Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of required experimental settings for the hard-to-change factors. In this research, we propose classes of equivalent estimation second-order response surface split-plot designs for which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Designs that possess the equivalence property enjoy the advantages of best linear unbiased estimates and design selection that is robust to model misspecification and independent of the variance components. We present a generalized proof of the equivalence conditions that enables the development of several systematic design construction strategies and provides the ability to verify numerically that a design provides equivalent estimates, resulting in a broad catalog of designs. We explore the construction of balanced and unbalanced split-plot versions of the central composite and Box-Behnken designs. In addition, we illustrate the utility of numerical verification in generating D-optimal and minimal point designs, including split-plot versions of the Notz, Hoke, Box and Draper, and hybrid designs. Finally, we consider the practical implications of analyzing a near-equivalent design when a suitable equivalent design is not available. By simulation, we compare methods of estimation to provide a practitioner with guidance on analysis alternatives when a best linear unbiased estimator is not available. Our goal throughout this research is to develop practical experimentation strategies for restricted randomization that are consistent with the philosophy of traditional response surface methodology. / Ph. D.

Tsunami and storm surge are two of the main destructive and costly natural hazards faced by coastal communities around the world. To enhance coastal resilience and to develop effective risk management strategies, accurate and efficient tsunami and storm surge prediction models are needed. However, existing physics-based numerical models have the disadvantage of being difficult to satisfy both accuracy and efficiency at the same time. In this dissertation, several surrogate models are developed using statistical and machine learning techniques that can rapidly predict a tsunami and storm surge without substantial loss of accuracy, with respect to high-fidelity physics-based models. First, a tsunami run-up response function (TRRF) model is developed that can rapidly predict a tsunami run-up distribution from earthquake fault parameters. This new surrogate modeling approach reduces the number of simulations required to build a surrogate model by separately modeling the leading order contribution and the residual part of the tsunami run-up distribution. Secondly, a TRRF-based inversion (TRRF-INV) model is developed that can infer a tsunami source and its impact from tsunami run-up records. Since this new tsunami inversion model is based on the TRRF model, it can perform a large number of tsunami forward simulations in tsunami inversion modeling, which is impossible with physics-based models. And lastly, a one-dimensional convolutional neural network combined with principal component analysis and k-means clustering (C1PKNet) model is developed that can rapidly predict the peak storm surge from tropical cyclone track time series. Because the C1PKNet model uses the tropical cyclone track time series, it has the advantage of being able to predict more diverse tropical cyclone scenarios than the existing surrogate models that rely on a tropical cyclone condition at one moment (usually at or near landfall). The surrogate models developed in this dissertation have the potential to save lives, mitigate coastal hazard damage, and promote resilient coastal communities. / Doctor of Philosophy / Tsunami and storm surge can cause extensive damage to coastal communities; to reduce this damage, accurate and fast computer models are needed that can predict the water level change caused by these coastal hazards. The problem is that existing physics-based computer models are either accurate but slow or less accurate but fast. In this dissertation, three new computer models are developed using statistical and machine learning techniques that can rapidly predict a tsunami and storm surge without substantial loss of accuracy compared to the accurate physics-based computer models. Three computer models are as follows: (1) A computer model that can rapidly predict the maximum ground elevation wetted by the tsunami along the coastline from earthquake information, (2) A computer model that can reversely predict a tsunami source and its impact from the observations of the maximum ground elevation wetted by the tsunami, (3) A computer model that can rapidly predict peak storm surges across a wide range of coastal areas from the tropical cyclone's track position over time. These new computer models have the potential to improve forecasting capabilities, advance understanding of historical tsunami and storm surge events, and lead to better preparedness plans for possible future tsunamis and storm surges.

