For the last five years, I have designed and delivered a special course: Research Project in Industrial Mathematics.
This course was initiated by NSF-funded MAA PIC Math (Preparation for Industrial Careers in Mathematics) Program in 2017.
This course provides a unique educational experience by introducing students to the ways that advanced mathematics and statistics are used in the real world to analyze and solve complex problems. The students work in small teams on real problems, which are directly provided by business and industry. Most of the projects are data enabled and machine-learning oriented.

PROJECTS ADVISED

Spring 2020 Using Matrix and Tensor Factorizations for Analyzing Radiation Transport Data
Industrial Sponsor: Pacific Northwest National Laboratory, Richland, WA
Description and results

Students:
Research Project in Industrial Mathematics - Capstone
Emma Galligan ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math
Grant Johnson ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math
DeAndre Lesley ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math

Research Project in Industrial Mathematics
Seth Garcia ('21) DB BS Electrical Engineering/2nd Major Computational Math
Petar Grigorov ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math
Brittney Marzen ('20) DB BS Computational Mathematic/Daytona Space Studies Minor

Description: The Disruptive Technologies Group in the National Security Directorate of Pacific Northwest National Laboratory is enthusiastic to collaborate with students at Embry-Riddle Aeronautical University on a research project whose goal is to develop quantitative methods for characterizing features in radiation transport simulation data and comparing features across different computational approaches.

Understanding how radiation particles are transported throughout a system and interact with shielding is extremely computationally expensive. Reduced order models (ROMs) can be used to significantly increase the speed of these calculations. This project focuses on analysis of the simulated radiation transport for Cobalt-60, Cesium-137, and Technetium-99. A ROM may be developed from several formalisms and then analyzing the feature vectors of each.

The methods considered here include developing algorithms afor principal component analysis (PCA), non-negative matrix factorization (NNMF), and CP tensor decomposition (CPT). The tests students conducted focused on investigated the similarities between vectors, the effects of noise on reconstructing the data, and the ability of each ROM to identify the different sources of radiation. The conclusion from this analysis plus the qualitative features of each method indicate the CPT is the best method for developing a ROM to describe the data.

Major outcomes:

  • Results were presented at 2020 ERAU Discovery Day
  • Grant Johnson was awarded the Department of Energy Computational Science Graduate Fellowship to support his doctoral studies in plasma physics at Princeton University
  • Emma Galligan is currently persuing her PhD at Georgia State in Astronomy
  • Petar Grigorov is currently persuing his PhD at George Washington University in Physics with concentration in high energy astrophysics

Spring 2020 Enchance the functionality of Personal Weather Stations using Data Analytics
Industrial Sponsor: WeatherFlow Inc, Daytona Beach, FL
Description and results

Students:
Research Project in Industrial Mathematics - Capstone
Evelyn Taylor (‘20) DB BS Computer Science/2nd Major Computational Math
Research Project in Industrial Mathematics
Kade Mahoney ('20) DB BS Computational Mathematic/Daytona Physics Minor
Hailey DeNys (‘21) DB BS Computational Mathematic

Description: Description: WeatherFlow, a personal weather systems company, collaborated with undergraduate students at Embry-Riddle Aeronautical University to find a way to enhance visualization of real time meteorological data.

Students used the meteorological data from WeatherFlow network to develop a new feature to enhance the user interface experience by creating a real time display of the weather in relation to a principal station. Temperature and rain were tracked in a grid structure with ten-mile intervals from ten to fifty miles along the eight cardinal directions. This visualization tool will give users a new understanding of their local conditions allowing them to better plan their daily activities.

