Applied Mathematics Commons^™

Non-Contact Wind Turbine Blade Crack Detection Using Laser Doppler Vibrometers, Ali Zabihi, Farhood Aghdasi, Chadi Ellouzi, Nand Kishore Singh, Ratneshwar Jha, Chen Shen

Henry M. Rowan College of Engineering Departmental Research

In response to the growing global demand for both energy and a clean environment, there has been an unprecedented rise in the utilization of renewable energy. Wind energy plays a crucial role in striving for carbon neutrality due to its eco-friendly characteristics. Despite its significance, wind energy infrastructure is susceptible to damage from various factors including wind or sea waves, rapidly changing environmental conditions, delamination, crack formation, and structural deterioration over time. This research focuses on investigating non-destructive testing (NDT) of wind turbine blades (WTBs) using approaches based on the vibration of the structures. To this end, WTBs are first …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations and Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill

Master's Theses

We numerically investigate the effects that Environmental, Social, and Governance (ESG) scores have on portfolio optimization with Modern Portfolio Theory assumptions and how ESG scores correlate with the market returns of a rated company's stock. Additionally, we review and analyze a research paper published in the Journal of Financial Economics regarding ESG investing titled “Responsible investing: The ESG-efficient frontier” by Pedersen, Fitzgibbons, and Lukasz. Our overall goal is provide insight for socially responsible inclined investors, to help them understand what ESG scores tell us and how those scores may effect their overall investment returns."

Bidding Strategy For A Wind Power Producer In Us Energy And Reserve Markets, Anne Stratman

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

Wind power is one of the world's fastest-growing renewable energy resources and has expanded quickly within the US electric grid. Currently, wind power producers (WPPs) may sell energy products in US markets but are not allowed to sell reserve products, due to the uncertain and intermittent nature of wind power. However, as wind’s share of the power supply grows, it may eventually be necessary for WPPs to contribute to system-wide reserves. This paper proposes a stochastic optimization model to determine the optimal offer strategy for a WPP that participates in the day-ahead and real-time energy and spinning reserve markets. The …

Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair

Graduate Theses and Dissertations

We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.

Modeling Prices In Limit Order Book Using Univariate Hawkes Point Process, Wenqing Jiang

LSU New Orleans Theses and Dissertations

This thesis presents a time-changed geometric Brownian price model with the univariate Hawkes processes to trace the price changes in a limit order book. Limit order books are the core mechanism for trading in modern financial markets, continuously collecting outstanding buy and sell orders from market participants. The arrival of orders causes fluctuations in prices over time. A Hawkes process is a type of point process that exhibits self-exciting behavior, where the occurrence of one event increases the probability of other events happening in the near future. This makes Hawkes processes well-suited for capturing the clustered arrival patterns of orders …

Cost-Risk Analysis Of The Ercot Region Using Modern Portfolio Theory, Megan Sickinger

Master's Theses

In this work, we study the use of modern portfolio theory in a cost-risk analysis of the Electric Reliability Council of Texas (ERCOT). Based upon the risk-return concepts of modern portfolio theory, we develop an n-asset minimization problem to create a risk-cost frontier of portfolios of technologies within the ERCOT electricity region. The levelized cost of electricity for each technology in the region is a step in evaluating the expected cost of the portfolio, and the historical data of cost factors estimate the variance of cost for each technology. In addition, there are several constraints in our minimization problem to …

Analysis And Construction Of Artificial Neural Networks For The Heat Equations, And Their Associated Parameters, Depths, And Accuracies., Shakil Ahmed Rafi

Graduate Theses and Dissertations

This dissertation seeks to explore a certain calculus for artificial neural networks. Specifically we will be looking at versions of the heat equation, and exploring strategies on how to approximate them.

Our strategy towards the beginning will be to take a technique called Multi-Level Picard (MLP), and present a simplified version of it showing that it converges to a solution of the equation (^∂/_∂t u_d ) (t, x) = (∇² _x u_d)(t, x).

We will then take a small detour exploring the viscosity super-solution properties of solutions to such …

Modeling Vibration Stiffness: An Analytical Extension Of Hertzian Theory For Angular Contact Bearings With A Thin Viscoelastic Coating, Davis R. Burton

Honors Theses

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila

Faculty Publications

This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …

Bayesian Estimation Of Reproduction Numbers From Distributions Of Outbreaks Sizes: Branching Process Approach, Alberta Araba Johnson

Theses and Dissertations

The Generalized Poisson distribution is useful in modeling epidemiological processes as a branching stochastic processes problem. Our goal is to construct accurate and reliable estimators for the reproduction number (R0) (i.e., the number of secondary infections), particularly in the context of disease outbreaks modeled by a Galton-Watson process. Towards this goal, we construct the classical Bayes estimator, the Maximum Likelihood estimator, and the Empirical Bayes (EB) estimator under the Square Error Loss function in Chapter II. We prove that the Empirical Bayes estimator is asymptotically optimal and estimate the rate of convergence. We then proceed to monotonize the Empirical Bayes …

