earthquake ground-motion duration estimation using general...

Scientia Iranica A (2018) 25(5), 2425{2439

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Earthquake ground-motion duration estimation usinggeneral regression neural network

S. Yaghmaei-Sabegh�

Department of Civil Engineering, University of Tabriz, Tabriz, Iran.

Received 22 May 2016; received in revised form 4 February 2017; accepted 13 March 2017

KEYWORDSGround motionduration;Signi�cant duration;GeneralizedRegression NeuralNetwork (GRNN);RBF network;Iran.

Abstract. Accurate prediction of earthquake duration could control seismic design ofstructures. In this paper, a new simple method was developed to estimate such an importantparameter by employing Arti�cial Neural Networks (ANN) capability. A GeneralizedRegression Neural Network (GRNN) as a special class of RBF networks was implementedin this study to reduce the number of computation steps required for the searching processon sparse datasets. This network with quick-design capability does not need to imposea prescribed form to map the observed data. The independent variables used in thepredictive model of this study included earthquake magnitude, distance measure, and siteconditions. The designed models were trained using the 950 accelerograms recorded atIranian plateau. The performance of the proposed approach was compared with predictedresults of feedforward backpropagation networks. Analyses show that the designed GRNNperforms well in estimating earthquake record duration and can be applied to predictcommon measures of earthquake ground-motion duration.

© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

Amplitude parameters, such as peak ground accelera-tion or spectral acceleration, are widely used param-eters in most seismic design codes. Nevertheless, theduration of strong motions could enlarge the extentof earthquake damage to structures. According tovarious studies, seismic response of a structure de-pends on a structural framing system and earthquakecharacteristics including amplitude and duration [1-4].Ground-motion duration signi�cantly a�ects ductilitymeasure, the amount of cumulative damage incurredby the structures, dissipated energy [5,6], input energyamount, and the level of damage done to a structure.It is noted that the role of duration depends on several

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doi: 10.24200/sci.2017.4217

factors such as the structural model and damage metricused in the analysis [7]. From a geotechnical point ofview, duration of input motion is expected to play aninstrumental role in evaluating soil's seismic response,liquefaction potential, and lateral spread displacementresulting from soil liquefaction [8-10]. Ground-motionduration has also an imperative role in the assessmentof potential losses in future earthquakes as in theHAZUS standardized framework, where duration isexplicitly taken into account [11,12].

Several researches, conducted in the past, at-tempted to obtain the earthquake ground-motion du-ration based on regional (local) predictive equations.These predictive equations, typically �t into a strongground-motion data by conventional regression meth-ods, could be developed for typical de�nitions of theground-motion duration. Kempton and Stewart [3]proposed signi�cant duration prediction equationsbased on a random e�ects regression procedure withrespect to di�erent parameters: magnitude, distance

2426 S. Yaghmaei-Sabegh/Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 2425{2439

from site to source, soil site condition, and one morefactor that re ects near-�eld e�ects. Bommer et al. [2]employed the global database of Next Generation ofAttenuation (NGA) to present new updated empiricalequations. Recently, Yaghmaei-Sabegh et al. [13] devel-oped a new predictive model by a nonlinear regressionanalysis based on earthquake ground-motion recordsobtained in Iran. According to the basic seismologicaltheory, earthquake record duration depends on thecomplex fracture mechanism on the fault plane andseismic wave radiation characteristics. Thus, utilizingan appropriate physically based representation for sucha multi-faceted parameter would be very di�cult andmay require a deep understanding of di�erent param-eters that control ground-motion duration. For thisreason, di�erent mathematical functions often in thenonlinear forms have been adopted in the associatedliterature. To overcome this concern, the purpose ofthis paper is to develop a simple tool for estimatingthe duration of earthquake records. To this end, asimple and e�cient framework is designed based onhigh capability of GRNN neural networks.

By increasing the computational power of engi-neering software, di�erent computer-based searchingalgorithms, including K-means, Genetic Programming(GP), Arti�cial Neural Networks (ANNs), and au-toregressive integrated moving average (ARIMA), arevastly used in both seismology and earthquake engi-neering [14-17]. This paper shows that the nonlinearnature and high �tting ability of a special class ofnetworks, named Generalized Regression Neural Net-works (GRNN), make it very suitable particularly whiledi�erent factors in uence the prediction results. Asan advantage for a GRNN, design-decisions about thelayers numbers and unit number of the hidden layerscould be removed.

