NEURAL-NETWORK BASED ESTIMATION OF NORMALIZED RESPONSE SPECTRA

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1 ISET Journal of Earthquake Technology, Paper No. 517, Vol. 48, No. 2-4, June-Dec. 2011, pp NEURAL-NETWORK BASED ESTIMATION OF NORMALIZED RESPONSE SPECTRA C.R. Arjun and Ahok Kumar Department of Earthquake Engineering Indian Intitute of Technology Roorkee Roorkee ABSTRACT Thi paper focue on the application of neural network a an alternative computational tool for the etimation of normalized repone pectra for the horizontal ground motion with magnitude M JMA 5 and hypocentral ditance le than 50 km. The feaibility of uing the perceptron neural network in etimating ite-pecific repone pectra and the effect of the geophyical propertie of the ite i examined. Two neural-network model are propoed for generating normalized repone pectra, uch that thoe conider the effect of local ite condition. Model 1 i developed with ix input (i.e., magnitude, hypocentral ditance, primary wave velocity, hear wave velocity, N-value obtained by the tandard penetration tet (SPT), and denity of oil), wherea Model 2 i developed with three input (i.e., magnitude, hypocentral ditance, and hear wave velocity). A expected, a better performance i obtained from (neural-network) Model 1 in term of accuracy and efficiency. The reult obtained from thi tudy are very encouraging and have a potential to replace the commonly ued regreion approach. KEYWORDS: Neural Network, Repone Spectra, Hypocentral Ditance, Shear Wave Velocity, Regreion Approach INTRODUCTION Repone pectrum i a fundamental engineering tool in the dynamic analyi and deign of tructure. The concept of repone pectrum, introduced originally by Biot (1941) and later popularized by Houner (1941), decribe the maximum repone of a erie of damped, linear elatic, ingle-degreeof-freedom ocillator to a particular ground motion a a function of the natural period of vibration or the circular frequency of the ocillator. A repone pectrum form the bai for the tructural engineer intereted to know the repone of tructure ubjected to a ground motion reulting from an earthquake. For deign purpoe, eimic code provide a deign pectrum that decribe the level of eimic reitance required for deign, baed on the tatitical analyi of the repone pectra for an enemble of ground motion. The deign pectrum contain all the information on ground motion amplitude and frequencie and hence can be directly ued to deign a tructure for earthquake load (Gupta, 1990). In the pat, over 80 tudie have been carried out for the etimation of (deign) repone pectral ordinate (Dougla, 2001, 2002). A majority of the publihed prediction model for the generation of acceleration repone pectra are baed on regreion analyi. One of the way of evaluating ite-dependent pectra i by decribing the ite itelf. The mot commonly ued method to claify ite i according to the hear wave velocity recorded at the recording tation. The literature on the ite-dependent pectra i voluminou (e.g., Kuribayahi et al., 1972; Mohraz et al., 1973; Seed et al., 1976; Mohraz, 1976; Trifunac, 1976; Iwaaki et al., 1980; Trifunac, 1990; Lee and Trifunac, 1995; Borcherdt, 1994) and hence a review of thi literature i not covered in thi paper. In thi work, an attempt i made to incorporate all the reported ite effect at the Kyohin Net recording tation. Neural network are ued a an alternative tool for generating the repone pectral ordinate by uing the actual eimic data without any implification and aumption, intead of the commonly ued regreion approach. To the bet of the knowledge of the author, thi i the firt time that neural network are ued for etimating normalized repone pectra by uing the detailed oil propertie and ite characteritic at the recording tation. Thi paper provide a neural-network baed approach for etimating the ite-dependent repone pectra baed on earthquake record and ite characteritic. The firt part of the paper i concerned with the compilation and proceing of trong-motion data for the Japanee earthquake record from the

2 74 Neural-Network Baed Etimation of Normalized Repone Spectra Kyohin Net databae. The econd part of the paper preent the application of artificial neural network to predict repone pectral ordinate with ix input a well a with three input, along with the imulation reult for each model. Finally, the trained network with three input i teted for a few ignificant US earthquake and the reult are preented. In an earlier work (Arjun and Kumar, 2009) the author of the preent paper have developed an artificial neural network in the form of a multilayer perceptron model to predict peak ground acceleration with different training parameter. Alo, the firt author (Arjun, 2008) ha ued artificial neural network for predicting the trong ground motion parameter that are of primary ignificance in earthquake engineering. INFORMATION ON RECORDING