'ector Lg/Lb are assigned to the columns as
independent input variables while relative local scour depth
Ds/y1 is used as dependent output variable. Therefore, a Ds/
y1 model of output variable is developed by using GEP. 4.3. MLR model The same training data sets for building GEP and ANN mod-
els are used also to build the multiple regression model. The
following equation is obtained to correlate the relative scour
depth with the other independent parameters (Froude number
and relative position of current de'ector). D1=y1 ¼ 0:57 þ 1:6eð5'F1  3:2eð3'ðLg=Lb' þ 1:13eð3'ðLg=Lb' 0:2 ð2' 5. Discussion of results Numerical results using GEP, ANNs, and multiple linear
regressions (MLR) techniques are plotted versus the experi-
mental results; Figs. 4 and 5 show the experimental data versus
numerical results using GEP for both train and test data sets,
respectively. The same plots are prepared for ANNs tech-
niques (Figs. 6 and 7) and MLR (Figs. 8 and 9). The statistical Figure 7 Experimental data versus the output of ANN model for test data set. Table 3 Results of GEP, ANN, and MLR Models. Model Data set R 2 Stander error AMRE ¼ ABS DsðMeasured'Dsðmodeloutput' DSðMeasured'   (Absolute mean relative error) GEP Train data 0.86 0.11 0.08 Test data 0.96 0.08 0.07 ANN Train data 0.71 0.25 0.12 Test data 0.74 0.20 0.13 MLR (Eq. (2)) Train Data 0.64 0.50 0.14 Test data 0.67 0.25 0.20 Figure 8 Experimental data versus the output of MLR model for train data set. Figure 9 Experimental data versus the output of MLR model for test data set. 720 Y.A.M. Moussa results of model predictions for training and testing sets are
given in Table 3. It is clear that GEP model predicted the scour
depth for both training and testing set with lower error AMRE
(0.08 and 0.07) and higher accuracy R 2 (0.86 and 0.96), respec- tively. Table 3 shows that the outperforming of the GEP model
is considered the best one compared to ANNs and MLR
models. The numerical results for GEP model are presented versus the experimental data for different relative positions of current
de'ector (Lg/Lb = 0:0.76), Fig. 10. This figure shows that
GEP expresses well the experimental data for different relative
position of current de'ector. The best location of the current
de'ector to have minimum local scour depth equals (Lg/Lb),
0.37, Fig. 11. 6. Conclusions A mathematical model between is generated by Gene expression
programming (GEP) for the purpose of predicting local scour
depth downstream stilling basin through trapezoidal channel. The stilling basin is provided with current de'ector placed at
different relative positions to control the local scour depth. In
addition, an artificial neural network (ANN) and multiple lin-
ear regression (MLR) models are implemented to predict the
scour depth downstream the hydraulic structures. From this
study, it is clearly found that the Gene expression programming
model simulate the local scour depth downstream stilling basin
effectively compared to the other models (ANN, MLR). GEP
model is showing well the effect of current de'ector on the scour
formed through the trapezoidal channel section. Acknowledgement The Author would like to express his appreciation to Engineer-
ing Marowa Shaheen, Ministry of Water Resources and Irriga-
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Post Doctorate fellow with Hydroscience and
Engineering, college of Engineering, Univer-
sity of Iowa, USA. Currently, he is an asso-
ciate professor at college of engineering,
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Document Outline

Modeling of local scour depth downstream hydraulic structures in trapezoidal channel using GEP and ANNs 1 Introduction 2 Overviews of ANNs and GEP 2.1 The artificial neural networks 2.2 Gene expression programming 3 Theoretical background 4 Modeling of local scour depth using ANNs, GEP and MLR 4.1 ANNs model 4.2 GEP model 4.3 MLR model 5 Discussion of results 6 Conclusions Acknowledgement References


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