# Peak Ground Acceleration Prediction by Artificial Neural Networks for Northwestern Turkey

Authors: Kemal Günaydın; Ayten Günaydın
Journal: Mathematical Problems in Engineering
 (2008)

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## Abstract

Three different artificial neural network (ANN) methods, namely, feed-forward back-propagation (FFBP), radial basis function (RBF), and generalized regression neural networks (GRNNs) were applied to predict peak ground acceleration (PGA). Ninety five three-component records from 15 ground motions that occurred in Northwestern Turkey between 1999 and 2001 were used during the applications. The earthquake moment magnitude, hypocentral distance, focal depth, and site conditions were used as inputs to estimate PGA for vertical (U-D), east-west (E-W), and north-south (N-S) directions. The direction of the maximum PGA of the three components was also added to the input layer to obtain the maximum PGA. Testing stage results of three ANN methods indicated that the FFBPs were superior to the GRNN and the RBF for all directions. The PGA values obtained from the FFBP were modified by linear regression analysis. The results showed that these modifications increased the prediction performances.


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## Body

## 1. Introduction

Knowing the characteristics  of ground  motions in a specified region is vital for the design
of engineering structures. Peak ground acceleration (PGA) is commonly used to
define the ground motions. Based on the historical ground motion records,
several empirical equations were suggested through regression analysis for
the estimation of PGA [1–7]. Different
combinations of the earthquake characteristics and site condition were generally
taken into consideration by the authors during the derivation of the equations.
Douglas [8] performed an extensive analysis
for earlier empirical formulas. As a result of this investigation very little
agreement has been reached in the past 30 years of ground motion estimation
relation studies since each formula had been derived based on the available data
which varied greatly with geographical regions. The empirical attenuation
relationships based on Turkish strong ground motion data were proposed by Aydan
et al. [9], Inan et al. [10], Aydan [11], Gülkan and Kalkan [12], and Ulusay et
al. [13].Northwestern Turkey, which includes the Marmora region,
is a densely populated and industrialized region of the country. In recent
years, two destructive earthquakes Kocaeli (1999) (the moment magnitude,Mw=7.4)
and Düzce (1999) (Mw=7.1) occurred in this area. As a result of comprehensive
records from these ground motions, their aftershocks and other recent earthquakes,
several investigations were performed to evaluate the PGA of this region. Some
of these investigations were summarized as follows: Özbey [14]
developed an attenuation relationship for peak horizontal acceleration using
data from the Kocaeli (1999) and the Düzce (1999) earthquakes. Akyol et
al. [15] evaluated attenuation and site effects of the 69 microearthquakes
recorded at six stations located in different geological conditions in the city
of Bursa, Marmora region, Turkey. Durukal [16]
compared not only horizontal peak accelerations from the Kocaeli and Düzce earthquakes
with the attenuation relationships derived by Boore et al. [3], Campbell [4], Sadigh et al. [5], and Atkinson and Boore [17] but also vertical peak
accelerations from these earthquakes with the formulas of Campbell [4],
and Atkinson and Boore [17]. From these comparisons, the author concluded
that the attenuation relationships relied heavily on extrapolation from larger
distances and smaller magnitude earthquakes to define ground motion predictions
in the distance and magnitude range and could not yield correct values in the near
field for large magnitude events. Fukushima et al. [18] investigated
attenuation characteristics of PGA recorded on different sites during the
Kocaeli (1999) and Düzce (1999) earthquakes and found that the PGA data of the
Kocaeli earthquake showed good agreement with the attenuation relation derived
by Fukushima
and Tanaka [19]. Özbey et al. [20] used 195 recordings from 17 recent
earthquakes including the Kocaeli (1999) and Düzce (1999) earthquakes and their aftershocks to develop empirical
attenuation relationships of PGA and 5% damped spectral acceleration for Northwestern Turkey. Özel et al. [21]
evaluated PGA values recorded on 19 different sites during the largest
aftershock (Mw=5.8) of the Kocaeli (1999) earthquake by using the empirical
attenuation relationships derived by Fukushima
and Tanaka [22] and Ansal [23].Artificial
neural networks (ANNs),
however, are not defined as a specific equation form. They can infer solutions
to problems having nonlinear and complex interaction among the variables and
find functional relationship between the input and output of dataset. In recent
years, considerable researches, some of which referenced in this paragraph,
were performed to evaluate the PGA and response spectra of ground motions by
using ANN methods. Dai and MacBeth [24, 25] used ANN to pick seismic arrivals
from local earthquakes data. Dai and MacBeth [26] developed a back-propagation
neural network to identify P- and S-arrivals from three-component recordings of
local earthquake data. Giacinto et al. [27] applied the neural networks to evaluate earthquake
risk for real geological structures. Ghaboussi and Lin [28] proposed a new
method using the ANN to generate artificial earthquake accelerograms from
response spectra. Lin
and Ghaboussi [29] applied stochastic neural networks to generate multiple
spectrum accelerograms from response spectra or design spectra. Kerh and Chu [30] estimated PGA at
two main line sections of Kaohsiung Mass Rapid Transit in Taiwan by using three
models of the FFBP structured different combination of  epicentral distance,  focal depth, and earthquake magnitude in the
input layer and verified their results by using microtremor records. They also
compared their results with those of available empirical formulas in the
literature. Lee and Han [31] used five ANN-based models to generate artificial
earthquake and response spectra. Baziar and Ghorbani [32] developed a neural
network model to predict the horizontal ground displacement in both ground
slope and free face conditions due to liquefaction-induced lateral spreading. Kerh
and Ting [33]  applied back-propagation neural networks obtained from different input
combinations of epicentral distance, focal depth, and magnitude to predict PGA along the high-speed rail system in Taiwan. Alves [34] used
neural networks for earthquake forecasting. Barrile et al. [35] predicted
seismic sequences of aftershocks occurred after a great earthquake by using
radial basis function neural network. Liu et al. [36] evaluated the peak ground
velocity for West America region. The authors
used the earthquake magnitude, epicentre distance, site intensity, and site
condition as inputs. As a result of this study, input parameters were ordered
as earthquake magnitude, epicentral distance, and soil condition with respect
to the importance of them on the peak ground velocity variations. Amiri and
Bagheri [37] used wavelet multiresolution analysis and radial basis function
neural network to generate artificial earthquake accelerograms from response
spectrum.The
present study aimed at developing the PGA estimation models for Northwestern Turkey by using ANN methods. The PGA was
modelled as function of earthquake moment magnitude (Mw), hypocentral
distance (HD), focal depth (FD), and site conditions (SCs) for vertical, E-W and N-S directions,
separately. The direction of the maximum PGA of the three components was also
used as input to develop the maximum PGA model. Each model was calculated by
using three different ANN methods such as FFBP, RBF, and GRNN. The result
showed that the models of FFBP gave the best prediction performance under the
conditions of used data. In order to improve prediction performance, the PGA
values of FFBP were modified by the regression analysis.