Variational Bias Sampling For Collaborative Filtering Recommender Systems, Prisca Stephens

Theses and Dissertations

Advancements in digitalization has yielded enormous growth of data on online platforms, overwhelming users with multitude of options to choose from. Recommender systems narrow down these options to a few relevant ones thereby facilitating the decision-making processes for users. This study presents a framework for integrating variational bias sampling into model-based collaborative filtering techniques for recommender systems. Variational bias sampling is a novel and unique way to account for random factors that affect explicit ratings in collaborative filtering recommender systems. A Gaussian distribution is used to model all the possible random factors that could affect ratings. Sampling user and item …

The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos

Theses and Dissertations

The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing high-stakes testing. The framework of the study is grounded in the theory of mathematical education (knowledge of mathematics educators to teach), the theory of mathematical learning (understanding how students learn mathematics), and social constructivism. The study seeks ways to teach all students, mainly the minority, to learn …

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

Electronic Theses and Dissertations

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Convergence Estimate Of Minimal Residual Methods And Random Sketching Of Krylov Subspace Methods, Peter Westerbaan

All Dissertations

This study concerns two main issues in numerical linear algebra: convergence estimate of minimal residual methods based on explicit construction of approximate min-max polynomials for in- definite matrices, and development and analysis of Krylov subspace methods using non-orthonormal basis vectors based on random sketching. For a matrix A with spectrum Λ(A), it is well known that the min-max polynomial problem min max |pk (z)| pk ∈Pk, pk (0)=1, z∈Λ(A) is used to bound the relative error of Krylov subspace minimum residual methods or similar methods. For a symmetric positive definite matrix A, the min-max polynomial for the Conjugate Gradient (CG) …

Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa

All Dissertations

Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …

Domain Decomposition Methods For Fluid-Structure Interaction Problems Involving Elastic, Porous, Or Poroelastic Structures, Hemanta Kunwar

All Dissertations

We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and Schwarz waveform relaxation (SWR) method using Robin transmission conditions (or the Robin method), for solving fluid-structure interaction systems involving elastic, porous, or poroelastic structure. These methods allow us to formulate the coupled system as a space-time interface problem and apply iterative algorithms directly to the evolutionary problem. Each time-dependent fluid and the structure subdomain problem is solved independently, which enables the use of different time discretization schemes and time step sizes in the subsystems. This leads to an efficient way of simulating time-dependent multiphysics phenomena. For the fluid-porous …

System Identification For Motion Control Of Unmanned Aerial Vehicles Platform, Raj Ramesh Agarwal

Theses and Dissertations

Comprehensive research on Unmanned Aerial Vehicles (UAV) system identification for motion control parameters is presented in this thesis, with a focus on the necessity of precise control and improved performance. Using Pseudorandom Binary Sequence (PRBS) and Normally Distributed Random Numbers, it presents a unique technique for excitation of UAV dynamic systems. It also shows how effective random signals are in time-domain identification for precise control in a range of flying circumstances. The piece of research includes a thorough analysis and implementation of various approaches and its further improvements, highlighting the benefits and drawbacks of each. These approaches include the free …

Approximation Via Degree Reduction Of Nonlinearities With Applications To Turbulent Flows, Flame Fronts, And Magnetohydrodynamics, Matthew Enlow

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems." More specifically, in …

Sol-Gel Synthesis And Microstructure Characterization Of Nio-Tio2 Semiconductor, Godlisten N. Shao

Tanzania Journal of Engineering and Technology (TJET)

NiO-TiO2 is a fascinating p-n semiconducting binary metal oxide with unique electronic and optical properties. The NiO-TiO2 has been synthesized using complicated preparation methods and expensive precursors that hamper their large-scale production. The present study reports the preparation of NiO-TiO2 semiconductor with improved physicochemical properties. NiO-TiO2 samples were prepared through one-pot sol-gel synthesis process followed by sintering of the as-synthesized materials at temperatures ranging from 600 to 1000 °C. The role of thermal treatment and NiO content on the microstructures was exquisitely studied. The microstructure of the NiO-TiO2 samples was examined by Raman spectroscopy, XRD, XRF, SEM-EDAX, high resolution TEM, …

General Hydrogeochemical Characterization Of Groundwater In Coastal Aquifers Of Kilwa Kisiwani Oceanic Island, South East Tanzania, Simon R Melchioly

Tanzania Journal of Engineering and Technology (TJET)

The main objective of this study was to determine the hydrogeochemical processes controlling the groundwater chemistry on the Island and assess its suitability for human consumption and irrigation. The methodology used in the study include hydrogeological assessment of the study area and laboratory analysis for general physico-chemical parameters of groundwater. Other parameters such as Soluble sodium percentage (SSP) or % Na+, Sodium Adsorption Ratio (SAR), Magnesium adsorption ratio (MAR), Residual sodium carbonate (RSC), hydrochemical facies classification, and Water Quality Index (WQI) were calculated using empirical formulae. The effects of salinization of groundwater were classified using the chloride-Bicarbonate (Cl/HCO3) and the …

Thermogravimetric Analysis And Chemical Kinetics Of Waste Tires, Mahir Mohammed Said

Tanzania Journal of Engineering and Technology (TJET)

The focus of this paper is to analyse the pyrolysis reaction of waste tires. The pyrolysis was studied experimentally using thermal and chemical kinetics. The tires were pyrolyzed using thermogravimetry at a temperature range of 200 to 600°C, with heating rates of 10, 20, and 50°C/min. The activating energy was observed to increase with increased temperature. The highest activating energy was 101.02 kJ/mol at a heating rate of 50°C/min.

