One of the most significant challenges faced when modeling mass transfer from contaminant source zones is uncertainty regarding parameter estimates. These rate parameters are of particular importance because they control the connectivity between a simulated contaminant source zone and the aqueous phase. Where direct observation has fallen short, this study attempts to interpret field data using an inverse modeling technique for the purpose of constraining mass transfer processes which are poorly understood at the field scale. Inverse modeling was applied to evaluate parameters in rate-limited models for mass transfer. Two processes were analyzed: (i) desorption of hydrophobic contaminants and (ii) multicomponent Non-Aqueous Phase Liquid (NAPL) dissolution. Desorption was investigated using data obtained from elution experiments conducted with weathered sediment contaminated with 2,4,6 trinitrotoluene (TNT) (Sellm and Iskandar, 1994). Transport modeling was performed with four alternative source models, but predictive error was minimized by two first-order models which represented sorption/desorption using a Freundlich isotherm. The results suggest that first-order/Freundlich models can reproduce dynamic desorption attributed to high-and-low relative energy sorption sites. However, additional experimentation with the inversion method suggests that mass constraints are required in order to appropriately determine mass transfer coefficients and sorption parameters. The final portion of this research focused on rate-limited mass transfer from multicomponent NAPLs to the aqueous phase. Previous work has been limited to bench and intermediate scale findings which have been shown to inadequately translate to field conditions. Two studies were conducted in which numerical modeling was used to reproduce dissolution from multicomponent NAPL sources. In the first study, a model was generated to reproduce dissolution of chloroform (TCM), trichloroethylene (TCE) and tetrachloroethylene (PCE) observed during an emplaced-source field experiment conducted within a flow cell (Broholm et al., 1999). In the second study, a methodology was developed for analyzing benzene, toluene, ethylbenzene and xylene (BTEX) data during a field-scale mass transfer test conducted within a vertically-smeared source zone (Kavanaugh, 2010). The findings suggest that the inversion technique, when provided appropriate characterization of site and source parameters and when given appropriate dataset resolution, represents a viable method for parameter determination. Furthermore, the findings of this research suggest that inversion-based modeling provides an innovative predictive method for determining mass transfer parameters for multicomponent mixtures at the field scale. / Ph. D.

Rail vehicle designers and analysts can benefit from the results of vehicle parameter estimation. Using this technique, they can determine the effects of suspension design decisions, and they can reduce the amount of on-track testing required to qualify new designs for service. This work addresses two major issues: the determination of parameter identifiability and the estimation of rail vehicle parameters from laboratory tests. Usually, the identifiability issue should be addressed first since identifiability determines the number of independent parameters that can be estimated. The general issues of identifiability and parameter estimation are discussed. Two identifiability tests are explored in-depth, as is a Bayesian least-squares parameter estimation method. Laboratory tests from a lightweight intermodal rail vehicle with single-axle trucks provided the data for the parameter estimation. The test setup and a simple vehicle mathematical model provided the structure for the identifiability determination. This work shows that identifiability and estimation issues closely interact. Even if a system is not identifiable, the Bayesian estimation method can return results. Thus, the Bayesian method can instill false confidence in the validity of the estimation results. Estimation of experimental data with a linear model provided values within one percent for the mass and damped natural frequency, and ten percent for the peak amplitude. Excellent agreement with the experimental data was obtained for frequencies above the resonant peak and for very low frequencies. Error at frequencies slightly below the resonant peak, however, indicated the vehicle contained significant nonlinearities. To achieve closer agreement between model response and test response at these frequencies, a nonlinear vehicle model is needed. / Master of Science

