In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis. / Graduate

abstract: This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017

Etanol é um dos combustíveis renováveis mais importantes e contribui com a redução dos impactos negativos causados pela utilização de combustíveis fósseis por todo o mundo. É obtido principalmente pela fermentação dos açúcares provenientes da cana-de-açúcar e do milho. O produto da fermentação possui aproximadamente 96,5% molar de água, e um dos desafios é a obtenção econômica de um produto com pureza acima dos 99% molar em etanol para a utilização no setor de transporte. O presente trabalho tem por objetivo a otimização do processo de destilação extrativa do etanol utilizando glicerol como agente extrator. Esse solvente é um subproduto no processo de produção do diesel renovável, e estudou-se sua viabilidade como substituto do solvente derivado de fontes naturais não-renováveis, etileno glicol. Vinte e duas diferentes configurações de colunas de destilação simples e complexas foram avaliadas nesta investigação. O recente modelo de coeficientes de atividade F-SAC foi ajustado para a melhor representação de dados de equilíbrio líquido-vapor e de coeficiente de atividade em diluição infinita coletados na literatura. A predição do modelo F-SAC foi superior comparando-se a outros modelos de atividade. A média na diferença absoluta, quando comparado ao modelo NRTL chegou a valores aproximadamente 47% menores. O modelo do processo foi construído em um simulador baseado em equações, onde balanços de massa e de energia são resolvidas simultaneamente, buscando possíveis alterações para a redução do consumo energético e aumento na produtividade. A influência dos principais parâmetros do processo foi avaliada via simulações e descobriu-se que uma configuração e operação ótimas do sistema por destilação extrativa podem gerar significativa redução no consumo energético do processo. A economia em termos energéticos pode atingir valores de até 10% quando comparados com a melhor configuração disponível na literatura. / Ethanol is one of the most important renewable fuels and contributes to reducing the negative impacts caused by the use of fossil fuels worldwide. It is mainly obtained by the fermentation of sugars from sugar cane and corn. The fermentation broth has approximately 96.5% of water molar, and an economic challenge is to obtain a product with purity above 99% of ethanol molar to use in the transportation sector. The present work aims at optimizing the process of extractive distillation of ethanol using glycerol as extracting agent. This solvent is a byproduct in the renewable diesel production and was then studied as an alternative for ethylene glycol, the curently used non-renewable solvent. Twenty-two different configurations of simple and complex column sequences were evaluated in this investigation. The recent F-SAC activity coefficient model was adjusted to the best representation of vapor-liquid equilibrium and infinite dilution activity coefficient data from the literature. The prediction of the F-SAC model was superior when compared with other activity coefficient models. The average absolute difference was up to 47% smaller when compared with the NRTL model. The process model was built on an equation-based simulator, where mass and energy balances are solved simultaneously, looking for possible changes to reduce the energy demands and raise the production. The influence of the main process parameters was evaluated via simulations and we have found that an optimal operation of the system by extractive distillation with glycerol can lead to significant reduction in the energy consumption of the process. The energy savings could reach values up to 10% when compared with the best configuration available in the literature using ethylene glycol as entrainer.

abstract: Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

Etanol é um dos combustíveis renováveis mais importantes e contribui com a redução dos impactos negativos causados pela utilização de combustíveis fósseis por todo o mundo. É obtido principalmente pela fermentação dos açúcares provenientes da cana-de-açúcar e do milho. O produto da fermentação possui aproximadamente 96,5% molar de água, e um dos desafios é a obtenção econômica de um produto com pureza acima dos 99% molar em etanol para a utilização no setor de transporte. O presente trabalho tem por objetivo a otimização do processo de destilação extrativa do etanol utilizando glicerol como agente extrator. Esse solvente é um subproduto no processo de produção do diesel renovável, e estudou-se sua viabilidade como substituto do solvente derivado de fontes naturais não-renováveis, etileno glicol. Vinte e duas diferentes configurações de colunas de destilação simples e complexas foram avaliadas nesta investigação. O recente modelo de coeficientes de atividade F-SAC foi ajustado para a melhor representação de dados de equilíbrio líquido-vapor e de coeficiente de atividade em diluição infinita coletados na literatura. A predição do modelo F-SAC foi superior comparando-se a outros modelos de atividade. A média na diferença absoluta, quando comparado ao modelo NRTL chegou a valores aproximadamente 47% menores. O modelo do processo foi construído em um simulador baseado em equações, onde balanços de massa e de energia são resolvidas simultaneamente, buscando possíveis alterações para a redução do consumo energético e aumento na produtividade. A influência dos principais parâmetros do processo foi avaliada via simulações e descobriu-se que uma configuração e operação ótimas do sistema por destilação extrativa podem gerar significativa redução no consumo energético do processo. A economia em termos energéticos pode atingir valores de até 10% quando comparados com a melhor configuração disponível na literatura. / Ethanol is one of the most important renewable fuels and contributes to reducing the negative impacts caused by the use of fossil fuels worldwide. It is mainly obtained by the fermentation of sugars from sugar cane and corn. The fermentation broth has approximately 96.5% of water molar, and an economic challenge is to obtain a product with purity above 99% of ethanol molar to use in the transportation sector. The present work aims at optimizing the process of extractive distillation of ethanol using glycerol as extracting agent. This solvent is a byproduct in the renewable diesel production and was then studied as an alternative for ethylene glycol, the curently used non-renewable solvent. Twenty-two different configurations of simple and complex column sequences were evaluated in this investigation. The recent F-SAC activity coefficient model was adjusted to the best representation of vapor-liquid equilibrium and infinite dilution activity coefficient data from the literature. The prediction of the F-SAC model was superior when compared with other activity coefficient models. The average absolute difference was up to 47% smaller when compared with the NRTL model. The process model was built on an equation-based simulator, where mass and energy balances are solved simultaneously, looking for possible changes to reduce the energy demands and raise the production. The influence of the main process parameters was evaluated via simulations and we have found that an optimal operation of the system by extractive distillation with glycerol can lead to significant reduction in the energy consumption of the process. The energy savings could reach values up to 10% when compared with the best configuration available in the literature using ethylene glycol as entrainer.

