Genetic programming for prediction of local scour at vertical bridge abutment

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Special Issue: 02 | Dec-2013, Available @ http://www.ijret.org 74
GENETIC PROGRAMMING FOR PREDICTION OF LOCAL SCOUR AT
VERTICAL BRIDGE ABUTMENT
S. A. Begum1
, A. K. Md. Fujail2
, A. K. Barbhuiya3
1
Department of Computer Science, Assam University, Silchar, Assam, India
2
Department of Computer Science, Assam University, Silchar, Assam, India
3
Department of Civil Engineering, National Institute of Technology, Silchar, Assam, India
Abstract
Local scour around bridge abutment is a common problem encountered worldwide. Extensive laboratory and field studies have been
carried out in this field and the equations derived so far are applicable to particular circumstances only. This paper presents an
alternative to the empirical equations for Prediction of Local Scour at Vertical Bridge Abutment in the form of genetic programming
(GP). The performance of the developed models has been evaluated using Root Mean Square Error and Correlation Coefficient. The
accuracy of the trained model has been compared with the empirical formulae available in the literature. The performance of GP
model is found to be more accurate than the empirical equations.
Keywords: Genetic programming, neural network, scour depth, abutment.
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1. INTRODUCTION
Scour is the erosion caused by water of the soil around
obstruction. The magnitude of the scour is multiplied when the
natural flow is disturbed due to the presence of some
obstructions like bridge pier, bridge abutment, spur etc. Failure
of bridges due to local scour at their foundation is a common
occurrence and each year a large amount is spent to repair or
replace bridges whose foundations have been undercut by the
scouring action of stream flow [1, 2]. Bridge foundation
consists of abutments and piers. Probably the number of
existing bridge abutments is much more than the numbers of
bridge piers as most of the bridges are of single span. In a
report, published by the Department of Scientific and Industrial
Research (DSIR) of New Zealand [3], it is reported that almost
50% of total expenditure was made to repair and maintain
bridge damage, out of which 70% was spent to repair abutment
scour. Thus, scour around bridge abutment is a severe hazard
to the performance of bridges. Considerable investigations on
pier scour have been carried out and a reliable design method
is now available [4]. However, evaluating scour around
abutment is in preliminary stage. It is essential to understand
the scour in the design of foundations of structures as well as
scour protection work. Without a detailed understanding of
scour, failures are more likely to occur. Extensive experimental
investigation has been conducted to understand the complex
process of scour and to determine a method of predicting scour
depth for various abutment situations but no generic formula
has been developed yet that can be applied to all abutment
conditions to determine the extent of scour that may develop.
Although, numerous empirical formulae have been presented
to estimate equilibrium scour depth at bridge abutment [5-6],
each varies significantly, highlighting the fact that there is a
lack of knowledge in predicting scour depth and that a more
universal solution would be beneficial. Only a few number of
studies relating to the application of soft computing methods in
the field of scour around bridge abutment are available in the
literature. Kheireldin [7] used the artificial neural network
(ANN) to predict the maximum local scour depth around
bridge abutments. It reported that the ANN approach
performed well for one set of data and its performance was not
satisfactory for another set of data. Begum et al. [8] developed
Radial basis function (RBF) network to predict scour depth
around vertical bridge abutment and it is reported that the
performance of RBF network is much better than the existing
empirical formulae. Begum et al. [9] also developed Multilayer
perceptron (MLP) and RBF network to predict scour around
semicircular abutment. In the experimental results, it is shown
that ANN models perform better than empirical equations.
In this paper we present an alternative approach for Prediction
of Local Scour at Vertical Bridge Abutment in the form of
Genetic Programming (GP).
2. GENETIC PROGRAMMING
GP is an extension to genetic algorithms (GAs) proposed by
Koza [10] who defines GP as a domain-independent problem-
solving approach in which computer programs are evolved to
solve or approximately solve problems based on the Darwinian
principle. GP creates computer programs that consist of
variables and several mathematical operators (function) sets as
the solution. The function set of the model can be composed of
arithmetic operations (+, −, /, *) and function calls (such as ex,

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sin, cos, log, ln, sqrt, power). In the present GP
implementation, two-point string crossover and single point
mutation is used. In crossover, a segment of random position
and random length is selected in both parents and exchanged
between them. In mutation, an operator or operand is replaced
with another operator symbol over the same set. The fitness of
a GP individual may be computed by using the equation
2
1
( ) (1)
N
i i
i
E o t

