APPLICATION OF NEURAL NETWORK TO PREDICT STRONG GROUND MOTION FOR HIMALAYAN REGION

* Arjun Kumar 1 , Himanshu Mittal 2 , Rajiv Sachdeva 3 Rohtash Kumar 4 . 1. Department of Civil Engineering, Arni University, Kathgarh, (H.P), India. 2. # 207, Back suit, Global Change Center National Taiwan University. 3. Department of Earthquake Engineering, Indian Institute of Technology Roorkee-247667. 4. Department of Geophysics, Banaras Hindu University Varanasi. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

To design engineering structures at a particular region, it requires the information about the characteristics of strong ground motion. Peak Ground Acceleration (PGA) is most frequently used parameter to characterize such ground motions. Ground motion predictions using regression analysis are commonly used for estimating these loading conditions by using strong ground motion data from previous recorded earthquakes. Artificial Neural Networks (ANNs) are efficient computing models which have shown their strengths in solving many complex problems in numerous fields. A data set of 398 strong ground motion records from 69 earthquakes (3.0≤M≤6.8) occurred in Himalayan region is used in this study. Multi-layer perceptron architecture with the error back-propagation learning algorithm has been adopted to estimate peak ground accelerations for the Himalayan earthquakes. The PGAs predicted by the ANN have been compared with PGAs obtained by regression analysis. From these observations it has been concluded that the perceptron model is quite promising for the estimation of peak ground acceleration. Results of the predicted PGA have indicated that ANN is a promising tool for the estimation of peak ground acceleration at a site.

Introduction:-
Strong Ground Motion (SGM) record at a particular site during an occurrence of earthquake is a result of complexnon linear combination of many factors (Sachdeva, 2014). Ground motion associated with a peak ground acceleration of 0.05g or higher is considered as strong ground motion (Chen and Scawthorn, 2003). For design of engineering structures for a specified region the information about the characteristics of strong ground motion is of paramount importance. Peak Ground Acceleration (PGA) is most frequently used parameter to characterize such ground motions. Ground Motion Prediction Equations (GMPE's) are commonly used for estimating these loading conditions by using strong ground motion data from previous recorded earthquakes. A very little agreement has been reached in the past 30 years of ground motion estimation relation studies and the scatter could not be reduced to requisite level. This is more because the relations not only depends upon data selection, characterization of source, path or site or the regression technique employed but also on the purpose for which equation is intended to be used.
Artificial Neural Networks (ANNs) are efficient computing models which have shown their strengths in solving many complex problems in numerous fields. They have the versatility to approximate a wide range of complex functional relationships between sets of input and output data. The purpose of this study is to predict strong ground motion parameters using ANN that are of primary significance in earthquake engineering. In this study, sets of Multilayer Perception (MLP) neural network model are trained to predict the PGA. Neuro Intelligence (Neural Network Simulator) software has been used to model ANN and the standard back-propagation supervised training scheme is used to train all networks. A data set of 398 strong ground motion records from 69 earthquakes (3.0≤M≤6.8) occurred in Himalayan region are used in this study. A comparision of PGA values obtained from neural network and regression analysis have made.

Acceleration Data:-
Two types of data sets collected from the Himalaya region have been used in the study. The first data set of 144 records from 10 earthquakes (5.2≤M≤6.8) as shown in Figure 1 became available from strong motion array comprised of strong motion accelerographs (SMA-1 of Kinematrics) in the Himalaya region. The purpose of deploy these instruments is to record the strong ground motion due to moderate and large-sized earthquakes occurring in the Himalayan region (Chandrasekharan, 1991). At each station the threshold level (trigger level) to sense the ground motion was set about 0.01 g. The analog recordings of these earthquakes were manually digitized using a semi automatic digitizer and digital data was processed adopting standard processing procedures (Trifunac, 1976). The data was converted to a uniform sampling rate of 0.02 seconds and band-pass filtered (0.17-0.20 Hz; 25-27 Hz) using an Ormsby filter (Chandrasekaran and Das, 1992).
The second data set of 254 records from 59 earthquakes of magnitude range (3.0≤M≤6. The earthquakes considered for training neural network are shown in Table 1. The magnitude distance distribution of these earthquakes is shown in Figure 4.