  • Results were presented at 2020 ERAU Discovery Day
  • Kade Mahoney currently is Associate Software Engineer at Northrop Grumman
  • Evelyn Taylor currently is Software Engineer at Amazon
  • Hailey DeNys got Co-op internship at JEA for Summer 2020

Spring - Fall 2020 Dynamic Pricing Algorithm Project
Industrial Sponsor: OneSky, Daytona Beach, FL
Description and results

Spring 2020 Students:
Research Project in Industrial Mathematics - Capstone
Allison Acosta ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math
Paige Rasmussen ('21) DB BS Computational Mathematic

Research Project in Industrial Mathematics
Payton Boliek ('20) DB BS Computational Mathematic/Daytona Comp Science Minor
Mariah Marin ('21) DB BS Computational Mathematic

Fall 2020 Students:
Research Project in Industrial Mathematics - Capstone
Payton Boliek ('20) DB BS Computational Mathematic/Daytona Comp Science Minor
Betiay Babacan ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math

Description: OneSky Flight supports the technology needs of four established private jet brands; Flexjet, Sentient Jet, PrivateFly, and Sirio. One key function required by these businesses is trip pricing. This is the exercise of determining the appropriate price for a trip, considering many factors. Today, this process is manual. The ultimate goal of this project is to create a dynamic pricing tool that generates an appropriate price for trips in the US and EU. There is a large part of this project that needs to be addressed: Event Calendar. The Event Calendar includes a factor for each day of the year. These factors are based on the events/holidays that happen throughout the year and their impact on the demand for days on and surrounding the events/holidays.

In order to build the list of possible events that affect the intensity of flights extended data analysis was performed. Along with processing 3 years of raw flight data (~8,000,000 single flights), students did independent research on theory behind dynamic pricing. Team determined the patterns in raw data and identify anomalies as possible event, mapping them and sorting them in holidays, sport events, extreme weather events, etc. based on open sources, also recognized the local and global patterns before identification. The corresponding quantitatively model for model of dynamic pricing algorithm was developed. It is the hierarchical model with primary and secondary factors: considering normal weekly traffic, seasonal increments, and day of the week of a selected event. With given three years of flight history, model was build using any two years and validated using third on: the prediction of demand for third year was modeled and compared with third year actual data.

Major outcomes:

  • Results were presented at 2020 ERAU Discovery Day
  • Payton Boliek got internship as Operations Analyst Intern at Lockheed Martin for Summer 2020
  • Paige Rasmussen got internship at Lockheed Martin for Summer 2020

Spring 2020 Identifying Individual Voter Sub-Ethnicity
Industrial Sponsor: Florida Democratic Party, Daytona Beach, FL
Description and results

Students:
Research Project in Industrial Mathematics - Capstone
Ian Mungovan ('20) DB BS Aerospace Engineering/Daytona Astronomy Minor
Liana Parker ('20) DB BS Computational Mathematic/ Business Admin Minor

Research Project in Industrial Mathematics
Richard Beredo ('21) DB BS Electrical Engineering/Daytona Military Science Minor

Description: The Democratic performance in Florida among voters regressed in the 2016-2018 election cycle. Most of the regression was caused by the low turnout of Hispanic voters in the southern sector of Florida. The Florida Democratic Party teamed up with students at Embry-Riddle Aeronautical University on a research project that could help to analyze trends by examining Democratic Hispanic performance level based on sub ethnicity. First step towards it aims to develop an algorithm to analyze and predict possible Hispanic sub-ethnicity.

Dealing with over 11 million records on all voters registered in Florida, students was able to combine public information on population data for all zip codes and data on 1000 most popular first names and 1000 most popular last names for all 16 Hispanic subethnicities to build algorithm to estimate the probability of each subethnicity for each Hispanic origin voter. With given prediction the further analysis on each subethnicity activity and party affiliation is in progress.