STATIONS AND DATA PROCESSING TECHNIQUE Japanee ground motion record from the Kyohin Net (K-NET) databae are elected for thi tudy, a K-NET provide detailed oil propertie and ite characteritic at almot all the recording tation. K- NET i a dene trong-motion network, coniting of over 1,000 recording tation deployed all over Japan at free-field ite at the interval of approximately 25 km. Each tation ha a digital trong-motion accelerometer with a wide frequency band and a wide dynamic range. The K-NET data i openly available on regitration through their web-ite 1. Almot all the ite in thi databae have the oil condition (e.g., tandard penetration value (SPT), denity) available, including the P- and S-wave velocity tructure obtained from the downhole meaurement. A majority of the K-NET tation are located on thick edimentary ite in the urban area. The accelerometer at a tation i placed on a concrete bae and it houing i made of fiber reinforced platic (FRP). The layout of a typical obervatory i hown in Figure 1. All tation operated by K-NET have K-NET95 accelerometer, with 108 db dynamic range and the maximum meaurable acceleration of 2000 Gal (20 m/ 2 ). Each accelerometer i a triaxial, force balance accelerometer (i.e., V403BT model by Akahi Co.) with a natural frequency of 450 Hz and critical damping ratio of The reolution of the A/D converter i 18 bit with the ampling frequency of 100 Hz. The reolution of the accelerometer i 15 mgal (0.15 mm/ 2 ). The repone characteritic curve of the accelerograph, which include the effect of anti-aliaing filter in digitization, are hown in Figure 2. The cutoff frequency of the filter i 30 Hz. Fig. 1 The layout of typical obervatory 1 1

3 ISET Journal of Earthquake Technology, June-December Fig. 2 Repone characteritic curve of K-NET95 accelerograph 1 Baeline correction i an important part of the data proceing procedure and i eentially required for the correction of error due to noie. A baeline correction of all uncorrected acceleration time hitorie i performed by uing the leat-quare line of the time hitory. Correction are alo applied in frequency domain by filtering the high- and low-frequency component of the accelerogram. All accelerogram are band-pa filtered by removing the frequencie below 0.1 Hz and the frequencie above 30 Hz. A ixth-order Butterworth band-pa function in frequency domain (commonly called a frequency filter) i ued for the above filtering operation. For the dynamic analyi of tructure, the frequency range of interet i uually below 30 Hz, and hence a frequency limit of 30 Hz i acceptable. The low value of the frequency limit i critical only when the recorded event i in the near-field of a large earthquake. The objective of thi tudy i to ue the K-NET databae a input to a neural network, and not to tudy the noie characteritic of the databae. Hence, a filter with the band limit of Hz i applied. A the natural frequency of all accelerograph i very high, there i no need of any intrument repone correction. SITE INFORMATION The mot commonly ued parameter to claify the ite i the average hear wave velocity in the top 30 m of the earth, V 30. The National Earthquake Hazard Reduction Program (NEHRP) in USA alo ue V 30 to define variou ite categorie. K-NET provide the velocity tructure beneath the ite baically to a depth of m by uing the downhole meaurement method. Apart from the P- and S- wave velocity tructure, at each tation the N-value of SPT, the bulk denity value of oil, and oil profile are reported. A typical oil data at the recording tation i given in Figure 3. The average value of the hear wave velocity, primary wave velocity, SPT blow count and the denity of oil, i.e., ν, ν, p N, ρ, repectively, are ued a the input to a neural network. The averaging i done in accordance with Section of the NEHRP recommended proviion for eimic regulation for new building and other tructure (FEMA, 2003): ν, ν,n, ρ = p n n i= 1 d di di di di,,, ν ν N ρ i= 1 i pi i i where ν i denote the hear-wave velocity of oil, blow count, and ρ i the denity of oil, in the layer i; the number of layer of the imilar oil material, for which data i available. i (1) ν pi the primary-wave velocity of oil, N i the SPT d i denote the depth of the layer i; and n denote