## 2. Artificial Neural Network Method

### 2.1. Feed-Forward Back-Propagation Networks

Feed-forward back-propagation (FFBP) networks have
three components: an input layer, one or more hidden layers, and an output
layer (see Figure1). Each layer consists of one or more neurons (nodes). In
the calculation process of problem solving, all input nodes are collected at
each hidden node after being multiplied by weights. Later, a bias is attached
to this sum, transformed through a nonlinearity function, and transferred to
the next layer. There are several functions such as hyperbolic tangent, sigmoid
and linear functions that can be used as transfer function. The same procedure
can be followed in this layer to provide the network output results consequently.
As the forward processing arrives at the output layer, the overall error
between the network output and the actual observation is calculated. The error
at the output layer propagates backward to the input layer through the hidden
layer in the network to obtain the final desired outputs. During the forward
pass all the synaptic weights of the networks are fixed. During the backward
pass, on the other hand, all the synaptic weights are adjusted in accordance
with an error-correction rule [38]. Figure 1 shows a typical FFBP structure
used in this study. There are
one input layer having xn neurons, one hidden layer having hm neurons, and one output layer having yl neurons. Every node in the layer is connected with that in the next layer by
interconnection strength, or weight (w).
Input-to-hidden and hidden-to-output weights are named as wij and wik, respectively. Mathematically the output of network (yk) is computed by the equation
(2.1)yk=f˜[∑j=1mwjk⋅f[∑i=1n(wij⋅xi+b1)]+b2],k=1,2,3,…,l,
where b1 is the first layer bias, b2 is the second layer bias,
f(⋅)
is
activation function between input and hidden layers, and
f˜(⋅)
is activation function between hidden and
output layers. The tangent sigmoid (tan-sigmoid), logarithmic sigmoid
(log-sigmoid), and linear activation functions [38] are tried for both
f(⋅)
and
f˜(⋅)
to obtain the best prediction performance. The  f(⋅)
and
f˜(⋅)
types used in this study are presented in
Section 4.Figure 1
Schematic diagram of an FFBP.The back-propagation network (BPN) proposed
by Rumelhart et al. [39] is used for learning model. The aim of this model is
to minimize iteratively the global error or mean sum squared error (MSE), E, defined by
(2.2)E=12P∑p=1P∑k=1l(Tpk−ypk),p=1,2,3,…,P,
where Tpk is the target (observed) output at kth
output node of pth pattern, ypk is the predicted output
at kth output node of pth pattern, P is total number of training patterns. The global error (E) at the
output layer propagates backward from the output to hidden layer in order to
adjust the weights in each layer of the network during each iteration. The
iterations are repeated until a specified convergence is reached or a given
number of iterations are over.Each step in the learning phase is called a
Learning Epoch. In the present study Levenberg-Marquardt algorithm [40, 41] is
used. It minimizes E while it tries
to keep small the step between the old weights configuration (Wold) and the updated one (Wnew). This algorithm can be
written as follows:
(2.3)Wnew=Wold−[JTJ+γI]−1JTE(Wold),
where J is the Jacobian of the error function E, I is the identity matrix, and γ is the parameter used to define the iteration
step value [42].  The adaptive learning rate,
which changes during the training stage dynamically, is used here. The learning
rate takes values changing from 0 to 1. For each epoch, if performance decreases
toward the goal, then the learning rate is increased by the factor learning
increment. If performance increases, the learning rate is adjusted by the
factor learning decrement. Throughout all FFBP simulations, the performance
goal is taken as 0.00001. After the training phase of the network has been
successfully accomplished, performance of the trained model is tested with a
different dataset. Details of the concept
of FFBP networks and description of various training algorithms can be seen in Haykin
[38], Bishop and Hinton [43], and Principe et al. [44].The training
input and output data of models are normalized by(2.4)xni=a⋅xi−xminxmax−xmin+b,
where xi is the observed data obtained from ith
record, xni is normalized value of ith record, xmax and xmin are the maximum
and minimum values, respectively. Different values can be assigned for scaling
factors a and b. There are no fixed rules as to which standardization approach
should be used in particular circumstances [45, 46]. In this study, different a and b values were tried to obtain the best prediction performance,
then, a=0.6 and b=0.2 were taken. Thus, both input and output
data were normalized within the range 0.2–0.8. The relative
better node numbers of the hidden layer were found by trial and error because
there was no theory about the nodes numbers yet. The networks training were
stopped after maximum 10000 epochs.


