Proceedings of Coastal Engineering, JSCE, Vol.3, 2012, November

APPLICIBILITY OF A NEW DATA MINING
PREDICTION MODEL OF SCOURING AROUNDPILES
Samaneh Ghazanfari Hashemi1, Testsuya Hiraishi2
1Dept. of Civil and Earth Resources Engineering, Kyoto University, samanehghh@gmail.com
2Dept. Of Civil and Earth Resources Engineering, Kyoto University, hiraishi.tetsuya.2c@kyoto-u.ac.jp

Regarding the complexity of the scouring of piles due to waves, existing models do not always
provide acceptable results in predictions of scour hole properties. This study addresses two alternative
approaches to estimate the wave-induced scour depth around vertical piles. To assess the performance of
two data mining approaches: Artificial Neural Networks (ANN) and Support Vector Machines, data setscollected in the filed or laboratory were used. Controlling parameters of scouring such as
Keulegan-Carpenter, pile Reynolds number, etc. were used as inputs and the amounts of scouring aroundeach set of pile data were predicted as outputs of the models. Results of data mining approaches werecompared by those of empirical approaches to assess the applicability of data mining models. Results
indicate that data mining models provide better prediction than other models.
Key Words: scouring, piles, waves, soft computing models, Artificial Neural Networks, Support Vector Machines

1. INTRODUCTION
Various arrangements of pile groups are widely
being used as supports of marine structures. As piles
are located on erodible beds of the sea, scouring is athreat to such structures and the scour depth aroundpile groups should be considered well in theirdesigns. The arrangement of the piles in addition totheir geometry, sediment and wave characteristics
should be considered to estimate the scour depth
around a group of vertical piles. Regarding theimportance of prediction of scour depth, several
empirical formulae have been presented to predict
equilibrium scour depth around piles, but suchapproaches which are mostly based on dimensional
analysis and data correlation of laboratory tests do
not always produce reasonable results for field
conditions or even for laboratory cases.
Prediction of wave-induced scour depth arounda single pile has been studied by (Hebrich et al.
1984; Sumer et al. 1992, 1993; Kobayashi & Oda
1994, Ayoublu et al., 2010, etc).
Scour around groups of vertical piles due towaves has been investigated by (Sumer & Fredsoe,1998; Bayram & Larson, 2000)
Experimental investigations made by Sumer &Fredsoe (1998) showed the importance of thearrangement in a pile group scour. Their study also
showed that the equilibrium scour depth is governedby G/D and KC number, where G is the gap
between the piles, D is the pile diameter and KC is
Keulegan–Carpenter number
Considering the complexity of modeling and theimportance of scouring phenomena this study aims
to assess new alternative approaches to predictscouring around single piles as well as pile groups.

2. CONTROLLING PARAMETERS AND
EMPIRICALFORMULASOFSCOURING DUE TO WAVES
Wave-induced scour around a single piledepends on several groups of variables such as thecharacteristics of the wave, the sediment properties
and geometry of the pile. Thus, the following
functional relationship can be used to describe theequilibrium scour depth for a single pile (Sumer etal., 1992b):

S = f (T , d 50 ,U m ,U fm , D , s ,υ )(1)

where S is the equilibrium scour depth, T is thewave period, d50 is the medium sediment diameter,- 21 -

Um is the maximum undisturbed orbital velocity at
the sea bottom just above the wave boundary, Ufm isthe shear velocity at the undisturbed bed given by
U fm = (0.5f )0.5U m
in which f is the wave
friction factor, D is the pile diameter, s is thespecific gravity of sediments and ᶹ is the kinematics
viscosity. Using the dimensional analysis, the above
relationship can be presented in non-dimensional
form as follows (Sumer et al., 1992b):

Table 1 Empirical formulae applied in this study
FormulaS= 1.3{1 − exp[ −0.043( KC − 4.2)]} for KC ≥ 4.2 (a) *DeS= 1.3{1 − exp[ −0.054(KC − 3.3)]} for KC ≥ 3.3 (b)De* Myrhaug & Rue (2005) for single piles
S= 0.023KC **De** Bayram & Larson (2000)for pile groups

S= f (R e, N s , θ , KC )D(2)Where Re is the pile Reynolds number, Ns is thesediment number, ɵ is the Shield’s parameter and
KC is the Keulegan–Carpenter number defined asfollows:

