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This thesis contributes to influence analysis in nonlinear regression and in particular the detection of influential observations. The focus is on a regression model with a known mean function, which is nonlinear in its parameters and where the function is chosen according to the knowledge about the process generating the data. The error term in the regression model is assumed to be additive. The main goal of this thesis is to work out diagnostic measures for assessing the influence of observations on various results from a nonlinear regression analysis. The obtained results comprise diagnostic tools for detecting observations that, individually or jointly with some other observations, are influential on the parameter estimates. Moreover, assessing conditional influence, i.e. the influence of an observation conditional on the deletion of another observation, is of interest. This can help to identify influential observations which could be missed due to complex relationships among the observations. Novelties of the proposed diagnostic tools include the possibility to assess influence of observations on a specific parameter estimate and to assess influence of multiple observations. A further emphasis of this thesis is on the observations' influence on the outcome of a hypothesis testing procedure based on Rao's score test. An innovative solution to the problem of visual identification of influential observations regarding the score test statistic obtained in this thesis is the so called added parameter plot. As a complement to the added parameter plot, new diagnostic measures are derived for assessing the influence of single and multiple observations on the score test statistic.

Modelos não lineares como o Logístico e o Gompertz são amplamente usados para descrever vários processos biológicos por meio da curva de crescimento dada pela equação do modelo. O objetivo deste trabalho foi ajustar o modelo Chanter, assim como o Logístico e o Gompertz, utilizando um conjunto de dados do fruto do cacaueiro. O modelo Chanter é um híbrido entre o modelo Logístico e o modelo Gompertz cujos parâmetros podem ser interpretados similarmente. A comparação sobre a qualidade do ajuste entre os modelos foi feita utilizando as seguintes medidas estatísticas: o critério de informação de Akaike (AIC), o critério Peso de Akaike, o critério de informação de Bayes (BIC), o desvio padrão residual (DPR) e as medidas de não linearidade vício de Box e curvatura de Bates e Watts além de um estudo de simulação. Verificou-se que o modelo Chanter dentre os modelos estudados neste trabalho é o mais adequado para o ajuste dos dados do fruto do cacaueiro. / Nonlinear models such as Logistic and Gompertz are widely used to describe several biological processes using a growth curve given by the equation of the model. The objective of this work was to adjust the Chanter model, as well as the Logistic and the Gompertz, using a data set of cocoa fruit. The Chanter model is a hybrid between the Logistic model and the Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaike information criterion (AIC), the Akaike weight criterion, Bayes information criterion (BIC), residual standard deviation (RSD), and measures of non-linearity Box addiction and Bates and Watts curvature as well as a simulation study. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.

Predictive anisotropy is a phenomenon referring to unequal predictability of surface wind components in different directions. This study addresses the question of whether predictive anisotropy resulting from statistical prediction is influenced by physical factors or by types of regression methods (linear vs nonlinear) used to construct the statistical prediction. A systematic study of statistical predictability of surface wind components at 2109 land stations across the globe is carried out. The results show that predictive anisotropy is a common characteristic for both linear and nonlinear statistical prediction, which suggests that the type of regression method is not a major influential factor. Both strong predictive anisotropy and poor predictability are more likely to be associated with wind components characterized by relatively weak and non-Gaussian variability and in areas characterized by surface heterogeneity. An idealized mathematical model is developed separating predictive signal and noise between large-scale (predictable) and local (unpredictable) contributions to the variability of surface wind, such that small signal-to-noise ratio (SNR) corresponds to low and anisotropic predictability associated with non-Gaussian local variability. The comparison of observed and simulated statistical predictability by Regional Climate models (RCM) and reanalysis in the Northern Hemisphere indicates that small-scale processes that cannot be captured well by RCMs contribute to poor predictability and strong predictive anisotropy in observations. A second idealized mathematical model shows that spatial variability in specifically the minimum directional predictability, resulting from local processes, is the major contributor to predictive anisotropy. / Graduate