4 76 Neural-Network Baed Etimation of Normalized Repone Spectra Fig. 3 Site information at FURUDONO ite 1 PREDICTIVE MODELS FOR GENERATING RESPONSE SPECTRA USING NEURAL NETWORKS Artificial neural network are efficient computing model wherein the olution to a problem i learned from a et of example. One of the major hortcoming of neural network i that thoe are conidered a a black box, ince there i no atifactory explanation of their behavior for finding a olution (Benitez et al., 1997). There are many definition of an artificial neural network (ANN). It i a maively parallelditributed proceor made up of imple proceing unit, which have a natural tendency of toring experiential knowledge and making it available for ue (Haykin, 1994). The mot powerful feature of a neural network involving upervied learning i the input-output mapping. In a upervied learning algorithm the output i known and given to the neural network during the training proce o that the neural network can adjut weight in uch a way that the actual output move cloer to the deired output. After the training, the neural network i teted by giving only the input value, to ee how cloe it output i to the deired value. Backpropagation i one of the mot commonly ued algorithm for training the multilayer ANN. Many reearcher have ued the multilayer feedforward neural network in tructural dynamic, epecially in the field of earthquake trong ground motion problem (e.g., Lee and Han, 2002; Tehranizadeh and Safi, 2004; Ghaboui and Lin, 1998; Kerh and Chu, 2002; Kerh and Ting, 2005; Kerh et al., 2011). A multilayer neural network conit of an input layer, one or more hidden layer, and an output layer. The relationhip between the input and output of a neural network can be linear a well a non-linear. Thi relationhip in any network require a function, known a the activation function or the tranfer function. There are everal activation function, uch a tep function, linear function, hyperbolic tangent function, and igmoid function. The tranfer function ued in thi tudy are decribed below. Hyperbolic Tangent Tranfer Function: The hyperbolic tangent tranfer function, hown in Figure 4 and ued for the hidden unit of the multilayer perceptron neural network, ha the form F( x ) = ( x) tanh α, where α i the lope parameter. Thi function take the input in form of any value between minu and plu infinity and limit the output to the range ( 1, 1). Sigmoid Tranfer Function: The igmoid tranfer function ha the form F x ( e α x ) ( ) = Thi tranfer function take the input in form of any value between minu and plu infinity and limit the output to the range (0, 1). Thi tranfer function i ued in thi tudy for the output layer and i hown in Figure 5.

5 ISET Journal of Earthquake Technology, June-December Output F Input x Fig. 4 Hyperbolic tangent tranfer function Output F Input x Fig. 5 Sigmoid tranfer function The backpropagation algorithm provide a precription for changing the weight. The input ignal propagate through the neural network in a forward direction, layer by layer. During the forward phae, an input vector i preented to the network, reulting in an output at the output layer. During thi phae, the weight are not modified and they are all fixed. In the backpropagation phae the weight are adjuted baed on the error between the actual and deired output. The hidden layer aid in extracting the higherorder tatitic, which tend to be ueful when the input layer i large. Alo, the ue of hidden layer implie that the information needed to compute the output i filtered before paing it on to the next layer. The ize of hidden layer i one of the mot important conideration, while olving the multilayer feedforward neural network. Chooing the number of neuron in the hidden layer i an art and i dependent on the complexity of the deired input-output mapping. The following equation i ued for the adjutment of connection weight: w n = η E w + α w n 1 j (2) ( ) ( ) ( ) ij ij ij where wij ( n) and wij ( n 1) are the weight increment between the node i and j during the n th and ( n 1) th epoch (or iteration), repectively, η i the learning rate, and α i the momentum. The momentum factor and learning rate are ued to accelerate the peed of learning without leading to ocillation. The theory of backpropagation algorithm i decribed in the neural-network related book (e.g., Haykin, 1994; Hagan et al., 1996). The objective of the training algorithm i to adjut the weight, uch that the network perform well, i.e., the quantitative meaurement of the network performance decreae. Network are trained in thi tudy by uing the gradient decent with momentum learning cheme, which focue on uing the error between the network output and the deired output. The learning algorithm adapt the weight of the ytem baed on the error until the ytem produce the deired output. The oftware NeuroSolution, Verion 5.0 (NeuroDimenion, 2003) i ued here for the imulation of neural network model. The error criteria family in NeuroSolution compute the different error meaure that can be ued to train the network. In thi tudy the criterion ued i the L2 norm or the mean quared error (MSE) criterion defined below. In thi criterion the quared difference between the ytem output and the deired ignal i imply averaged a N 1 MSE = ( x ) 2 i yi 2 (3) N i = 1

