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In some survival analysis of medical studies, there are often long term survivors who can be considered as permanently cured. The goals in these studies are to estimate the cure probability of the whole population and the hazard rate of the noncured subpopulation. The existing methods for cure rate models have been limited to parametric and semiparametric models. More specifically, the hazard function part is estimated by parametric or semiparametric model where the effect of covariate takes a parametric form. And the cure rate part is often estimated by a parametric logistic regression model. We introduce a non-parametric model employing smoothing splines. It provides non-parametric smooth estimates for both hazard function and cure rate. By introducing a latent cure status variable, we implement the method using a smooth EM algorithm. Louis' formula for covariance estimation in an EM algorithm is generalized to yield point-wise confidence intervals for both functions. A simple model selection procedure based on the Kullback-Leibler geometry is derived for the proposed cure rate model. Numerical studies demonstrate excellent performance of the proposed method in estimation, inference and model selection. The application of the method is illustrated by the analysis of a melanoma study. / Ph. D.

The following is an exploration into the optimal guidance and control of gun-launched guided projectiles. Unlike their early counterparts, modern-day gun-launched projectiles are capable of considerable accuracy. This ability is enabled through the use of control surfaces, such as fins or wings, which allow the projectile to maneuver towards a target. These aerodynamic features are part of a control system which lets the projectile achieve some effect at the target. With the advent of very high velocity guns, such as the Navy's electromagnetic railgun, these systems are a necessary part of the projectile design. This research focuses on a control scheme that uses the projectile's angle of attack as the single control in the development of an optimal control methodology that maximizes impact velocity, which is directly related to the amount of damage in icted on the target. This novel approach, which utilizes a reference trajectory as a seed for an iterative optimization scheme, results in an optimal control history for a projectile. The investigation is geared towards examining how poor an approximation of the true optimal solution that reference trajectory can be and still lead to the determination of an optimal control history. Several different types of trajectories are examined for their applicability as a reference trajectory. Although the use of aerodynamic control surfaces enables control of the projectile, there is a potential down side. With steady development of guns with longer ranges and higher launch velocities, it becomes increasingly likely that a projectile will y into a region of the atmosphere (and beyond) in which there is not sufficient air ow over the control surfaces to maintain projectile control. This research is extended to include a minimum dynamic pressure constraint in the problem; the imposition of such a constraint is not examined in the literature. Several methods of adding the constraint are discussed and a number of cases with varying dynamic pressure limits are evaluated. As a result of this research, a robust methodology exists to quickly obtain an optimal control history, with or without constraints, based on a rough reference trajectory as input. This methodology finds its applicability not only for gun-launched weapons, but also for missiles and hypersonic vehicles. / Doctor of Philosophy / As the name implies, optimal control problems involve determining a control history for a system that optimizes some aspect of the system's behavior. In aerospace applications, optimal control problems often involve finding a control history that minimizes time of ight, uses the least amount of fuel, maximizes final velocity, or meets some constraint imposed by the designer or user. For very simple problems, this optimal control history can be analytically derived; for more practical problems, such as the ones considered here, numerical methods are required to determine a solution. This research focuses on the optimal control problem of a gun-launched guided projectile. Guided projectiles have the potential to be significantly more accurate than their unguided counterparts; this improvement is achieved through the use of a control mechanism. For this research, the projectile is modeled using a single control approach, namely using the angle of attack as the only control for the projectile. The angle of attack is the angle formed between the direction the projectile is pointing and the direction it is moving (i.e., between the main body axis and the velocity vector of the projectile). An approach is then developed to determine an optimal angle of attack history that maximizes the projectile's final impact velocity. While this problem has been extensively examined by other researchers, the current approach results in the analytical determination of the costate estimates that eliminates the need to iterate on their solutions. Subsequently, a minimum dynamic pressure constraint is added to the problem. While extensive investigation has been conducted in the examination of a maximum dynamic pressure constraint for aerospace applications, the imposition of a minimum represents a novel body of work. For an aerodynamically controlled projectile, (i.e., one controlled with movable surfaces that interact with the air stream), dropping below a minimum dynamic pressure may result in loss of sufficient control. As such, developing a control history that accommodates this constraint and prevents the loss of aerodynamic control is critical to the ongoing development of very long range, gun-launched guided projectiles. This new methodology is applied with the minimum dynamic pressure constraint imposed and the resulting optimal control histories are then examined. In addition, the possibility of implementing other constraints is also discussed.

A phasor-only estimator carries with it intrinsic improvements over its SCADA analogue with respect to performance and reliability. However, insuring the quality of the data stream which leaves the linear estimator is crucial to establishing it as the front end of an EMS system and network applications which employ synchrophasor data. This can be accomplished using a two-fold solution: the pre-processing of phasor data before it arrives at the linear estimator and the by developing a synchrophasor-only dynamic state estimator as a mechanism for bad data detection and identification. In order to realize these algorithms, this dissertation develops a computationally simple model of the dynamics of the power system which fits neatly into the existing linear state estimation formulation. The algorithms are then tested on field data from PMUs installed on the Dominion Virginia Power EHV network. / Ph. D.

