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In this thesis appropriate statistical methods to overcome two types of problems that occur during parameter estimation in chemical engineering systems are studied. The first problem is having too many parameters to estimate from limited available data, assuming that the model structure is correct, while the second problem involves estimating unmeasured disturbances, assuming that enough data are available for parameter estimation. In the first part of this thesis, a model is developed to predict rates of undesirable reactions during the finishing stage of nylon 66 production. This model has too many parameters to estimate (56 unknown parameters) and not having enough data to reliably estimating all of the parameters. Statistical techniques are used to determine that 43 of 56 parameters should be estimated. The proposed model matches the data well. In the second part of this thesis, techniques are proposed for estimating parameters in Stochastic Differential Equations (SDEs). SDEs are fundamental dynamic models that take into account process disturbances and model mismatch. Three new approximate maximum likelihood methods are developed for estimating parameters in SDE models. First, an Approximate Expectation Maximization (AEM) algorithm is developed for estimating model parameters and process disturbance intensities when measurement noise variance is known. Then, a Fully-Laplace Approximation Expectation Maximization (FLAEM) algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities and measurement noise variances in nonlinear SDEs. Finally, a Laplace Approximation Maximum Likelihood Estimation (LAMLE) algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear SDEs. The effectiveness of the proposed algorithms is compared with a maximum-likelihood based method. For the CSTR examples studied, the proposed algorithms provide more accurate estimates for the parameters. Additionally, it is shown that the performance of LAMLE is superior to the performance of FLAEM. SDE models and associated parameter estimates obtained using the proposed techniques will help engineers who implement on-line state estimation and process monitoring schemes. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2013-12-23 15:12:35.738

A great interest in 3-D modeling in Geographic Information Technologies (GIS) has emerged in recent years, because many GIS related implementations, ranging from urban area design to environmental analysis require 3-D models. Especially the need for 3-D models is quite urgent in urban areas. However, numerous applications in GIS only represent two-dimensional information. The GIS community has been struggling with solving complex problems dealing with 3-D objects using a 2-D approach. This research focused on finding most accurate method which is used for getting height information that is used in 3D modeling of man made structures in urban areas. The first method is estimating height information from floor numbers of the buildings data from municipal database systems. The second method is deriving heights of buildings from Digital Elevation Model (DEM) that is generated from stereo satellite images. The third method is measuring height values of the buildings from 3D view of stereo IKONOS satellite images by operators. The comparisons between these three methods are done with respect to height data collected from field study, and according to these comparisons, the amount of the error is determined. The error is classified according to floor numbers of buildings, so that, the quantified errors can be applied for similar works in future. Lastly, the third method is utilized by the assistance of 10 people who have different experience level about 3D viewing, in order to see the error amount changes according to different operators. Several results are presented with a discussion of evaluation of the methods applied. It is found that, if there is an updated floor number database, obtaining building height is the most accurate way from this database. The second most accurate method is found to be getting height information by using 3D view of stereo IKONOS images through experienced users.