6 78 Neural-Network Baed Etimation of Normalized Repone Spectra where xi and y i are the actual and predicted value, and N denote the number of data point in the analyi. The topping criterion hould be uch that it addree the problem of generalization. Thi i done by topping the training at the point of maximum generalization. The training et i uually divided into two et: the training et and the cro-validation et. The training i topped when the error in the crovalidation et i mallet. Thi will be the point of maximum generalization. A total of 1,850 horizontal component of earthquake record from the Kyohin Net databae of 145 earthquake, having magnitude M JMA value more than 5.0 and hypocentral ditance le than 50 km, are conidered in thi tudy. The geometric mean of the two horizontal component at each recording tation i conidered for the computation of repone pectral ordinate. Thi lead to a et of 925 pectra that will be ued for training and teting the neural network. 1. Implementation Detail of Individual Model For generating a repone pectrum by uing ANN, neural network model are created in two phae. In the firt phae, the magnitude of earthquake, M, JMA hypocentral ditance H, average SPT blow count N, average primary wave velocity v p, average hear wave velocity v, and average denity of oil, ρ are ued a the ix input variable. In the econd phae, a neural network with three node on the input layer i created, uch that thi repreent the magnitude of earthquake, M, JMA hypocentral ditance H, and the average hear wave velocity v. In both the phae, the output layer conit of 55 repone pectrum ordinate with 5 percent critical damping ratio. Table 1 how the 55 time period elected from 0.03 to 10 for thee ordinate. It may be mentioned that in the databae conidered, the value of M JMA range from 5 to 7.1, H from 0 to 50 km, N from 1 to 99, v p from 450 to 3590 m/, v from 85 to 1676 m/ and ρ from 1125 to 2425 kg/m 3. Table 1: Time Period Selected for Repone Spectrum Ordinate Period () Ordinate Period () Ordinate Period () Ordinate RS(1) RS(20) RS(39) RS(2) RS(21) RS(40) RS(3) RS(22) RS(41) RS(4) RS(23) RS(42) RS(5) RS(24) RS(43) RS(6) RS(25) RS(44) RS(7) RS(26) RS(45) RS(8) RS(27) RS(46) RS(9) RS(28) RS(47) RS(10) RS(29) RS(48) RS(11) RS(30) RS(49) RS(12) RS(31) RS(50) RS(13) RS(32) RS(51) RS(14) RS(33) RS(52) RS(15) RS(34) RS(53) RS(16) RS(35) RS(54) RS(17) RS(36) RS(55) RS(18) RS(37) RS(19) RS(38)

7 ISET Journal of Earthquake Technology, June-December The total et of 925 pectra i divided into three et: (1) training et, (2) validation et, and (3) teting et. The training et, coniting of about 80% of the data et, i ued to train the network; the validation et, coniting of about 10% of the data et, i ued for the purpoe of monitoring the training proce and to guard againt overtraining; and the teting et, coniting of about 10% of the data et and not ued in the training proce, i ued to judge the performance of the trained network. The training i topped when the cro-validation error begin to increae, i.e., when the cro-validation error become minimum. 2. Neural Network Model 1 The ANN model with ix node on the input layer a decribed in the previou ection i created. A et of 825 pectra i elected randomly from the total et of 925 pectra for training and cro validation, and the remaining pectra are ued to tet the performance of the trained network. Four different data et of 825 pectra are created and randomized. Thee data et are trained independently and the data et, which give the minimum mean-quare error (MSE), i conidered for teting the network. Parametric tudie are carried out in order to evaluate the optimum value of the hidden node and learning parameter. The variou parameter ued for training the network are given in Table 2. Figure 6 how one hidden layer network model, with 51 hidden neuron, ix input neuron and 55 output neuron. Table 2: Parameter for Neural Network with One Hidden Layer for Six Input Decription Hidden layer Output layer Tranfer Function TanhAxon SigmoidAxon Learning Rule Momentum Momentum Step Size Momentum M H RS(1) RS(2) N ν ν p RS(54) ρ RS(55) Fig. 6 Neural network architecture with ix input The network with 51 hidden node in the hidden layer how the bet performance (with minimum MSE). The reult obtained after teting the network are compared by plotting the actual and predicted value of the repone pectral ordinate. A typical et of reult are hown graphically in Figure 7. The efficiency of reult obtained from the teted network i categorized a (a) excellent matching for MSE le than 0.1, (b) very good matching for MSE le than 0.2 and more than 0.1, (c) good matching for MSE le than 0.3 and more than 0.2, and (d) incorrect matching for MSE more than 0.3. The efficiency of reult o categorized i tabulated in Table 3. It i oberved from thi table that the prediction of the trained neural network i quite atifactory and therefore Model 1 ha the potential to fully replace the empirical regreion technique. It may be noted that 71% excellent matching i hown by the normalized repone pectra predicted by an ANN with ix input.