### 2.2. Radial Basis Function Networks

Radial basis function (RBF) networks were introduced
into the neural networks literature by Broomhead and Lowe [47]. The RBF
consists of three layers, namely, input, hidden and output. It is a feed-forward
network and has only one hidden layer (Figure 2). The input layer is made up of
source nodes (sensory units) that connect the network to its environment. The
second layer applies a nonlinear transformation from the input space to the
hidden space; in most applications the hidden space is of high dimensionality. The
output layer is linear, supplying the response of the network to the activation
pattern (signal) applied to the input layer [38]. The input to each RBF neuron is treated as a measure of the difference
between data and a “centre”, which is a parameter of its transfer function (Figure
2). The transfer function of the neuron indicates the influence of data points
at the centre. Generally this function is Gaussian and its centres can be
chosen either randomly from the training data or they are iteratively trained
or derived using techniques like K-means, Max-Min algorithms, Kohonen self
organizing maps [38, 48]. After this unsupervised learning and cluster
formations, the weights between the hidden and output layer neurons are
determined by multiple regression in a supervised manner. The concept of such a
fragmented learning is borrowed from certain biological neurons (doing, say,
visual recognition), which function on the basis of “locally tuned response” to
sensing. The RBF does not involve iterative training and hence much of the
training time is saved [49]. The output y of an RBF is
computed by the equation
(2.5)y=f(x)=∑i=1mwi⋅G∥x−ci∥+wo,
where m is number of hidden nodes (i=1,2,3,…,m), wi is connection weights between the hidden neuron and output neuron, x is input feature vector, c is centre of the respective field, ∥x−ci∥ is the Euclidian distance between the
prediction location (ci),
and each known data location (x) and G∥x−ci∥ is radial basis function. The general class of
radial basis function is Gaussian as given by (2.6):
(2.6)G∥x−ci∥=−exp(−∑i=1m∥xi−ci∥2σi2),
where σi is the width of the Gaussian function indicating selectivity of the neuron. In
this study, the exact design RBF creating as many hidden neurons as there were
input vectors was used
[50]. Different spread constants were examined to find the best estimation
performance of the RBF with zero error on training vectors.Figure 2
Schematic diagram of an RBF.


### 2.3. Generalized Regression Neural Networks

The generalized regression neural network
(GRNN) was proposed by Specht [51] and reinvented by Schiøler and
Hartmann [52]. The GRNN is Specht's term for Nadaraya-Watson kernel
regression [53, 54]. It is based on established statistical principles and
converges with an increasing number of samples asymptotically to the optimal
regression surface [55].Since the principle of the GRNN has been
well documented in the literature [38, 51, 56], it is briefly explained in this
section. As shown in Figure 3, the GRNN consists of four
layers, including the input layer, pattern layer, summation layer, and output
layer. Each input unit in the input layer corresponds to individual process
parameter. The input layer is fully connected to the second, pattern layer,
where each unit represents a training pattern and its output is a measure of
the distance of the input from the stored patterns. Each pattern layer unit is
connected to the two neurons in the summation layer: S- and D-summation neurons.
The S-summation neuron
computes the sum of the weighted outputs of the pattern layer while the D-summation neuron calculates the unweighted outputs of
the pattern neurons. The connection weight between the ith neuron in the
pattern layer and the S-summation neuron
is yi, the
target output value corresponding to the ith input pattern. For D-summation
neuron, the connection weight is unity. The output layer merely divides the
output of each S-summation neuron
by that of each D-summation neuron,
yielding the predicted value to an unknown input vector x as
(2.7)y^(x)=∑i=1nyiexp[−D(x,xi)]∑i=1nexp[−D(x,xi)],
where n indicates
the number of training patterns and the Gaussian D function in (2.7) is defined as
(2.8)D(x,xi)=∑j=1p(xj−xijζ)2,
where p indicates
the number of elements of an input vector. The xj and xij represent the jth element of x and xi, respectively. The
ζ is generally referred to as the spread, whose
optimal value is experimentally determined. It should be noted that in conventional
GRNN applications all units in the pattern layer have the same single spread [57].
The GRNN performance is controlled only by the spread factor during the
training. In this study, different spreads were tried to obtain the best
prediction performance.Figure 3
Schematic diagram of a GRNN.