The collection of biological data has been limited by instrumentation, the complexity of the systems themselves, and even the ability of graduate students to stay awake and record the data. However, increasing measurement capabilities and decreasing costs may soon enable the collection of reasonably sampled time course data characterizing biological systems, though in general only a subset of the system's species would be measured. This increase in data volume requires a corresponding increase in the use and interpretation of such data, specifically in the development of system identification techniques to identify parameter sets in proposed models. In this paper, we present the results of identifiability analysis on a small test system, including the identifiability of parameters with respect to different measurements (proteins and mRNA), and propose a working definition for "biologically meaningful estimation". We also analyze the correlations between parameters, and use this analysis to consider effective approaches to determining parameters with biological meaning. In addition, we look at other methods for determining relationships between parameters and their possible significance. Finally, we present potential biologically meaningful parameter groupings from the test system and present the results of our attempt to estimate the value of select groupings. / Master of Science

Estimation methods such as the Kalman filter identify best state estimates based on certain optimality criteria using a model of the system and the observations. A common assumption underlying the estimation is that the noise is Gaussian. In practical systems though, one quite frequently encounters thick-tailed, non-Gaussian noise. Statistically, contamination by this type of noise can be seen as inducing outliers among the data and leads to significant degradation in the KF. While many nonlinear methods to cope with non-Gaussian noise exist, a filter that is robust in the presence of outliers and maintains high statistical efficiency is desired. To solve this problem, a new robust Kalman filter framework is proposed that bounds the influence of observation, innovation, and structural outliers in a discrete linear system. This filter is designed to process the observations and predictions together, making it very effective in suppressing multiple outliers. In addition, it consists of a new prewhitening method that incorporates a robust multivariate estimator of location and covariance. Furthermore, the filter provides state estimates that are robust to outliers while maintaining a high statistical efficiency at the Gaussian distribution by applying a generalized maximum likelihood-type (GM) estimator. Finally, the filter incorporates the correct error covariance matrix that is derived using the GM-estimator's influence function. This dissertation also addresses robust state estimation for systems that follow a broad class of nonlinear models that possess two or more equilibrium points. Tracking state transitions from one equilibrium point to another rapidly and accurately in such models can be a difficult task, and a computationally simple solution is desirable. To that effect, a new robust extended Kalman filter is developed that exploits observational redundancy and the nonlinear weights of the GM-estimator to track the state transitions rapidly and accurately. Through simulations, the performances of the new filters are analyzed in terms of robustness to multiple outliers and estimation capabilities for the following applications: tracking autonomous systems, enhancing actual speech from cellular phones, and tracking climate transitions. Furthermore, the filters are compared with the state-of-the-art, i.e. the <i>H_â</i>-filter for tracking an autonomous vehicle and the extended Kalman filter for sensing climate transitions. / Ph. D.

Link adaptation is important to guarantee robust and reliable wireless communications with- out wasting valuable radio resources. This technique has become more feasible with the recent appearance of Software Defined Radios (SDRs), which allow easy reconfiguration of their parameters via software. As the environment changes over time, the transmitter needs to be able to effectively estimate its performance under different radio input parameters to be able to find a close to optimal solution. In most wireless communications, an equalizer is implemented at the receiver to estimate the channel impulse response. This estimate can be fed back to the transmitter via a feedback channel, which can in turn help generate a sub-optimal transmission solution for the current situation. In this thesis, a link adaptation method is proposed that uses Orthogonal Frequency-Division Multiplexing (OFDM) in conjunction with blind channel estimation. With the use of OFDM, it can be assumed that the frequency fading at each subcarrier is approximately flat. In addition, under the assumption that the channel is quasi-stationary, the Bit Error Rate (BER) at each subcarrier can be estimated by using the well-known BER formulas for an Additive White Gaussian Noise (AWGN) channel. However, the effect of imperfect channel estimation must also be taken into account. A novel OFDM blind channel estimator is developed. Finally, both simulations and real over-the-air results are presented. / Master of Science

In previous studies, evidence of thermal wave behavior was found in heterogeneous materials. Thus, the overall goal of this study was to experimentally verify those results, and develop a parameter estimation scheme to estimate the thermal properties of various heterogeneous materials. Two types of experiments (Experiments 1 and 2) were conducted to verify the existence or non-existence of thermal wave behavior in heterogeneous materials. In Experiment 1 sand, ion exchanger, and sodium bicarbonate were used as test materials, while processed meat (bologna) was used in Experiment 2. The measured temperature profiles of the samples were compared with the parabolic and hyperbolic heat conduction model results. The values of thermal diffusivity and thermal conductivity were obtained using the Box-Kanemasu parameter estimation method which is based on the comparison between temperature measurements and the solutions of the theoretical model. Overall, no clear experimental evidence was found to justify the use of hyperbolic heat conduction models rather than parabolic for the materials tested. Further comprehensive experimentation using different heating rates is warranted to definitely identify the accurate type of heat conduction process associated with such materials, and to describe the physical mechanisms which produce wave-like heat conduction in heterogeneous materials. / Master of Science