8 80 Neural-Network Baed Etimation of Normalized Repone Spectra (a) (b) (c) Fig. 7 Typical plot of acceleration repone pectra predicted by ANN with ix input for (a) M = 5.3, H = 30 km, N = 99, v p = 1730 m/, v = m/, ρ = 2.1 g/cm 3, (b) M = 5.0, H = 18.3 km, N = 80, v p = 1374 m/, v = 334 m/, ρ = 2.1 g/cm 3 and (c) M = 5.1, H = 31.4 km, N = 7, v p = 930 m/, v = m/, ρ = 1.6 g/cm 3 Table 3: Efficiency of Six-Input Baed Network S. No. Efficiency Percentage 1 Excellent Matching 71 2 Very Good Matching 17 3 Good Matching 8 4 Incorrect Matching 4 3. Neural Network Model 2 Except the K-Net databae of Japan, no other country provide detailed oil-condition data at the recording tation. Only few countrie provide the value of average hear wave velocity recorded at their recording tation. For the ue of trained network baed on the Japanee trong-motion data in other countrie, it i eential to train the network with average hear wave velocity repreenting the ite a one of the input. Model 2 i developed in a manner imlar to that of Model 1, but with only three input, i.e., M, H and. JMA v The network i deigned with 3 input node, 55 output node and 58 hidden node (i.e., with the cheme). The training parameter in Model 2 are imilar to thoe of Model 1. A typical et of reult are hown graphically in Figure 8.

9 ISET Journal of Earthquake Technology, June-December Fig. 8 (a) (b) Typical plot of acceleration repone pectra predicted by ANN with three input for (a) M = 5.2, H = 42 km, v = m/ and (b) M = 5.1, H = 39.6 km, v = m/ The efficiency of reult obtained from the teted network i categorized in a imilar manner a that for the ix input and i tabulated in Table 4. It may be oberved that with three input, 60% of the repone pectra predicted how excellent matching. However, the ANN with three input i not able to predict harp variation at the repone pectrum peak. Table 4: Efficiency of Three-Input Baed Network S. No. Efficiency Percentage 1 Excellent Matching 60 2 Very Good Matching 20 3 Good Matching 14 4 Incorrect Matching 6 4. Teting of Trained Neural Network Model 2 for Few Significant US Earthquake Motion A decribed in the previou ection, only few countrie provide the value of average hear wave velocity v recorded at their tation. One uch organization i California Strong Motion Intrumentation Program (CSMIP). In thi tudy, proceed data from the CSMIP databae i conidered. It ha been found by Katumata (1996) that the average difference between M JMA and moment magnitude M w i not ignificant for the earthquake in the magnitude range of 5 to 7. The trong-motion record conidered from the CSMIP databae are (a) Loma Prieta earthquake (with M w = 7.0) of October 17, 1989, recorded at Eureka Canyon road, Corralito, (b) Big Bear earthquake (with M w = 6.4) of June 28, 1992, recorded at Civic Center ground, Big Bear lake, (c) Northridge earthquake (with M w = 6.7) of January 17, 1994, recorded at Cedar Hill Nurery A, Tarzana, and (d) Parkfield earthquake (with M w = 6.0) of September 28, 2004, recorded at Gold Hill 3W, Parkfield. The acceleration repone pectra predicted by Model 2 for the horizontal motion in thee cae are preented in Figure 9. It i oberved that the repone pectra predicted for thee motion (recorded in USA) are quite cloe to the actual pectra and that MSE i le than 0.1 for the Big Bear, Northridge, and Parkfield earthquake motion and le than 0.2 for the Loma Prieta earthquake motion. SUMMARY AND CONCLUSIONS The uefulne of conidering the ite effect reported by the Kyohin Net databae ha been illutrated by implementing neural network a an alternative predictive tool. Two multilayer perceptron neural network model with back-propagation learning cheme have been generated with variable hidden