Parametric modeling has many applications. These applications include data estimation and interpolation, modern spectral estimation, and data encoding. This research applies parametric modeling to radar cross section data in an attempt to encode it as well as preserve its spectrum. Traditionally, radar data has been processed through Fourier spectral estimation techniques. These methods not only require large amounts of data, for good spectral estimates, but assume the unobserved data values are zero which leads to spectral smearing. Modern spectral estimation methods alleviate these problems by basing the spectral estimate on a parametric model fit to the data set. The spectral estimate is then derived from the parameters of the model. For models which give a good fit to the data, a good spectral estimate can be made. The most common parametric models are the autoregressive moving-average (ARMA), the moving-average (MA) and the autoregressive (AR) model. These models represent filters, which when excited by a white Gaussian noise sequence give some output sequence. If the parameters of the models and the noise sequence are selected properly, a desired output data sequence can be modeled. The variance of the white noise is often small compared to the variance of the data sequence. This means that the model parameters plus the noise can be stored with fewer bits than the original data sequence while maintaining the same amount of accuracy in the data. The model parameters and noise sequence can be used to reproduce the original data sequence. Further, if only the spectrum of the data is of interest, only the noise variance plus the parameters need to be stored. This could lead to an even greater amount of data reduction. Most high resolution radar data applications require only that the spectrum of the data be preserved which makes modern spectral estimation appealing. This research project applies parametric modeling and modern spectral estimation to high resolution radar data as a means of encoding it. Several different parametric modeling techniques are evaluated to see which would be most useful in radar data encoding. The Burg AR parametric model was chosen due to its computational efficiency and its good spectral estimates. The Burg method applied to two radar range profile data sets gave a reduction in data storage by a factor of four. Further encoding was achieved by fitting the Burg AR parameters to a set of basis functions. This produced an additional data reduction by a factor of 36, for a total compression factor of 144. The latter led to some distortion of the high resolution range profiles, yet targets were still sufficiently characterized. / Master of Science

This work focuses on the development of a system to noninvasively estimate blood perfusion using thermal methods. This is accomplished by the combination of a bioprobe, biothermal model, and parameter estimation techniques. The probe consists of a heat flux sensor and surface thermocouple placed in contact with tissue while the opposite side is cooled by jets of room temperature air. The biothermal model predicts the temperature and heat flux within tissue and probe based upon the input of blood perfusion and the thermal contact resistance between probe and tissue. Parameter estimation techniques are developed that use the model to simultaneously estimate blood perfusion and contact resistance based on experimental heat flux and/or temperature. A gradient based system minimizes a sum of squares error function based on either or both heat flux and temperature. This system is tested on human forearms and in controlled flow rate experiments using tissue phantoms. Blood perfusion estimates from the controlled experiments are positively correlated with experimental flow rate. Experimental measurements and statistical analysis show distinct variations in the heat flux signal and rises in perfusion estimates with increasing flow rate. This research validates the use of thermal and parameter estimation methods to develop a practical, noninvasive probe to clinically measure blood perfusion. / Master of Science

The use of delayed drainage in land subsidence modeling greatly complicates model calibration, particularly when the thickness of the fine-grained interbeds varies throughout the modeled region. This thesis documents two separate projects (chapters) related to the use of delayed drainage in groundwater flow and subsidence modeling with parameter estimation. The overall goal of these projects was to better understand how delayed drainage affects accurate parameter estimation and how it is currently affecting the subsidence processes occurring in Las Vegas Valley. Chapter 1 describes an investigation on the value of subsidence data for groundwater model calibration considering delayed drainage. The calibration results of 13 hydraulic parameters of a synthetic conceptual model evaluated for 24 test cases indicate that (1) the inverse of the square of the observation values is a reasonable method to weight the observations, (2) spatially abundant subsidence data typically produce superior parameter estimates even with observation error under constant and cyclical pumping, (3) when subsidence data are limited and combined with drawdown data, outstanding results are obtained for constant pumping conditions. However, for cyclical pumping with observation errors, the best parameter estimates are achieved when multiple years of seasonal subsidence data are provided. The results provide useful suggestions for real-world calibration problems. Chapter 2 outlines the development of an updated flow and subsidence model for Las Vegas Valley covering the entire period of development of the basin. The new model includes a subsidence package that takes into account delayed drainage of fine-grained interbeds. Previous models used subsidence packages that assumed instantaneous equilibration of heads across all hydrogeologic units. The new model resulted in an agreement with measured water-level and improved the simulation of land subsidence. The analysis shows that the typical residual subsidence in Las Vegas Valley can be accurately simulated by incorporating delayed drainage in a long-term model. The study also indicates the need for more sophisticated modeling practices that use delayed drainage with parameter estimation processes to accurately calibrate flow and subsidence models. / Master of Science

Mathematical models of viral infections have been informing virology research for years. Estimating parameter values for these models can lead to understanding of biological values. This has been successful in HIV modeling for the estimation of values such as the lifetime of infected CD8 T-Cells. However, estimating these values is notoriously difficult, especially for highly complex models. We use Bayesian inference and Monte Carlo Markov Chain methods to estimate the underlying densities of the parameters (assumed to be continuous random variables) for three models of influenza. We discuss the advantages and limitations of parameter estimation using these methods. The data and influenza models used for this project are from the lab of Dr. Amber Smith in Memphis, Tennessee. / Master of Science

