Earthquake Engineering Problems in Parallel Neuro Environment

Transcription

1 Earthquake Engineering Problems in Parallel Neuro Environment Sanjay Singh IBM Global Services India Pvt. Ltd., Bangalore and Sudhirkumar V Barai Department of Civil Engineering, IIT Kharagpur skbarai@civil.iitkgp.ernet.in URL: 1

2 Presentation Outline Introduction Genesis of the Problem Objectives ANN And Parallel Computing Environment Autoregressive Moving Average Models Handling Nonstatoinary Processes Data Collection Development of Neuro-Models: Present Study Performance of Neuro-Models Discussion Conclusions 2

3 Introduction Earthquake Ground Motion Simulation Stochastic Models Neural-Networks and Earthquake Ground Motion 3

4 Genesis of the Problem Replacing the modeling process step by step Difficulties in handling large data sets and Neural Network Parameters Increase in computational time 4

5 Objectives Replace the ARMA model by ANN. Expedite the process of training Neural-Networks. Simulation on Parallel Computing Environment. Generation of Earthquake Acceleration 5

6 Artificial Neural Networks (ANN) Different approach to simulation problems Inspired by the neuronal architecture of brain A family of highly interconnected neurons 6

7 Parallel Computing Environment Processing tasks - distributed among the processors Processors work in parallel Processors communicate sequentially Considerable reduction in computational time 7

8 Handling Non-stationary Processes Earthquake ground motion is a non-stationary process. Both the frequency and the intensity changes with time. A non-stationary process has a change in variance as a function of time. A Variance envelope is constructed to transform the process. 8

9 Data Collection 100 strong earthquake records. Locations: North-Eastern part of India, Himanchal Pradesh and Uttaranchal. Acceleration data points - at the interval of 0.02 seconds. Corrected data can directly be used for the analysis purpose. 9

10 Implementation on PARAM

11 Performance of Neuro Models 11

12 Part 1: Construction of ARMA Models Using ANN 12

13 Construction of ARMA Models Step 1: Estimation of the variance function. Step 2: Construction of a stationary series by transforming the non-stationary series according to the various functions determined in step 1. Step 3: Estimation of an ARMA model from the stationary series obtained in step 2. Step 4: Validation of the modeling procedure. Variance is determined by squaring the series and applying Box-Cox transformation. 13

14 Recording Station - Baithalangso Acceleration series 14

15 Transformed square acceleration with estimated variance polynomial 15

16 ANN for Variance Function Estimation Polynomial Variance Model h () 2 k t = β + β t + β t β A fourth-order polynomial model describes the data well. Initial information - input parameters and polynomial coefficients as output parameters. kt 16

17 Input Features Magnitude Focal Depth Epicentral Dist. GM Components Hidden Layers Two Layers Sigmoid Activation Function Output Features Polynomial Coefficients β, β, β, β, β ARMA Model Parameters φ, φ, φ, φ, θ,c Neural Network Architecture 17

18 Polynomial Coefficient Prediction 18

19 Average Error in Training Patterns Typical Testing Example Error 19

20 Comparison of estimated and predicted standard deviation as a function of time 20

21 Acceleration Series after Variance Stabilization 21

22 ANN for ARMA Model Estimation The ARMA (4, 1) appeared to give a reasonable fit. Z = φ Z + φ Z + φ Z + φ Z + a θ a + c t 1 t 1 2 t 2 3 t 3 4 t 4 t 1 t 1 In developing ANN for ARMA model estimation, initial information is used as input variables and the ARMA model parameters are chosen as the output variables 22

23 Input Features Magnitude Focal Depth Epicentral Dist. GM Components Hidden Layers Two Layers Sigmoid Activation Function Output Features Polynomial Coefficients β, β, β, β, β ARMA Model Parameters φ, φ, φ, φ, θ,c Neural Network Architecture 23

24 ARMA Model Parameter Prediction 24

25 Average Error in Training Patterns Typical Testing Example Error 25

26 Part 2: Simulating Earthquake Acceleration using ANN 26

27 Simulated of Earthquake Acceleration Stationary series are first generated from the fitted ARMA models Multiplied by the estimated standard deviation function. ANN models - to predict the ARMA model coefficients and the standard deviation function. Artificial accelerogram - reproduced by the multiplication of two. 27

28 Simulated Acceleration from ARMA (4, 1) 28

29 Simulated Acceleration from ANN 29

30 Discussion Neural networks simulations were carried out using Parallel Neuro Simulator developed on PARAM The ANN models showed the satisfactory results, the maximum error in training patterns is 6.19%. 30

31 Computational Time Comparison ANN for variance estimation ANN for ARMA parameters estimation 31

32 Conclusions The proposed approach - attempt to relate the recording site characteristics with the accelerogram. More input parameters can enhance the prediction capabilities of ANN. The spectra for the observed and simulated series match quite well. Selection of ANN parameters in parallel environment. Significant reduction in computational time. 32

33 33

34 References Chang, M.K., Kwaitkowski J.W., Nau R.F., Oliver R.M. and Pister K.S. (1982). ARMA models for earthquake ground motions, Earthquake Eng. Struct. Dyn., 10, Lee, S. C. and Han, S.W. (2002). Neural-network-based models for generating artificial earthquakes and response spectra, Computers and Structures 80, Ghaboussi, J. and Lin, C. (1998). New method of generating spectrum compatible accelerograms using neural networks, Earthquake Eng Struct Dyn., 27, Haykin S. (1994). Neural networks: a comprehensive foundation. Englewood Cliffs, NJ: Prentice-Hall International, Inc;

35 References Polhemus N.W. and Cakmak A. S. (1981). Simulation of earthquake ground motions using autoregressive moving average (ARMA) models. Earthquake Engg. Struct. Dyn., 9, Roverso D. (2000). Neural Ensembles for Event Identification, in Proceedings of Safeprocess'2000, the 4th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes. Lee, S. C. and Han, S.W. (2002). Neural-network-based models for generating artificial earthquakes and responsespectra, Computers and Structures 80,