Design And Optimization Of An Azeotropic Distillation Pilot Plant For The Production Of Pure Ethanol, Samwel V. Manyele

Tanzania Journal of Engineering and Technology (TJET)

This study aimed to design an azeotropic distillation plant using Aspen Plus® V10 software and determine optimal process conditions for producing pure ethanol greater than 95% from pre-concentrated near-azeotropic ethanol-water solution. The non-random two-liquid Redlich-Kwong thermodynamic model was the base method for property analysis and performance prediction. Modelling and simulation of the converged process were conducted for fixed column variables (R = 5, N = 12 and p = 1 atm). Plant operating parameters were varied in the range of 0 to 1 for the pre-heater vapour fraction, 2 to 10 for the column feed plates (NFP), 2 to 6 …

Enhanced Post Deposition Annealing Conditions On The Fabrication Of High Quality Thermochromic Vanadium Dioxide Films, Nuru R. Mlyuka

Tanzania Journal of Engineering and Technology (TJET)

Sputter deposition of thermochromic VO2 thin films for smart window applications has been faced with several challenges including the need for high deposition temperature, extremely precise and narrow range of oxygen/argon flow ratio and target poisoning during sputtering. Deposition of VO2 at room temperature without oxygen followed by post-deposition annealing has been cited as one of the potential mitigations to the challenge. In this study, the effects of post-deposition annealing conditions on the structural, electrical and optical properties of VO2 thin films are reported. The films were prepared on soda lime glass substrates using DC magnetron sputtering of metallic vanadium …

Optimization Pump As Turbine Coupled To A Self-Excited Induction Generator Using Multi-Objective Genetic Algorithm, Emanuel J. Nyirenda

Tanzania Journal of Engineering and Technology (TJET)

As a way of accelerating the deployment of affordable and clean renewable energy generation technologies, applying a pump working as a turbine coupled to a self-excited induction generator is gaining popularity in various areas including energy recovery and micro hydro systems. However, it is currently challenging to predict the performance of the PAT-SEIG system and there is no agreed-upon rule on the selection of the appropriate system to be installed at a particular site. This paper has presented multi-objective optimization to select the best operating point of the PAT-SEIG system. The results show that the peak efficiencies for the PAT …

Optimal Load Shedding During Service Restoration In Electrical Secondary Distribution Network Based On Reinforcement Learning, Rukia J. Mwifunyi

Tanzania Journal of Engineering and Technology (TJET)

Increased stress in traditional power systems results in blackouts due to voltage instability attributed to a mismatch between available capacity and load demand, especially in distribution networks. Service restoration schemes are designed to return power supply to the affected parts of the networks. The availability of insufficient supply is a complex problem that requires operational experience or an automatic system. The stochastic nature of load demand significantly impacts service restoration as it results in increased restored demand in case a fault occurs during off-peak hours and helps reduce overload if the fault occurs during peak hours. The study adopts an …

Evaluation Of Cybersecurity In Remote Working Settings For Mobile Network Operators, Victoria Mahabi

Tanzania Journal of Engineering and Technology (TJET)

Cybersecurity has increasingly been a primary concern to people as technology advances and allows them to work remotely. This study thus evaluated the cybersecurity posture for organisations that have opted for remote working culture, whereas emerging cyber threats, practices to combat them, and appropriate guidelines for managing cyber threats were discussed. The study used a descriptive design with a quantitative approach from 118 information technology personnel working for Tanzania's three major mobile network operators (MNOs). SPSS analysed the collected data. The study revealed that predominant cyber-threats affecting MNOs in remote working include human errors, phishing attacks, malicious domains, denial of …

Study Of The Effects Of Thermal Aging Coupled With Shot-Peening Treatment Of Carbonitrided Din 1.6587 Low Alloy Steel On Retained Austenite And Residual Stresses, Richard J. Katemi

Tanzania Journal of Engineering and Technology (TJET)

This work investigated the effects of thermal aging and shot-peening of carbonitrided 1.6587 steel grade on retained austenite and residual stresses. After carbonitriding samples contained maximum of 0.87% carbon, 0.34% nitrogen and 50 mass. -% retained austenite. Thermal aging conditions investigated were -30°C, 90°C and 150°C while the aging period were 14, 96 and 720 hours. After thermal aging, some of the samples were subjected to shot-peening treatment using standard cut wire shots StD – G3 - 0.6 mm VDFI 8001 with intensity in the range of 0.25 to 0.30 mmA and coverage of 1.00 to 1.24 x 98%. It …