Stochastic Analysis of the LMS Algorithm for System Identification with Subspace Inputs

This paper studies the behavior of the low rank LMS adaptive algorithm for the general case in which the input transformation may not capture the exact input subspace. It is shown that the Independence Theory and the independent additive noise model are not applicable to this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to the Independence Theory model). The new theory is applied to a network echo cancellation scheme which uses partial-Haar input vector transformations. Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the Independence Theory based model available in the literature

A non-separable stochastic model for pulse-like ground motions

A phenomenological non-separable non-stationary stochastic model is proposed to represent near-fault pulse-like ground motions (PLGMs) by means of a parametrically defined evolutionary power spectrum (EPSD). Numerical data pertaining to ensembles of EPSD compatible realizations and considering statistical analysis of peak elastic and inelastic spectral ordinates demonstrate the applicability of the model to capture the salient effects of PLGMs to structural responses. To this aim, the model parameters are calibrated against a field recorded PLGM. Further numerical data considering stochastic processes compatible with the response spectrum of the European aseismic code (EC8) are furnished to demonstrate the potential of the proposed model for including near-fault effects to spectrum compatible representations of the seismic action. It is foreseen that this model can be a useful tool in accounting for the low-frequency content of PLGMs in both Monte Carlo simulation-based analyses and in statistical linearization based studies

Which univariate time series model predicts quicker a crisis? The Iberia case

In this paper four univariate models are fitted to monthly observations of the number of passengers in the Spanish airline IBERIA from January 1985 to October 1994. During the first part of the sample, the series shows an upward trend which has a rupture during 1990 with the slope changing to be negative. The series is also characterized by having seasonal variations. We fit a deterministic components model, the Holt-Winters algorithm, an ARIMA model and a structural time series model to the observations up to December 1992. Then we predict with each ofthe models and compare predicted with observed values. As expected, the results show that the detenninistic model is too rigid in this situation even if the within-sample fit is even better than for any of the other models considered. With respect to Holt-Winters predictions, they faH because they are not able to accornmodate outliers. Finally, ARIMA and structural models are shown to have very similar prediction performance, being flexible enough to predict reasonably well when there are changes in trend