Artificial Neural Network:-
Artificial neural networks are among the most powerful learning models that are capable of establishing a mapping relationship between the given sets of inputs and outputs. The theoretical background on neural networks (NN) can be found in a large volume of literature (e.g., Zurada, 1992;Hagan et al., 1996;Bishop, 1995;Mehrotra et al., 1996;Haykin, 1994;Demuth et al., 2006;Arjun and Kumar, 2009).
In this study, multi-layer feedforward neural networks, commonly referred to as multilayer perceptrons (MLPs) have been used. It has a layered architecture consisting of input, hidden, and output layers. The input signal propagates through the network in a forward direction on a layer-by-layer basis. The output of each layer is transmitted to the input of neurons in the next layer through weighted links. The hidden layer aids in performing useful complex computations by extracting progressively more meaningful features from the input layer. Figure 3 shows a onehidden-layer MLP with D inputs, K hidden processing elements and M outputs (i.e., MLP (D-K-M)).
Training and weight adaptation is done in MLPs in a supervised manner with a highly popular algorithm known as the error back-propagation algorithm. Back-propagation learning consists of two phases. During the first phase, inputs presented to the input layer propagate through the network, layer by layer, to the output layer, where the error between the desired output and the network output is calculated. During this phase, the weights are not modified, and they remain constant. During the second phase, the error signal is propagated backwards from the output layer through the network to the input layer. During this stage, the weights are adjusted in such a way that the actual output moves closer to the desired output.
Networks have been trained in this study by using the gradient descent with momentum learning scheme, which focuses on using the error between the network output and the desired output. The learning algorithm adapts the weights of the system based on the error until the system produces the desired output. The error criterion used is the 2 L -norm or mean squared error (MSE) criterion. It simply computes the difference between the system output and the desired signal and squares it. The stopping criteria should be such that it addresses the problem of generalization. This has been done by stopping the training at the point of maximum generalization. The training set is usually divided into two sets: the training and the cross-validation sets. The training is stopped when the error in the crossvalidation set is smallest. This will be the point of maximum generalization.

Application of ANN for estimating PGA:-
A data set of 398 strong ground motion records from 69 earthquakes (3.0≤M≤6.8) occurred in Himalayan region is used in this study. Figure 4 gives the scatter plot of magnitude versus hypocentral distance of the data used. The neural network is trained and tested using the data. The total set of 398 values has been divided into three sets: 1. training set, 2. validation set, and 3. testing set.
The training set, which is about 80% of the complete dataset, has been used to train the network; the validation set, which is about 10%, has been used for the purpose of monitoring the training process, and to guard against overtraining; and the testing set, which is about 10%, has been used to judge the performance of the trained network. The training was stopped when the cross-validation error began to increase, i.e., when the cross-validation error was minimum.
A [2-2-1] architecture with 9 weights have been selected which have 3.25 fitness. The training error is 0.35; validation error is 0.27 and testing error is 0.31 for this architecture. A correlation of 0.73 is obtained between the actual PGA and predicted PGA ( Figure 5). Then estimated PGAs for magnitude 6.8 were compared with actual and that obtained from regression analysis. A good correlation has been observed between predicted by ANN and that obtained from regression analysis.

Conclusions:-
A multi-layer perceptron architecture with the error back-propagation learning algorithm has been adopted to estimate peak ground accelerations for the Himalayan earthquakes. The PGAs predicted by the ANN have been compared with PGAs obtained by regression analysis. From these observations it has been concluded that the perceptron model is quite promising for the estimation of peak ground acceleration. Results of the predicted PGA have indicated that ANN is a promising tool for the estimation of peak ground acceleration at a site. The performance of networks may be improved by carrying a detailed parametric study on the optimal network to be used for predicting the peak ground acceleration. Future work may also examine the application of hybrid artificial intelligence techniques.