The purpose of this paper is an attempt toestablish a suitable platform to compare capabilitiesof Multi-Layer Feed-Forward (MLFF) and GRNN net-works for accurate prediction of ground-motion recordduration as a complex problem in seismology. The needfor GRNN implementation for the purpose of this studyis demonstrated by presenting the prediction resultsof backpropagation multi-layer feed-forward networks.This paper consists of six di�erent sections. The studyof this paper could facilitate a good condition for read-ers to compare the prediction abilities of multi-layerfeed-forward neural network and GRNN models withregard to a complex case study in seismology wheretraining data are limited. Following the introduction, adescription of the arti�cial neural networks applicationsin seismology and earthquake engineering is providedin Section 2. Theoretical background of implementednetwork is laid out in this section, too. Section 3reviews di�erent de�nitions for ground-motion dura-tion. Results of analysis in training and testing steps

are discussed in Section 4. This section also includesthe details of the ground-motion records and datasetanalysis. The prediction ability of MLFF network asthe most popular ANN is evaluated and compared withothers in Section 5. Di�erent performance evaluationindices, i.e., root mean square error, correlation coef-�cients, and e�ciency factor between estimated andobserved dataset, are used in the analysis. A summaryof conclusions drawn in this study is reported in the�nal section of the current paper.

2. Arti�cial neural networks and applications

Capability of Arti�cial Neural Network (ANN) tomodel complex features was used successfully in thepast when conventional linear functions were not ableto demonstrate high-dimensional inputs. The applica-tions of arti�cial neural networks as a powerful toolhave been evaluated broadly in seismology, earthquakeand geotechnical engineering, and geosciences.

McCulloch, a neurobiologist, and Pitts, a statis-tician [18], initiated the �rst arti�cial neuron as abinary threshold unit in 1943. An ANN deducesessential features of biological neurons and their inter-connections and takes a di�erent approach to solve aspeci�c problem than that of conventional algorithmiccomputer, which follows a set of instructions in orderto solve the problem. Neurons (or cells) supply parallelprocessing nature of arti�cial neural networks to solvea complex problem [19]. Each neuron is responsible forcarrying out received impulses from input cells to theother cells. Neural networks are able to learn duringtraining process to achieve the generalization ability,which is useful for future predictions. In this regard,neural networks could be considered as a practicaltool for pattern recognition and function approxima-tion applications. Multi-Layer Feed-Forward (MLFF)neural network, referred to as multi-layer perceptron,Kohenen's Self-Organizing Maps (SOM), and RBF net-works are di�erent types of neural networks, normallyapplied to solve such a problem.

In a MLFF network, which is a most popularANN architecture, feedforward style, typically, is usedto form connections among hidden layer neurons withthose of input and output layers. The error backprop-agation (BP) algorithm as a highly popular algorithmfor feedforward networks uses a local gradient to reacha minimum value of prediction error. The MLFF wasemployed widely in the past researches as a predictorof unknown functional relations for di�erent applica-tions in both seismology and earthquake engineering.Pioneering researches by Dysart and Pulli [20] and Daiand MacBeth [21] were focused on the application ofBP-MLFF in regional seismic event classi�cation andidenti�cation of seismic arrival types. Application of aback-propagation neural network in system identi�ca-