Re =Ns =UmD

νUmg (s − 1)d 50

U fm2 D(s − 1) gd 50
U T
KC = mD

θ=3. RESEARCH APPROACH(3)

Two data mining approaches of Artificial NeuralNetworks (ANN) and Support Vector Machines aswell as empirical formulae were applied to predictscour hole properties around piles due to waves. A
brief introduction of each data mining method isgiven below:

(4)

(5)
(6)

The non-dimensional parameters should include theeffect of various physical processes occurring
during the scour, i.e. flow–seabed interaction,
flow–structure interaction and sediment transport. InEquation (2) the Reynolds number andKeulegan–Carpenter number describe the flow
pattern around piles, whereas the Shield’s parameterand sediment number represent the mutual effects offlow on the seabed. For a group of vertical piles, inaddition to the above parameters, spacing between
the piles (G), number of piles normal to the flow (n)and number of piles parallel to the flow (m) are also
important in the estimation of scour depth aroundpile groups. Considering these new parameters, themaximum scour depth S normalized by pile
diameter D can be best expressed as follows( Ghazanfari-Hashemi et al. (2011)):

SG m= f (R e , N s , θ , KC , , )DD n(1) DATA SET
In case of single piles, Laboratoray data ofSubhasish et al. (2006) and Sumer et al. (1992), andin case of pile groups laboratory data of Sumer andFredsoe (1998) and field data of Bayram and Larson(2000) were used respectively.

(7)

The existing empirical approaches for estimating
scour depth at pile groups are given in Table 1 forsingle piles and group piles.

(1) ARTIFICAIL NEURAL NETWORK (ANN)ANN is the most famous data-mining approachthat imitates some functions of the human brain.
Neural networks are the general-purpose computing
tools that can solve complex nonlinear problems
The network comprises of a large number of simple
processing elements linked to each other byweighted connections according to a specified
architecture. These networks learn from the training
data by adjusting the connection weights .he
connection of neurons to each other can be carriedout in various configurations. Hence, the simplest
way of modeling a neural network consists of threelayers: input layer, hidden layer and output layer.
The optimum topology of ANN is usually
determined by a trial-and-error procedure.
(2) SUPPORT VECTOR MACHINES (SVM)
Recently, a new soft computing approach named
Support Vector Machines (SVM) has beensuccessfully applied in problems such as the runoff
modeling (Bray & Han, 2004), prediction of storm
surge (Rjasekaran et al., 2008), and prediction ofsignificant wave height (Mahjoobi & Mosabbeb,2009).
In support vector regression the objective is to find afunction f(x) which has at most ε deviation from the- 22 -actually obtained targets yi for all the training data{(x 1 , y 1 ),..., (x i , y i )} and at the same time is as flat as
possible. In other words, errors are negligible aslong as they are less than ε and any deviation larger
than this is not accepted. f(x) can be expressed as(Smola & Scholkopf, 2003):
f ( x ) = (w , x ) + b , w ∈ X , b ∈ R(8)where w is a weight vector (w ∈ R n ); b is additivenoise ( b ∈ R ) and (w , x ) denote dot points in X.
Flatness of the regression function f ( x ) can beachieved by smaller values of w. To achieve that,the minimization problem can be written as aconvex optimization problem:
12min imize 2 w
y − (w , x i ) − b ≤ εsubject to  i(w , x i ) + b − y i ≤ ε(9)The optimization problem can be feasible if theerror on any training data is less than εm12min imize w + C (ξi + ξi* )
2i =1

∑

 y − (w , x ) − b ≤ ε + ξ(10)iii
 i
subject to (w i , x i ) + b − y i ≤ ε + ξ i**ξi , ξ i ≥ 0
where ζi and ζ*i are slack variables and the constant
C>0 determines the trade-off between the flatness off (x ) and the tolerable amount larger than ε which
is defined by the user.
Nonlinear support vector regressions can be used incomplex and nonlinear problems. Solving nonlinear
problems can be achieved by mapping the data intoa higher-dimensional feature space with the help ofkernel functions.
The problem of support vector regression in thefeature space can be written as (11) in the feature
space as;mf (x ) = ∑ (α i −α i* )K (x i , x ) + b

fewer parameters than ANN which leads it to be
trained more rapidly (Mahjoobi & Mosabbeb, 2009;
Ghazanfari-Hashemi et al., 2011)