## 2.1. Feed-Forward Back-Propagation Networks

Feed-forward back-propagation (FFBP) networks have
three components: an input layer, one or more hidden layers, and an output
layer (see Figure1). Each layer consists of one or more neurons (nodes). In
the calculation process of problem solving, all input nodes are collected at
each hidden node after being multiplied by weights. Later, a bias is attached
to this sum, transformed through a nonlinearity function, and transferred to
the next layer. There are several functions such as hyperbolic tangent, sigmoid
and linear functions that can be used as transfer function. The same procedure
can be followed in this layer to provide the network output results consequently.
As the forward processing arrives at the output layer, the overall error
between the network output and the actual observation is calculated. The error
at the output layer propagates backward to the input layer through the hidden
layer in the network to obtain the final desired outputs. During the forward
pass all the synaptic weights of the networks are fixed. During the backward
pass, on the other hand, all the synaptic weights are adjusted in accordance
with an error-correction rule [38]. Figure 1 shows a typical FFBP structure
used in this study. There are
one input layer having xn neurons, one hidden layer having hm neurons, and one output layer having yl neurons. Every node in the layer is connected with that in the next layer by
interconnection strength, or weight (w).
Input-to-hidden and hidden-to-output weights are named as wij and wik, respectively. Mathematically the output of network (yk) is computed by the equation
(2.1)yk=f˜[∑j=1mwjk⋅f[∑i=1n(wij⋅xi+b1)]+b2],k=1,2,3,…,l,
where b1 is the first layer bias, b2 is the second layer bias,
f(⋅)
is
activation function between input and hidden layers, and
f˜(⋅)
is activation function between hidden and
output layers. The tangent sigmoid (tan-sigmoid), logarithmic sigmoid
(log-sigmoid), and linear activation functions [38] are tried for both
f(⋅)
and
f˜(⋅)
to obtain the best prediction performance. The  f(⋅)
and
f˜(⋅)
types used in this study are presented in
Section 4.Figure 1
Schematic diagram of an FFBP.The back-propagation network (BPN) proposed
by Rumelhart et al. [39] is used for learning model. The aim of this model is
to minimize iteratively the global error or mean sum squared error (MSE), E, defined by
(2.2)E=12P∑p=1P∑k=1l(Tpk−ypk),p=1,2,3,…,P,
where Tpk is the target (observed) output at kth
output node of pth pattern, ypk is the predicted output
at kth output node of pth pattern, P is total number of training patterns. The global error (E) at the
output layer propagates backward from the output to hidden layer in order to
adjust the weights in each layer of the network during each iteration. The
iterations are repeated until a specified convergence is reached or a given
number of iterations are over.Each step in the learning phase is called a
Learning Epoch. In the present study Levenberg-Marquardt algorithm [40, 41] is
used. It minimizes E while it tries
to keep small the step between the old weights configuration (Wold) and the updated one (Wnew). This algorithm can be
written as follows:
(2.3)Wnew=Wold−[JTJ+γI]−1JTE(Wold),
where J is the Jacobian of the error function E, I is the identity matrix, and γ is the parameter used to define the iteration
step value [42].  The adaptive learning rate,
which changes during the training stage dynamically, is used here. The learning
rate takes values changing from 0 to 1. For each epoch, if performance decreases
toward the goal, then the learning rate is increased by the factor learning
increment. If performance increases, the learning rate is adjusted by the
factor learning decrement. Throughout all FFBP simulations, the performance
goal is taken as 0.00001. After the training phase of the network has been
successfully accomplished, performance of the trained model is tested with a
different dataset. Details of the concept
of FFBP networks and description of various training algorithms can be seen in Haykin
[38], Bishop and Hinton [43], and Principe et al. [44].The training
input and output data of models are normalized by(2.4)xni=a⋅xi−xminxmax−xmin+b,
where xi is the observed data obtained from ith
record, xni is normalized value of ith record, xmax and xmin are the maximum
and minimum values, respectively. Different values can be assigned for scaling
factors a and b. There are no fixed rules as to which standardization approach
should be used in particular circumstances [45, 46]. In this study, different a and b values were tried to obtain the best prediction performance,
then, a=0.6 and b=0.2 were taken. Thus, both input and output
data were normalized within the range 0.2–0.8. The relative
better node numbers of the hidden layer were found by trial and error because
there was no theory about the nodes numbers yet. The networks training were
stopped after maximum 10000 epochs.