 
Where ti = value returned by a chromosome and oi = target
value for the ith fitness case.
In the present work, the maximum size of the program is
restricted by setting the maximum depth of the tree. The best
individual of the trained GP model can be identified based on
Eq. 1 and can be converted into a functional representation.
A few number of studies related to the application of GP in
hydraulic engineering are available in literature. Guven and
Gunal [11] used GP to predicted local scour downstream of
hydraulic structures. It was reported that the performance of
GP was found more effective when compared to regression
equations and ANNs in predicting the scour depth at bridge
piers. Guven et al.[12] applied linear genetic programming
(LGP) to predict scour around circular piles and the results
were better than Adaptive neuro fuzzy inference system
(ANFIS) and regression-based equations. Azamathulla et al.
[13] estimated the scour depth around pier with GP. The
performance of GP was found to be more effective when
compared with the results of regression equations and ANNs
modeling in predicting the scour depth around pipelines.
Azamathulla et al. [14] also developed LGP model to compute
scour below submerged pipeline. The results were better as
compared to ANFIS and regression-based equations.
Azamathulla [15] implemented GP model for prediction of
scour depth downstream of sills. It was able to provide better
estimation than existing predictors.
3. GP TO PREDICT MAXIMUM LOCAL SCOUR
DEPTH AROUND ABUTMENT
Maximum equilibrium local scour depth around an abutment in
a steady flow of uniform, cohesionless sediment depends on
variables characterizing the fluid, flow, bed sediment and
abutment. Thus, the maximum equilibrium scour depth can be
described by the following functional relationship [16]:
dse = f 1(U, ρ, ρs, g, l, ν, h, d50) (2)
where, U = average approach flow velocity, ρ = mass density
of the fluid, ρs = mass density of the sediment, g = gravitational
acceleration, l = abutment length, ν = kinematic viscosity,
h=approaching flow depth, d50 = median grain size, dse =
equilibrium scour depth.
Since, ρ, ρs, g and ν are constant for given sediment and fluid,
the relationship between dse and its dependent variables can be
expressed as:
dse = f 2(l, d50, h, U) (3)
The dataset for training the GP models were collected from the
literature [16]. It consists of an experimental database
comprising of five sets of data for vertical wall abutments. The
dataset contains four independent parameters: l, d50, h and U
and one dependent parameter dse i.e. depth of the scour. The
whole dataset consists of 99 samples out of which 79 samples
are considered for training and 24 samples are considered for
testing.
The GP model is implemented in MATLAB 7.9 environment.
To develop the model, l, d50, h and U are considered as input
parameter and dse is considered as output parameter. The
arithmetic operators (+, −, *, /) and mathematical functions
(square root, power, log, exponentiation) were used. The
population size of the model is specified as 150 and the
maximum number of nodes in the GP tree was specified as
300. The tournament size was set as 2%. To get the optimal
solution, GP model was tested with upto 4000 generations.
4. EXPERIMENTAL RESULTS
The performance of GP in training and testing sets is validated
in terms of correlation coefficient (CC) and root mean square
error (RMSE).
 
2
1
1
(4)
n
i i
i
RMSE o t
n 
 
  
   
1
2 2
1 1
(5)
n
i i
i
n n
i i
i i
o o t t
CC
o o t t

 
 

 

 
where, oi and ti are network and target output for the ith
input
pattern, and o , t are the average of network and target
outputs and n is the total number of events considered. The
model having minimum RMSE and maximum CC during
testing is selected as optimum. Some of the training and testing
cases are tabulated in Table 1.

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Table 1 Training and Testing cases of GP (Population
Size=150, Tournament Size=0.02)
Gener
ation
Training Testing
RMSE CC RMSE CC
1000 0.0821 0.9153 0.0752 0.9153
2000 0.0647 0.9472 0.0596 0.9472
3000 0.0492 0.9648 0.0351 0.9648
4000 0.0510 0.9680 0.0373 0.9680
From table 1, it is seen that the GP model with 3000 generation
provides the minimum RMSE and maximum CC for the
training and testing case data and thus considered as the best
case for the present experimentation. For the best case, the
generated GP tree is shown is shown in Fig. 1. The
corresponding arithmetic expression is as follows:
1
4
4 1 2 3 1*log( )*(log( ) ) (6)
x
xe
sed x x x e x x   
Fig. 1 GP Tree
The best case of the GP model and the result of two of the
empirical equations available in the literatures (Appendix A)
are tabulated in Table 2. For the best case training and testing
of GP model the actual versus the predicted scour depth is
plotted in Fig 2. From Fig. 2, it is seen that the predicted values
are within ±20% from the observed values. From Table 2, it is
observed that the GP model is able to provide better results
than the empirical equations developed by Froehlich [5] and
Kandasamy et al. [6].
Table 2 GP versus empirical equations
Method RMSE CC
Froehlich[5] 0.3009 0.4018
Kandasamy and
Melville[6]
0.1676 0.7054
GP 0.0351 0.9648
(a)
(b)
Fig. 2 The best case training and testing of GP Model
5. CONCLUSIONS
In the present work, GP is employed to predict the local scour
at vertical bridge abutment. The GP model with population size
of 150, tournament size=0.02 and 3000 iteration is found to be
optimal. The performance of the present GP model is
compared with two of the existing empirical equations over the
same dataset. The GP tree and the mathematical expression
generated by the best case GP model are also presented. From
the results, it is observed that the predicted scour depth of the

