In global energy and industrial market, petroleum refining industry accounts for a major share. Through proper planning and the use of adequate mathematical models for the different processing units, many profit improving opportunities can be realized. The increasing crude oil price has also made refining of crude oil blends to be a common practice. This thesis aims to provide useful insight for planning of the integrated refinery subsystems. The main subsystems referred to are (1) The crude oil unloading subsystem (2) The production and product blending subsystem and (3) The product distribution subsystem. Aspen HYSYS® was first used to develop a rigorous model for crude distillation unit (CDU) and vacuum distillation unit (VDU). The rigorous model was validated with pilot plant data from literature. The information obtained from the rigorous model is further used to develop a model for planning of the CDU and VDU. This was combined with models (obtained from empirical correlations) for fluid catalytic cracker (FCC) and hydrotreater (HDT) units to form a mathematical programming planning model used for refinery production and product blending subsystem planning. Since two different types of crude were considered, the optimum volumetric mixing ratio, the sulphur content at that mixing ratio and the CDU flow rate were determined. The yields fraction obtained from the rigorous model were then used to generate regression model using least square method. The sulphur composition of the crude oil was used as independent variable in the regression model. The generated regression models were then used to replace the regular fixed yield approach in a refinery planning model and the results compared. From the results obtained, the proposed method provided an alternative and convenient means for estimating yields from CDU and VDU than the regular fixed yield approach. The proposed aggregate model for the production and products blending subsystem was integrated with the modified scheduling model for the crude unloading subsystem developed by Lee et al. (1996) and products distribution model developed by Alabi and Castro (2009) for refinery planning. It was found that the regression model could be integrated in a refinery planning model and that the CDU flow rate was maximised as compared to the non- integrated system.

The ability to predict accurately the critical quality characteristics of aircraft engines is essential for modeling the degradation of engine performance over time. The acceptable margins for error grow smaller with each new generation of engines. This paper focuses on turbine gas temperature (TGT). The goal is to improve the first principles predictions through the incorporation of the pure thermodynamics, as well as available information from the engine health monitoring (EHM) data and appropriate maintenance records. The first step in the approach is to develop the proper thermodynamics model to explain and to predict the observed TGTs. The resulting residuals provide the fundamental information on degradation. The current engineering models are ad hoc adaptations of the underlying thermodynamics not properly tuned by actual data. Interestingly, pure thermodynamics model uses only two variables: atmospheric temperature and a critical pressure ratio. The resulting predictions of TGT are at least similar, and sometimes superior to these ad hoc models. The next steps recognize that there are multiple sources of variability, some nested within others. Examples include version to version of the engine, engine to engine within version, route to route across versions and engines, maintenance to maintenance cycles within engine, and flight segment to flight segment within maintenance cycle. The EHM data provide an opportunity to explain the various sources of variability through appropriate regression models. Different EHM variables explain different contributions to the variability in the residuals, which provides fundamental insights as to the causes of the degradation over time. The resulting combination of the pure thermodynamics model with proper modeling based on the EHM data yield significantly better predictions of the observed TGT, allowing analysts to see the impact of the causes of the degradation much more clearly. / Doctor of Philosophy / AEM is major civilian aircraft gas turbine engine manufacturer, serving different airliners and airlines. However, one of its newest models has had performance issues; the engines degraded faster than their in-house model had anticipated, leading to more frequent maintenance and causing significant financial losses to the company. The key objectives of our research project are to produce a model that has higher predictive capabilities than AEM's in-house predictive model (DTGT), and develop a model selection algorithm that allows for direct comparisons among models of vastly different architecture. There are three major components to our research: 1) interdisciplinary studies merging the theory of thermodynamics and regression, 2) the sequential modeling, and 3) the modified Mallows's Cp. We propose a layered sequential approach to the regression modeling, where one regression model is followed by another regression on the residuals of the previous model. We also propose the modified Mallows's Cp, a modification of the Mallows's Cp, as a viable model selection criterion. Our results demonstrated that the sequential approach both outperformed the AEM's in-house model and was found to be more useful than the traditional multiple linear regression. Our results also demonstrated that the modified Mallows's Cp prefer smaller number of parameters than other standard model selection criterion without sacrificing predictive capabilities of its models.

This thesis sumarizes in detail general linear regression model, including testing statistics for coefficients, submodels, predictions and mostly tests of outliers and large leverage points. It describes how to include categorial variables into regression model. This model was applied to describe saturation of photographs of bread, where input variables were, type of flour, type of addition and concntration of flour. After identification of outliers it was possible to create mathematical model with high coefficient of determination, which will be usefull for experts in food industry for preliminar identification of possible composition of bread.