Maximum likelihood spectrum estimation with applications to failure detection and system identification
Abstract
This thesis is concerned with the utility of the information in the family of Capon's maximum likelihood spectra (1969) for estimating a mixed spectrum consisting of point masses corresponding to a deterministic random process, plus arbitrary unknown continuous spectrum corresponding to a regular random process. A popular setting for this type of mixed spectrum is the signal-plus-noise problem wherein the signal consists of harmonic or sinusoidal components and the noise is colored and without such components. A mixed spectrum identification technique has been developed. This technique provides an improved identification of the point spectrum, as well as procedures for subsequently recovering the continuous spectrum. Subsequent to investigating this single channel signal-plus-noise problem we extended the utility of our new approach to a larger class of settings in mechanical engineering. To our knowledge this extension provides the first rigorous approach to extracting system identification and coherence information from rotating machinery. Based on the comparative results we conclude that this new technique is an extremely valuable tool in system identification and coherence analysis. Our results demonstrate that in mixed spectrum settings it performs significantly better than FFT and AR methods for system identification including both magnitude and phase. Moreover, it is robust with respect to the amount of available data. Our results also highlighted the limitations and dangers of blindly applying FFT and AR methods in mixed spectrum settings. Without consideration of the information of point spectrum extremely erroneous results can be obtained.
Degree
Ph.D.
Advisors
Sherman, Purdue University.
Subject Area
Mechanical engineering
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