## 2.2. Radial Basis Function Networks

Radial basis function (RBF) networks were introduced
into the neural networks literature by Broomhead and Lowe [47]. The RBF
consists of three layers, namely, input, hidden and output. It is a feed-forward
network and has only one hidden layer (Figure 2). The input layer is made up of
source nodes (sensory units) that connect the network to its environment. The
second layer applies a nonlinear transformation from the input space to the
hidden space; in most applications the hidden space is of high dimensionality. The
output layer is linear, supplying the response of the network to the activation
pattern (signal) applied to the input layer [38]. The input to each RBF neuron is treated as a measure of the difference
between data and a “centre”, which is a parameter of its transfer function (Figure
2). The transfer function of the neuron indicates the influence of data points
at the centre. Generally this function is Gaussian and its centres can be
chosen either randomly from the training data or they are iteratively trained
or derived using techniques like K-means, Max-Min algorithms, Kohonen self
organizing maps [38, 48]. After this unsupervised learning and cluster
formations, the weights between the hidden and output layer neurons are
determined by multiple regression in a supervised manner. The concept of such a
fragmented learning is borrowed from certain biological neurons (doing, say,
visual recognition), which function on the basis of “locally tuned response” to
sensing. The RBF does not involve iterative training and hence much of the
training time is saved [49]. The output y of an RBF is
computed by the equation
(2.5)y=f(x)=∑i=1mwi⋅G∥x−ci∥+wo,
where m is number of hidden nodes (i=1,2,3,…,m), wi is connection weights between the hidden neuron and output neuron, x is input feature vector, c is centre of the respective field, ∥x−ci∥ is the Euclidian distance between the
prediction location (ci),
and each known data location (x) and G∥x−ci∥ is radial basis function. The general class of
radial basis function is Gaussian as given by (2.6):
(2.6)G∥x−ci∥=−exp(−∑i=1m∥xi−ci∥2σi2),
where σi is the width of the Gaussian function indicating selectivity of the neuron. In
this study, the exact design RBF creating as many hidden neurons as there were
input vectors was used
[50]. Different spread constants were examined to find the best estimation
performance of the RBF with zero error on training vectors.Figure 2
Schematic diagram of an RBF.


## 2.3. Generalized Regression Neural Networks

The generalized regression neural network
(GRNN) was proposed by Specht [51] and reinvented by Schiøler and
Hartmann [52]. The GRNN is Specht's term for Nadaraya-Watson kernel
regression [53, 54]. It is based on established statistical principles and
converges with an increasing number of samples asymptotically to the optimal
regression surface [55].Since the principle of the GRNN has been
well documented in the literature [38, 51, 56], it is briefly explained in this
section. As shown in Figure 3, the GRNN consists of four
layers, including the input layer, pattern layer, summation layer, and output
layer. Each input unit in the input layer corresponds to individual process
parameter. The input layer is fully connected to the second, pattern layer,
where each unit represents a training pattern and its output is a measure of
the distance of the input from the stored patterns. Each pattern layer unit is
connected to the two neurons in the summation layer: S- and D-summation neurons.
The S-summation neuron
computes the sum of the weighted outputs of the pattern layer while the D-summation neuron calculates the unweighted outputs of
the pattern neurons. The connection weight between the ith neuron in the
pattern layer and the S-summation neuron
is yi, the
target output value corresponding to the ith input pattern. For D-summation
neuron, the connection weight is unity. The output layer merely divides the
output of each S-summation neuron
by that of each D-summation neuron,
yielding the predicted value to an unknown input vector x as
(2.7)y^(x)=∑i=1nyiexp[−D(x,xi)]∑i=1nexp[−D(x,xi)],
where n indicates
the number of training patterns and the Gaussian D function in (2.7) is defined as
(2.8)D(x,xi)=∑j=1p(xj−xijζ)2,
where p indicates
the number of elements of an input vector. The xj and xij represent the jth element of x and xi, respectively. The
ζ is generally referred to as the spread, whose
optimal value is experimentally determined. It should be noted that in conventional
GRNN applications all units in the pattern layer have the same single spread [57].
The GRNN performance is controlled only by the spread factor during the
training. In this study, different spreads were tried to obtain the best
prediction performance.Figure 3
Schematic diagram of a GRNN.