S. Yaghmaei-Sabegh/Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 2425{2439 2427

tion (sti�ness and damping coe�cients) and structuralresponse prediction due to earthquake excitation canbe found in the literature [22,23]. Kuzniar et al. [24]implemented capability of MLFF neural networks toconstruct response spectra based on mining tremorsdata. Gentili and Bragato [25] proposed a BP-MLFFneural network system to forecast earthquakes locationoccurred in Italy. Asencio-Corte's et al. [26] evaluatedthe e�ciency of neural networks for the prediction ofearthquake sizes according to �ve databases in Japan.In 2005, in Taiwan, Kern and Ting [27] predicted peakground acceleration values by considering MLFF neuralnetworks as a soft computing tool. Ahmad et al. ap-plied an arti�cial neural network to develop attenuationrelationships for peak Parameters as Ground Acceler-ation (PGA) [28]. They considered real earthquakedata to demonstrate the accuracy of designed networkto model local attenuation characteristics. Arjun andKumar [29] presented a new application of MLFFneural network to estimate earthquake record durationin Japan. Recently, Liu et al. [30] applied a neuralnetwork as a classi�er along with wavelet transform tostructural damage diagnosis. Alari� et al. [31] useda feedforward neural network (consisting of 3 layers)to predict earthquakes magnitude in northern Red Seaarea. As another application, high ability of neuralnetworks was used for earthquake prediction based oncorrelated information with earthquake occurrence inthe past [32-34]. Panakkat and Adeli [35] proposeda neural network model to provide useful informationabout events location and time of occurrence for majorearthquakes in the California. Despite wide appli-cations of this type of neural networks, there are anumber of disadvantages in using BP-MLFF models.The architectural design of MLFF neural networks,including optimal number of neurons in each of hiddenlayers, is di�cult. For lower number of nodes, thenetwork does not obtain the right results. In contrast,increasing the number of units increases the number ofweights [36] and, hence, the processing time in trainingstep; sometimes, it is weakens the generalization abilityof the network. Typically, it can take a large numberof iterations to converge to the preferred values and,consequently, require too much time, particularly whena large-sized network is needed.

The feasibility of using Generalized RegressionNeural Networks (GRNN) is examined in this article topredict earthquake ground-motion duration. More in-formation about RBF and GRNN networks is presentedin Sections 2.1, and 2.2. Details of the mathematicaltheory of neural networks were extensively documentedin [37].

2.1. RBF-based modelsA Radial Basis Function network (RBF) learns usinga supervised training technique and consists of a single

hidden layer associated with basis functions modellinga Gaussian response surface. Indeed, RBF networkperforms a nonlinear mapping when the data are loadedonto interior con�guration of network. The advancedcapability of RBF networks in civil engineering andseismological problems has been shown in estimatingdesign parameters [38], identi�cation and control ofstructures [39,40], prediction of building interferencee�ects [41], earthquake magnitude prediction [42],seismic data inversion problem [43] in stress-strainapproximation of plain concrete [44], and, recently, forestimation of earthquake occurrence model [45].

2.2. GRNN-based modelA statistical technique called \kernel regression" per-forms a fundamental role in the proceeding core ofGRNN, which will be used for prediction herein. Asa main advantage over traditional regression methods,GRNN, like kernel methods in general, does not need toimpose a prescribed form to map the observed data. Infact, GRNN model is able to construct an appropriaterepresentation based on probability density function ofthe input data, facilitating smooth transition amongstdi�erent observations [46]. Training time of GRNNwhich is a memory-based network is short, because thebandwidths of the parameters used in the analysis aresimply considered [47]; therefore, the precise settingis not needed [48]. Figure 1 demonstrates a typicalarchitecture of GRNN consisting of four layers. Theinput and output layers in GRNN are similar tothose of most neural networks. However, there is nocomputational role in the neurons of input layer inthis type of network, where data are simply passed tothe pattern layer units. Pattern and summation layersare two computational parts of GRNN that completethe structure of GRNN. Neurons are assigned to all oftraining datasets in the pattern layer to compute theEuclidean distance based on the center-point positionof neurons. Finally, the RBF kernel function has beenapplied to this processing layer. The summation layercontains two neurons: S-summation and D-summationneurons, which compute the sum of weighted and un-weighted outputs, respectively. The summation andoutput layers produce a normalization of output set.

The predicted target value (y) can be explainedas follows:

Figure 1. A typical architecture of generalized regressionneural network.


y =Pnj=1 yj exp[�D(xi; xij)]Pnj=1 exp[�D(xi; xij)]

; (1)

where yi is the weight connection between the ith unitin the pattern layer and the summation layer, n is thenumber of training cases (xij), parameter xi is inputvalue for testing cases, and function D is described asfollows:

D(xi; xij) =pXi=1

(xi � xij)2

2�2 ; (2)

in which p indicates the unit number of each in-put vector, � is called \smoothing" or \bandwidth"parameter which a�ects prediction performance of aGRNN and is frequently calibrated for each model [49].More information about GRNN model can be foundin [48,50]. The main features of GRNN in functionapproximation could be summarized as follows:

i) The simplicity in design where there is no need tode�ne a learning rule;

ii) Anticipating high performance often even based onsmall amount of data;

iii) Low cost of CPU processing;iv) Removing the decision-making step on architec-

tural design of network.

