FIRST PRINCIPLES MODELLING OF POINT DEFECT DISORDER AND DIFFUSION IN ThO2

  This dissertation investigates the thermodynamics and transport of vacancies and interstitials of oxygen (O) and thorium (Th) in thorium dioxide (ThO2) with varying charge states from neutral to maximum, with respect to temperature and oxygen pressure. The study also explores the impact of varying fractions of uranium (U) as a cation (y) on the defect disorder in mixed oxide fuels (Th1-yUyO2). Understanding the properties of point defects in these oxides lays a strong foundation, as defects influence the properties of bulk materials, such as thermal transport. To accomplish the stated objectives of this dissertation, the research is structured into three sections that employ first principles density functional theory (DFT) and phonon calculations. The first section focuses on the structure, internal energy of formation, and vibrational entropy of point defects in ThO2. The results demonstrate that defect energetics increase with an increase in defect charge for O interstitials and Th vacancies, while the opposite is true for O vacancies and Th interstitials. The lowest internal energy of formation shifts from O vacancies of charge 2+ to O interstitials and Th vacancies at various temperature ranges of 0 to 600 K, 600 to 1300 K, and 1300 to 2000 K. The second section develops a model to calculate the defect disorder and off-stoichiometry in ThO2±x and Th1-yUyO2±x. The model shows that ThO2 exists mainly as a hypo-stoichiometric oxide between 1200 K to 2900 K for oxygen pressures ranging from 10-30 to 10 atm, with O defects dominating this off-stoichiometric regime. The addition of U increases the thermodynamic window over which Th1-yUyO2 is hyper-stoichiometric, with O vacancies dominating in the hypo-stoichiometric regime, and cation vacancies and O interstitials dominating at low and high temperatures, respectively. Specifically, at low U content and low temperatures, U vacancies dominate hyper-stoichiometry, while at high U content and low temperatures, Th vacancies are dominant. This research facilitates the comprehension of the intricate changes in structural and defect equilibria that take place during nuclear fuel irradiation, where the fuel is not in a stoichiometric condition. The third section of the dissertation investigates migration barriers and diffusivities of defects and of O and Th in ThO2. Results indicate that the migration energy of a point defect is dependent on its charge state. The average diffusivity of O vacancies exceeds that of O interstitials, while the similar is true for Th vacancies and Th interstitials above 1650 K. The self-diffusion coefficient of O and Th increases with temperature and is influenced by oxygen pressure, showing a close agreement with experimental and molecular-dynamics-based computational data. At 1500 K, the self-diffusivity of O and Th in ThO2 is 7.47 x 10-16 m2s-1 and 4.48 x 10-23 m2s-1 , respectively, while at 2500 K, the values increase to 1.06 x 10-12 m2s-1  and 2.28 x 10-17 m2s-1 , respectively. The chemical diffusion coefficients of defects decrease initially and then plateau as the hypo-stoichiometry in the oxide increases. These findings serve as a fundamental framework for understanding the diffusion-controlled processes of defects, which affect the radiation tolerance and microstructural evolution of ThO2 as a nuclear fuel.   </ol

Approximation of centroid end-points and switch points for replacing type reduction algorithms

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik-Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process

Switch point finding using polynomial regression for fuzzy type reduction algorithms

Karnik-Mendel (KM) algorithm is the most widely used type reduction (TR) method in literature for the design of interval type-2 fuzzy logic systems (IT2FLS). Its iterative nature for finding left and right switch points is its Achilles heel. Despite a decade of research, none of the alternative TR methods offer uncertainty measures equivalent to KM algorithm. This paper takes a data-driven approach to tackle the computational burden of this algorithm while keeping its key features. We propose a regression method to approximate left and right switch points found by KM algorithm. Approximator only uses the firing intervals, rnles centroids, and FLS strnctural features as inputs. Once training is done, it can precisely approximate the left and right switch points through basic vector multiplications. Comprehensive simulation results demonstrate that the approximation accuracy for a wide variety of FLSs is 100%. Flexibility, ease of implementation, and speed are other features of the proposed method

Linear approximation of Karnik-Mendel type reduction algorithm

Karnik-Mendel (KM) algorithm is the most used and researched type reduction (TR) algorithm in literature. This algorithm is iterative in nature and despite consistent long term effort, no general closed form formula has been found to replace this computationally expensive algorithm. In this research work, we demonstrate that the outcome of KM algorithm can be approximated by simple linear regression techniques. Since most of the applications will have a fixed range of inputs with small scale variations, it is possible to handle those complexities in design phase and build a fuzzy logic system (FLS) with low run time computational burden. This objective can be well served by the application of regression techniques. This work presents an overview of feasibility of regression techniques for design of data-driven type reducers while keeping the uncertainty bound in FLS intact. Simulation results demonstrates the approximation error is less than 2%. Thus our work preserve the essence of Karnik-Mendel algorithm and serves the requirement of lowcomputational complexities

Forecasting bike sharing demand using fuzzy inference mechanism

Forecasting bike sharing demand is of paramount importance for management of fleet in city level. Rapidly changing demand in this service is due to a number of factors including workday, weekend, holiday and weather condition. These nonlinear dependencies make the prediction a difficult task. This work shows that type-1 and type-2 fuzzy inference-based prediction mechanisms can capture this highly variable trend with good accuracy. Wang-Mendel rule generation method is utilized to generate rule base and then only current information like date related information and weather condition is used to forecast bike share demand at any given point in future. Simulation results reveal that fuzzy inference predictors can potentially outperform traditional feed forward neural network in terms of prediction accuracy

Effect of different initializations on EKM algorithm

As an integral part of interval type-2 fuzzy logic system (IT2FLS), type reduction (TR) plays a vital role in determining the performance of IT2FLS. Out of many type reduction algorithms, only Karnik-Mendel type TR algorithms capture the essence of interval type-2 fuzzy sets in type reduction. Enhanced Karnik-Mendel (EKM) algorithm is the most commonly used TR algorithm. In this work, we propose three new initializations for EKM algorithm. It is shown they are performing better than EKM and one of the proposed initializations significantly outperforms others. The performance gain can be upto 40% as per comprehensive simulation results demonstrated in this paper. Our findings are justified by computational time savings and iteration requirement for switch point search