In this work minimally supported D-optimal designs for response surface models with spatially correlated errors are studied. The spatially correlated errors describe the correlation between two measurements depending on their distance d through the covariance function C(d)=exp(-rd). In one dimensional design space, the minimally supported D-optimal designs for polynomial models with spatially correlated errors include two end points and are symmetric to the center of the design region. Exact solutions for simple linear and quadratic regression models are presented. For models with third or higher order, numerical solutions are given. While in two dimensional design space, the minimally supported D-optimal designs are invariant under translation¡Brotation and reflection. Numerical results show that a regular triangle on the experimental region of a circle is a minimally supported D-optimal design for the first-order response surface model.

A mixture experiment is an experiment in which the q-ingredients {x_i,i=1,2,...,q} are nonnegative and ubject to the simplex restriction £Ux_i=1 on the (q-1)-dimensional probability simplex S^{q-1}. It is usually assumed that the observations are uncorrelated, although in many applications the observations are correlated. We study the difference between the ordinary least square estimator and the Gauss Markov estimator under correlated observations. It is shown that for certain models and a special covariance structure for the mixture experiments, the unknown parameter vector for the ordinary least square estimators and the Gauss Markov estimators are the same. Moreover, we also show that the corresponding optimal designs may be obtained from previous D- and A-optimal designs for uncorrelated observations. The models studied here includ Scheff'e models, log contrast models, models containing homogeneous functions, and models containing inverse terms.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-05-10T18:12:21Z No. of bitstreams: 1 IsabelleViegas.pdf: 3633888 bytes, checksum: 9ca9d98ac32b28eabeb6aca7328c6155 (MD5) / Made available in DSpace on 2017-05-10T18:12:21Z (GMT). No. of bitstreams: 1 IsabelleViegas.pdf: 3633888 bytes, checksum: 9ca9d98ac32b28eabeb6aca7328c6155 (MD5) Previous issue date: 2016-02-23 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / Since some pure biodiesels do not reach the minimum oxidative stability of 8 h, specified by RANP 45/2014, the blend of unsaturated biodiesels with others mainly saturated becomes an alternative to work around this problem. The present work presented a study on binary, ternary and quaternary mixtures of biodiesel from soybean, corn, babassu and palm, aiming to improve oxidative stability. The 71 mixtures were designed by simplex-lattice and simplex-centroid designs, and the samples were divided into calibration set (50 samples) and validation set (21 samples) by the sample set partitioning based on joint x-y distances (algorithm SPXY). Six polynomial models were adjusted and statistically compared: linear, quadratic, special cubic, full cubic, special quartic and full quartic models. The quadratic equation was set to be remodeled and it presented correlation coefficients (r) 0.9879 and 0.9569 for calibration and validation steps, respectively, with Root Mean Squared Error (RMSE) of 0.64 h for calibration and 0.71 h for validation. The quadratic equation was used to plot the contour map of the oxidative stability of the mixtures, allowing to study the property behavior and to choose mixtures of biodiesels from babassu, soybean, corn and palm that reach any value of oxidative stability in the calibration range, that was from 5.08 h to 20.88 h. / Uma vez que alguns biodieseis puros não atingem a estabilidade oxidativa mínima de 8 h especificada pela RANP 45/2014, a mistura de biodieseis insaturados com outros majoritariamente saturados se torna uma alternativa para contornar esse problema. O presente trabalho apresentou um estudo de misturas binárias, ternárias e quaternárias de biodieseis de soja, milho, babaçu e dendê, visando melhorias na estabilidade oxidativa. As 71 misturas foram delineadas por planejamento em rede simplex e centroide simplex, e as amostras foram divididas nos conjuntos de calibração (50 amostras) e de validação (21 amostras) pelo particionamento de amostras baseado nas distâncias x-y dos conjuntos (algoritmo SPXY). Seis modelos polinomiais foram ajustados e comparados estatisticamente: linear, quadrático, cúbico especial, cúbico completo, quártico especial e quártico completo. A equação quadrática foi selecionada para ser remodelada e apresentou coeficientes de correlação (r) de 0,9879 e 0,9569 para as etapas de calibração e de validação, respectivamente, com a raiz do erro médio quadrático (RMSE) de 0,64 h para calibração e 0,71 h para validação. A equação quadrática foi utilizada para traçar os mapas de contorno de estabilidade oxidativa das misturas, possibilitando o estudo do comportamento da propriedade e a seleção de misturas dos biodieseis de babaçu, soja, milho e dendê que atinjam qualquer valor de estabilidade oxidativa na faixa de calibração do modelo, que foi de 5,08 h a 20,88 h.

This thesis deals with problem of experimental identification using principles of artificial intelligence and development of nonlinear models. It shows how to estimate parameters of nonlinear models and it compares different types of nonlinear models based on analytical analysis which were developed from measured data in simulation and real system motors with flexible component.

À mesure que les performances intrinsèques des bâtiments s’améliorent, les usages énergétiques non réglementés, que nous associons à une notion d’intensité énergétique des usages, prennent de plus en plus d’importance dans le bilan des consommations des bâtiments. De plus, les bâtiments performants font apparaître des problématiques au niveau de l’exploitation des installations. Ces constats nous permettent d’affirmer qu’il est aujourd’hui important de proposer un cadre pour le suivi et l’optimisation de la sobriété énergétique des usages et l’exploitation performante pour la maîtrise des consommations énergétiques réelles des bâtiments. Cette thèse propose tout d’abord de développer des modèles polynomiaux de prédiction de la consommation énergétique tous usages en fonction des facteurs caractérisant l’intensité d’usage, la qualité d’usage et la qualité d’exploitation. Pour cela, nous utilisons le logiciel EnergyPlus afin de réaliser des simulations énergétiques dynamiques (SED) sur des valeurs de paramètres définis par la méthode des plans d’expérience D-optimaux. Le modèle polynomial créé permet alors d’effectuer, avec un faible temps de calcul, une propagation des incertitudes sur les consommations d’énergie calculées. Pour ce faire, nous utilisons les données mesurées en exploitation dans le cadre de la mesure et de la vérification de la performance énergétique, associées à une incertitude concernant leur valeur. Nous pouvons alors déterminer l’incertitude globale sur les consommations énergétiques et identifier les pistes pour la réduire, permettant ainsi un meilleur suivi et encadrement de la consommation énergétique réelle. / Since building envelope and MEP systems characteristics regularly improve, the weight of non-regulatory energy end-uses increases. These energy end-uses are typically associated with tenants or owners’ activities. In addition, high performance buildings show new issues related to HVAC systems operations. Therefore, it is important to evaluate and improve non-regulatory energy end-uses energy as well as HVAC systems operations efficiencies. We have developed polynomial energy models that can predict energy consumption as a function of building’s activities characteristics and HVAC systems operations factors. We used EnergyPlus software in order to build reliable energy models along with the D-optimum design of experiments method (DOE). Then, we used measurement and verification (M&V) data, associated with probability functions, to determine the associated uncertainty of the calculated energy consumption. Finally, we combine the latter with the polynomial modeling error to calculate the energy consumption global uncertainty, with the goal to identify strategies to reduce it.