CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Combustion Instability and Active Control: Alternative Fuels, Augmentors, and Modeling Heat Release

Experimental and analytical studies were conducted to explore thermo-acoustic coupling during the onset of combustion instability in various air-breathing combustor configurations. These include a laboratory-scale 200-kW dump combustor and a 100-kW augmentor featuring a v-gutter flame holder. They were used to simulate main combustion chambers and afterburners in aero engines, respectively. The three primary themes of this work includes: 1) modeling heat release fluctuations for stability analysis, 2) conducting active combustion control with alternative fuels, and 3) demonstrating practical active control for augmentor instability suppression. The phenomenon of combustion instabilities remains an unsolved problem in propulsion engines, mainly because of the difficulty in predicting the fluctuating component of heat release without extensive testing. A hybrid model was developed to describe both the temporal and spatial variations in dynamic heat release, using a separation of variables approach that requires only a limited amount of experimental data. The use of sinusoidal basis functions further reduced the amount of data required. When the mean heat release behavior is known, the only experimental data needed for detailed stability analysis is one instantaneous picture of heat release at the peak pressure phase. This model was successfully tested in the dump combustor experiments, reproducing the correct sign of the overall Rayleigh index as well as the remarkably accurate spatial distribution pattern of fluctuating heat release. Active combustion control was explored for fuel-flexible combustor operation using twelve different jet fuels including bio-synthetic and Fischer-Tropsch types. Analysis done using an actuated spray combustion model revealed that the combustion response times of these fuels were similar. Combined with experimental spray characterizations, this suggested that controller performance should remain effective with various alternative fuels. Active control experiments validated this analysis while demonstrating 50-70\% reduction in the peak spectral amplitude. A new model augmentor was built and tested for combustion dynamics using schlieren and chemiluminescence techniques. Novel active control techniques including pulsed air injection were implemented and the results were compared with the pulsed fuel injection approach. The pulsed injection of secondary air worked just as effectively for suppressing the augmentor instability, setting up the possibility of more efficient actuation strategy.