Major outcomes:

  • Results were presented at 2020 ERAU Discovery Day

Fall 2019 Characterizing Seismic Events through Data Analytics
Industrial Sponsor: Nevada National Security Site, Las Vegas, NV
Description and results

Research Project in Industrial Mathematics - Capstone
Students:
Kasey Friedenreich ('19) DB BS Computational Mathematic/Daytona Elect Comp Eng Minor
Joseph Uy ('21) DB BS Computational Mathematic/Global Conflict Studies/Daytona Military
Kade Mahoney ('20) DB BS Computational Mathematic/Daytona Physics Minor

Description: The Signal Processing and Applied Mathematics research group at the Nevada National Security Site, is seeking to collaborate with students at Embry-Riddle Aeronautical University to develop advanced data analytics methods for characterizing seismic events in the southwest United States as near-field earthquakes, far-field earthquakes, or non-natural seismic events, using publicly available seismic data.

Students performed independent research on theory of seismic activities and data available. Learned how to read seismic data, determine location, distances, and original magnitude. Collected additional data of known events for comparison and testing purposes. With the given data for 5 stations and 30 days history with interval of one minute, there was a large amount of data to be processed, filtered, and visualized. Students have located and characterized manually all events, approximately 90 events in the given 30 days period.

Major outcomes:

  • Kasey Friedenreich is currently an Electrical Engineer at Northrop Grumman Aerospace Systems
  • Kade Mahoney is currently an Associate Software Engineer at Northrop Grumman Aerospace Systems

Fall 2018 - Spring 2019 Predictive Analytics in Child Welfare
Industrial Sponsor: Partnership for Strong Families, Gainesville, FL
This project was supported by ERAU IGNITE grant
Description and results

Students:
Research Project in Industrial Mathematics - Capstone
Daniel Oldham ('19) DB BS Computational Mathematic/Daytona Appl Meteor Minor
Maegan Revak ('19) DB BS Computational Mathematic
Orobosa Ero ('19) DB BS Computational Mathematic/Daytona Business Admin Minor

Research Project in Industrial Mathematics
Daniel Oldham ('19) DB BS Computational Mathematic/Daytona Appl Meteor Minor (Fall 2018)
Betiay Babacan ('20) DB BS Astronomy & Astrophysics/2nd Major Computational Math
Geoffrey Mount ('19) DB BS Computer Engineering/Daytona Applied Math Minor
Nathan Foster ('21) DB BD Computer Science

Description: The Partnership for Strong Families (PSF) is a child welfare organization headquartered in Gainesville, Florida helping to serve 13 counties in northern Florida. DCF estimates that, within PSF's area, approximately 45 children are removed every month from their parents' (or guardians') care. There is a clear need to identify, as early as possible, children who are at risk. The purpose of this project is to examine removals within PSF's area over the last 7 years and to potentially identify factors that lead to a child's re-entry into the state shelter system.

Students successfully used statistical analysis, data mining, and machine learning techniques to determine multiple factors in child welfare service records that could lead to a child entering the foster care system multiple times. The factors included ages, removal types, disabilities, demographics, case details, relatives, and caregivers involved. Students also built multiple machine learning models and prediction schemes that facilitated further understanding of statistically significant insights about the cases.

Major outcomes:

Results were presented by:
Daniel Oldham at ERAU STUDENT RESEARCH SYMPOSIUM (SRS), November 19, 2018, Daytona Beach, FL
Daniel Oldham at Florida Undergraduate Research Conference, February 22-23, 2019, Jacksonville, FL
Daniel Oldham at National Conference on Undergraduate Research, April 10-13, 2019, Atlanta, GA
Nathan Foster and Daniel Oldham at 2019 ERAU Discovery Day

Results were published:
Oldham, D., Foster, N., & Berezovski, M. (2019). Data Mining and Machine Learning to Improve Northern Florida’s Foster Care System. Beyond: Undergraduate Research Journal, 3(1), 3.

