Optimal-adaptive filters for modelling spectral shape, site amplification, and source scaling

Optimal filtering techniques have been used successfully in various areas in science and engineering. They are based on statistical properties of the signal and the noise, and stochastic approximation theory. In addition to filtering, optimal filters can also be used for smoothing, prediction, and system identification. This paper introduces some applications of optimal filtering techniques to earthquake engineering by using the so-called ARMAX models. Three applications are presented: (a) spectral modelling of ground accelerations, (b) site amplification (i.e., the relationship between two records obtained at different sites during an earthquake), and (c) source scaling (i.e., the relationship between two records obtained at a site during two different earthquakes). A numerical example for each application is presented by using recorded ground motions. The results show that the optimal filtering techniques provide elegant solutions to above problems, and can be a useful tool in earthquake engineering.