The first chapter explains the motivation for measuring rod function, in particular the rod’s dynamic recovery from a substantial bleach which results in so-called ‘rate limited’ recovery of sensitivity. The physiological processes that underpin the replenishment of the rod photopigment are described and discussed, and explain the way in which rod function can act as a marker for retinal health. Overall, this chapter explains why rod function is worthy of further investigation.Then follows a description of the experimental methods used in the study of rod function, presented in later chapters. The psychophysical procedures are described and a new method of dark adaptation measurement is presented. The key feature of this technique is a red background.Nonlinear mathematical models are used to describe the reduction in visual thresholds with time following a bleach. Chapter three describes the difficulties associated with numerical methods of nonlinear regression and presents a novel, multi start algorithm that extracts the parameters of interest from a model that adequately describes dark adaptation in the healthy normal subject.Chapter 4 verifies the algorithm presented in chapter 3, which is shown to be reliable and robust. A series of numerical experiments are performed to evaluate some of the characteristics of the algorithm’s performance.In chapter five, a series of experiments are presented to investigate the possible effect of a luminous background on dark adaptation (DA). The first experiment tests whether the rod system can detect a dim red background and the second, whether the rod thresh olds, when measured against light emitted by a red light emitting diode (LED), were linear. The third explores whether the background had any effect on the recovery of rod sensitivity. Finally, conventional contrast sensitivity is used to investigate the recovery from a photo bleach.A novel laboratory based apparatus was used to measure dark adaptation in a group of 36 subjects and the results of these measurements are presented in chapter six. The aim here was to see if the data collected were comparable with the dark adaptation data in the literature. These subjects were asked to make two visits so that an assessment of the test retest reliability of the method could be made. The method is shown to be reliable and capable of characterising the recovery of the visual system after a photo bleach.Although inherently flexible the analogue apparatus was prone to subject driven variability. Greater consistency of measurement was achieved using a digital device developed in partnership with an industry partner, Elektron (UK). This device, described in chapter seven provided fine control of many of the experimental parameters. It was used to measure the dark adaptation of a young healthy group of 21 people.This study uses new methodological approaches, both experimental and statistical, that are robust and reliable to facilitate investigation of rod function, and presents new findings about the early phase of rod sensitivity recovery.

In this thesis work the hydrogenation kinetics of phenanthrene inhibited by the basic nitrogen compound acridine and the non-basic carbazole was investigated. Based on a transient reactor model a steady state plug flow model was developed and kinetic parameters were estimated through nonlinear regression to experimental data. The experimental data was previously collected from hydrotreating of phenanthrene in a bench-scale reactor packed with a commercial NiMo catalyst mixed with SiC. As a first two-step solution, the yields of the hydrogenation products of phenanthrene were predicted as a function of conversion, which subsequently was used to calculate concentration profiles as a function of position in reactor. As a second improved solution, the concentration profiles were calculated directly as a function of residence time, and these results were then used for further analysis. Reaction network 2 in figure 7 was considered sufficient to describe the product distribution of phenanthrene, with a pseudo-first-order rate law for the nitrogen compounds. Both solution methods provided similar results which gave good predictions of the experimental data, with a few exceptions. These cases could be improved by gathering more experimental data or by investigating the effect of some model assumptions. The two-step method thus proved useful in evaluating the phenanthrene reaction network and providing an initial estimate of the parameters, while the onestep method then could give a more precise solution by calculating all parameters simultaneously. As expected, acridine was shown to be more inhibiting than carbazole, both in the produced concentration profiles and estimated parameters. A possible saturation effect was also seen in the inhibition behavior, where adding more nitrogen compounds only had a small additional effect on the phenanthrene conversion. The Mears and Weisz-Prater criteria were found to be inversely proportional to the concentrations of the nitrogen compounds and otherwise only depend on rate constants, with values well below limits for diffusion controlled processes. Sensitivity analyses also supported that the global minimum had been found in the nonlinear regression solution.