In this work we develop and analyze algorithms motivated by the parameter estimation problem corresponding to a multilayer aquifer/interbed groundwater flow model. The parameter estimation problem is formulated as an optimization problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and differentiability properties of the map. For differentiability, we expand existing results on Fréchet sensitivity analysis to convection diffusion equations and groundwater flow equations. This is achieved by proving that the Fréchet  derivative of the solution operator is Hilbert-Schmidt, under smoothness assumptions for the parameter space. In addition, we approximate this operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant changes in the solutions, as well as applications to uncertainty quantification. Numerical results complement our theoretical findings. / Ph. D.

Bayesian parameter estimation is a popular method to address inverse problems. However, since prior distributions are chosen based on expert judgement, the method can inherently introduce bias into the understanding of the parameters. This can be especially relevant in the case of distributed parameters where it is difficult to check for error. To minimize this bias, we develop the idea of a minimally corrective, approximately recovering prior (MCAR prior) that generates a guide for the prior and corrects the expert supplied prior according to that guide. We demonstrate this approach for the 1D elliptic equation or the elliptic partial differential equation and observe how this method works in cases with significant and without any expert bias. In the case of significant expert bias, the method substantially reduces the bias and, in the case with no expert bias, the method only introduces minor errors. The cost of introducing these small errors for good judgement is worth the benefit of correcting major errors in bad judgement. This is particularly true when the prior is only determined using a heuristic or an assumed distribution. / Master of Science

In this dissertation, we seek to improve the dynamic modeling and control of autonomous underwater vehicles (AUVs). We address nonlinear hydrodynamic modeling, simplifying modeling assumptions, and robust control for AUVs. In the literature, various hydrodynamic models exist with varying model complexity and with no universally accepted model. We compare various hydrodynamic models traditionally employed to predict the motion of AUVs by estimating model coefficients using least-squares and adaptive identifier techniques. Additionally, we derive several dynamic models for an AUV employing varying sets of simplifying assumptions. We experimentally assess the efficacy of invoking typical assumptions to simplify the equations of motion. For robust control design, we develop a procedure for designing robust attitude controllers based on loop-shaping ideas. We specifically address the challenge of adjusting the desired actuator bandwidth in a loop-shaping design framework. Finally, we present a novel receding horizon H-infinity control algorithm to improve the control of autonomous vehicle systems working in high-disturbance environments, employing a Markov jump linear system framework to model the stochastic and non-stationary disturbances experienced by the vehicle. Our main results include a new Bounded Real Lemma for stability analysis and an output feedback H-infinity control synthesis algorithm. This work uses numerical simulations and extensive field trials of autonomous underwater vehicles to identify and verify dynamic models and to validate control algorithms developed herein. / Ph. D. / In this dissertation, we seek to improve the dynamic modeling and control of autonomous underwater vehicles (AUVs). We compare different models employed to predict the motion of AUVs, and we derive several dynamic models for an AUV employing varying sets of simplifying assumptions. We experimentally assess the efficacy of invoking typical assumptions to simplify the equations of motion. For robust control design, we develop a procedure for designing robust controllers that do not produce excessive fin movements. Finally, we present a novel robust control algorithm to improve the control of autonomous vehicle systems working in high-disturbance environments. This work uses numerical simulations and extensive field trials of autonomous underwater vehicles to identify and verify dynamic models and to validate control algorithms developed herein.

We consider uncertainty quantification using surrogate Gaussian processes. We take a previous sampling algorithm and provide a closed form expression of the resulting posterior distribution. We extend the method to weighted least squares and a Bayesian approach both with closed form expressions of the resulting posterior distributions. We test methods on 1D deconvolution and 2D tomography. Our new methods improve on the previous algorithm, however fall short in some aspects to a typical Bayesian inference method. / Master of Science / Parameter uncertainty quantification seeks to determine both estimates and uncertainty regarding estimates of model parameters. Example of model parameters can include physical properties such as density, growth rates, or even deblurred images. Previous work has shown that replacing data with a surrogate model can provide promising estimates with low uncertainty. We extend the previous methods in the specific field of linear models. Theoretical results are tested on simulated computed tomography problems.