## 3. Description of Data

As presented in Table1, fifteen ground motions
that occurred at Northwestern region of Turkey  between 1999-2000 were used in
the ANN applications. Maps of study area were given in Figures 4(a) and 4(b).
95 PGA records resulting from the ground motions were downloaded from web sites
of the Consortium of Organizations for Strong Motion Observation Systems
(COSMOSs, 2008) for east-west (E-W), north-south (N-S), and Up-Down (U-D)
directions. The records were determined from 11 accelerograph stations operated
by Boğaziçi University’s Kandilli Observatory and Earthquake
Research Institute (see Table 2 and Figure 4(b)).Table 1
Strong ground motions used for PGA estimations.
EarthquakeDateEarthquake locationMwFD (km)Record numbersLatitude (N°)Longitude (E°)İzmit-Kocaeli17.08.199940.727029.99007.415.0010Akyazi-Adapazarı17.08.199940.640030.65005.515.301Cinarcik-Yalova19.08.199940.590029.08005.011.54Hendek-Adapazari22.08.199940.740030.68005.05.403Hendek-Akyazi23.08.200040.680030.10005.815.309İzmit31.08.199940.750029.92005.217.709İzmit13.09.199940.770030.10005.819.6010Marmara Sea20.09.199940.690027.58005.016.4010Sapanca-Adapazarı11.11.199940.740030.27005.722.0010Düzce12.11.199940.774631.18707.110.0010Duzce Aftershock12.11.199940.750031.10005.210.007Duzce Aftershock12.11.199940.740031.05005.410.007Kaynaşlı-Bolu12.11.199940.750031.36005.010.001Hendek-Adapazari27.11.199940.710030.70005.010.002Northeast of Bolu02.14.200040.900031.75005.015.702Table 2
Recording stations used in this study.
Station no.Station nameLatitude (N°)Longitude (E°)772Yarimca Pektim, Yarimca40.763929.7620ARCArcelik, Darica40.823629.3607770Heybeliada Hospital, Heybeliada40.868829.0875BURTofas Factory, Bursa40.260529.0680769Yapi-Kredi Plaza, Levent41.081129.0111777Fatih Tomb, Fatih41.019728.9500779Yesilkoy Airport, Yesilkoy40.982228.8200768Nuclear Research Center, K. Cekmece41.023728.7594767Ambarli Thermic Power Plant, Ambarli40.980928.6926766Botas Gas Terminal, M. Ereglisi40.992027.9796DARArslan Cimento Factory, Darica40.756929.3673Figure 4
(a) Seismicity map of Turkey (http://neic.usgs.gov/). (b) Location map of the recording stations and earthquakes occurred in Northwestern Turkey.The local site conditions at an accelerograph station can affect the strong motion recorded. The widely accepted method of reflecting these effects is to classify the recording stations based
on shear-velocity (Vs). But, information on Vs is
currently lacking for most stations in Turkey. In order to categorize site
conditions in Turkey some studies were performed
by researchers, namely, Zaré
and Bard [58], Gülkan and Kalkan [12], Ulusay et al. [13], and Özbey et al.
[20]. In the present study, site conditions (SCs) given in the web site of
COSMOS were used as rock, stiff, and soft. Since the SC was taken into consideration
during the estimation of PGA some records lacking the SC in the web site were
not downloaded.The training of the networks was performed
using 72 sets of data. Testing of networks was done using 23 datasets that were randomly
selected among the whole data. As depicted in Figures5(a) and 5(b), the Mw and FD values of test and train data varied in the range of 5.2 to 7.4 and 5.4
to 22 km,
respectively. The HD values were given in the Figure 5(c). Figure 5(d) illustrated
the site conditions of train and test data (selected as SC=1 for rock, SC=3 for
stiff soil, and SC=5 for soft soil). The other numbers could also be selected
for SC. As seen in this figure the site conditions were commonly soft and stiff
soil types.  Figures 5(e)–5(g) showed the PGA values for E-W, N-S, and U-D
directions, respectively. The maximum PGA records of the three components were
given in Figure 5(h).Record values of (a)Mw, (b) FD, (c) ED, (d) SC, (e) PGA for E-W direction, (f) PGA for N-S direction, (g) PGA for U-D direction, (h) maximum PGA of the three directions.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4. Results and Discussions