A novel fabrication process is presented which allows for three-dimensionally independent features to be etched in silicon using SF6 gas in a deep reactive ion etcher (DRIE) after a single etch step. The mechanism allowing for different feature depths and widths to be produced over a wafer is reactive ion etch lag, where etch rate scales with the exposed feature size in the mask. A modified Langmuir model has been developed relating the geometry of the exposed areas in a specific mask pattern as well as the etch duration to the final depth and width of a channel that is produced after isotropic silicon etching. This fabrication process is tailored for microfluidic network design, but the capabilities of the process can be applied elsewhere. A characterization of an Alcatel DRIE tool is also presented in order to enhance RIE lag by varying etch process parameters, increasing the variety of channel sizes that can be fabricated. High values of flow rate, coil power, and pressure were found to produce this effect. The capability of the modeled process for creating a microchip cooling device for high-heat flux applications was also investigated. Using meander channels, heat flux in excess of 100W/cm2 were cooled using 750µL/s flow rate of water through the chip. This single-mask process reduces risk of damage to the chip and provides the capability to cool high-heat-flux microprocessors for the next 10 years, and for an even longer time once the geometry of the channels is optimized. / Master of Science

In the Canadian Prairies recurring droughts are one of the realities which can have significant economical, environmental, and social impacts. For example, droughts in 1997 and 2001 cost over $100 million on different sectors. Drought frequency analysis is a technique for analyzing how frequently a drought event of a given magnitude may be expected to occur. In this study the state of the science related to frequency analysis of droughts is reviewed and studied. The main contributions of this thesis include development of a model in Matlab which uses the qualities of Fuzzy C-Means (FCMs) clustering and corrects the formed regions to meet the criteria of effective hydrological regions. In FCM each site has a degree of membership in each of the clusters. The algorithm developed is flexible to get number of regions and return period as inputs and show the final corrected clusters as output for most case scenarios. While drought is considered a bivariate phenomena with two statistical variables of duration and severity to be analyzed simultaneously, an important step in this study is increasing the complexity of the initial model in Matlab to correct regions based on L-comoments statistics (as apposed to L-moments). Implementing a reasonably straightforward approach for bivariate drought frequency analysis using bivariate L-comoments and copula is another contribution of this study. Quantile estimation at ungauged sites for return periods of interest is studied by introducing two new classes of neural network and machine learning: Radial Basis Function (RBF) and Support Vector Machine Regression (SVM-R). These two techniques are selected based on their good reviews in literature in function estimation and nonparametric regression. The functionalities of RBF and SVM-R are compared with traditional nonlinear regression (NLR) method. As well, a nonlinear regression with regionalization method in which catchments are first regionalized using FCMs is applied and its results are compared with the other three models. Drought data from 36 natural catchments in the Canadian Prairies are used in this study. This study provides a methodology for bivariate drought frequency analysis that can be practiced in any part of the world.

In the Canadian Prairies recurring droughts are one of the realities which can have significant economical, environmental, and social impacts. For example, droughts in 1997 and 2001 cost over $100 million on different sectors. Drought frequency analysis is a technique for analyzing how frequently a drought event of a given magnitude may be expected to occur. In this study the state of the science related to frequency analysis of droughts is reviewed and studied. The main contributions of this thesis include development of a model in Matlab which uses the qualities of Fuzzy C-Means (FCMs) clustering and corrects the formed regions to meet the criteria of effective hydrological regions. In FCM each site has a degree of membership in each of the clusters. The algorithm developed is flexible to get number of regions and return period as inputs and show the final corrected clusters as output for most case scenarios. While drought is considered a bivariate phenomena with two statistical variables of duration and severity to be analyzed simultaneously, an important step in this study is increasing the complexity of the initial model in Matlab to correct regions based on L-comoments statistics (as apposed to L-moments). Implementing a reasonably straightforward approach for bivariate drought frequency analysis using bivariate L-comoments and copula is another contribution of this study. Quantile estimation at ungauged sites for return periods of interest is studied by introducing two new classes of neural network and machine learning: Radial Basis Function (RBF) and Support Vector Machine Regression (SVM-R). These two techniques are selected based on their good reviews in literature in function estimation and nonparametric regression. The functionalities of RBF and SVM-R are compared with traditional nonlinear regression (NLR) method. As well, a nonlinear regression with regionalization method in which catchments are first regionalized using FCMs is applied and its results are compared with the other three models. Drought data from 36 natural catchments in the Canadian Prairies are used in this study. This study provides a methodology for bivariate drought frequency analysis that can be practiced in any part of the world.

<p>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.</p><p>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. </p><p>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.</p><p>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.</p><p>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. </p><p>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. </p>