| The dissertation primarily investigates the characterization and discrimination of stochastic time series with an application to pattern recognition and fault detection. These techniques supplement traditional methodologies that make overly restrictive assumptions about the nature of a signal by accommodating stochastic behavior. The assumption that the signal under investigation is either deterministic or a deterministic signal polluted with white noise excludes an entire class of signals---stochastic time series. The research is concerned with this class of signals almost exclusively. The investigation considers signals in both the time and the frequency domains and makes use of both model-based and model-free techniques.;A comparison of two multivariate statistical discrimination techniques, one based on a traditional covariance statistic and one based on a more recently proposed periodogram based statistic, is carried out through simulation study. This investigation validates the utility of the periodogram based statistic over the covariance based statistic. The periodogram based statistic proves more useful in identifying statistical dissimilarities in multidimensional time series than the more traditional statistic.;Attention is then focused on using the periodogram based statistic as a distance measure for clustering and classifying time series, which is motivated by the periodogram method's increased discrimination capability. The test statistic is used in both clustering and classification algorithms, and the performance is evaluated though a simulation study. This measure proves capable of grouping like series together while simultaneously separating dissimilar series from one another.;Finally, the techniques are adapted to the time-domain where they are used to cluster multidimensional, non-stationary, climatological data. The non-stationary model accounts for seasonal means, seasonal standard deviations, and stochastic components. The statistical approach results in the development of a level-alpha test for assessing signal equality. This improves upon typical dendrogram techniques by defining a level under which the distance should be considered zero. Climatological time series from the west coast, Gulf of Mexico, and east coast are analyzed using the aforementioned techniques.;To complement the time series analysis work, some effort (Appendix A) is focused on improving the bachelor of science in the department of mechanical engineering via the undergraduate laboratories. This is accomplished by identifying desired outcomes and implementing specific improvements in the undergraduate laboratory courses over a period of four years. The effects of these improvements are quantified with survey results. Overall, the improvements are very well received and result in significant increases in student satisfaction. |
