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Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition

Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
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Description
Uncertainty is inherent in predictive decision-making, both with respect to forecasting plausible future conditions based on a historic record, and with respect to backcasting likely upstream states from downstream observations. In the first chapter, I evaluated the status of current water resources management policy in the United States (U.S.) with

Uncertainty is inherent in predictive decision-making, both with respect to forecasting plausible future conditions based on a historic record, and with respect to backcasting likely upstream states from downstream observations. In the first chapter, I evaluated the status of current water resources management policy in the United States (U.S.) with respect to its integration of projective uncertainty into state-level flooding, drought, supply and demand, and climate guidance. I found uncertainty largely absent and discussed only qualitatively rather than quantitatively. In the second chapter, I turned to uncertainty in the interpretation of downstream observations as indicators of upstream behaviors in the field of Wastewater-Based Epidemiology (WBE), which has made possible the near real-time, yet anonymous, monitoring of public health via measurements of biomarkers excreted to wastewater. I found globally, seasonality of air and soil temperature causes biomarker degradation to vary up to 13-fold over the course of a year, constituting part of the background processes WBE must address, or detrend, prior to decision-making. To determine whether the seasonal change in degradation rates was introducing previously unaccounted for uncertainty with respect to differences in observed summertime and winter-time populations, I evaluated demographic indicators recorded by the Census Bureau for correlation with their distance from all major wastewater treatment plants across the U.S. The analysis identified statistically significant correlation for household income, education attainment, unemployment, military service, and the absence of health insurance. Finally, the model was applied to a city-wide case study to test whether temperature could explain some of the trends observed in monthly observations of two opiate compounds. Modeling suggests some of the monthly changes were attributed to natural temperature fluctuation rather than to trends in the substances’ consumption, and that uncertainty regarding discharge location can dominate even relative observed differences in opiate detections. In summary, my work has found temperature an important modulator of WBE results, influencing both the type of populations observed and the likelihood of upstream behaviors disproportionally magnified or obscured, particularly for the more labile biomarkers. There exists significant potential for improving the understanding of empirical observations via numerical modeling and the application of spatial analysis tools.
ContributorsHart, Olga (Author) / Halden, Rolf (Thesis advisor) / Mascaro, Giuseppe (Committee member) / Renaut, Rosemary (Committee member) / Nelson, Keith (Committee member) / Arizona State University (Publisher)
Created2019