Inlet distortion research has become increasingly important over the past several years as demands for aircraft flight efficiency and performance has increased. To accommodate these demands, research progression has shifted the emphasis onto airframe-engine integration and improved understanding of engine operability in less than ideal conditions. Swirl distortion, which is considered a type of non-uniform inflow inlet distortion, is characterized by the presence of swirling flow in an inlet. The presence of swirling flow entering an engine can affect the compression systems performance and operability, therefore it is an area of current research. A swirl distortion generation device created by Virginia Tech, identified as the StreamVane, has the ability to produce various swirl distortion flow profiles. In its current state, the StreamVane methodology generates a design swirl distortion at the trailing edge of the device. However, in many applications the plane at which the researcher wants a desired distortion is downstream of the StreamVane trailing edge. After the distortion is discharged from the StreamVane it develops as it moves downstream. Therefore, to more accurately replicate a desired swirl distortion at a given downstream plane, distortion development downstream of the StreamVane must be considered. Currently Virginia Tech utilizes a numerical modeling design tool, designated StreamFlow, that generates predictions of how a StreamVane-generated distortion propagates downstream. However, due to the non-linear physics of the flow problem, StreamFlow cannot directly calculate an accurate inverse solution that can predict upstream conditions from a downstream boundary, as needed to design a StreamVane. To solve this problem, in this research, an efficient estimation process has been created, combining the use of the StreamFlow model with a Markov Chain Monte Carlo (MCMC) parameter estimation tool to estimate upstream flow profiles that will produce the desired downstream profiles. The process is designated the StreamFlow-MC2 Estimation Process. The process was tested on four fundamental types of swirl distortions. The desired downstream distortion was input into the estimation process to predict an upstream profile that would create the desired downstream distortion. Using the estimated design profiles, 6-inch diameter StreamVanes were designed then wind tunnel tested to verify the distortion downstream. Analysis and experimental results show that using this method, the upstream distortion needed to create the desired distortion was estimated with excellent accuracy. Based on those results, the StreamFlow-MC2 Estimation Process was validated. / Master of Science / Inlet distortion research has become increasingly important over the past several years as demands for aircraft flight efficiency and performance has increased. To accommodate these demands, research progression has shifted the emphasis onto airframe-engine integration and improved understanding of engine operability in less than ideal conditions. Swirl distortion, which is considered a type of non-uniform inflow inlet distortion, is characterized by the presence of swirling flow in an inlet. The presence of swirling flow entering an engine can affect the compression system’s performance and operability, therefore it is an area of current research. A swirl distortion generation device created by Virginia Tech, identified as the StreamVane™, has the ability to produce various swirl distortion flow profiles. In its current state, the StreamVane methodology generates a design swirl distortion at the trailing edge of the device. However, in many applications the plane at which the researcher wants a desired distortion is downstream of the StreamVane trailing edge. After the distortion is discharged from the StreamVane it develops as it moves downstream. Therefore, to more accurately replicate a desired swirl distortion at a given downstream plane, distortion development downstream of the StreamVane must be considered. Currently Virginia Tech utilizes a numerical modeling design tool, designated StreamFlow, that generates predictions of how a StreamVane-generated distortion propagates downstream. However, due to the non-linear physics of the flow problem, StreamFlow cannot directly calculate an accurate inverse solution that can predict upstream conditions from a downstream boundary, as needed to design a StreamVane. To solve this problem, in this research, an efficient estimation process has been created, combining the use of the StreamFlow model with a Markov Chain Monte Carlo (MCMC) parameter estimation tool to estimate upstream flow profiles that will produce the desired downstream profiles. The process is designated the StreamFlow-MC2 Estimation Process. The process was tested on four fundamental types of swirl distortions. The desired downstream distortion was input into the estimation process to predict an upstream profile that would create the desired downstream distortion. Using the estimated design profiles, 6-inch diameter StreamVanes were designed then wind tunnel tested to verify the distortion downstream. Analysis and experimental results show that using this method, the upstream distortion needed to create the desired distortion was estimated with excellent accuracy. Based on those results, the StreamFlow-MC2 Estimation Process was validated.

ITC/USA 2009 Conference Proceedings / The Forty-Fifth Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2009 / Riviera Hotel & Convention Center, Las Vegas, Nevada / We derive bounds on the performance of data-aided joint estimators for timing offset, carrier phase offset, and carrier frequency offset for use in an APSK packet-based communication link. It is shown that the Cramér-Rao Bound (CRB) is a function of the training sequence, the signal-to-noise ratio (SNR), and the pulse shape. We also compute APSK training sequences of different lengths that minimize the CRB for each of the parameters.