In the past few years, the demands for high speed semiconductor integrated circuits have warranted new techniques in their fabrication process which will meet the ever-shrinking dimensions. The gaseous plasma assisted etching is one of these revolutionary processes. However, the plasma and the etch process are very complex in nature. It has been very difficult to understand various species present in the plasma and their role in the etch reaction. In addition, the submicron geometries also require interconnect materials which will satisfy the necessary properties such as thermal stability and low electrical resistance. Titanium (Ti) and titanium nitride (TiN) are widely used as barriers between aluminum (Al) and silicon (Si) to prevent the destructive intermixing of these two materials. The process of patterning of the interconnect containing Ti and TiN along with Al has been a challenge to the semiconductor process engineers. Therefore, complete characterization of the plasma etch process of Ti and TiN films and development of mathematical models to represent the responses such as the etch rate and uniformity is necessary for a good understanding of the etching process. A robust and well controlled metal etch process usually results in good die yield per wafer and hence can translate into higher profits for the semiconductor manufacturer. The objective of this dissertation is to characterize the plasma etch processes of Ti and TiN films in chlorine containing plasmas such as BCl₃ and Cl₂/N₂ and to develop mathematical models for the etch processes using statistical experimental design and analysis technique known as Response Surface Methodology (RSM). In this work, classical experiments are conducted on the plasma etch process of Ti and TiN films by varying the process parameters, such as gas flow, radio frequency (RF) power, reaction pressure, and temperature, one parameter at a time, while maintaining the other parameters constant. The variation in the etch rate with the change in the process parameter of the film is studied and the results were explained in terms of the concepts of plasma. These experiments, while providing very good understanding of the main effects of the parameters, yield little or no information on the higher order effects or interaction between the process parameters. Therefore, modern experimental design and analysis techniques using computerized statistical methods need to be employed for developing mathematical models for these complex plasma etch processes. The second part of this dissertation concentrates on the Design and Analysis of Experiments using Response Surface Methodology (RSM) and development of models for the etch rate and the etch uniformity of the Ti and TiN films in chlorine-containing plasmas such as Cl₂/N₂ and Cl₂/N₂/BCl₃. A complete characterization of the plasma etch process of Ti and TiN films is achieved with the RSM technique and a well fitting and statistically significant models have been developed for the process responses, such as the etch rate and the etch uniformity. These models also provide a means for quantitative comparison of main effects, which are also known as first order effects, second order effects and two factor interactions. The models, thus developed, can be effectively used for an etch process optimization, prediction of the responses without actually conducting the experiments, and the determination of process window. This dissertation work has achieved a finite study of the plasma etch process of Ti and TiN films. There is tremendous potential and scope for further research in this area, limited only by the available resources for wafer processing. A few of the possibilities for further research is discussed in the next few sentences. The optimized process derived from the RSM technique needs to be implemented in the actual production process of the semiconductor ICs and its effects on the wafer topography, etch residue and the resulting die yield have to be studied. More research studies are needed to examine the effect of process parameters such as temperature, the size and shape of the etch chamber, the quality of the film being etched, among other parameters. It is worth emphasizing in this respect that this dissertation marks beginning of research work into the ever-increasing complexities of gas plasma. / Ph. D.

The FVS-Sn model was developed by the USDA Forest Service to project and report forest growth and yield predictions for the Southern United States. It is able to project forest growth and yield for different forest types and management prescriptions, but it is a relatively new, complex, and untested model. These limitations notwithstanding, FVS-Sn once tested and validated could meet the critical need of a comprehensive growth and yield model for the mixed hardwood forests of the southern Appalachian region. In this study, sensitivity analyses were performed on the FVS-Sn model using Latin hypercube sampling. Response surfaces were fitted to determine the magnitudes and directions of relationships between FVS-Sn model parameters and predicted 10-year basal area increment. Model sensitivities were calculated for five different test scenarios for both uncorrelated and correlated FVS-Sn input parameters and sub-models. Predicted 10-year basal area increment was most sensitive to parameters and sub-models related to the stand density index and, to a lesser degree, the large tree diameter growth sub-model. The testing procedures and framework developed in this study will serve as a template for further evaluation of FVS-Sn, including a comprehensive assessment of model uncertainties, followed by a recalibration for southern Appalachian mixed hardwood forests. / Master of Science

Nine independent and four dependent variables are used to build a response surface to calculate strip crown using the difference in the industry standard strip height measurements. The single element response surface in use provides the advantages of continuous derivatives and decouples rolling load from the determination of exit height. The data points to build the response surface are the product of a calibrated finite element model. The rolling dynamics in the finite element model creates a transient that requires nonlinear regression to find the system steady-state values. Weighted-least squares is used to build a response surface using isoparametric interpolation with the non-rectangular domain of the mill stands represented as a single element. The regression statistics, the 1-D projections, comparisons against other response surface models and the comparisons against an existing strip crown model are part the validation of the response surface generated. A four-high mill stand is modeled as a quarter-symmetry 3-D finite element model with an elastic-plastic material model. A comparison of the pressure distribution under the arc of contact with existing research supports the pressure distribution found with experiments conducted by Siebel and Lueg [16] and it also suggests the need for one improvement in the initial velocity for the strip in the finite element model. The strip exit heights show more sensitivity to change than strip exit crown in seven out of the nine independent variables, so a response surface built with the strip exit height is statistically superior to using the derived dependent variable strip exit crown. Sensitivity of strip exit crown and the strip exit heights to changes in work-roll crown are about equal. Backup-roll diameter sensitivity is small enough that oversampling for the mean trend has to be considered or ignore backup-roll altogether. Strip entry velocity is a new independent variable, unless the response surface is built from the derived variable, strip exit crown. A problem found is that the sensitivity of strip entry crown and work-roll crown requires a larger than typical incremental change to get a reliable measure of the change strip exit crown. A narrow choice of high and low strip entry crowns limits the usefulness of the final response surface. A recommendation is to consider the use of the strip cross-section as an exit crown predictor. / Master of Science

