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Physical Sciences and Mathematics Commons™
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- Optimal Design of Experiments (2)
- Uncertainty (2)
- ANOVA (1)
- Abcd system (1)
- Aerial imaging (1)
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- AlexNet (1)
- Asymptotics (1)
- Calibration (1)
- Cnoidal solutions (1)
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- Coordinate Exchange (1)
- Damage detection (1)
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- G-Optimality (1)
- History of probability (1)
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- Information Matrix (1)
- Jacobi elliptic functions (1)
- Likelihood estimation (1)
- Method of Semidefinite Relaxations (1)
- NLS-KdV system (1)
- Optimal Design (1)
- Optimization (1)
- Parametric bootstrap (1)
- Periodic solutions (1)
- Probability history (1)
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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen
Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen
All Graduate Reports and Creative Projects, Fall 2023 to Present
While often taught in high school and required as part of a college degree, statistics classes are sometimes viewed by students as an obstacle rather than a support for their overall goals. One way to increase student engagement in a statistics course is to use the history of statistics. Within the literature review, the advantages to using the history of statistics are discussed as well as the more extensive research on using the history of mathematics in mathematics courses. Included are instructional strategies for using the context around the development of mathematical ideas in math classrooms which can be extended …
Exploring Application Of The Coordinate Exchange To Generate Optimal Designs Robust To Data Loss, Asher Hanson
Exploring Application Of The Coordinate Exchange To Generate Optimal Designs Robust To Data Loss, Asher Hanson
All Graduate Theses and Dissertations, Fall 2023 to Present
The primary objective of this study is to evaluate the efficacy of the coordinate exchange (CEXCH) algorithm in the generation of robust optimal designs. The assessment involves a comparative analysis, wherein designs produced by the Point Exchange (PEXCH) Algorithm are employed as benchmarks for evaluating the efficiency of CEXCH designs. Three modified criteria, selected from the traditional alphabet criteria pool, are utilized to score each algorithm. To enhance the reliability of the comparative analysis, multiple rounds of validation are conducted, focusing on visual assessments, design scores, and criteria efficiencies. The findings from each round of validation contribute to a comprehensive …
Assessing Extant Methods For Generating G-Optimal Designs And A Novel Methodology To Compute The G-Score Of A Candidate Design, Hyrum John Hansen
Assessing Extant Methods For Generating G-Optimal Designs And A Novel Methodology To Compute The G-Score Of A Candidate Design, Hyrum John Hansen
All Graduate Theses and Dissertations, Fall 2023 to Present
Experimental designs are used by scientists to allocate treatments such that statistical inference is appropriate. Most traditional experimental designs have mathematical properties that make them desirable under certain conditions. Optimal experimental designs are those where the researcher can exercise total control over the treatment levels to maximize a chosen mathematical property. As is common in literature, the experimental design is represented as a matrix where each column represents a variable, and each row represents a trial. We define a function that takes as input the design matrix and outputs its score. We then algorithmically adjust each entry until a design …
Ianova: Multi-Sample Means Comparisons For Imprecise Interval Data, Zachary Rios
Ianova: Multi-Sample Means Comparisons For Imprecise Interval Data, Zachary Rios
All Graduate Theses and Dissertations, Fall 2023 to Present
In recent years, interval data has become an increasingly popular tool to solve modern data problems. Intervals are now often used for dimensionality reduction, data aggregation, privacy censorship, and quantifying awareness of various uncertainties. Among many statistical methods that are being studied and developed for interval data, the significance test is particularly of importance due to its fundamental value both in theory and practice. The difficulty in developing such tests mainly lies in the fact that the concept of normality does not extend naturally to interval data (due the range of an interval being necessarily non-negative), causing the exact tests …
On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels
On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels
All Graduate Theses and Dissertations, Fall 2023 to Present
A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields …
A Comprehensive Uncertainty Quantification Methodology For Metrology Calibration And Method Comparison Problems Via Numeric Solutions To Maximum Likelihood Estimation And Parametric Bootstrapping, Aloka B. S. N. Dayarathne
A Comprehensive Uncertainty Quantification Methodology For Metrology Calibration And Method Comparison Problems Via Numeric Solutions To Maximum Likelihood Estimation And Parametric Bootstrapping, Aloka B. S. N. Dayarathne
All Graduate Theses and Dissertations, Fall 2023 to Present
In metrology, the science of measurements, straight line calibration models are frequently employed. These models help understand the instrumental response to an analyte, whose chemical constituents are unknown, and predict the analyte’s concentration in a sample. Techniques such as ordinary least squares and generalized least squares are commonly used to fit these calibration curves. However, these methods may yield biased estimates of slope and intercept when the calibrant, substance used to calibrate an analytical procedure with known chemical constituents (x-values), carries uncertainty. To address this, Ripley and Thompson (1987) proposed functional relationship estimation by maximum likelihood (FREML), which considers uncertainties …
Exploring Optimal Design Of Experiments For Random Effects Models, Ryan C. Bushman
Exploring Optimal Design Of Experiments For Random Effects Models, Ryan C. Bushman
All Graduate Theses and Dissertations, Fall 2023 to Present
The majority of research in the field of optimal design of experiments has focused on producing designs for fixed effects models. The purpose of this thesis is to explore how the optimal design framework applies to nested random effects models. The object that is being optimized is the model information matrix. We explore the full derivation of the random effects information matrix to highlight the complexity of the problem and show how the optimization is a function of the model's parameters. In conjunction with this research, the ODVC (Optimal Design for Variance Components) package was built to provide tools that …
Anomaly Detection On Small Wind Turbine Blades Using Deep Learning Algorithms, Bridger Altice, Edwin Nazario, Mason Davis, Mohammad Shekaramiz, Todd K. Moon, Mohammad A. S. Masoum
Anomaly Detection On Small Wind Turbine Blades Using Deep Learning Algorithms, Bridger Altice, Edwin Nazario, Mason Davis, Mohammad Shekaramiz, Todd K. Moon, Mohammad A. S. Masoum
Electrical and Computer Engineering Faculty Publications
Wind turbine blade maintenance is expensive, dangerous, time-consuming, and prone to misdiagnosis. A potential solution to aid preventative maintenance is using deep learning and drones for inspection and early fault detection. In this research, five base deep learning architectures are investigated for anomaly detection on wind turbine blades, including Xception, Resnet-50, AlexNet, and VGG-19, along with a custom convolutional neural network. For further analysis, transfer learning approaches were also proposed and developed, utilizing these architectures as the feature extraction layers. In order to investigate model performance, a new dataset containing 6000 RGB images was created, making use of indoor and …