News article about the project:
Data Science Offers New Tools for Understanding Foster Care Outcomes

  • Daniel Oldham got Research Scholars Award
  • Daniel Oldham currently is Data Engineer at MassMutual
  • Daniel Oldham is currently persuing his Master degree in Database Management & Business Intelligence at Boston University
  • Geoffrey Mount currently is Computer Firmware Engineer at Cyient Inc
  • Orobosa Ero currently is Data Analyst at Nigeria federal budget office

Spring 2019 Satellite-Image Detection of Ships with Convolutional Neural Network
Description and results

Research Project in Industrial Mathematics - Capstone
Clayton Birchenough ('19) DB BS Aerospace Engineering/2nd Major Computational Math

Description: A convolutional neural network was built to provide automatic ship detection and localization from satellite images. The challenge of solving for the parameters of the neural network is a non-convex optimization problem with acceptable solutions and many deceptively acceptable solutions. To avoid deceptively acceptable solutions, different learning rate parameters, data augmentation methods, and neuron dropout rates were explored when training the network. Additionally, the effects of the number and order of convolutional, max pooling, and fully connected layers were varied to investigate the impacts on training and results.

Major outcomes:

  • Clayton Birchenough currently is Associate Engineer at Aerojet Rocketdyne

Spring 2019 Characterizing Seismic Events through Data Analytics
Industrial Sponsor: Nevada National Security Site, Las Vegas, NV
Description and results

Research Project in Industrial Mathematics
Students:
Jessica Haselwood ('21) DB BS Aerospace Engineering/Daytona Applied Math Minor
Roger Acchione ('20) DB BS Aerospace Engineering/2nd Major Computational Math
Nikolaus Rentzke ('21) DB BS Meteorology/2nd Major Computational Math
Nathaniel Arzola Lilly ('21) DB BS Mechanical Engineering/Daytona Applied Math Minor
Dhairya Chokshi ('21) DB BS Astronomy & Astrophysics/Daytona Applied Math Minor
Paige Rasmussen ('21) DB BS Computational Mathematic

Description: The Signal Processing and Applied Mathematics research group at the Nevada National Security Site, is seeking to collaborate with students at Embry-Riddle Aeronautical University to develop advanced data analytics methods for characterizing seismic events in the southwest United States as near-field earthquakes, far-field earthquakes, or non-natural seismic events, using publicly available seismic data.

Students performed independent research on theory of seismic activities and data available. Learned how to read seismic data, determine location, distances, and original magnitude. Collected additional data of known events for comparison and testing purposes. With the given data for 5 stations and 30 days history with interval of one minute, there was a large amount of data to be processed, filtered, and visualized. Students have located and characterized manually all events, approximately 90 events in the given 30 days period.

Major outcomes:

  • Nikolaus Rentzke got internship with NOAA Hurricane Research Division for Summer 2019 and Summer 2020
  • Jessica Haselwood got internship for Summer 2019 and Summer 2020
  • Paige Rasmussen got internship at Lockheed Martin for Summer 2019 and Summer 2020

Spring 2019 Unmanned Aerial Vehicle (UAV) DOF Dynamic Simulation Environment
Industrial Sponsor: Embedded Control Designs, MicaPlex, Daytona Beach, FL
Description and results

Research Project in Industrial Mathematics
Students:
Philip Giuliano ('21) DB BS Aerospace Engineering
Christopher Gutierrez ('20) DB BS Aerospace Engineering/Applied Math Minor/ CAD/CAM Minor
Eric Osorio ('19) DB BS Mechanical Engineering/Applied Math Minor
Eugenie Fontaine ('21) DB BS Aerospace Engineering Applied Math Minor/ Astronomy Minor
Nicolas Prulhiere ('20) DB BS Aerospace Engineering

Description: The goal of this project is the development of a 6 DOF dynamic simulation environment. This simulation environment will play an integral role in the development of flight software and mission planning for standard operations as well as R&D.

Students was able to create a completely software-based UAV simulation by utilizing a digital, on-board computer called ArduCopter and a 3D game engine, Unity, to test the success rate of a mission for various UAV models. The goal is to display the “thought processes” of ArduCopter and the actual behavior of the simulated UAV model. This data is analyzed to see the percent error between both data sets to determine a mission’s success rate. The data collected from the 3D simulation then used by ArduCopter to make necessary corrections and increase the chance of a successful mission.

