Doctor of Philosophy / Department of Statistics / James W. Neill / Checking the adequacy of a proposed parametric nonlinear regression model is important in order to obtain useful predictions and reliable parameter inferences. Lack of fit is said to exist when the regression function does not adequately describe the mean of the response vector. This dissertation considers asymptotics, implementation and a comparative performance for the likelihood ratio tests suggested by Neill and Miller (2003). These tests use constructed alternative models determined by decomposing the lack of fit space according to clusterings of the observations. Clusterings are selected by a maximum power strategy and a sequence of statistical experiments is developed in the sense of Le Cam. L2 differentiability of the parametric array of probability measures associated with the sequence of experiments is established in this dissertation, leading to local asymptotic normality. Utilizing contiguity, the limit noncentral chi-square distribution under local parameter alternatives is then derived. For implementation purposes, standard linear model projection algorithms are used to approximate the likelihood ratio tests, after using the convexity of a class of fuzzy clusterings to form a smooth alternative model which is necessarily used to approximate the corresponding maximum optimal statistical experiment. It is demonstrated empirically that good power can result by allowing cluster selection to vary according to different points along the expectation surface of the proposed nonlinear regression model. However, in some cases, a single maximum clustering suffices, leading to the development of a Bonferroni adjusted multiple testing procedure. In addition, the maximin clustering based likelihood ratio tests were observed to possess markedly better simulated power than the generalized likelihood ratio test with semiparametric alternative model presented by Ciprian and Ruppert (2004).

Evaluating data in capillary zone electrophoresis usually involves many steps that require using several different programmes. Apart from evaluating the electrophoreogram itself, it is usual to process the obtained data in some other way. For example, a suitable model is fit to the data in order to obtain physical and chemical parameters of the separation (e.g. stability constant in case of complexation). It is also important to know the accuracy of the evaluation (the calculation error). In this work, new parts of the Eval programme, originally developed for electrophoreogram evaluation, were implemented. The programme now automatically estimates the Haarhoff-van der Linde function (solution of continuity equation in capillary) parameters for analyte peak. Complexing agents are often used to improve the separation in the capillary zone electrophoresis. Complexation in the capillary can be described by its physical and chemical parameters. A new part was added to the Eval programme that allows the user to fit a rectangular hyperbole function to the obtained data. Thus, the regression parameters of this dependence can be gained. The programme can also draw profile diagrams for these parameters, from which the confidence intervals can be read. An option that allows two dependencies to be fitted at...

The aim of this thesis is a comprehensive description of the properties of a nonlinear least squares estimator for a nonlinear regression model with normally distributed errors and thorough development of various methods for constructing confidence regions and confidence intervals for the parameters of the nonlinear model. Due to the fact that, unlike the case of linear models, there is no easy way to construct an exact confidence region for the parameters, most of these methods are only approximate. A short simulation study comparing observed coverage of various confidence regions and confidence intervals for models with different curvatures and sample sizes is also included. In case of negligible intrinsic curvature the use of likelihood-ratio confidence regions seems the most appropriate.

[pt] Muitos problemas da área de aprendizagem automática tem por objetivo modelar a complexa relação existente num sisitema , entre variáveis de entrada X e de saída Y na ausência de um modelo teórico. A regressão por mínimos quadrados parciais PLS ( Partial Least Squares) constitui um método linear para resolução deste tipo de problema , voltado para o caso de um grande número de variáveis de entrada quando comparado com número de amostras. Nesta tese , apresentamos uma variante do algoritmo clássico PLS para o tratamento de grandes conjuntos de dados , mantendo um bom poder preditivo. Dentre os principais resultados destacamos um versão paralela PPLS (Parallel PLS ) exata para o caso de apenas um variável de saída e um versão rápida e aproximada DPLS (DIRECT PLS) para o caso de mais de uma variável de saída. Por outro lado ,apresentamos também variantes para o aumento da qualidade de predição graças à formulação não linear. São elas o LPLS ( Lifted PLS ), algoritmo para o caso de apenas uma variável de saída, baseado na teoria de funções de núcleo ( kernel functions ), uma formulação kernel para o DPLS e um algoritmo multi-kernel MKPLS capaz de uma modelagemmais compacta e maior poder preditivo, graças ao uso de vários núcleos na geração do modelo. / [en] The purpose of many problems in the machine learning field isto model the complex relationship in a system between the input X and output Y variables when no theoretical model is available. The Partial Least Squares (PLS)is one linear method for this kind of problem, for the case of many input variables when compared to the number of samples. In this thesis we present versions of the classical PLS algorithm designed for large data sets while keeping a good predictive power. Among the main results we highlight PPLS (Parallel PLS), a parallel version for the case of only one output variable, and DPLS ( Direct PLS), a fast and approximate version, for the case fo more than one output variable. On the other hand, we also present some variants of the regression algorithm that can enhance the predictive quality based on a non -linear formulation. We indroduce LPLS (Lifted PLS), for the case of only one dependent variable based on the theory of kernel functions, KDPLS, a non-linear formulation for DPLS, and MKPLS, a multi-kernel algorithm that can result in a more compact model and a better prediction quality, thankas to the use of several kernels for the model bulding.

Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-12-21T10:53:57Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Giovanne Steudel.pdf: 9400807 bytes, checksum: 8a6ed5c0cfacf8380363dfd4584186c1 (MD5) / Made available in DSpace on 2018-12-21T10:53:57Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Giovanne Steudel.pdf: 9400807 bytes, checksum: 8a6ed5c0cfacf8380363dfd4584186c1 (MD5) Previous issue date: 2018-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O objetivo deste trabalho é avaliar os efeitos na cinética de transformação e nas propriedades mecânicas dos aços inoxidáveis ferrítico AISI 430 (16-18% Cr) e superdúplex SAF 2507 (24-26% Cr), quando submetidos a tratamentos térmicos de envelhecimento em 475°C, assim fragilizados pela formação da fase alfa linha. Este fenômeno é conhecido por “fragilização de 475°C” e ocorre na ferrita de aços inoxidáveis ferríticos e dúplex, e nos aços martensíticos envelhecidos entre 300°C e 550°C. O acompanhamento e análise da cinética de formação de α’ nos dois aços inoxidáveis, o ferrítico AISI 430 e superdúplex SAF 2507, foram feitas com base em ajustes matemáticos por regressão não-linear via sete modelos sigmoidais de aplicação geral, os quais serão comparados ao modelo JMAK de transformação de fases difusivas elaborada por Johnson, Mehl, Avrami e Kolmogorov. Amostras do aço ferrítico foram submetidas a tratamentos térmicos de solubilização em forno tubular em 1050 °C e 30 minutos, e em 1150°C durante 30 minutos para o aço dúplex. Tratamentos de envelhecimento posteriores em 475°C por diversos períodos foram realizados. Verificou-se a evolução da “fragilização de 475°C” e, indiretamente, a formação de α’, por ensaios de dureza Vickers, de tração e de impacto instrumentado Charpy. Análises microestruturais e fractográficas foram feitas em microscopias óptica e eletrônica de varredura (MEV-FEG); análises cristalográficas por difração de elétrons retroespalhados (EBSD); e as análises químicas por espectroscopia por dispersão de energia (EDS). O aço superdúplex, com aproximadamente 25,2% Cr, apresentou cinética de fragilização mais rápida do que o ferrítico, com cerca de 16,6% Cr. O modelo sigmoidal que mais se adequou aos dados de dureza de ambos os aços foi o de Boltzmann; o qual também apresentou maior versatilidade de informações e melhor ajuste e capacidade preditiva do que o modelo JMAK. As tendências para tempos de envelhecimento crescentes do aço AISI 430 foram o aumento dos limites de escoamento e de resistência à tração, com dados de tensão na ruptura oscilando em função do tempo de envelhecimento, porém a literatura aponta aumento também da tensão de ruptura. A mudança de comportamento de dúctil para frágil (clivagem) do aço AISI 430, em função do prosseguimento da “fragilização de 475°C”, foi mais acentuada nos corpos de prova de impacto, em relação aos de tração. / The goal of this work is to evaluate the effects in the transformation kinetics and in the mechanical properties of the AISI 430 (16-18% Cr) ferritic and the SAF 2507 (24-26% Cr) superduplex stainless steels, when they undergo aging heat treatments at 475°C, thus embrittled by the formation of the alpha prime phase. This phenomenon is known as “475°C embrittlement” and it occurs in the ferrite of ferritic and duplex stainless steels, and in martensitic stainless steels aged between 300°C and 550°C. The monitoring and analysis of the kinetics of α’ formation in the AISI 430 and SAF 2507 steels was done based on mathematical fitting by means of nonlinear regression of seven sigmoidal models of general application, whose were compared to the JMAK model of diffusive phase transformations elaborated by Johnson, Mehl, Avrami and Kolmogorov. Ferritic steel samples were submitted to solubilization heat tratments in a tubular furnace at 1050°C for 30 minutes, and at 1150°C during 30 minutes for the duplex steel. Posterior aging treatments will hold at 475°C by various periods. The evolution of the “475°C embrittlement” and, indirectly, the formation of α’, were verified by the way of Vickers hardness, tensile and Charpy instrumented impact tests. Microstructural and fractographic analyses were done by optical and scanning electron microscopies (FEG-SEM); crystallographic analyses by electron backscattered diffraction (EBSD); and chemical analyses by energy dispersive spectroscopy (EDS). The superduplex steel, containing approximately 25,2% Cr, showed a faster embrittlement kinetics than the ferritic steel, with about 16,6% Cr. The sigmoidal model that better fitted to the hardness data of both steels was the Boltzmann one; which also showed greater versatility of information and a better fit and predictive ability than the JMAK model. The trends for rising aging times of the AISI 430 steel were the increase in the yield and ultimate tensile stresses, having oscillation in the breaking stress in function of the aging time, yet the literature claims that there is also a increase in the breaking stress. The change in the mechanical behavior from ductile to brittle (cleavage) of the AISI 430 steel, in function of the following of the “475°C embrittlement”, was more severe in the impact test specimens, compared to the tensile specimens.

