Obene, Pufinji Maclean (1990) On the use of time and correlation windows for non-parametric spectral analysis. PhD thesis, University of Warwick.

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Abstract

Design of time and correlation windows for non-parametric frequency response estimates.

The thesis deals with problems that arise in the field of spectral analysis due to finite observations of input and output records. In particular, it is concerned with the method of applying time and correlation windows in spectral analysis procedures to obtain non- parametric frequency response estimates of open-loop time invariant systems.

The thesis reviews and develops the sources of error that arise when frequency response techniques are applied directly to windowed records of input and output data to estimate the frequency response of open loop systems.

Having identified the cause of these errors, methods of eliminating or reducing them are studied. The techniques introduced, which are believed to be novel, involve the use of differing time windows for the input and output data records. Rather than the use of previously developed and ad-hoc symmetrical windows, it is shown that windows can be designed on the basis of some specified criterion such as maximum square coherence or minimum mean square error.

Another method of window selection is based on minimum a priori knowledge of the system characteristics which leads to further improvement in the frequency response estimates. These Least Mean Square Error Windows, are solved numerically and are shown to be superior to conventional, classical windows developed in the past.

Window carpentry and modelling of power spectral data

Careful mathematical modelling is always required in the design of modern suspension bridges, as these models are used to predict free vibrations and excitation responses. However, in order to validate any assumption made in the modelling and accuracy of the model parameters, full scale testing procedures need to be undertaken. From the spectrum of measured ambient responses of such large structures, it is necessary to determine the damping factor, resonant frequency and amplitude for each resonance.

Such high Q systems have very sharp spectral peaks and any smoothing; by splitting into segments or by smoothing over frequencies of estimates obtained from a single realisation, removes important fine spectral details.

By analysis and experiment, tests on known similar models show that least squares fitting on the windowed unsmoothed estimates reduces bias in the spectral estimates. It is also be shown that least squares fitting on the unsmoothed cumulative spectra further reduces this bias.

Both procedures, applied to ambient response data from the Humber suspension bridge, are found to differ consistently from earlier results. In particular estimates of damping factor are shown to be very much smaller than those based on smoothed spectral density measurements.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Spectrum analysis, Signal processing -- Mathematics, Time-series analysis, Frequency response (Dynamics), Spectral theory (Mathematics)
Official Date:	December 1990
Dates:	Date Event December 1990 Submitted
Institution:	University of Warwick
Theses Department:	Department of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Douce, J. L.
Sponsors:	Science and Engineering Research Council (Great Britain)
Format of File:	pdf
Extent:	v, 193 leaves : illustrations, charts
Language:	eng

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