Major outcomes:

  • Results were presented at ERAU COAS Math Department IAB meeting in 2019
  • Results were presented at 2019 ERAU Discovery Day
  • Eugenie Fontaine got internship as Systems Engineering intern with Boeing for Summer 2019 and Summer 2020
  • Christopher Gutierrez got internship as Test Engineer Intern at Northrop Grumman for Summer 2020

Spring 2019 Flying Routes Optimization
Industrial Sponsor: OneSky, MicaPlex, Daytona Beach, FL
Description and results

Students:
Research Project in Industrial Mathematics
Ada Chika ('19) DB BS Aerospace Engineering/2nd Major Computational Math/Flight Minor
Nicholas Parga ('21) DB BS Aerospace Engineering/2nd Major Computational Math
Timothy Mitchell ('19) DB BS Aerospace Engineering/2nd Major Computational Math
Ian Mungovan ('20) DB BS Aerospace Engineering/ Astronomy Minor
Ian Young ('21) DB BS Aerospace Engineering/ Space Studies Minor

Description: The ultimate goal for the OneSky Optimization project was to create a new fleet optimizer that works across all of the OneSky Flight five established private jet brands: Flexjet, Sentient Jet, SkyJet, PrivateFly, and Sirio. There are industry-specific rules and business-specific requirements that ERAU team working on this project will discuss with members of the OneSky Innovation Center in the MicaPlex.

Students successfully developed and built the new optimization algorithm using, by their choice, a modified version of Dijkstra’s algorithm to identify the most profitable routes for any requested trip. Algorithm includes connection to OneSky SQL server retrieving all the possible flight connections for each possible aircraft, identification of all viable flights for each leg considering constraints, assignment dollar value to each alternative and operational time constraints. The output is the most profitable route option: optimal trade-off between money and time without compromising quality. Students signed IP release to have access to SQL data base.

Major outcomes:

  • Results were presented at 2019 ERAU Discovery Day
  • Results were presented at ERAU COAS Math Department IAB meeting in 2019
  • Jose Gachancipa Parga got internship with Airbus for Summer 2019 and Summer 2020
  • Timothy Mitchell currently is Software Engineer at Wells Fargo

Spring 2018 Quantifying Uncertainties in Image Segmentation
Industrial Sponsor: Nevada National Security Site, Las Vegas, NV
Description and results

Research Project in Industrial Mathematics
Students:
Tori Hoff ('18) DB BS Computational Mathematic/Daytona Business Admin Minor
Jean-Lucien Gionet ('20) DB BS Aerospace Engineering/ Applied Math Minor/ Comp Math Minor

Description: The Signal Processing and Applied Mathematics research group at the Nevada National Security Site (NNSS) partnered with students at ERAU to characterize the effects of user interaction on supervised image segmentation.

Students were provided with a new statistical tool for image segmentation, called Locally Adaptive Discriminant Analysis (LADA) which has three primary user inputs, the training data, the window size (WS), and nearest neighbor (NN) values. The primary research objective was to determine the sensitivity of the tool in regards to the user inputs with regard to all other inputs and provide a set of parameters as a guide to optimize the results of segmentation with regards to the boundary definition between different classes within an acceptable margin of error. Students come up with recommendation on parameters and analysis of inputs mutual effect. Another important result was the identification of the failure in the provided application: for small WS and NN values the program was unable to handle the calculations required to output the appropriate matrices.

