Applied Mathematics Commons^™

Hybrid Electric Vehicle Energy Management Strategy With Consideration Of Battery Aging, Bin Zhou

Dissertations, Master's Theses and Master's Reports

The equivalent consumption minimization strategy (ECMS) is a well-known energy management strategy for Hybrid Electric Vehicles (HEV). ECMS is very computationally efficient since it yields an instantaneous optimal control. ECMS has been shown to minimize fuel consumption under certain conditions. But, minimizing the fuel consumption often leads to excessive battery damage. The objective of this dissertation is to develop a real-time implementable optimal energy management strategy which improves both the fuel economy and battery aging for Hybrid Electric Vehicles by using ECMS. This work introduces a new optimal control problem where the cost function includes terms for both fuel consumption …

Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan

Dissertations

Despite an extensive history of oceanic observation, researchers have only begun to build a complete picture of oceanic currents. Sparsity of instrumentation has created the need to maximize the information extracted from every source of data in building this picture. Within the last few decades, autonomous vehicles, or AVs, have been employed as tools to aid in this research initiative. Unmanned and self-propelled, AVs are capable of spending weeks, if not months, exploring and monitoring the oceans. However, the quality of data acquired by these vehicles is highly dependent on the paths along which they collect their observational data. The …

An Information Theory Model For Optimizing Quantitative Magnetic Resonance Imaging Acquisitions, Drew Mitchell

Dissertations and Theses (Open Access)

Quantitative magnetic resonance imaging (qMRI) is a powerful group of imaging techniques with a growing number of clinical applications, including synthetic image generation in post-processing, automatic segmentation, and diagnosis of disease from quantitative parameter values. Currently, acquisition parameter selection is performed empirically for quantitative MRI. Tuning parameters for different scan times, tissues, and resolutions requires some measure of trial and error. There is an opportunity to quantitatively optimize these acquisition parameters in order to maximize image quality and the reliability of the previously mentioned methods which follow image acquisition.

The objective of this work is to introduce and evaluate a …

Practical Modelling Of The Vanilla Option Volatility Smile, Jacob E. Shanley

Mathematics & Statistics ETDs

Many discussions on how best to model the standard American Option derivative focus solely upon the volatility smile modelling itself from a mathematical perspective. This thesis instead closely examines both the practical and mathematical implications of processing market data, modelling the volatility smile, and making real-world trading decisions from the results. In particular, it contains an analysis of market data processing algorithms, new volatility smile models, multiple empirically-driven weighting schemes, Gauss-Newton and Levenberg-Marquardt optimization algorithms, and various trading strategies. The top performing combinations found were those that involved the Smile and Twist volatility smile models, Volatility Width Vega Multiplier weighting …

Combinatorial Optimization: Introductory Problems And Methods, Erin Brownell

Honors Scholar Theses

This paper will cover some topics of combinatorial optimization, the study of finding the best possible arrangement of a set of discrete objects. These topics include the shortest path problem and network flows, which can be extended to solve more complex problems. We will also briefly cover some basics of graph theory and solving linear programming problems to give context to the reader.

Second-Order Generalized Differentiation Of Piecewise Linear-Quadratic Functions And Its Applications, Hong Do

Wayne State University Dissertations

The area of second-order variational analysis has been rapidly developing during the recent years with many important applications in optimization. This dissertation is devoted to the study and applications of the second-order generalized differentiation of a remarkable

class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to optimization and stability.

The first goal of this dissertation is to compute the second-order subdifferential of the functions described above, which will be applied in the study of the stability of composite optimization problems associated with piecewise linear-quadratic functions, known as extended …

Developing Optimization Techniques For Logistical Tendering Using Reverse Combinatorial Auctions, Jennifer Kiser

Electronic Theses and Dissertations

In business-to-business logistical sourcing events, companies regularly use a bidding process known as tendering in the procurement of transportation services from third-party providers. Usually in the form of an auction involving a single buyer and one or more sellers, the buyer must make decisions regarding with which suppliers to partner and how to distribute the transportation lanes and volume among its suppliers; this is equivalent to solving the optimization problem commonly referred to as the Winner Determination Problem. In order to take into account the complexities inherent to the procurement problem, such as considering a supplier’s network, economies of scope, …

Computational Methods In Civil Engineering, Nir Krakauer

Open Educational Resources

No abstract provided.