It is well known that, similar to an RBF network,GRNN model is not able to extrapolate. For thisreason, a GRRN designer should be aware of thisimportant matter to control the range of the selectedtraining data used in the analysis.

A review of the past research works illustratesdi�erent applications of GRNN in seismology andearthquake engineering. GRNN was applied to eval-uate soil composition based on CPT data by Kuropand Gri�n [51]. Hanna et al. [52] used high capacityof GRNN to estimate soil liquefaction potential basedon earthquake database of Turkey and Taiwan. In2011 and as an important procedure in site-speci�cseismic hazard assessment, a GRRN-based procedurewas suggested for site classi�cation [47]. The resultsof Yaghmaei-Sabegh and Tsang [47] were validatedwith borehole data that are normally used in the soilclassi�cation procedure. Their results revealed highe�ciency of GRNN model used for this purpose [47,53].

3. Overview of di�erent ground-motionduration de�nitions

As mentioned before, ground-motion duration mayinvolve many variables from source, path and sitee�ects; consequently, there is no general de�nitionfor this complex-multifaceted phenomenon among seis-mologists. Di�erent typical de�nitions, presented for

earthquake record duration in the past, could beput into three main groups: bracketed, uniform, andsigni�cant durations.

The bracketed duration measure (DB) is the timeduration of ground shaking that is de�ned as the timelength from the �rst and last excursions rather than aprecise pre-de�ned threshold of acceleration [1]. Thissimple de�nition is a sensitive measure for the accelera-tion threshold and can be unstable in some cases [1]. Itshould be noted that bracketed duration has been usedby di�erent researchers, taking into account di�erentlevels of acceleration as a threshold [2,54,55].

Uniform duration (DU ) is measured as the sum ofnumbers of discrete time intervals at the points whereacceleration is greater than a pre-de�ned threshold. Itis noted that the sensitivity of this de�nition is lowercompared with that of bracketed duration. Figures 2to 4 demonstrate the acceleration time history as wellas bracketed and uniform durations for a destruc-tive earthquake occurred at Tabas, northeast of Iran(recorded at Deyhook station).

Finally, signi�cant duration (DS) as an energy-based measure describes a continuous time window,which is de�ned based on two pre-de�ned Arias inten-

Figure 2. Acceleration time history of 1978 Tabasground-motion recorded at Deyhook station.

Figure 3. Bracketed duration (DB) estimated for 1978Tabas earthquake recorded at Deyhook station (Acc2 isthe square of the ground acceleration).


Figure 4. Uniform duration (DU ) estimated for 1978Tabas earthquake recorded at Deyhook station (Acc2 isthe square of the ground acceleration).

sity thresholds. The signi�cant duration illustrates thetime interval of ground-motion time history when themain part of input energy is imposed on the buildingsand is more stable than the bracketed and uniformduration measures. For these reasons, two genericmeasures of this de�nition are used in the predictionprocedure of this research as the time intervals ofArias Intensity between 5-95% and 5-75% (Ds�5�95%and Ds�5�75%), respectively. Figure 5 presents thesetwo common measures of signi�cant duration for theselected record at Deyhook station.

4. Estimating earthquake ground-motionduration

4.1. Model developmentThe primary step to design a GRNN model is toprovide a suitable large database used in learning andtesting process. The ground-motion records applied inthis work corresponded to 950 ground-motion recordsobtained at important earthquakes occurred in Iran,provided by Building and Research Center (BHRC).A review of the historical earthquakes in Iran demon-strates this fact that Iran has been located in one of

Figure 6. Magnitude versus closest site-source distanceof dataset used in this study.

the world's signi�cant seismic belt that has experiencedmany large events in the past [56].