Major outcomes:

  • Results were presented at ERAU COAS Math Department IAB meeting in 2018
  • Jean-Lucien Gionet got internship with Northrop Grumman for Summer 2018 and Summer 2019
  • Jean-Lucien Gionet currently is a Systems engineer level 2 for Northrop Grumman Aerospace Systems
  • Tory Hoff got internship with NNSS for summer 2018
    Results were published in: Luttman, A., Catenacci, J., Constantino, D., Hoff, T., Jackson, E., Putman, B., ... & Hoeller, M. (2018). Dynamic Test Prediction and Characterization through Modeling-Informed, Multi-Source Data Fusion, NLV-006-17, Year 2 of 3 (No. DOE/NV/03624-0246). Nevada National Security Site/Mission Support and Test Services LLC.
  • Tory Hoff is currently pursuing the PhD at Georgia Tech in Quantitative Psychology

Spring 2018 Data Analysis for Partnership For Strong Families
Industrial Sponsor: Partnership for Strong Families, Gainesville, FL
Description and results

Students:
Research Project in Industrial Mathematics - Capstone
Tori Hoff ('18) DB BS Computational Mathematic/Daytona Business Admin Minor
Research Project in Industrial Mathematics
Cynthia Butcher ('20) DB BS Astronomy & Astrophysics/Applied Math Minor
Maegan Revak ('19) DB BS Computational Mathematic

Description: The Partnership for Strong Families (PSF) is a child welfare organization headquartered in Gainesville, Florida helping to serve 13 counties in northern Florida. DCF estimates that, within PSF's area, approximately 45 children are removed every month from their parents' (or guardians') care. There is a clear need to identify, as early as possible, children who are at risk.

The purpose of this project is to study the data provided by Partnership for Strong Families (PSF) and identify any factors that could lead to a child being removed from his/her home multiple times.

Major outcomes:

  • Grace Butcher and Maegan Revak got IGNITE grant to continue the project for 2018-2019 academic year
  • Results were presented at ERAU COAS Math Department IAB meeting

Spring 2017 Mie Scattering Diagnostic
Industrial Sponsor: Nevada National Security Site, Las Vegas, NV
This project was supported by PIC Math program
Description and results

PICMath course - Research Project in Industrial Mathematics
Students:
Tilden Roberson ('19) DB BS Aerospace Engineering/ Applied Math Minor ('21) DB MS Aerospace Engineering
Clayton Birchenough ('19) DB BS Aerospace Engineering/2nd Major Computational Math
Arjunsinh Nakum ('20) DB BS Astronomy & Astrophysics/ Comp Science Minor
Joao Rocha Belmonte ('19) DB BS Mechanical Engineering/ Applied Math Minor
Sophie Jorgensen ('20) DB BS Aerospace Engineering/ Applied Math Minor/ Comp Math Minor

Description: The Signal Processing and Applied Mathematics Research Group at the Nevada National Security Site teamed up with Embry-Riddle Aeronautical University (ERAU) to collaborate on a research project under the framework of PIC math program with challenge to make a recommendation about whether to use a technique, used in the air quality industry, called Mie scattering, and repurpose this method to measure particle sizes that are emitted from a metal surface when it's shocked by explosives.

Using simulated data derived from Mie scattering theory and existing codes provided by NNSS students validated the simulated measurement system. The construction data procedure was implemented with an additional choice of discretization technique: randomly distributed particle radii and incrementally discretized particle radii. The critical regions of sensors position were determined.

Major outcomes:

  • Team presented results at 2017 MathFest as poster presentation
  • Results were presented at ERAU campus show case
  • Results were presented at 2018 ERAU Discovery Day
  • Clayton Birchenough won 2nd place for poster presentation at 2018 ERAU Discovery Day
  • Clayton Birchenough got internship with NNSS for summer 2017 and 2018.
  • Results were published in: Kasey Bray, Clayton Birchenough, Marylesa Howard, and Aaron Luttman. (2017) Mie scattering analysis, National Security Technologies, LLC internal report.
  • Clayton Birchenough currently is Associate Engineer at Aerojet Rocketdyne
  • Tilden Roberson got CO-OP with NASA’s Armstrong Flight Research Center for fall 2017
  • Tilden Roberson graduated ERAU with Master Degree in Aerospace Engineering at ERAU in 2021
  • Joao Rocha Belmonte got internship in Germany with MTU Aero Engines for fall 2017
  • Joao Rocha Belmonte is currently persuing his Master Degree in Mechanical Engineering at ERAU