10 82 Neural-Network Baed Etimation of Normalized Repone Spectra layer ize to predict the 5%-damped normalized repone pectra. The prediction abilitie of both the neural network model have been teted by uing mean-quare error a a tatitical meaure. For Model 1 71% of the predicted normalized repone pectra have hown excellent matching (i.e., MSE < 0.1), wherea Model 2 ha hown excellent matching in 60% cae. Although the neural network model in thi tudy have made acceptable prediction, the accuracy of neural network etimation may need further improvement with the availability of more data et from different location and by conidering reaonably uniform ditribution of record with repect to local ite effect while training the network. The model developed here may till erve a a ueful guide for evaluating the ite-pecific repone pectra, if detailed information of the local ite condition and potential fault ource are available within a hypocentral ditance of 50 km. At the preent tage of thi tudy, the effectivene of perceptron neural network ha been demontrated to predict the 5%-damped normalized repone pectra. However, it will be ueful to alo invetigate the application of the other type of artificial neural network. Further, in the preent tudy the velocity tructure, N -value of SPT and bulk denity of oil have been conidered over a maximum depth of 20 m and have not been extended to the top 30 m of the earth. However, in future tudie it i propoed that thee ite effect may be extrapolated to at leat 30-m depth (Boore, 2004). Alo, thi tudy ha been limited to the 5%-damped normalized repone pectra and therefore it could be extended to include the other value of damping. Another important apect that could be looked into i the incluion of fault mechanim a one more additional input to the neural network. (a) (b) Fig. 9 (c) Acceleration repone pectra predicted by Model 2 for (a) Loma Prieta earthquake, (b) Big Bear earthquake, (c) Northridge earthquake and (d) Parkfield earthquake motion (d)

11 ISET Journal of Earthquake Technology, June-December The traditional regreion approach model, to predict peak ground acceleration (PGA) and pectral acceleration (SA), have concentrated on finding the tandard deviation, which i really a meaure of the goodne of fit of the derived relationhip with the data ued and thu doe not provide an inight for the record not ued in the regreion analyi. However, the propoed neural network model with backpropagation learning have been teted alo for ome of the record not ued for the development of thee model. The tatitic of the reult preented in thi work are only for 10% of the data ued for teting. Hence, the neural network methodology can be a better alternative and can provide excellent reult compared to the conventional regreion approach for predicting PGA and SA. ACKNOWLEDGEMENTS The author wih to expre their incere thank to the Kyohin Net trong-motion network of Japan for providing u with an excellent earthquake databae for conducting thi reearch. In addition, the author thank the anonymou reviewer for their valuable comment and uggetion to enhance the quality of thi article. REFERENCES 1. Arjun, C.R. (2008). Application of Artificial Neural Network for Generating Strong Ground Motion Parameter, M.Tech. Thei, Department of Earthquake Engineering, Indian Intitute of Technology Roorkee, Roorkee. 2. Arjun, C.R. and Kumar, A. (2009). Artificial Neural Network-Baed Etimation of Peak Ground Acceleration, ISET Journal of Earthquake Technology, Vol. 46, No. 1, pp Benitez, J.M., Catro, J.L. and Requena, I. (1997). Are Artificial Neural Network Black Boxe?, IEEE Tranaction on Neural Network, Vol. 8, No. 5, pp Biot, M.A. (1941). A Mechanical Analyzer for the Prediction of Earthquake Stree, Bulletin of the Seimological Society of America, Vol. 31, No. 2, pp Boore, D.M. (2004). Etimating V S (30) (or NEHRP Site Clae) from Shallow Velocity Model (Depth < 30 m), Bulletin of the Seimological Society of America, Vol. 94, No. 2, pp Borcherdt, R.D. (1994). Etimate of Site-Dependent Repone Spectra for Deign (Methodology and Jutification), Earthquake Spectra, Vol. 10, No. 4, pp Dougla, J. (2001). A Comprehenive Worldwide Summary of Strong-Motion Attenuation Relationhip for Peak Ground Acceleration and Spectral Ordinate (1969 to 2000), ESEE Report 01-1, Civil Engineering Department, Imperial College of Science, Technology and Medicine, London, U.K. 8. Dougla, J. (2002). Errata of and Addition to ESEE Report No. 01-1: A Comprehenive Worldwide Summary of Strong-Motion Attenuation Relationhip for Peak Ground Acceleration and Spectral Ordinate (1969 to 2000), Department Report, Department of Civil & Environmental Engineering, Imperial College of Science, Technology and Medicine, London, U.K. 9. FEMA (2003). Recommended Proviion for Seimic Regulation for New Building and Other Structure, Report FEMA 450, Federal Emergency Management Agency, Wahington, DC, U.S.A. 10. Ghaboui, J. and Lin, C.