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In this dissertation we first consider a parallel linear model with correlated dual responses on a symmetric compact design region and construct locally optimal designs for estimating the location-shift parameter. These locally optimal designs are variant under linear transformation of the design space and depend on the correlation between the dual responses in an interesting and sensitive way. Subsequently, minimax and maximin efficient designs for estimating the location-shift parameter are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations. Thirdly, we consider a linear regression model with a one-dimensional control variable x and an m-dimensional response variable y=(y_1,...,y_m). The components of y are correlated with a known covariance matrix. The calibration problem discussed here is based on the assumed regression model. It is of interest to obtain a suitable estimation of the corresponding x for a given target T=(T_1,...,T_m) on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and the optimal value of calibration point x, say x_0, is considered to be the one which minimizes the weighted sum of squares of such deviations within the range of x. The objective of this study is to find a locally optimal design for estimating x_0, which minimizes the mean square error of the difference between x_0 and its estimator. It shows the optimality criterion is approximately equivalent to a c-criterion under certain conditions and explicit solutions with dual responses under linear and quadratic polynomial regressions are obtained.

The success of screening experiments hinges on the effect sparsity assumption, which states that only a few of the factorial effects of interest actually have an impact on the system being investigated. The development of a screening methodology to harness this assumption requires careful consideration of the strengths and weaknesses of a proposed experimental design in addition to the ability of an analysis procedure to properly detect the major influences on the response. However, for the most part, screening designs and their complementing analysis procedures have been proposed separately in the literature without clear consideration of their ability to perform as a single screening methodology. As a contribution to this growing area of research, this dissertation investigates the pairing of non-replicated and partially–replicated two-level screening designs with model selection procedures that allow for the incorporation of a model-independent error estimate. Using simulation, we focus attention on the ability to screen out active effects from a first order with two-factor interactions model and the possible benefits of using partial replication as part of an overall screening methodology. We begin with a focus on single-criterion optimum designs and propose a new criterion to create partially replicated screening designs. We then extend the newly proposed criterion into a multi-criterion framework where estimation of the assumed model in addition to protection against model misspecification are considered. This is an important extension of the work since initial knowledge of the system under investigation is considered to be poor in the cases presented. A methodology to reduce a set of competing design choices is also investigated using visual inspection of plots meant to represent uncertainty in design criterion preferences. Because screening methods typically involve sequential experimentation, we present a final investigation into the screening process by presenting simulation results which incorporate a single follow-up phase of experimentation. In this concluding work we extend the newly proposed criterion to create optimal partially replicated follow-up designs. Methodologies are compared which use different methods of incorporating knowledge gathered from the initial screening phase into the follow-up phase of experimentation.

"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

In environmental studies, measurements of interest are often taken on multiple variables. The results of spatial data analyses can be substantially affected by the spatial configuration of the sites where measurements are taken. Hence, optimal designs which result in data guaranteeing efficient statistical inferences need to be studied. We study optimal designs on two large classes of spatial regions with respect to three design criteria, which were prediction, covariance parameter estimation, and empirical prediction. The first class of regions includes those in the plane, where Euclidean distance is used. The performance of the optimal designs is compared to that of randomly chosen designs. Optimal designs for a small example and a relatively large example are obtained. For the small example, complete enumeration of all possible designs is computationally feasible. For the large example, the computational difficulty in searching for the optimal spatial sampling design is overcome by a simulated annealing algorithm. The second class of spatial regions includes streams and rivers, where the distance is defined as distance along the stream network. A moving average construction is used to establish valid covariance and cross-covariance models using stream distance. Optimal designs for small and large examples are obtained. An application of our methodology to a real stream network is included. We discuss the impact of asymmetry in the cross covariance function on the spatial multivariate design. The relationship between multivariate optimal design and univariate optimal design if the multivariate design is restricted to be completely collocated is studied. The efficiency lost if we consider the design that is optimal within the class of collocated designs is discussed.

This research is in three parts with different although related objectives. The first part developed an efficient, modified simulated annealing algorithm to solve the D-optimal (determinant maximization) design problem for 2-way polynomial regression with correlated observations. Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this research, we present an improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with the best design selected from the class of designs that are known to be D-optimal in the uncorrelated case: annealing results had generally higher D-efficiency than the best comparison design, especially when the correlation parameter was well away from 0. The second research objective, using Balanced Incomplete Block Designs (BIBDs), wasto construct weakly universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also constructed approximately weakly universal optimal block designs for the block-structured correlation. Lastly, we developed an improved Particle Swarm Optimization(PSO) algorithm with time varying parameters, and solved D-optimal design for linear regression with it. Then based on that improved algorithm, we combined the non-linear regression problem and decision making, and developed a nested PSO algorithm that finds (nearly) optimal experimental designs with each of the pessimistic criterion, index of optimism criterion, and regret criterion for the Michaelis-Menten model and logistic regression model.

This research is in three parts with different although related objectives. The first part developed an efficient, modified simulated annealing algorithm to solve the D-optimal (determinant maximization) design problem for 2-way polynomial regression with correlated observations. Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this research, we present an improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with the best design selected from the class of designs that are known to be D-optimal in the uncorrelated case: annealing results had generally higher D-efficiency than the best comparison design, especially when the correlation parameter was well away from 0. The second research objective, using Balanced Incomplete Block Designs (BIBDs), wasto construct weakly universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also constructed approximately weakly universal optimal block designs for the block-structured correlation. Lastly, we developed an improved Particle Swarm Optimization(PSO) algorithm with time varying parameters, and solved D-optimal design for linear regression with it. Then based on that improved algorithm, we combined the non-linear regression problem and decision making, and developed a nested PSO algorithm that finds (nearly) optimal experimental designs with each of the pessimistic criterion, index of optimism criterion, and regret criterion for the Michaelis-Menten model and logistic regression model.

This dissertation presents the concept of a small, low-cost, self-powered smart wireless sensor that can be used for monitoring current, temperature and voltage on a variety of utility assets. Novel energy harvesting approaches are proposed that enable the sensor to operate without batteries and to have an expected life of 20-30 years. The sensor measures current flowing in an asset using an open ferromagnetic core, unlike a CT which uses a closed core, which makes the proposed sensor small in size, and low-cost. Further, it allows the sensor to operate in conjunction with different assets having different geometries, such as bus-bars, cables, disconnect switches, overhead conductors, transformers, and shunt capacitors, and function even when kept in the vicinity of an asset. Two novel current sensing algorithms have been developed that help the sensor to autonomously calibrate and make the sensor immune from far-fields and cross-talk. The current sensing algorithms have been implemented and tested in the lab at up to 1000 A. This research also presents a novel self-calibrating low-cost voltage sensing technique. The major purpose of voltage sensing is detection of sags, swells and loss-ofpower on the asset; therefore, the constraint on error in measurement is relaxed. The technique has been tested through several simulation studies. A voltage sensor prototype has been developed and tested on a high voltage bus at up to 35 kV. Finally, a study of sensor operation under faults, such as lightning strikes, and large short circuit currents has been presented. These studies are conducted using simulations and actual experiments. Based on the results of the experiments, a robust protection circuit for the sensor is proposed. Issues related to corona and external electrical noise on the communication network are also discussed and experimentally tested. Further, optimal design of the energy harvester and a novel design of package for the sensor that prevents the circuitry from external electrical noise without attenuation of power signals for the energy harvester are also proposed.