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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 204
Modelling NonLinear Effects in Seismic Data from Estimates of Bispectra using Linear Prediction and Volterra Kernels A.A. Chanerley^{1}, H. Nabijou^{2}, N. Alexander^{3} and R. Sigbjornsson^{4}
^{1}School of Computing and Technology, University of East London, United Kingdom
A.A. Chanerley, H. Nabijou, N. Alexander, R. Sigbjornsson, "Modelling NonLinear 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", CivilComp Press, Stirlingshire, UK, Paper 204, 2007. doi:10.4203/ccp.86.204
Keywords: correction, seismic, recursive, bispectrum, least squares, inverse, Levinson, timehistory, 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 timehistory. 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 nonlinear fashion resulting in sum and difference frequencies; for instance in the case of quadratic phase coupling, where f_{3}=f_{1}+f_{2}, the appearance of f_{3} in the power spectrum is in fact a coupling artefact.
In order to estimate the bispectra of seismic timehistories using a nonlinear 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 nonlinear residue to which a secondorder Volterra model is fitted to estimate its kernel. The secondorder 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 LevinsonDurbin recursion in order to estimate the model coefficients and the secondorder Volterra kernel is estimated using the input output crossbispectrum. The magnitude of the secondorder 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 nonlinear behaviour. On the other hand these nonlinear effects may arise from coupling in the frequency content of the ground motion or the structure in which the accelerometer may be installed. References
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