Theses and Dissertations

Fall 2024

Kammammettu, Sanjula

years. The optimal transport problem seeks to transport probability mass from one probability distribution to another at the least total cost. This thesis uses this underlying concept in three main ways. Firstly, the optimal transport distance is used as a measure of similarity between probability

ambiguity on multimodal uncertainty that is modeled as a Gaussian mixture. An optimal transport variant for Gaussian mixtures is further used to construct an ambiguity set of distributions around this reference model, and a tractable formulation is presented. The superior performance of this proposed

formulation is contrasted with the established Wasserstein method on an illustrative study, as well as on a portfolio optimization problem. The thesis then uses the proposed formulation to tackle chance-constrained optimization in a distributionally robust setting, wherein the worst-case expected constraint

Fall 2012

Lin, Feng

potentials were effectively uniform. These two effects contributed to a more random distribution of zeta potentials on the bitumen droplet surfaces. Ultimately, it is the randomness of zeta potential, together with its average value (measured, for example, by electrophoresis), that determine the probability

) sliding along the surface of a much larger droplet (effectively a flat surface). Procedures were developed to allow direct quantification of the probabilities of coalescence between the two oil drops. The experimental parameters include: zeta potential of the bitumen drops (through manipulation of

solution pH and calcium ion concentration in the electrolyte), distance of shear contact, and shear speed. These parameters were varied to observe their effects on the probabilities of drop coalescence. Contrary to traditional DLVO theory, it was demonstrated that the coalescence of bitumen droplets was

Spring 2024

Mao, Yiren

locations. A binary relevance 3D CNN-LSTM autoencoder, employing different loss functions, showed marginal improvement but struggled to predict probability locations over a large horizon. Models trained on principal component analysis (PCA)-transformed and dynamic PCA (DPCA)-transformed data showed promise

in training but failed in testing. Models trained on PDFs without "dead voxels" (zero probability voxels independent of time) and atomic Cartesian coordinates perform well during training but encounter challenges in testing due to teacher forcing. Teacher forcing is a training method that can

. This work focuses on the development of machine learning (ML) models as proxy models for Car-Parrinello molecular dynamics (CPMD) metadynamics simulations in condensed-phase biomass reactions. Explicit solvation CPMD metadynamics simulation data of HMF undergoing protonation in a solution of dimethyl

Fall 2014

Gonzalez, Ruben T

another technique is a modification on Dempster-Shafer Theory. Evidence in previous work was considered to be a vector of discrete variables, and the resulting probability estimates consisted of discrete categorical distributions. However, most monitors have continuous outputs that are only discretized

While there has been much literature in the area of system monitoring and diagnosis, most of these techniques have a relatively small scope in terms of the faults and performance issues that they are built to detect. When implementing several monitors simultaneously on a single process, a single

problem can result in multiple alarms, making it difficult to single out the underlying cause. Recent work has been done on incorporating information from multiple monitoring systems by means of Bayesian diagnosis; however, work so far is still in its infancy. This thesis focuses on a number of techniques

Fall 2019

Ma, Yanjun

thesis forms a transition function for the constrained latent features. As a hierarchical extension of the hidden Markov model, it describes a dynamic model for the probabilities of discrete variables. By using the Beta distribution to replace the Gaussian distribution, the novel transition function

. Besides several probability models, novel inferencing algorithms are elaborated for different application scenarios. In most chemical processes, features with large inertia and small varying velocity are believed to be more informative. By imposing this modelling preferences as prior distributions of

model parameters, the first contribution of this thesis builds the dynamic latent features under a fully Bayesian framework. The preference for large inertia is implemented through a constraint and a prior distribution for the dynamic model of latent features, namely the transition function. The

Fall 2011

Qi, Fei

The large number of control loops in a modern industrial plant poses a serious challenge for operators and engineers to monitor these loops to maintain them at optimal conditions continuously. Much research has been done on control loop performance assessment and monitoring of individual components

missing pattern concept is introduced. The incomplete evidence problems are categorized into single missing pattern ones and multiple missing pattern ones. A novel method based on marginalization over an underlying complete evidence matrix (UCEM) is proposed to include the incomplete evidences into the

under the Bayesian framework. An approach to estimate the distributions of monitor readings with sparse historical samples is proposed to alleviate the intensive requirement of historical data. The statistical distribution functions for several monitoring algorithm outputs are analytically derived. A

Fall 2018

Li, Ruoxia

develop an estimator for the state PDF of arbitrary distribution. In this work, we develop an estimator based on a Gaussian mixture model (GMM) coupled with the ensemble Kalman filter (EnKF) specifically for estimation with multimodal state distributions.The second problem is that the conventional

a Gaussian distribution. This presents a challenge for Kalman-based state estimators such as the extended Kalman filter, since they model the state PDF as Gaussian. In order to achieve more accurate estimation, the modeling of the state distribution needs to be improved. The first problem is to

work, we develop a novel state estimation technique to incorporate inequality constraints for the case of Gaussian filters. Furthermore, we consider the constrained estimation for the case where the state PDF cannot be approximated with a Gaussian distribution. To this end, we develop a framework to

Spring 2017

Shen, Wenhan

and parameter uncertainties. Robust optimization (RO) approximation, a novel method dealing with joint chance constraints, is investigated to solve CCMPC problem. This method leads to results close to the true optimal and is not restricted to certain types of distribution. This work is further applied

on the steam assisted gravity drainage (SAGD) process. Constraint violations are greatly reduced by using the RO method. For system noises, the RO method can be directly applied with the inclusion of uncertainty sets. The type of uncertainty set is selected based on the distribution. Two-layer

optimization is proposed, one layer guarantees probability satisfaction and the other layer deals with optimizing the cost. Compared with traditional analytical methods, RO method is not limited to specific distribution and shows better performance in objective function. For parameter uncertainties, random

Spring 2013

Rueda-Velasquez, Rosa I

represents the maximum amount of large clusters in asphaltenes that could not be converted to lighter compounds under the evaluated cracking conditions. These analytical data for Cold Lake asphaltenes were transformed into probability density functions that described the molecular weight distributions of the

building blocks. These distributions were input for a Monte Carlo approach that allowed stochastic construction of asphaltenes and simulation of their cracking reactions to examine differences in the distributions of products associated to the molecular topology. The construction algorithm evidenced that a

significant amount of asphaltenes would consist of 3-5 building blocks. The results did not show significant differences between linear and dendritic molecular architectures, but suggested that dendritic molecules would experience slower reaction rates as they required more breakages to reach a given yield of

Spring 2023

Andrade Rossi, Ricardo

floc size distribution, and the morphology of populations of aggregates from breakage experiments that were conducted in a previous study (Gustavo Cifuentes, Aggregate Breakage in Laminar Couette Flow, 2022). These experiments were performed in a Taylor-Couette cell at laminar flow conditions. The

easier to separate than individual particles due to their larger size. Depending on the shear rate of the system, the hydrodynamic forces acting on flocs can break them into smaller fragments or induce their restructuring, which leads to the formation of small compact flocs. Aggregate breakage is an

mechanisms in shear flows. Therefore, the objective of the present work is to investigate the breakage and restructuring of populations of aggregates in laminar shear flow via a statistical approach. A population balance model (PBM) was developed to predict the evolution of the average aggregate size, the