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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 204

Modelling Non-Linear Effects in Seismic Data from Estimates of Bispectra using Linear Prediction and Volterra Kernels

A.A. Chanerley1, H. Nabijou2, N. Alexander3 and R. Sigbjornsson4

1School of Computing and Technology, University of East London, United Kingdom
2Department of Computing Communications Technology and Mathematics, London Metropolitan University, United Kingdom
3Department of Civil Engineering, University of Bristol, United Kingdom
4Institute for Earthquake Engineering, University of Iceland, Iceland

Full Bibliographic Reference for this paper
A.A. Chanerley, H. Nabijou, N. Alexander, R. Sigbjornsson, "Modelling Non-Linear Effects in Seismic Data from Estimates of Bispectra using Linear Prediction and Volterra Kernels", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 204, 2007. doi:10.4203/ccp.86.204
Keywords: correction, seismic, recursive, bispectrum, least squares, inverse, Levinson, time-history, spectra, Volterra, kernels, linear prediction.

Summary
This paper continues from recent work [1,2] on the correction of seismic data using system identification methods, which estimate the frequency responses of an accelerometer in order to reverse engineer and obtain a better estimate the ground motion time-history. The analytic and numerical methods used suggest that some of the resonant frequencies in the acceleration response spectra may be artefacts arising as a result of phase coupling. This occurs because frequency components interact in a non-linear fashion resulting in sum and difference frequencies; for instance in the case of quadratic phase coupling, where f3=f1+f2, the appearance of f3 in the power spectrum is in fact a coupling artefact.

In order to estimate the bispectra of seismic time-histories using a non-linear model, the parameters of the linear part of the total model are first estimated using a linear predictive coding approach. The linear model is then transformed to the time domain and used to remove the linear component from the data. The remainder is then the non-linear residue to which a second-order Volterra model is fitted to estimate its kernel. The second-order kernel transform is therefore the parametric approach in estimating the bispectrum. Using this approach produces some useful results of peak frequencies for a relatively small number of model coefficients. The LPC uses the Levinson-Durbin recursion in order to estimate the model coefficients and the second-order Volterra kernel is estimated using the input output cross-bispectrum. The magnitude of the second-order Volterra kernels transform is then used to identify the interacting frequency spectra of the seismic event.

The source of the coupled frequencies may come from the accelerometer. These instruments may be subject to inherent non-linear behaviour. On the other hand these non-linear effects may arise from coupling in the frequency content of the ground motion or the structure in which the accelerometer may be installed.

References
1
A.A. Chanerley and N.A. Alexander, "An Approach to Seismic Correction which includes Wavelet De-noising", in Proceedings of the Third International Conference on Engineering Computational Technology, B.H.V. Topping and Z. Bittnar, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 44, 2002. doi:10.4203/ccp.75.44
2
N.A. Alexander, A.A. Chanerley and N. Goorvadoo, "A Review of Procedures used for the Correction of Seismic data", in Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing, B.H.V. Topping, (Editor), Civil-Comp Press, Stirling, United Kingdom, paper 39, 2001. doi:10.4203/ccp.73.39

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