Spectral Methods in the Identification of Time Series

The analysis of time series is a very important element in much of the systems work carried out at IIASA and elsewhere. The basic principles of time series analysis were laid down by Box and Jenkins in 1970 in an approach which divided model building into three stages: model identification, parameter estimation and model validation. However, while there are many formal approaches to parameter estimation and several formal methods for model validation, the only available tool for model identification is currently visual inspection of the time series plot and autocorrelation function. This is evidently the weakest point of the Box-Jenkins methodology. In an attempt to remedy this, Andrzej Lewandowski proposes here a new approach to Box-Jenkins model identification. In contrast to the existing tools, this approach is based on spectral methods and involves frequency analysis of ARMA models. It differs from the standard spectral approach presented in textbooks on time series analysis, although it is based on a principle well known in control engineering and circuit theory. This method provides a means of analyzing time series in some depth using only a pencil, a piece of paper, and a pocket calculator

Geoacoustic inversion in laterally varying shallow-water experiments using high-resolution wavenumber estimation

Thesis (Ph. D. in Applied Ocean Sciences)--Joint Program in Applied Ocean Physics and Engineering (Massachusetts Institute of Technology, Dept. of Ocean Engineering; and the Woods Hole Oceanographic Institution), February 2002.Includes bibliographical references (leaves 161-170).Sound propagation in shallow water is highly dependent on the interaction of the sound field with the bottom. In order to fully understand this problem, it is necessary to obtain reliable estimates of bottom geoacoustic properties that can be used in acoustic propagation codes. In this thesis, perturbative inversion methods and exact inverse methods are discussed as a means for inferring geoacoustic properties of the bottom. For each of these methods, the input data to the inversion is the horizontal wavenumber spectrum of a point-source acoustic field. The main thrust of the thesis work concerns extracting horizontal wavenumber content for fully three-dimensionally varying waveguide environments. In this context, a high-resolution autoregressive (AR) spectral estimator was applied to determine wavenumber content for short aperture data. As part of this work, the AR estimator was examined for its ability to detect discrete wavenumbers in the presence of noise and also to resolve closely spaced wavenumbers for short aperture data. As part of a geoacoustic inversion workshop, the estimator was applied to extract horizontal wavenumber content for synthetic pressure field data with range-varying geoacoustic properties in the sediment. The resulting wavenumber content was used as input data to a perturbative inverse algorithm to determine the sound speed profile in the sediment. It was shown using the high-resolution wavenumber estimator that both the shape and location of the range-variability in the sediment could be determined.(cont.) The estimator was also applied to determine wavenumbers for synthetic data where the water column sound speed contained temporal variations due to the presence of internal waves. It was shown that reliable estimates of horizontal wavenumbers could be obtained that are consistent with the boundary conditions of the waveguide. The Modal Mapping Experiment (MOMAX), an experimental method for measuring the full spatial variability of a propagating sound field and its corresponding modal content in two-dimensions, is also discussed. The AR estimator is applied to extract modal content from the real data and interpreted with respect to source/receiver motion and geometry. For a moving source, it is shown that the wavenumber content is Doppler shifted. A method is then described that allows the direct measure of modal group velocities from Doppler shifted wavenumber spectra. Finally, numerical studies are presented addressing the practical issues associated with using MOMAX type data in the exact inversion method of Gelfand-Levitan.by Kyle M. Becker.Ph.D

Proceedings of the Workshop on Identification and Control of Flexible Space Structures, volume 1

Identification and control of flexible space structures were studied. Exploration of the most advanced modeling estimation, identification and control methodologies to flexible space structures was discussed. The following general areas were discussed: space platforms, antennas, and flight experiments; control/structure interactions - modeling, integrated design and optimization, control and stabilization, and shape control; control technology; control of space stations; large antenna control, dynamics and control experiments, and control/structure interaction experiments