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Rapid environmental changes linked to human-induced increases in atmospheric greenhouse gas concentrations have been observed on a global scale over recent decades. Given the relative certainty of continued change across many earth systems, the information output from climate models is an essential resource for adaptation planning. But in the face of many known modeling deficiencies, how confident can we be in model projections of future climate? It stands to reason that a realistic simulation of the present climate is at least a necessary (but likely not sufficient) requirement for a model’s ability to realistically simulate the climate of the future. Here, I present the results of three studies that evaluate the 20th century performance of global climate models from phase 5 of the Coupled Model Intercomparison Project (CMIP5). The first study examines precipitation, geopotential height, and wind fields from 21 CMIP5 models to determine how well the North American monsoon system (NAMS) is simulated. Models that best capture large-scale circulation patterns at low levels usually have realistic representations of the NAMS, but even the best models poorly represent monsoon retreat. Difficulty in reproducing monsoon retreat results from an inaccurate representation of gradients in low-level geopotential height across the larger region, which causes an unrealistic flux of low-level moisture from the tropics into the NAMS region that extends well into the post-monsoon season. The second study examines the presence and severity of spurious Gibbs-type numerical oscillations across the CMIP5 suite of climate models. The oscillations can appear as unrealistic spatial waves near discontinuities or sharp gradients in global model fields (e.g., orography) and have been a known problem for decades. Multiple methods of oscillation reduction exist; consequently, the oscillations are presumed small in modern climate models and hence are rarely addressed in recent literature. Here we quantify the oscillations in 13 variables from 48 global climate models along a Pacific ocean transect near the Andes. Results show that 48% of nonspectral models and 95% of spectral models have at least one variable with oscillation amplitude as large as, or greater than, atmospheric interannual variability. The third study is an in-depth assessment model simulations of 20th century monthly minimum and maximum surface air temperature over eight US regions, using mean state, trend, and variability bias metrics. Transparent model performance information is provided in the form of model rankings for each bias type. A wide range in model skill is at the regional scale, but no strong relationships are seen between any of the three bias types or between 20th century bias and 21st century projected change. Using our model rankings, two smaller ensembles of models with better performance over the southwestern U.S. are selected, but they result in negligible differences from the all-model ensemble in the average 21st century projected temperature change and model spread. In other words, models of varied quality (and complexity) are projecting very similar changes in temperature, implying that the models are simulating warming for different physical reasons. Despite this result, we suggest that models with smaller 20th century biases have a greater likelihood of being more physically realistic and therefore, more confidence can be placed in their 21st century projections as compared to projections from models that have demonstrably poor skill over the observational period. This type of analysis is essential for responsibly informing climate resilience efforts.

This work presents a study on modeling error estimates in linear elastic structures of heterogeneous materials. The employed formulation is based on a theory of a posteriori estimation of modeling errors and uses the Finite Element Method as numerical tool. The evaluated modeling errors consist of global errors based on energy norm and local errors in quantities of interest induced by replacing the fine-scale micromechanical properties of the material by homogenized or effective properties. These effective properties are determined from different micromechanical models and considered in the surrogate physical models of the heterogeneous materials. The quantities of interest may be, for example, averaged stress or strain on chosen regions, such as surfaces of inclusions, and interfacial displacements. Several numerical examples involving structures of heterogeneous materials are analyzed and the results are presented to demonstrate the performance of the formulation in the evaluation of global and local modeling errors. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta um estudo sobre estimativas de erro de modelagem em estruturas elásticas lineares de materiais heterogêneos. A formulação empregada é baseada em uma teoria de avaliação de erro de modelagem à posteriori e utiliza o Método dos Elementos Finitos como ferramenta numérica. Os erros de modelagem avaliados consistem em erros globais, baseados em norma energia, e erros locais, em quantidades de interesse, induzidos pela substituição das propriedades micromecânicas do material em escala refinada por propriedades efetivas homogeneizadas. Estas propriedades efetivas são determinadas a partir de diferentes modelos da micromecânica e consideradas nos modelos físicos substitutos dos materiais heterogêneos. As quantidades de interesse podem ser, por exemplo, tensões médias ou deformações sobre a região escolhida, tais como superfície de inclusões e deslocamentos nas interfaces. Diversos exemplos numéricos envolvendo estruturas de materiais heterogêneos são analisados e os resultados são apresentados para demonstrar o desempenho da formulação na avaliação de erros de modelagem global e local.

Oceanic microwave remote sensing provides the data necessary for the estimation of significant geophysical parameters such as the near-surface vector wind. To obtain accurate estimates, a precise understanding of the measurements is critical. This work clarifies and quantifies specific uncertainties in the scattered power measured by an active radar instrument. While there are many sources of uncertainty in remote sensing measurements, this work concentrates on three significant, yet largely unstudied effects. With a theoretical derivation of the backscatter from an ocean-like surface, results from this dissertation demonstrate that the backscatter decays with surface roughness with two distinct modes of behavior, affected by the size of the footprint. A technique is developed and scatterometer data analyzed to quantify the variability of spaceborne backscatter measurements for given wind conditions; the impact on wind retrieval is described in terms of bias and the Cramer-Rao lower bound. The probability density function of modified periodogram averages (a spectral estimation technique) is derived in generality and for the specific case of power estimates made by the NASA scatterometer. The impact on wind retrieval is quantified.