Updated database of this paper covers theground-motion duration data, recently used byYaghmaei-Sabegh et al. [13] to develop a new predic-tive model in Iran. The overall range for momentmagnitude in the dataset is from 3.75 to 7.7 withthe closest site-source distance ranging from 1.5 to370 km. Figures 6 and 7 demonstrate the magnitudeof earthquakes used in this study against distance mea-sure along with the location distribution of importantearthquakes across the study area, Iran. The totalset of 950 values used for the modelling is separatedinto two data bins. Eighty percent of dataset has beenadopted as training set and 20% of data can best covertesting set of analysis.

In the proposed models, an earthquake ground-motion duration parameter is described as a functionof three independent variables: earthquake size, dis-tance from source to site, and soil type, i.e., Ds =f(M;R; S). Two di�erent models have been presentedseparately for two generic measures of signi�cant du-ration (Ds�5�95% and Ds�5�75%). The closest site-source distance is used also as a distance measure

Figure 5. Signi�cant duration estimated for 1978 Tabas earthquake recorded at Deyhook station (Ds�5�95% andDs�5�75%) [13].


Figure 7. Location distribution of major earthquakesused in this study for the prediction of earthquake-groundmotion duration [13].

herein. Site e�ect in the proposed duration model isconsidered to be based on soil classi�cation schemeadopted in the Iranian seismic design code (Standard2800). Four soil classes have been de�ned in thiscode based on average shear wave velocity, which iscompatible with site classes in 2003 NEHRP [57].Dummy variables 0 and 1 are used simply in theprediction process for rock and soil sites, respectively.

4.2. ResultsThe only factor that needs to be selected to designGRNN model is the smoothing parameter that a�ectsthe predicted value of the designed neural network.Generally, smoother prediction would be expectedwhen the smoothing parameter is larger. In addition,generalization capability of designed network decreasesfor small value of smoothing parameter, which is notan enviable quality for future predictions. Therefore,the suitable value of this parameter, which is oftenexperimentally determined, will play a signi�cant rolein design implementation of this type of networks. Inthis study, di�erent values of smoothing parameterranging from 0 to 1 have been examined; �nally, basedon prediction performance, the value of � = 0:7 hasbeen intended through a calibration process. It isworth noting that choosing an appropriate value forsmoothing parameter will be more important if thenumber of observation may be small enough to predicta complex phenomenon.

The e�ciency and robustness of designed net-works have been checked based on three statisticalindices named root mean square error, correlationcoe�cients, and e�ciency factor. These indices are

Figure 8. Predicted values of signi�cant durationDs�5�95% versus observed values in training set.

Figure 9. Predicted values of signi�cant durationDs�5�95% versus observed values in testing set.

de�ned as follows:

RMSE =

sPNi=1(Xi � Yi)2

N; (3)

R =PNi=1�Xi � �X

� �Yi � �Y

�qPNi=1�Xi � �X

�2PNi=1�Yi � �Y

�2 ; (4)

EF =PNi=1�Xi � �X

�2 �PNi=1�Yi � �Y

�2PNi=1�Xi � �X

�2 : (5)

In these equations, Xi and Yi are de�ned as theobserved and predicted values; �X and �Y are the meanvalues of the observed and predicted data, respec-tively [58]. N is the number of data in dataset analysis.The three well-known indices, used in this study, re ectthe degree of �t for the proposed models and couldevaluate the ANN output error between the actual andpredicted outputs. Figures 8 through 11 illustrate theability of designed network while presenting scatter


Table 1. Performance of designed GRNN for predicting Ds�5�95% and Ds�5�75%.

Duration Training set Testing setR EF RMSE (sec) R EF RMSE (sec)

Ds�5�95% 0.88 0.77 4 0.79 0.73 4.1Ds�5�75% 0.89 0.78 2.54 0.76 0.75 2.68

Figure 10. Predicted values of signi�cant durationDs�5�75% versus observed values in training set.