-C.J. (1998). New Method of Generating Spectrum Compatible Accelerogram Uing Neural Network, Earthquake Engineering & Structural Dynamic, Vol. 27, No. 4, pp Gupta, A.K. (1990). Repone Spectrum Method in Seimic Analyi and Deign of Structure, Blackwell Scientific Publication, Inc., Boton, U.S.A. 12. Hagan, M.T., Demuth, H.B. and Beale, M. (1996). Neural Network Deign, PWS Publihing Company, Boton, U.S.A. 13. Haykin, S. (1994). Neural Network: A Comprehenive Foundation, Prentice-Hall International, Inc., New Jerey, U.S.A. 14. Houner, G.W. (1941) Calculating the Repone of an Ocillator to Arbitrary Ground Motion, Bulletin of the Seimological Society of America, Vol. 31, No. 2, pp

12 84 Neural-Network Baed Etimation of Normalized Repone Spectra 15. Iwaaki, T., Kawahima, K. and Saeki, M. (1980). Effect of Seimic and Geotechnical Condition on Maximum Ground Acceleration and Repone Spectra, Proceeding of the Seventh World Conference on Earthquake Engineering, Itanbul, Turkey, Vol. II, pp Katumata, A. (1996). Comparion of Magnitude Etimated by the Japan Meteorological Agency with Moment Magnitude for Intermediate and Deep Earthquake, Bulletin of the Seimological Society of America, Vol. 86, No. 3, pp Kerh, T. and Chu, D. (2002). Neural Network Approach and Microtremor Meaurement in Etimating Peak Ground Acceleration due to Strong Motion, Advance in Engineering Software, Vol. 33, No , pp Kerh, T. and Ting, S.B. (2005). Neural Network Etimation of Ground Peak Acceleration at Station along Taiwan High-Speed Rail Sytem, Engineering Application of Artificial Intelligence, Vol. 18, No. 7, pp Kerh, T., Huang, C. and Gunaratnam, D. (2011). Neural Network Approach for Analyzing Seimic Data to Identify Potentially Hazardou Bridge, Mathematical Problem in Engineering, Vol. 2011, Article Kuribayahi, E., Iwaaki, T., Iida, Y. and Tuji, K. (1972). Effect of Seimic and Suboil Condition on Earthquake Repone Spectra, Proceeding of the International Conference on Microzonation, Seattle, Wahington, D.C., U.S.A., pp Lee, S.C. and Han, S.W. (2002). Neural-Network-Baed Model for Generating Artificial Earthquake and Repone Spectra, Computer & Structure, Vol. 80, No , pp Lee, V.W. and Trifunac, M.D. (1995). Peudo Relative Velocity Spectra of Strong Earthquake Ground Motion in California, Report CE 95-04, Univerity of Southern California, Lo Angele, U.S.A. 23. Mohraz, B. (1976). A Study of Earthquake Repone Spectra for Different Geological Condition, Bulletin of the Seimological Society of America, Vol. 66, No. 3, pp Mohraz, B., Hall, W.J. and Newmark, N.M. (1973). A Study of Vertical and Horizontal Earthquake Spectra, Report WASH-1255 (prepared for U.S. Atomic Energy Commiion, Wahington, DC, U.S.A.), Nathan M. Newmark Conulting Engineering Service, Urbana, U.S.A. 25. NeuroDimenion (2003). NeuroSolution: Reference Manual, Verion 5.0, NeuroDimenion, Inc., Gaineville, U.S.A. 26. Seed, H.B., Uga, C. and Lymer, J. (1976). Site-Dependent Spectra for Earthquake-Reitant Deign, Bulletin of Seimological Society of America, Vol. 66, No. 1, pp Tehranizadeh, M. and Safi, M. (2004). Application of Artificial Intelligence for Contruction of Deign Spectra, Engineering Structure, Vol. 26, No. 6, pp Trifunac, M.D. (1976). Preliminary Empirical Model for Scaling Fourier Amplitude Spectra of Strong Ground Acceleration in Term of Earthquake Magnitude, Source-to-Station Ditance and Recording Site Condition, Bulletin of the Seimological Society of America, Vol. 66, No. 4, pp Trifunac, M.D. (1990). How to Model Amplification of Strong Earthquake Motion by Local Soil and Geologic Site Condition, Earthquake Engineering & Structural Dynamic, Vol. 19, No. 6, pp