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.

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>

Nos últimos anos grande número de modelos computacionais tem sido propostos com o intuito de descrever o movimento de solutos no perfil do solo, apesar disso, o que se observa é que existe grande dificuldade em se modelar esses fenômenos, para que o modelo possa predizer o processo de deslocamento e retenção dos solutos na natureza. Para tanto, o objetivo deste trabalho foi utilizar um modelo estatístico para descrever o transporte dos solutos no perfil do solo. Dessa forma, foi realizado um experimento em laboratório e observado os níveis de potássio e nitrato ao longo do perfil dos solos Latossolo Vermelho Amarelo e Nitossolo Vermelho. Para inferir sobre essas variáveis foram consideradas duas abordagens. Para a primeira abordagem foi utilizado um modelo de regressão não linear para cada uma das variáveis, cujos parâmetros do modelo apresentam uma interpretação prática, na área de solos. Para esse modelo foi realizado um esboço sobre a não linearidade do mesmo para verificar as propriedades assintóticas dos estimadores dos parâmetros. Para o método de estimação foi considerado, o método de mínimos quadrados e o método de bootstrap. Além disso, foi realizada uma análise de diagnóstico para verificar a adequação do modelo, bem como identificar pontos discrepantes. Por outro lado, para outra abordagem, foi utilizado um modelo multiresposta para analisar o comportamento das variáveis nitrato e potássio ao longo do perfil dos solos, conjuntamente. Para esse modelo foi utilizado o método da máxima verossimilhança para encontrar as estimativas dos parâmetros do modelo. Em ambas as situações, observou-se a adequação dos modelos para descrever o comportamento dos solutos nos solos, sendo uma alternativa para os pesquisadores que trabalham com estudo de solos. O modelo logístico com quatro parâmetros se destacou por apresentar melhores propriedades, como medidas de não linearidade e boa qualidade de ajuste. / In the last years, several computational models have been proposed to describe the movement of solutes in the soil profile, but what is observed is that there is great difficulty in model these phenomena, so that model can predict the displacement process and retention of solutes in nature. Thus, the aim of this study was to use a statistical model to describe the transport of solutes in the soil profile. Therefore, an experiment was conducted in the laboratory and observed levels of potassium and nitrate along the depth of soil Oxisol (Haplustox) and Hapludox,. To make inferences about these variables were considered two approaches. For the first approach was utilized a non-linear regression model for each variable and the model parameters have a practical interpretation on soil. For this model we performed a sketch on the nonlinearity of the model to check the asymptotic properties of parameter estimators. To estimate the parameters were considered the least squares method and the bootstrap method. In addition, we performed a diagnostic analysis to verify the adequacy of the model and identify outliers. In the second approach considered was using a multi-response model to analyze the behavior of the variables nitrate and potassium throughout the soil profile together. For this model we used the maximum likelihood method to estimate the model parameters. In both cases, we observed the suitability of the models to describe the behavior of solutes in soils, being an alternative for researchers working on the study of soils. The logistic model with four parameters stood out with better properties, such as non-linearity and good fit.

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.

No description available.

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data are unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. Therefore, several Regional Flood Frequency Analysis (RFFA) methods are applied to the Ceyhan Basin. Dalyrmple (1960) Method is applied as a common RFFA method used in Turkey. Multivariate statistical techniques which are Stepwise and Nonlinear Regression Analysis are also applied to flood statistics and basin characteristics for gauging stations. Rainfall, Perimeter, Length of Main River, Circularity, Relative Relief, Basin Relief, Hmax, Hmin, Hmean and H&Delta / are the simple additional basin characteristics. Moreover, before the analysis started, stations are clustered according to their basin characteristics by using the combination of Ward&rsquo / s and k-means clustering techniques. At the end of the study, the results are compared considering the Root Mean Squared Errors, Nash-Sutcliffe Efficiency Index and % difference of results. Using additional basin characteristics and making an analysis with multivariate statistical techniques have positive effect for getting accurate results compared to Dalyrmple (1960) Method in Ceyhan Basin. Clustered region data give more accurate results than non-clustered region data. Comparison between clustered region and non-clustered region Q100/Q2.33 reduced variate values for whole region is 3.53, for cluster-2 it is 3.43 and for cluster-3 it is 3.65. This show that clustering has positive effect in the results. Nonlinear Regression Analysis with three clusters give less errors which are 29.54 RMSE and 0.735 Nash-Sutcliffe Index, when compared to other methods in Ceyhan Basin.