Figure 11. Predicted values of signi�cant durationDs�5�75% versus observed values in testing set.

plots of the predicted values against observed valuesfor predictive models of Ds�5�95% and Ds�5�75%. Ob-served/estimated = 1 line is also superimposed on the�gures. Table 1 indicates the results of comparisons ofGRNN performances for training and testing dataset.It is revealed that the values of the RMSE and EFof Ds�5�95% and Ds�5�75% models are close to eachother, and the designed GRNN model could predictthese two parameters almost with similar accuracy.The total residual as another indicator is employedto evaluate the performance of soft computing predic-tions by GRNN. Figures 12 and 13 show the residual%vspace*0.5cm scattering plot for signi�cant dura-

Figure 12. The distribution of residuals between theobserved and predicted signi�cant durations (Ds�5�95%)for the proposed model with respect to (a) closestsite-source distance and (b) magnitude.

tions in logarithmic units (ln(observed)�ln(predicted))based on the predictive models for Ds�5�95% andDs�5�75% against magnitude and distance measures.The spread of residuals in these �gures representsthe variability of individual data values, which coulddemonstrate the quality of a predictor. Residuals ofthe proposed models for Ds�5�95% and Ds�5�75% varyin the range of �1:5 to 1 showing less scattering thanthe predicted results of models of Bommer et al. [2].The residuals for both de�nitions of signi�cant durationdo not show any trend with magnitude or distance,con�rming that the �tting procedure is robust andappropriate. Similar conclusion was made throughthe work of Bommer et al. [2] when their suggestedfunctional form was used in the analysis (see Figures 1and 2 in [2]).

The scatter plot of residuals between the observedand predicted values against soil site conditions isillustrated in Figure 14. From inspection of this �gure,the same prediction quality could be recognized for rockand soil sites.

A more comprehensive comparison made betweendi�erent ground-motion duration prediction equations


Figure 13. The distribution of residuals between theobserved and predicted signi�cant durations (Ds�5�95%)for the proposed model with respect to (a) closestsite-source distance and (b) magnitude.

Figure 14. The distribution of residuals between theobserved and predicted signi�cant durations for theproposed model with respect to site conditions.

is shown in Figures 15 and 16. In order to obtainan accurate evaluation and based on the validity ofpredicted values, models prepared in this paper havebeen re-examined with respect to the predictions in aspeci�ed distance (taken as 30 km) at rock sites fordi�erent values of magnitude ranging from 4.5 to 8.Results of the predicted values based on recentlypublished empirical relationships by Bommer et al. [2]and Yaghmaei-Sabegh et al. [13] have been superim-

Figure 15. Comparison of the proposed GRNN model forsigni�cant duration Ds�5�95% at a �xed distance measure(R = 30 km) on rock sites.

Figure 16. Comparison of the proposed GRNN model forsigni�cant duration Ds�5�75% at a �xed distance measure(R = 30 km) on rock sites.

Figure 17(a). Variation of signi�cant duration Ds�5�95%in distance for moment magnitude Mw = 7 at rock sites.

posed onto these �gures. According to Figures 15and 16, the suggested model is well matched withmodels of Bommer et al. [2] and Yaghmaei-Sabeghet al. [13], recon�rming the validity of ANN modelsdesigned in this paper. However, some discrepancycould be observed among three models which might berelated to the database size and their di�erent features.Plotting of the logarithmic scale has been adopted forthese �gures consistent with other publications in thispath. Figure 17(a) shows the variation of signi�cant


Figure 17(b). Variation of signi�cant duration Ds�5�95%in moment magnitude for rock and soft sites at a �xeddistance measure (R = 30 km).

duration Ds�5�95% in distance for moment magnitudeMw = 7 at rock sites based on the proposed modeland predictions of Bommer et al. [2]. Good agreementbetween the models, particularly for distance largerthan 10 km could be observed in this �gure. Variationof signi�cant duration Ds�5�95% in moment magnitudefor rock and soft sites at a �xed distance measure(R = 30 km) is presented in Figure 17(b). This�gure may possibly highlight soil e�ects on earthquakeduration for strong earthquakes.

5. Comparative analysis of GRNN andBP-MLFF models

The prediction capability of Multi-Layer Feed-Forward(MLFF) network as the most popular ANN is evaluatedin this section to show that there is a need for develop-ing GRNN model. The structure of the implementedfeedforward neural network is shown in Figure 18. Asalready discussed in Section 2 of the current paper,these types of neural networks were extensively appliedin the past; however, �nding the number of neuronsforming hidden layers remains one of the unsolved tasksin the application of such networks. Neurons numberin hidden layers, which controls the generalizationcapability of network, plays an important role in designof a MLFF. A single hidden layer, although withdi�erent neurons numbers, was used in the analysisto highlight this matter herein. The Kolmogorov'stheorem [59,60] could be considered as a simple rule

Figure 18. Architecture of MLFF network used in thisstudy .