Despite the growing promise of pharmaceutical research, inferior experimentation or interpretation of data can inhibit breakthrough molecules from finding their way out of research institutions and reaching patients. This thesis provides evidence that better characterization of pre-clinical and clinical data can be accomplished using non-linear mixed effect modeling (NLMEM) and more effective experiments can be conducted using optimal design (OD).  To demonstrate applicability of NLMEM and OD in pre-clinical applications, in vitro ligand binding studies were examined. NLMEMs were used to evaluate precision and accuracy of ligand binding parameter estimation from different ligand binding experiments using sequential (NLR) and simultaneous non-linear regression (SNLR). SNLR provided superior resolution of parameter estimation in both precision and accuracy compared to NLR.  OD of these ligand binding experiments for one and two binding site systems including commonly encountered experimental errors was performed.  OD was employed using D- and ED-optimality.  OD demonstrated that reducing the number of samples, measurement times, and separate ligand concentrations provides robust parameter estimation and more efficient and cost effective experimentation. To demonstrate applicability of NLMEM and OD in clinical applications, a phase advanced sleep study formed the basis of this investigation. A mixed-effect Markov-chain model based on transition probabilities as multinomial logistic functions using polysomnography data in phase advanced subjects was developed and compared the sleep architecture between this population and insomniac patients. The NLMEM was sufficiently robust for describing the data characteristics in phase advanced subjects, and in contrast to aggregated clinical endpoints, which provide an overall assessment of sleep behavior over the night, described the dynamic behavior of the sleep process. OD of a dichotomous, non-homogeneous, Markov-chain phase advanced sleep NLMEM was performed using D-optimality by computing the Fisher Information Matrix for each Markov component.  The D-optimal designs improved the precision of parameter estimates leading to more efficient designs by optimizing the doses and the number of subjects in each dose group.  This thesis provides examples how studies in drug development can be optimized using NLMEM and OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development. / <p>My name should be listed as "Charles Steven Ernest II" on cover.</p>

Please read the abstract in the section 00front of this document / Thesis (PhD(Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

The objective in this work is to build a rapid and automated numerical design method that makes optimal design of robots possible. In this work, two classes of optimal robot design problems were specifically addressed: (1) When the objective is to optimize a pre-designed robot, and (2) when the goal is to design an optimal robot from scratch. In the first case, to reach the optimum design some of the critical dimensions or specific measures to optimize (design parameters) are varied within an established range. Then the stress is calculated as a function of the design parameter(s), the design parameter(s) that optimizes a pre-determined performance index provides the optimum design. In the second case, this work focuses on the development of an automated procedure for the optimal design of robotic systems. For this purpose, Pro/Engineer© and MatLab© software packages are integrated to draw the robot parts, optimize them, and then re-draw the optimal system parts.

This thesis solves estimation and control problems in computational neuroscience, mathematically dealing with the first-passage times of diffusion stochastic processes. We first derive estimation algorithms for model parameters from first-passage time observations, and then we derive algorithms for the control of first-passage times. Finally, we solve an optimal design problem which combines elements of the first two: we ask how to elicit first-passage times such as to facilitate model estimation based on said first-passage observations. The main mathematical tools used are the Fokker-Planck partial differential equation for evolution of probability densities, the Hamilton-Jacobi-Bellman equation of optimal control and the adjoint optimization principle from optimal control theory. The focus is on developing computational schemes for the solution of the problems. The schemes are implemented and are tested for a wide range of parameters.

abstract: Bivariate responses that comprise mixtures of binary and continuous variables are common in medical, engineering, and other scientific fields. There exist many works concerning the analysis of such mixed data. However, the research on optimal designs for this type of experiments is still scarce. The joint mixed responses model that is considered here involves a mixture of ordinary linear models for the continuous response and a generalized linear model for the binary response. Using the complete class approach, tighter upper bounds on the number of support points required for finding locally optimal designs are derived for the mixed responses models studied in this work. In the first part of this dissertation, a theoretical result was developed to facilitate the search of locally symmetric optimal designs for mixed responses models with one continuous covariate. Then, the study was extended to mixed responses models that include group effects. Two types of mixed responses models with group effects were investigated. The first type includes models having no common parameters across subject group, and the second type of models allows some common parameters (e.g., a common slope) across groups. In addition to complete class results, an efficient algorithm (PSO-FM) was proposed to search for the A- and D-optimal designs. Finally, the first-order mixed responses model is extended to a type of a quadratic mixed responses model with a quadratic polynomial predictor placed in its linear model. / Dissertation/Thesis / Doctoral Dissertation Statistics 2020