The PGA values were estimated by using three
different ANN methods such as FFBP, RBF, and GRNN. Four models were developed
for each ANN method. Models (i), (ii), and (iii) were used to determine the PGA
values for E-W, N-S, and U-D directions, respectively. The input layer of these
models consisted of four nodes representing theMw, FD, HD, and SC
values. The SC values in the models were used as 1, 3, and 5 for rock soil,
stiff soil, and soft soil, respectively. Model (iv) was developed for
estimation of maximum PGA values of the three components. The direction of
maximum PGA (D) was varied for each record. Thus, the D (selected as D=1 for
E-W direction, D=2 for N-S direction, and D=3 for U-D direction) from a record
was also used as input in this model. Inputs and outputs of each model were
given in the second and third columns of Table 3, respectively. A program
including MATLAB neural network toolbox was coded to train and test the models
for each ANN method.Table 3
The final architectures of the models (i), (ii), (iii), (iv).
ModelInputsOutputsFFBP methodGRNN methodRBF methodhmf(⋅)f˜(⋅)Spread valuesSpread values(i)Mw, FD, HD and SCPGA for E-W5tan-sigmoidlog-sigmoid0.0150.022(ii)Mw, FD, HD and SCPGA for N-S5log-sigmoidlog-sigmoid0.0620.039(iii)Mw, FD, HD and SCPGA for U-D2tan-sigmoidlog-sigmoid0.0760.018(iv)Mw, FD, HD, SC and DMax. PGA7log-sigmoidlog-sigmoid0.280.060The models of the FFBP had one hidden layer
in this paper. The node numbers of the hidden layer (hm), the transfer function between input and hidden
layers, f(⋅), and the transfer
function between hidden and output layers, f˜(⋅), which gave the best testing performance,
were presented in the forth, fifth, and sixth columns of Table 3, respectively.
Similarly the spread values providing the most satisfactory testing performance
for models of the GRNN were given in the seventh column. Spread constants of the
models for the RBF with zero error on training vectors were given in last
column of Table 3. The training simulation performance of models of FFBP was evaluated in terms of
the MSE values calculated from (2.2).
The error graphs for models (i), (ii), (iii), and (iv) were presented in Figures
6(a), 6(b), 6(c), and 6(d), respectively. These figures showed that the networks
had good convergence during the training data.The training error graphs (a) for model (i), (b) for model (ii), (c) for model (iii)
and (d) for model (iv).
(a)(b)(c)(d)The
correlation coefficients (R), the
root mean square error (RMSE), and
the mean average error (MAE) used to
evaluate the accuracy of each model are defined as
(4.1)R=∑i=1n(Xi−X¯)−(Yi−Y¯)∑i=1n(Xi−X¯)2⋅∑i=1n(Yi−Y¯)2,(4.2)RMSE=1n∑i=1n(Xi−Yi)2,(4.3)MAE=1n∑i=1n|Xi−Yi|,
where Xi is observed PGA value at ith record, Yi is predicted PGA value at ith record, n is total number of
testing data, X¯ and Y¯ are the mean of Xi and Yi, respectively.TheR measures the degree of linear
association between the target and the realized outcome but the extreme values
heavily affect it. The RMSE is
specially suited for iterative algorithms and is a better measure for high
values. The MAE has the advantage
that it does not distinguish between the over- and underestimation and does not
get too much influence by higher values [59, 60]. The R, RMSE, and MAE statistics of the models of each ANN in the test period were given in Table 4.
According to the
highest R and the smallest RMSE and MAE viewpoint, the models (i), (ii), and (iv) of FFBP showed the
best performance. Although the R value
of model (iii) of FFBP was the highest, the RMSE and MAE values of model (iii) of GRNN
were the smallest.Table 4
R, RMSE, and MAE values of each ANN method for
models (i), (ii), (iii), and (iv) in the test period.
ModelFFBP methodGRNN methodRBF methodRRMSE (cm/s/s)MAE (cm/s/s)RRMSE (cm/s/s)MAE (cm/s/s)RRMSE (cm/s/s)MAE (cm/s/s)(i)0.9985.524.060.87237.3516.690.36258.1727.50(ii)0.95018.698.080.89122.9110.220.48143.6116.99(iii)0.99913.555.600.9718.102.850.21930.7111.91(iv)0.99218.6110.890.89541.5717.790.55050.4827.21The PGA estimates were plotted with
observed values in the form of the time series and scatter plot. Figures7(a, b), 7(c, d), 7(e, f),
and 7(g, h) were drawn for models (i), (ii), (iii), and (iv), respectively.  Figures 7(a) and 7(b) showed that the model of
FFBP gave the best PGA prediction performance considering the highest
correlation coefficient that was also given in the scatter plot, and the most agreements of the
estimated with observed PGA values. The second best performance was provided from the GRNN.  The RBF gave a
quite poor performance.  As illustrated in Figures 7(c) and 7(d), the results of
RBF were the poorest. Although the results of FFBP and GRNN gave similar values
for especially PGA < 50 cm/s/s, the estimation performance of FFBP (R=0.950
for PGA > 50 cm/s/s was better than that of GRNN (R=0.891). Figures 7(e) and 7(f)
indicated that the FFBP and GRNN provided good prediction performances for
PGA < 20 cm/s/s. The GRNN gave more satisfactory results than the FFBP for
PGA > 20 cm/s/s while the correlation coefficient of FFBP results (R=0.999) was superior to that of
GRNN results (R = 0.971). The RBF predictions were unsatisfactory as seen from
this figure. It was concluded from Figures 7(g) and 7(h) that the testing stage
results determined by the FFBP method were more satisfactory than the other
methods. The second best performance was provided by the GRNN. The performance
of RBF ranked as the third.Observed and predicted PGA values (a, b) for E-W direction, (c, d) for N-S direction, (e, f) for U-D direction, (g, h) for maximum PGA direction in test period.
(a)(b)(c)(d)(e)(f)(g)(h)The
exact design RBF used in the applications is structured with zero training error on the
design vectors hence it generates negative values for low PGA estimations. The GRNN,
on the other hand, does not provide negative predictions. The GRNNs learn in one pass
through the data and can generalize from samples as soon as they are stored. The
FFBP requires an iterative training period differing from the RBF and GRNN.Although the models of FFBP yielded considerably
high correlation coefficients greater than 0.95, the predicted PGA values did
not closely agree with observed PGA values except for E-W direction. A linear
fit line was plotted for each model of FFBP in Figures8(a), 8(c), 8(e), and 8(g).
Therefore, some modifications were carried out as follows. We perform linear
curve fitting of the form y=a⋅x+b to determine equations of these lines, that
were given in (4.4)–(4.7), where y is predicted PGA value from the FFBP
and x is observed PGA as follows:
(4.4)y=0.9518⋅x−1.3243,formodel(i),(4.5)y=0.6839⋅x+3.1888,formodel(ii),(4.6)y=0.5877⋅x+1.8049,formodel(iii),(4.7)y=1.2346⋅x−0.5589,formodel(iv).
Equation of the exact lines in the scatter
plots can be written as
(4.8)y=x.
The predicted PGA values of models for the FFBP
were modified by (4.9)–(4.12) to determine
the same exact and fit lines as follows:
(4.9)z=y+0.0482⋅x+1.3243,formodel(i),(4.10)z=y+0.3161⋅x−3.1888,formodel(ii),(4.11)z=y+0.4123⋅x−1.8049,formodel(iii),(4.12)z=y−0.2346⋅x+0.5589,formodel(iv),
where z is modified PGA values. As seen in
scatter plots of each model, the fit lines plotted by using modified PGA values
(z) were identical with exact lines.
These lines were named as modified lines in the figures. The R, RMSE, and MAE statistics of modified models were given in Table 5. Good
correlation was observed between the modified lines and modified PGA values
(R = 0.998 for model (i), R = 0.980 for model (ii), R = 0.996 for model (iii), and
R = 0.988 for model (iv)). The RMSE and MARE values of modified models (see
Table 5) also showed better performance than those of models of FFBP (see Table 4) with these modifications and the PGA prediction performance of each model
was considerably increased. The PGA values of model (i) of FFBP and modified
model (i) were nearly identical with those of observed data (see Figures 8(a)
and 8(b)). As illustrated in Figures 8(c) and 8(d) the model (ii) gave good
agreement with observed values except for the fist two test numbers. Although modified
model (ii) gave more convenient results for high PGA values (PGA > 100 cm/s/s) than the model (ii) of FFBP, it gave a slightly poorer performance for
small PGA values (PGA < 5 cm/s/s). Figure 8(e) showed that the model (iii)
results of FFBP had similar trend with observed values while modified model
(iii) results were fairly closed to observed values.  It can be concluded from Figure 8(g) that
modified model (iv) results provided better prediction performance than the
model (iv) of FFBP.Table 5
R, RMSE, and MAE values of modified models in the test period.
ModelRRMSE (cm/s/s)MAE (cm/s/s)(i)0.9983.642.86(ii)0.9809.546.02(iii)0.9962.661.73(iv)0.9889.516.80Comparison of FFBP and modified FFBP models and observed PGA values (a, b) for E-W direction, (c, d) for N-S direction, (e, f) for U-D direction, (g, h) for maximum PGA direction.
(a)(b)(c)(d)(e)(f)(g)(h)Models (v), (vi), (vii) of each ANN method were
developed to show the effects of SC on the PGA prediction performance for E-W,
N-S, and U-D directions, respectively. Models (viii) and (ix) were structured
to check the SC and D effects on the maximum PGA prediction performance. The
input variables of each model were given in the second column of Table6. In order to compare these
models with the models (i), (ii), (iii), and (iv), the same hm, f(⋅) and f˜(⋅) for the models of FFBP, and the same spread
values for the models of  RBF and GRNN,
which were given in Table 3, were used. The performance evaluation criteria (R, RMSE, and MAE) of models of each ANN method
were given in Table 6. As seen in this table, the models (v), (vi), (vii), (viii), and (ix)
gave a poorer prediction performance than the models (i), (ii), (iii), (iv)
used the SC and D in the input layer (see Table 4) under the conditions of used
ANN structures.Table 6
R, RMSE, and MAE values of each ANN method for
models (v), (vi), (vii), (viii), and (ix) in the test period.
ModelInputsOutputsFFBP methodGRNN methodRBF methodRRMSE (cm/s/s)MAE (cm/s/s)RRMSE (cm/s/s)MAE (cm/s/s)RRMSE (cm/s/s)MAE (cm/s/s)(v)Mw, FD and HDPGA for E-W0.85644.4518.460.82946.8918.630.48755.6829.79(vi)Mw, FD and HDPGA for N-S0.12233.2216.430.10932.9516.620.06647.2726.73(vii)Mw, FD and HDPGA for U-D0.09398.3893.610.93314.225.270.75121.8710.16(viii)Mw, FD and HDMax. PGA0.89529.5515.180.88245.2919.380.56361.5237.75(ix)Mw, FD, HD and SCMax. PGA0.66746.2721.940.80336.5615.350.0750.4895.93