In American rail operations, rails fail due to the combined effects of rail wear due to repetitive wheel contact and the growth of surface and sub-surface cracks and flaws. Rail maintenance includes frequent uncoupled wear and ultrasonic inspections that determine the amount of wear that the rail has undergone and the presence of cracks and flaws. A rail is removed from service when its wear reaches a pre-determined wear limit or a flaw is detected in its cross section. In rail research, the life of a rail is typically estimated using fracture mechanic or fatigue methods and an assumed flaw geometry. Multiple models ranging from complex elastic-plastic finite element models to simplified representations of a beam on an elastic foundation have been developed to predict the life of a rail. The majority of rail failure models do not incorporate rail wear into their analysis, and assume an unworn rail geometry. In order to account for rail wear, certain models adopt simplified rail geometries that uncouple rail wear into top-wear and side-wear. This thesis presents a rail failure model that describes the combined effects of rail wear and crack growth through the development of a functional relationship between input variables describing the geometry, loading, and material properties of a given rail and output variables describing the life characteristics of the rail. This relationship takes the form of multiple response surfaces estimating the desired output variables. Finite element models incorporating worn rail profiles and an assumed crack geometry corresponding to a detail fracture are combined to determine the state of stress and strain at the assumed flaw. Strain-life fatigue methods and fracture mechanic concepts are used to develop the output variables necessary to describe the life of the rail using the finite element model results. The goals of this research are to predict the remaining fatigue life and estimate the crack-growth rate of the rail based on the minimum number of geometry, loading, and material property independent variables. The outputs developed to describe the rail's remaining life are intended to be used for the decision making for rail removal. / Master of Science

This dissertation addresses the surging global demand for sustainable energy alternatives and biobased products, driven by population growth and the imperative to shift away from finite fossil fuels amidst climate change. The research centers on the catalytic upgrading of rice straw bio-oil, employing bimetallic magnetic nano-catalysts on rice straw-derived biochar to align with the imperative for environmentally conscious energy solutions. In the initial phase, the study systematically explores upgrading processes using varied alcohols, specifically ethanol, and butanol, under mild conditions to enhance bio-oil quality. The detailed evaluation of catalyst composition reveals a notable reduction in oxygen content, coupled with a significant increase in energy density and calorific value. The upgraded bio-oil not only exhibits heightened stability but also undergoes a substantial shift towards a more desirable hydrocarbon-rich composition. The second part of the research optimizes upgrading process parameters catalyst concentration, reaction holding time, and reaction temperature using Response Surface Methodology based on the Box-Behnken experimental design. This optimization refines the catalytic upgrading process, enhancing its efficiency and reliability. Beyond catalytic efficacy, the study considers the magnetic recovery of catalysts for potential reuse, emphasizing sustainability on a broader scale. Set against the backdrop of global energy challenges, this research significantly contributes to advancing the understanding of bimetallic magnetic nano-catalysts. The dissertation unfolds in two parts, with the first segment focusing on Catalytic Upgrading of Rice Straw Bio-Oil via Esterification in Supercritical Ethanol Over Bimetallic Catalyst (CuO-Fe3O4/AcB), involving the variation of Cu and Fe metals on Rice Straw Biochar without hydrogen gas. The exploration continues with the Upgrading of Rice Straw Bio-Oil in Butanol and hydrogen gas Over a Sustainable Magnetic Bimetallic Nano-Catalyst (ZrO2-Fe3O4/AcB). The integrated analytical approach, utilizing XRD, SEM, FT-IR for synthesized catalysts, alongside GC-MS and the Bomb Calorimeter for bio-oil samples, establishes a nuanced understanding crucial for optimizing catalytic performance in sustainable biofuel production.

Neural networks are being used increasingly often as alternatives to traditional statistical models. As a result, their performance needs to be examined in a statistical framework. Following a brief overview of many types of neural networks, details concerning the implementation of the single hidden layer feedforward neural network (SHLFNN) are presented. The focus of the presentation is on the application of this network in a regression setting. One area where the SHLFNN is being used more frequently is in response surface modeling based on designed experiments. Due to the small sample sizes typically employed by response surface designs, the ability of the SHLFNN to accurately approximate the underlying model is questionable. The results of a simulation which compares the performance of the SHLFNN with that of a second order polynomial model are presented. Finally, methods are explored for combining the SHLFNN model with a linear model. Such a combined model has advantages over each of its components. The combined model will be able to approximate any underlying nonlinear function better than a linear model, and it will allow for easy assessment of the impact of any effects of interest to the researcher, an ability that is lost when only the SHLFNN model is used. / Ph. D.