Orientador: Miriam Harumi Tsunemi / Resumo: Em inúmeras situações práticas a relação entre uma variável resposta e uma ou mais covariáveis é curvada. Dentre as diversas formas de representar esta curvatura, Royston e Altman (1994) propuseram uma extensa famı́lia de funções denominada de Polinômios Fracionários (Fractional Polynomials - FP ). Bové e Held (2011) im- plementaram o paradigma bayesiano para FP sob a suposição de normalidade dos erros. Sua metodologia é fundamentada em uma distribuição a priori hiper − g (Liang et al., 2008), que, além de muitas propriedades assintóticas interessantes, garante uma predição bayesiana de modelos consistente. Nesta tese, compara-se as abordagens clássica e Bayesiana para PF a partir de dados reais disponı́veis na litera- tura, bem como por simulações. Além disso, propõem-se uma abordagem Bayesiana para modelos FPs em que a potência, diferentemente dos métodos usuais, pode as- sumir qualquer valor num determinado intervalo real e é estimada via métodos de simulação HMC (Monte Carlo Hamiltoniano) e MCMC (Métodos de Monte Carlo via Cadeias de Markov). Neste modelo, para o caso de um FP de segunda ordem, ao contrário dos modelos atualmente disponı́veis, apenas uma potência é estimada. Avalia-se este modelo a partir de dados simulados e em dados reais, sendo um deles com transformação de Box-Cox. / Abstract: In many practical situations the relationship between the response variable and one or more covariates is curved. Among the various ways of representing this curvature, Royston and Altman (1994) proposed an extended family of functions called Fractional Polynomials (FP). Bov´e and Held (2011) implemented the Bayesian paradigm for FP on the assumption of error normality. Their methodology is based on a hyperg prior distribution, which, in addition to many interesting asymptotic properties, guarantees a consistent Bayesian model average (BMA). In addition, a Bayesian approach is proposed for FPs models in which power, unlike the usual methods, can obtain any numerical real interval value and is estimated via HMC (Monte Carlo Hamiltonian) and MCMC (Markov chain Monte Carlo). In this model, in the case of a second-order FP, unlike the currently available models, only one power is estimated. This model is evaluated from simulated data and real data, one of them with Box-Cox transformation. / Doutor