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GP model is more accurate than the empirical equations for the
dataset used in the present work.
FUTURE WORK
The present GP configuration can further be fine tuned to
improve the performance and results may be compared with
ANN models (viz. MLP, RBF and Bayesian Network) with the
same dataset.
ACKNOWLEDGEMENTS
One of the author (AKMF) gratefully acknowledges UGC and
Ministry of Minority affairs for the award of Maulana Azad
National Fellowship for the research work.
REFERENCES
[1] B. W. Melville, A. J. Sutherland, Design method for
local scour at bridge piers,J. Hydraul. Eng., ASCE,
vol. 114, No. 10, pp. 1210-1226, October 1988.
[2] D. S. Jeng, S. M. Bateni, E. Lockett, Neural network
assessment for scour depth around bridge piers,
Research Report No R855, Department of Civil
Engineering, Environmental Fluids/Wind Group, The
University of Sydney, November 2005.
[3] G. H. Macky, Survey of roading expenditure due to
scour. CR 90_09, Department of Scientific and
Industrial Research, Hydrology Centre, Christchurch,
New Zealand, 1990.
[4] S. M. Bateni, S. M. Borghei, D. S. Jeng, Neural network
and neuro-fuzzy assessment for scour depth around
bridge piers, Eng. Appl. Artif. Intell., vol. 20, No. 3, pp.
401–414, April 2007.
[5] D.C. Froehlich, Local scour at bridge abutments. Proc.
Natl. Conf. Hydraulic Engineering (New Orleans, LA:
Am. Soc. Civil Eng.), pp. 13–18, 1989.
[6] J.K. Kandasamy, B.W. Melville, Maximum local scour
depth at bridge piers and abutments, J. Hydraul.
Research, 36(2), pp. 183-198, 1998.
[7] K.A. Kheireldin, “Neural Network Modeling for Clear
Water Scour around Bridge Abutments”. J. Water
Science, 25(4), pp. 42-51, 1999.
[8] S.A. Begum, A.K. Md. Fujail, A.K. Barbhuiya, Radial
Basis Function to predict scour depth around bridge
abutment, IEEE Proceedings of the 2011 2nd
National
Conference on Emerging Trends and Applications in
Computer Science, (Shillong, Meghalaya, India), ISBN
No. 978-1-4244-9581-8, pp. 76-82, 2011.
[9] S.A. Begum, A.K. Md. Fujail, A.K. Barbhuiya,
Artificial Neural Network to Predict Equilibrium Local
Scour Depth around Semicircular Bridge Abutments,
6th
SASTech, Malaysia, Kuala Lumpur, 2012.
[10] J. Koza, Genetic programming: On the programming
of computers by means of natural selection, MIT Press,
Cambridge, Mass, 1992.
[11] A. Guven, and M. Gunal, “Genetic programming
approach for prediction of local scour downstream of
hydraulic structures.” J. Irrig.Drain. Eng., 134(2), pp.
241–249, 2008.
[12] A. Guven and H. Md. Azamathulla and N. A. Zakaria.
Linear genetic programming for prediction of circular
pile scour. Ocean Engineering, 36(12-13), pp. 985-991,
2009
[13] H. Md. Azamathulla and A. Ab Ghani, N. A. Zakaria
and A. Guven, Genetic Programming to Predict Bridge
Pier Scour. Journal of Hydraulic Engineering,
136(3):165-169, 2010
[14] H. Md. Azamathulla, A. Guven and Y. K. Demir,
Linear genetic programming to scour below submerged
pipeline. Ocean Engineering, 38(8-9), pp. 995-1000,
2011.
[15] H. Md. Azamathulla, Gene expression programming
for prediction of scour depth downstream of sills,
Journal of Hydrology, 2012, In Press.
[16] S. Dey, A. K. Barbhuiya, Time Variation of Scour at
Abutments, Journal of Hydraulic Engineering, 131(1),
pp. 11-23, 2005.
APPENDIX A:
Author Formula
Froehlich
[5]
0.63 0.43
1.16 1.87
0.78 1se
s r g
d l h
K K F
h h d
     
    
   
Where, Ks=abutment shape factor, K
=abutment alignment factor,
Fr=approaching flow Froude number, g =
geometric standard deviation
Kandasam
y and
Melville
[6]
1
2
n n
se sd K K h l 

Where, Ks is the shape factor, K2 = 5 and n =
1 for h/l <=0.04; K2 = 1 and n = 0.5 for 0.04
< h/l < 1 and K2 = 1 and n = 0 for h/l> 1

Genetic programming for prediction of local scour at vertical bridge abutment

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Genetic programming for prediction of local scour at vertical bridge abutment