## 5. Conclusions

In this study, the PGA values were estimated
for Northwestern Turkey by using three different
ANN methods such as FFBP, RBF, and GRNN. The earthquake moment
magnitude, epicentral distance, focal depth, and site conditions of strong motions were utilized as
input parameters for predicting the PGA values for east-west, north-south,
vertical directions. The direction of the maximum PGA of the three components
was also added to the input layer to obtain the maximum PGA. The PGA values in
each direction were calculated from each ANN method, separately. From these
calculations, it was found that the model estimates of RBF were the poorest
while those of FFBP were the best from the highestR and the smallest RMSE and MAE viewpoint. Although the GRNN
gave considerably good performance for PGA > 20 cm/s/s in vertical direction,
it gave lower estimation performance than the FFBP for other directions and
maximum PGA values.Mathematical
differences among the ANN methods can be briefly explained as follows. The RBFs generate negative
values for low PGA estimations while the GRNN does not provide negative
predictions. The GRNNs
learn in one pass through the data and can generalize from samples as soon as
they are stored. The FFBP has an iterative training period differing from the
RBF and GRNN. Mathematical details can be found in Section2.Although the models of FFBP yielded high
correlation coefficients (R) providing information for linear dependence
between observations and corresponding estimations, the predicted PGA values  were not fairly close to the observed values except for E-W direction. Thus, the predicted PGA values
of FFBP were modified by linear regression analysis and more sensitive
prediction performances were obtained.This paper showed that the ANN methods could
be applied successfully to derive the PGA models for Northwestern
Turkey under used test and train data conditions. With further
investigation, using more data from this region these models can be improved.



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*Source: 919420-2008-12-22.xml*