Os controladores eletrônicos de pulverização visam minimizar a variação das taxas de insumos aplicadas no campo. Eles fazem parte de um sistema de controle, e permitem a compensação da variação de velocidade de deslocamento do pulverizador durante a operação. Há vários tipos de controladores eletrônicos de pulverização disponíveis no mercado e uma das formas de selecionar qual o mais eficiente nas mesmas condições, ou seja, em um mesmo sistema de controle, é quantificar o tempo de resposta do sistema para cada controlador específico. O objetivo desse trabalho foi estimar os tempos de resposta para mudanças de velocidade de um sistema eletrônico de pulverização via modelos de regressão não lineares, estes, resultantes da soma de regressões lineares ponderadas por funções distribuição acumulada. Os dados foram obtidos no Laboratório de Tecnologia de Aplicação, localizado no Departamento de Engenharia de Biossistemas da Escola Superior de Agricultura \"Luiz de Queiroz\", Universidade de São Paulo, no município de Piracicaba, São Paulo, Brasil. Os modelos utilizados foram o logístico e de Gompertz, que resultam de uma soma ponderada de duas regressões lineares constantes com peso dado pela função distribuição acumulada logística e Gumbell, respectivamente. Reparametrizações foram propostas para inclusão do tempo de resposta do sistema de controle nos modelos, com o objetivo de melhorar a interpretação e inferência estatística dos mesmos. Foi proposto também um modelo de regressão não linear difásico que resulta da soma ponderada de regressões lineares constantes com peso dado pela função distribuição acumulada Cauchy seno hiperbólico exponencial. Um estudo de simulação foi feito, utilizando a metodologia de Monte Carlo, para avaliar as estimativas de máxima verossimilhança dos parâmetros do modelo. / The electronic controllers spray aimed at minimizing the variation of inputs rates applied in the field. They are part of a control system, and allow for compensation for variation spray travel speed during operation. There are several types of electronic spray controllers on the market and one way to select which more efficient under the same conditions, ie in the same system of control, is to quantify the system response time for each specific driver. The objective of this study was to estimate the response times for changes in speed of an electronic spraying system via nonlinear regression models, these resulting from the sum of weighted linear regressions for cumulative distribution functions. Data were obtained on the Application Technology Laboratory, located in the Department of Biosystems Engineering from College of Agriculture \"Luiz de Queiroz\", University of Sao Paulo, in Piracicaba, Sao Paulo, Brazil. The models used were the logistic and Gompertz, resulting from a weighted sum of two constant linear regressions with weight given by the cumulative distribution function logistics and Gumbell respectively. Reparametrization been proposed for inclusion in the control system response time models, in order to improve the statistical interpretation and inference of the same. It has also been proposed a non-linear regression model two-phase which is the weighted sum of constant linear regressions weight given by a cumulative distribution function exponential hyperbolic sine Cauchy in which a simulation study was conducted using the methodology of Monte Carlo to evaluating the maximum likelihood estimates of the model parameters.

This research addresses fleet-sizing for reusable containers that are used for protection, transportation, and storage of parts between a component plant and assembly plant. These reusable containers are often expensive and occupy a large amount of storage space when empty and full. Having a large container fleet comes with higher acquisition, maintenance, and storage costs, but decreases production down time caused by the lack of containers needed for storage. A quantitative model of these trade-offs will permit decision makers to maintain desired production levels at minimum cost. In this dissertation, the relationship between container fleet size and production down time caused by container shortages is researched. Utilizing both theoretical and empirical approaches, two analytical models that include relevant operational parameters and stochastic components are developed. The first is a container fleet sizing model, and the second model estimates production stoppages as a function of container fleet size. The formulas are shown to be accurate and provide decision makers with the tools to better plan and manage specific applications. The formulas also provide general insight into the factors that affect container fleet size and production stoppage due to container shortages. / Graduation date: 2012

The presence of vibration is an important problem in many engineering applications. Various passive techniques have traditionally been used in order to reduce waves and vibrations, and their harmful effects. Passive techniques are, however, difficult to apply in the low frequency region. In addition, the use of passive techniques often involve adding mass to the system, which is undesirable in many applications. As an alternative, active techniques can be used to manipulate system dynamics and to control the propagation of waves and vibrations. This thesis deals with modeling, estimation and active control of systems that have resonant dynamics. The systems are exposed to stochastic disturbances. Some of them excite the system and generate vibrational responses and other corrupt measured signals. Feedback control of a beam with attached piezoelectrical elements is studied. A detailed modeling approach is described and system identification techniques are employed for model order reduction. Disturbance attenuation of a non-measured variable shows to be difficult. This issue is further analyzed and the problems are shown to depend on fundamental design limitations. Feedforward control of traveling waves is also considered. A device with properties analogous to those of an electrical diode is introduced. An `ideal´ feedforward controller based on the mechanical properties of the system is derived. It has, however, poor noise rejection properties and it therefore needs to be modified. A number of feedforward controllers that treat the measurement noise in a statistically sound way are derived. Separation of overlapping traveling waves is another topic under investigation. This operation also is sensitive to measurement noise. The problem is thoroughly analyzed and Kalman filtering techniques are employed to derive wave estimators with high statistical performance. Finally, a nonlinear regression problem with close connections to unbalance estimation of rotating machinery is treated. Different estimation techniques are derived and analyzed with respect to their statistical accuracy. The estimators are evaluated using the example of separator balancing.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies. / February 2009