4. SCOUR DEPTH PREDICTIONS
The data set was separated into two input
categories as inputs for prediction of the scour
depth: single piles (Re, Ns, ɵ, KC) and group ofpiles (Re, Ns, ɵ, KC, G/D, m/n). Scour depth
normalized by pile diameter (S/D) was predicted asthe output.
Both sets of single and group pile data weredivided into two subsets for training and testing
phases. The total number of single pile data was 88
and those of group piles were 102 data points. In
both cases 80% of the data were used for training
phase and 20% were used in validation.
(1) ANN MODEL
A Multi-Layer Perceptron (MLP) with Back
Propagation (BP) learning algorithm was used totrain the network structure of the single pilescouring prediction. The number of neurons forinput, hidden and output layers was 4, 2 and 1
respectively.
Likewise, a Multi-Layer Perceptron (MLP) withBack Propagation (BP) learning algorithm was used
to train the network structure of the group pilescouring prediction. The number of neurons for
input, hidden and output layers was 6, 1 and 1
respectively.
The performances of models were assessed
quantitatively using the following statisticalparameters: coefficient of correlation (CC), root
mean square error (RMSE) and scatter index (SI)which are defined as the following relationships
CC =∑ (T i −T i )(Oi − Oi )22
∑ (T i −T i ) ∑ (Oi − Oi )N
∑ (Oi -T i )2
RMSE = i =1N(12)

(13)

(11)

i =1

where α and αi* are Lagrangian Parameters.
In addition to the choice of a kernel, SVM
requires the setting up of kernel-specific parameters.
Furthermore, optimum values of the regularization
parameter C and the size of error in the sensitivezone need to be determined. The choice of theseparameters controls the complexity of theprediction. SVM needs less computational time andRMSE
Ti(14)

Bias = O −Tii(15)SI =In the above formulae, Oi and Ti represent targetand network outputs for the i th output, respectively;
O and T are the average of target and networkii- 23 -outputs and Ni is the total number of data points. Ahigher value of CC and smaller values of RMSE andSI mean a better model performance.
Fig. 1 and Fig. 2 show the comparison between
the measured and predicted values of scour depth incase of single and group piles.
(2) SVM MODELThe SVM model requires setting of a few
user-defined parameters, such as the regularization
parameter (C) and the type of kernel (polynominalor RBF).

minimizing in case of single pile and the value of
C=3.44 and ε=0.00001 in case of pile groups.
Fig. 3 and Fig. 4 show the comparison between
the measured and predicted values of scour depth
for single pile. In Fig. 5 and Fig. 6 the comparisons
between the measured and predicted values of scour
depth by different approaches are shown.

5. RESULTS AND DISCUSSIONS
Table 2 presents a summary of the results of all
approaches (data mining and empirical approaches)
and their error statistics. Comparison of results andtheir related statistical errors indicate that data
mining approaches outperform the empirical ones
not only in single piles but also in case of pilegroups. The comparisons of all applied approaches
were also shown in Fig. 5 and Fig. 6.
Regarding Table 2, it can be concluded that

Fig. 1 Comparison between the observed and predicted
normalized scour depth of single piles by the ANN modelFig. 3 Comparison between the observed and predicted
normalized scour depth of single piles by the SVM modelFig. 2 Comparison between the observed and predicted
normalized scour depth of group piles by the ANN model

In this study, the regularization parameter C and thesize of error in sensitive zone parameters control thecomplexity of prediction. A value of C=350 and
ε=0.010 were selected based on the process of error- 24 -Fig. 4 Comparison between the observed and predicted
normalized scour depth of group piles by the SVM model

SVM and ANN can be introduced as high reliable
alternative approaches for empirical ones in
prediction of pile scour depths due to waves.
REFERENCES

Fig. 5 Comparison of measured and predicted normalized
scour depth for single pile using different approaches.

Fig. 6 Comparison of measured and predicted normalized
scour depth for pile groups using different approaches
Table 2 Summary of results by all approaches

CCSVM
ANN
Myrhaung&Rue(2005)
SVM
ANN
Bayram&Larson(2000)

0.97340.96020.0871
0.0696

0.0643-0.0884

0.94250.14920.14050.90500.85280.32140.3956-0.04630.01500.1176

1.25260.0154

Pile group

Single pile

Approach

RMSE

BIAS

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(Received June 15, 2012)- 25 -