Crystallisation is gaining a lot of interest in pharmaceutical industry to help designing active ingredients with tailored physicochemical properties. Many factors have been found to affect the crystallisation process, including process parameters and material attributes. Several studies in the literature have discussed the role of these parameters in the crystallisation process. A comprehensive study is still missing in this field where all the significant terms are taken into consideration, including the square effect and the interaction terms between different parameters. In this study, a thorough investigation into the main factors affecting crystallisation of a polymeric system, processed via injection moulding, was presented and a sample of response optimisation was introduced which can be mimicked to suite a specific need. Three grades of pure polyethylene oxide; 20K, 200K and 2M, were first characterised using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), powder X-ray diffraction (PXRD) and shear rheometry. The onset of degradation and the rate varied according to molecular weight of polyethylene oxide (PEO). The peak melting temperature and the difference in enthalpy between melting and crystallisation were both in a direct proportion with PEO molecular weight. PEO200K and PEO2M struggle to recrystallise to the same extent of the original state at the tested cooling rates, while PEO20K can retain up to a similar crystallinity degree when cooled at 1 °C/min. Onset of crystallisation temperature (Tc1) was high for PEO2M and the difference between the 20K and 200K were pronounced at low cooling rate (20K is higher than 200K). The rheometer study showed that PEO2M has a solid-like structure around melting point which explains the difficulty in processing this grade at a low temperature via IM. PEO20K was almost stable within the strain values studied (Newtonian behaviour). For higher grades, PEO showed a shear thinning behaviour. The complex viscosity for PEO2M is characterised by a steeper slope compared to PEO200K, which indicates higher shear thinning sensitivity due to higher entanglement of the longer chains. For binary blends of PEO, the enthalpy of crystallisation studied by DSC was in direct proportion to the lowest molecular weight PEO content (PEOL %) in PEO20K/200K and PEO20K/2M blends. The effect of PEOL% on Tc1 became slightly pronounced for PEO20K-2M blends where Tc1 exhibited slight inverse proportionality to PEOL% and it became more significant for PEO200K-2M blends. It was interesting to find that Tc1 for the blends did not necessarily lie between the values of the homopolymers. In all binary blends, Tc1 was inversely proportional to cooling rate for the set of cooling rates tested. Thermal analysis using hot stage polarised light microscopy yields different behaviours of various PEO grades against the first detection of crystals especially where the lowest grade showed highest detection temperature. Visual observation of PEO binary blends caplets processed at various conditions via injection moulding (IM) showed the low-quality caplets processed at mould temperature above Tc1 of the sample. The factors affecting crystallisation of injection moulded caplets were studied using response surface methodology for two responses; peak melting temperature (Tm) and relative change in crystallinity (∆Xc%) compared to an unprocessed sample. Mould temperature (Tmould) was the most significant factor in all binary blend models. The relationship between Tmould and the two responses was positive non-linear at the Tmould ˂ Tc1. Injection speed was also a significant factor for both responses in PEO20K-200K blends. For Tm, the injection speed had a positive linear relationship while the opposite trend was found for ∆Xc%. The interaction term found in the RSM study for all models was only between the injection speed and the PEOL % which shows the couple effect between these two factors. Molecular effect was considered a significant factor in all ∆Xc% models across the three binary blends. The order of ∆Xc% sensitivity to the change in PEOL% was 3, 5 and 7 % for 20K-200K, 200K-2M and 20K-2M.

Ces derniers temps, des procédés commerciaux basés sur la technologie photocatalytique, sont arrivés sur le marché, afin de satisfaire la demande croissante du traitement de l’air intérieur. L’objectif de ce présent travail est de développer une nouvelle méthodologie pour évaluer l’efficacité de ce nouveau procédé. Pour l’étude de l’application de la photocatalyse au traitement de l’air intérieur, un dispositif expérimental a été mis au point et deux méthodes analytiques ont été développées (ATD-GCMS et GC-PDHID). La performance de la dégradation photocatalytique du 2-propanol et du toluène à faibles concentrations (ppbv) a été étudiée. L’influence des différents paramètres (humidité relative, débit, concentration initiale, etc.) et leurs interactions sur la conversion, la formation des intermédiaires et la minéralisation au CO2 a été établie / Many commercial systems based in the photocatalytic technology have reached the market recently in order to address the growing demand for improve poor indoor air qualities. The present work deals with the development of a new methodology in order to evaluate the efficiency of this process. For the study of photocatalytic oxidation for indoor air applications, an experimental set-up was designed and two analytical tools (ATD-GC-MS and GC-PDHID) were developed. The performance of the photocatalytic treatment of 2-propanol and toluene at indoor air concentrations levels (ppbv) were realised. The influence of several parameters and their interactions effects on the conversion, by-product formation and mineralization to CO2 were established