(or initial guess) to recommend the neurons number ofhidden layer (NHN):

NHN = 2NIN + 1; (6)

where NIN represents the input neurons numbers.Thus, the neurons number in the hidden layer basedon Kolmogorov's theorem was taken as 2 � 3 + 1 = 7,since there are three input neurons. Consequently,the training analysis started based on seven units inthe hidden layer to learn the target mapping andcontinued by increasing neurons numbers to 9, 12,15, and 18. A trial-and-error approach led to anoptimal network architecture. The backpropagation(BP) learning scheme [61] which includes two phases ofpropagation and weight updating was adopted in thisstudy as a common training technique in ANNs. TheLevenberg-Marquardt training process as a variationof the Newton method was followed to train thedesigned BP-MLFF networks with di�erent architec-tures. Weights were selected randomly for each traininganalysis. The tan-sigmoid function was adopted hereinas an activation function of neurons in the hiddenlayer. Training and testing datasets were chosen similarto GRNN model. The predicted results of designedBP-MLFF models with di�erent processing units arepresented in Figures 19 and 20. Results contain theprediction of two common measures of signi�cant dura-tion: Ds�5�95% and Ds�5�75% separately. Accordingto these �gures, when there are few neurons (as theANN con�guration of 3-7-1), the network could notpredict large values of signi�cant duration well. Hence,the designed network does not model nonlinear featuresof function and the learning process may fail miserably.On the other side, with an increase in the neuronsnumber of the hidden layer, the prediction capacityis improved; however, the network loses its ability togeneralize.

Similar to GRNN models, the performance ofground-motion duration predictions resulting fromtraining and testing data set is evaluated by the threeindices: RMSE, R, and EF. Results are summarizedin Tables 2 and 3 for Ds�5�95% and Ds�5�75%, re-spectively. The maximum values of EF and R alongwith the lowest value of RMSE achieved based on theresults of testing dataset show the higher generalizationability of networks with 7 and 9 neurons amongothers. Comparison of Tables 2 and 3 with Table 1demonstrates higher performance of GRNN modelsobviously. This important result could be concludedbased on the total three evaluation indices used inthis paper. As an example, E�ciency Factor (EF) ofGRNN model for prediction of Ds�5�95% is 0.78 and0.74 in training and testing datasets where the lowercorresponding values of 0.53 and 0.51 are calculatedfor BP-MLFF networks in the best case. Root mean


Figure 19. Observed values of Ds�5�95% versus predicted values by BP-MLFF networks with di�erent number of neuronsin the hidden layer.

square error increases signi�cantly when the BP-MLFFnetworks are applied to the prediction procedure. It isworth noting that the purpose of this section of paperis not to suggest a suitable structure for a BP-MLFFnetwork. However, the results of BP-MLFF networks

con�rm that the prediction ability of such networksis very sensitive to the structure of designed networkand is lower than GRNN performance. In this regard,designing and training of various networks to reachsatisfactory results are required. As a result, due to the


Figure 20. Observed values of Ds�5�75% versus predicted values by BP-MLFF networks with di�erent number of neuronsin the hidden layer.

complex nature of earthquake ground-motion duration,prediction of such kinds of data with conventionalBP-MLFF is di�cult and requires special care whereGRNN is a powerful technique that could resolve thisproblem simply.

6. Summary and conclusions

Improvement of predictive models, which are ableto relate given ground motion characteristics to theseismological parameters, has been known to be a


Table 2. Performance of designed BP-MLFF for predicting Ds�5�95%.

BP-MLFFtopology

Training set Testing set

R EF RMSE (sec) R EF RMSE (sec)

3-7-1 0.726 0.47 6.27 0.720 0.52 6.35

3-9-1 0.683 0.53 6.60 0.660 0.51 7.10

3-12-1 0.767 0.41 5.85 0.641 0.33 7.56

3-15-1 0.762 0.42 5.92 0.642 0.49 6.90

3-18-1 0.700 0.34 5.35 0.612 0.15 8.15

Table 3. Performance of designed BP-MLFF for predicting Ds�5�75%.