Optimization And Control Of An Array Of Wave Energy Converters, Jianyang Lyu

Dissertations, Master's Theses and Master's Reports

This study explored optimal configuration of both the array layout and the dimension of each WEC in the array. The array contains heaving buoys with full interaction and exact hydrodynamics. Optimization of dimension was done on each WEC in the array with a given optimal layout, and a higher q-factor was achieved. Both impedance matching optimal control and derivative control were employed, which provides both theoretical maximum energy and a more realistic case. Then the work was expanded to optimization of both the array layout and the dimension of each WEC in the array. An average of 39.21% higher q-factor …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

Prediction And Optimal Scheduling Of Advertisements In Linear Television, Mark J. Panaggio, Pak-Wing Fok, Ghan S. Bhatt, Simon Burhoe, Michael Capps, Christina J. Edholm, Fadoua El Moustaid, Tegan Emerson, Star-Lena Estock, Nathan Gold, Ryan Halabi, Madelyn Houser, Peter R. Kramer, Hsuan-Wei Lee, Qingxia Li, Weiqiang Li, Dan Lu, Yuzhou Qian, Louis F. Rossi, Deborah Shutt, Vicky Chuqiao Yang, Yingxiang Zhou

Mathematical Sciences Faculty Research

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of "impressions" in the target demographic. However, because the number of impressions for a given program is not known a priori and because …

Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, Juan Sebastian Martinez, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

Multi-objective optimization (MOO) problems arise frequently in science and engineering situations. In an optimization problem, we want to find the set of input parameters that generate the set of optimal outputs, mathematically known as the Pareto frontier (PF). Solving the MOO problem is a challenge since expensive experiments can be performed only a constrained number of times and there is a limited set of data to work with, e.g. a roll-to-roll microwave plasma chemical vapor deposition (MPCVD) reactor for manufacturing high quality graphene. State-of-the-art techniques, e.g. evolutionary algorithms; particle swarm optimization, require a large amount of observations and do not …

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Graduate Student Theses & Dissertations

In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.

In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, …

Optimal Control And Its Application To The Life-Cycle Savings Problem, Tracy A. Taylor

Theses and Dissertations

Throughout the course of this thesis, we give an introduction to optimal control theory and its necessary conditions, prove Pontryagin's Maximum Principle, and present the life-cycle saving under uncertain lifetime optimal control problem. We present a very involved sensitivity analysis that determines how a change in the initial wealth, discount factor, or relative risk aversion coefficient may affect the model the terminal depletion of wealth time, optimal consumption path, and optimal accumulation of wealth path. Through simulation of the life-cycle saving under uncertain lifetime model, we are not only able to present the model dynamics through time, but also to …

Shape Optimization For Drag Minimization Using The Navier-Stokes Equation, Chukwudi Paul Chukwudozie

LSU Master's Theses

Fluid drag is a force that opposes relative motion between fluid layers or between solids and surrounding fluids. For a stationary solid in a moving fluid, it is the amount of force necessary to keep the object stationary in the moving fluid. In addition to fluid and flow conditions, pressure drag on a solid object is dependent on the size and shape of the object. The aim of this project is to compute the shape of a stationary 2D object of size 3.5 m2 that minimizes drag for different Reynolds numbers. We solve the problem in the context of shape …

Optimization Schemes For The Inversion Of Bouguer Gravity Anomalies, Azucena Zamora

Open Access Theses & Dissertations

Data sets obtained from measurable physical properties of the Earth structure have helped advance the understanding of its tectonic and structural processes and constitute key elements for resource prospecting. 2-Dimensional (2-D) and 3-D models obtained from the inversion of geophysical data sets are widely used to represent the structural composition of the Earth based on physical properties such as density, seismic wave velocities, magnetic susceptibility, conductivity, and resistivity. The inversion of each one of these data sets provides structural models whose consistency depends on the data collection process, methodology, and overall assumptions made in their individual mathematical processes. Although sampling …

Reformulations For Control Systems And Optimization Problems With Impulses, Jacob Blanton

LSU Doctoral Dissertations

This dissertation studies two different techniques for analyzing control systems whose dynamics include impulses, or more specifically, are measure-driven. In such systems, the state trajectories will have discontinuities corresponding to the atoms of the Borel measure driving the dynamics, and these discontinuities require further definition in order for the control system to be treated with the broad range of results available to non-impulsive systems. Both techniques considered involve a reparameterization of the system variables including state, time, and controls. The first method is that of the graph completion, which provides an explicit reparameterization of the time and state variables. The …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, Quan Yuan, Zhixin Yang

Mathematics Faculty Research Publications

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.

Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *

COURI Symposium Abstracts, Spring 2012

Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …

A Study On Facility Planning Using Discrete Event Simulation: Case Study Of A Grain Delivery Terminal, Sarah M. Asio

Department of Industrial and Management Systems Engineering: Dissertations, Theses, and Student Research

The application of traditional approaches to the design of efficient facilities can be tedious and time consuming when uncertainty and a number of constraints exist. Queuing models and mathematical programming techniques are not able to capture the complex interaction between resources, the environment and space constraints for dynamic stochastic processes. In the following study discrete event simulation is applied to the facility planning process for a grain delivery terminal. The discrete event simulation approach has been applied to studies such as capacity planning and facility layout for a gasoline station and evaluating the resource requirements for a manufacturing facility. To …

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …

Optimization In The Undergraduate Curriculum, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

A discussion of how an optimization course fits into the undergraduate mathematics curriculum

Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter

Mathematical Sciences Technical Reports (MSTR)

Optimally designing radiotherapy and radiosurgery treatments to increase the likelihood of a successful recovery from cancer is an important application of operations research. Researchers have been hindered by the lack of academic software that supports head-to-head comparisons of different techniques, and this article addresses the inherent difficulties of designing and implementing an academic treatment planning system. In particular, this article details the algorithms and the software design of Radiotherapy optimAl Design (RAD).

Doppler-Only Multistatic Radar, Dustin G. Mixon

Theses and Dissertations

In order to estimate the position and velocity of a target, most multistatic radar systems require multiple independent target measurements, such as angle-of-arrival, time-of-arrival, and Doppler information. Though inexpensive and reliable, Doppler-only systems have not been widely implemented due to the inherent nonlinear problem of determining a target’s position and velocity from their measurements. We solve this problem. In particular, we first establish the lack of observability in the Doppler-only bistatic system, thereby demonstrating the need for multiple transmitters and/or receivers. Next, for a multistatic system with a sufficient number of transmitter-receiver pairs, we invoke classical optimization techniques, such as …

Modeling Basketball Free Throws, Andrew Lang, Joerg M. Gablonsky

College of Science and Engineering Faculty Research and Scholarship

This paper presents a mathematical model for basketball free throws. It is intended to be a supplement to an existing calculus course and could easily be used as a basis for a calculus project. Students will learn how to apply calculus to model an interesting real-world problem, from problem identification all the way through to interpretation and verification. Along the way we will introduce topics such as optimization (univariate and multiobjective), numerical methods, and differential equations.

Multiple Comparison Pruning Of Neural Networks, Donald E. Duckro

Theses and Dissertations

Reducing a neural network's complexity improves the ability of the network to be applied to future examples. Like an overfitted regression function, neural networks may miss their target because of the excessive degrees of freedom stored up in unnecessary parameters. Over the past decade, the subject of pruning networks has produced non-statistical algorithms like Skeletonization, Optimal Brain Damage, and Optimal Brain Surgery as methods to remove connections with the least salience. There are conflicting views as to whether more than one parameter can be removed at a time. The methods proposed in this research use statistical multiple comparison procedures to …

Trigonometric Transforms For Image Reconstruction, Thomas M. Foltz

Theses and Dissertations

This dissertation demonstrates how the symmetric convolution-multiplication property of discrete trigonometric transforms can be applied to traditional problems in image reconstruction with slightly better performance than Fourier techniques and increased savings in computational complexity for symmetric point spread functions. The fact that the discrete Fourier transform a circulant matrix provides an alternate way to derive the symmetric convolution-multiplication property for discrete trigonometric transforms. Derived in this manner, the symmetric convolution-multiplication property extends easily to multiple dimensions and generalizes to multidimensional asymmetric sequences. The symmetric convolution-multiplication property allows for linear filtering of degraded images via point-by-point multiplication in the transform domain …

Linear Time Optimization Algorithms For P4-Sparse Graphs, Beverly Jamison, Stephan Olariu

Computer Science Faculty Publications

Quite often, real-life applications suggest the study of graphs that feature some local density properties. In particular, graphs that are unlikely to have more than a few chordless paths of length three appear in a number of contexts. A graph G is P₄-sparse if no set of five vertices in G induces more than one chordless path of length three. P₄-sparse graphs generalize both the class of cographs and the class of P₄-reducible graphs. It has been shown that P₄-sparse graphs can be recognized in time linear in the size of the …