BP-MLFFtopology

Training set Testing set

R EF RMSE (sec) R EF RMSE (sec)

3-7-1 0.701 0.51 3.85 0.640 0.50 4.20

3-9-1 0.660 0.56 4.06 0.650 0.49 4.10

3-12-1 0.741 0.45 3.60 0.620 0.35 4.40

3-15-1 0.720 0.48 3.75 0.620 0.33 4.42

3-18-1 0.771 0.40 3.44 0.610 0.29 4.48

very imperative step in seismic hazard analysis. Inthis article, a new arti�cial network-based scheme wasproposed to estimate earthquake record duration. AGeneralized Regression Neural Network (GRNN) wasimplemented in the analysis and examined to pre-dict a multi-faceted parameter of \earthquake groundmotion-duration". Designed models were presentedfor two typical de�nitions of signi�cant ground-motionduration de�ned based on 5-95% and 5-75% AriasIntensity (Ds�5�95% and Ds�5�75%). Di�erent modelswere trained using the 950 ground motions recordedat active tectonic regions of Iran. Results of analysisshowed good �tting with the training and testingrecords.

Unlike BP-MLFF network that needs too muchconvergence time, the time process of designed GRNNin this work is less than 5 seconds. It should be notedthat the speed of convergence in nonlinear least squareregression algorithm is dependent on the quality ofan initial guess for the solution, which is not easy inall cases. The proposed method in this paper is ableto remove the main shortcoming of the conventionalmethod used to develop ground motion prediction(GMPEs) equations. The only parameter that needsto be selected for the general regression neural networkis the smoothing parameter, playing a signi�cant rolein reaching an accurate prediction. Di�erent valuesof this parameter were examined for general practicalapplication of the proposed model. According to theanalysis results, the smoothing parameter � = 0:7was preferred to predict earthquake duration in therecommended models.

Based on the results of this paper, the easy-to-use proposed GRNN model is found to be moree�ective in the prediction purpose of a complex pa-rameter in seismology, ground-motion duration. Thismodel could provide more accurate results than themodels established based on BP-MLFF networks. TheGRNN network gives the best generalization perfor-mance when RMSE takes 4.1, 2.68 values for twocommon measures of signi�cant duration: Ds�5�95%and Ds�5�75%, respectively, whereas the BP-MLFFnetwork gives higher values of 6.35 and 4.1. E�ciencyfactor of GRNN model for prediction of Ds�5�95% is0.78 and 0.74 in training and testing datasets, respec-tively, where the lower corresponding values of 0.53and 0.51 were calculated for BP-MLFF networks inthe best case. Finding the number of neurons formingthe hidden layers of MLFF networks remains as one ofthe unsolved tasks in the application of such networks.Therefore, designing and training of various networksto reach satisfactory results are required in most cases,particularly when the nature of data is complex. Thecomparative results of this article showed that theproposed GRNN model could solve such a problemsimply and reduce the analysis time, too. Note thatthe proposed GRNN could resolve an unsuccessfulprediction of BP-MLFF in long duration; however, thepredicted duration with GRNN is underestimated forlonger observation.

It is worth noting that the current paper wasfocused mainly on the capability of arti�cial neuralnetworks; as for future works, a comparison of accuracyof the proposed method and other classical techniques


as autoregressive integrated moving average (ARIMA)could be useful.

Acknowledgement

The contributions of BHRC are acknowledged to pro-vide earthquake database of this study.

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Biography

Saman Yaghmaei-Sabegh obtained his PhD degreefrom Iran University of Science and Technology andwas awarded the Elite Prize by the university in 2006and 2007. He is currently an Associate Professor atThe University of Tabriz and has been a VisitingScholar at The University of Melbourne, Australiasince 2007. He is a Member of the Iranian EarthquakeEngineering Association. He has published more than40 technical articles and has won award in the 14thInternational Conference on Earthquake Engineeringin 2008 as a young researcher.

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