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Full-Text Articles in Physical Sciences and Mathematics

Machine Learning Land Cover And Land Use Classification Of 4-Band Satellite Imagery, Lorelei Turner [*], Torrey J. Wagner, Paul Auclair, Brent T. Langhals Jan 2022

Machine Learning Land Cover And Land Use Classification Of 4-Band Satellite Imagery, Lorelei Turner [*], Torrey J. Wagner, Paul Auclair, Brent T. Langhals

Faculty Publications

Land-cover and land-use classification generates categories of terrestrial features, such as water or trees, which can be used to track how land is used. This work applies classical, ensemble and neural network machine learning algorithms to a multispectral remote sensing dataset containing 405,000 28x28 pixel image patches in 4 electromagnetic frequency bands. For each algorithm, model metrics and prediction execution time were evaluated, resulting in two families of models; fast and precise. The prediction time for an 81,000-patch group of predictions wasmodels, and >5s for the precise models, and there was not a significant change in prediction time when a …


Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith Dec 2021

Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith

AFIT Patents

A passive microscopic Fabry-Pérot Interferometer (FPI) sensor an optical fiber a three-dimensional microscopic optical structure formed on a cleaved tip of an optical fighter that reflects a light signal back through the optical fiber. The reflected light is altered by refractive index changes in the three-dimensional structure that is subject to at least one of: (i) thermal radiation; and (ii) volatile organic compounds.


Ionospheric F-Layer Dipole Flute Instability Effects On Electromagnetic Scattering In A Magnetohydrodynamic Plasma, Andrew J. Knisely Nov 2021

Ionospheric F-Layer Dipole Flute Instability Effects On Electromagnetic Scattering In A Magnetohydrodynamic Plasma, Andrew J. Knisely

Theses and Dissertations

The ionosphere has significant impact on radio frequency (RF) applications such as satellites, over-the-horizon radar, and commercial communication systems. The dynamic processes effecting the behavior of the ionic content leads to a variety of instabilities that adversely affect the quality of RF signals. In the F-layer ionosphere, flute instability persists, appearing as two radial regions of high and low density perturbations elongated along the earth's geomagnetic field lines. The sizes of flute structures are comparable to the wavelengths in the high frequency spectrum. The objective is to characterize the high frequency scattering of an incident field by developing a 3D …


Method Of Making Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith Oct 2021

Method Of Making Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith

AFIT Patents

A method of making passive microscopic Fabry-Pérot Interferometer (FPI) sensor includes forming a three-dimensional microscopic optical structure on a cleaved tip of an optical fiber that reflects a light signal back through the optical fiber. The reflected light is altered by refractive index changes in the three-dimensional structure that is subject to at least one of: (i) thermal radiation; and (ii) volatile organic compounds.


Efficient, Dual-Particle Directional Detection System Using A Rotating Scatter Mask, Robert Olesen, Bryan V. Egner, Darren E. Holland, Valerie Martin, James E. Bevins, Larry W. Burggraf, Buckley E. O'Day Iii Jul 2021

Efficient, Dual-Particle Directional Detection System Using A Rotating Scatter Mask, Robert Olesen, Bryan V. Egner, Darren E. Holland, Valerie Martin, James E. Bevins, Larry W. Burggraf, Buckley E. O'Day Iii

AFIT Patents

A directional radiation detection system and an omnidirectional radiation detector. The omnidirectional radiation detector detects radiation comprising at least one of: (i) gamma rays; and (ii) neutron particles. A radiation scatter mask (RSM) of the radiation detection system includes a rotating sleeve received over the omnidirectional radiation detector and rotating about a longitudinal axis. The RSM further includes: (i) a fin extending longitudinally from one side of the rotating sleeve; and (ii) a wall extending from the rotating sleeve and spaced apart from the fin having an upper end distally positioned on the rotating sleeve spaced apart or next to …


Synthetic Aperture Radar Image Recognition Of Armored Vehicles, Christopher Szul [*], Torrey J. Wagner, Brent T. Langhals Jun 2021

Synthetic Aperture Radar Image Recognition Of Armored Vehicles, Christopher Szul [*], Torrey J. Wagner, Brent T. Langhals

Faculty Publications

Synthetic Aperture Radar (SAR) imagery is not affected by weather and allows for day-and-night observations, however it can be difficult to interpret. This work applies classical and neural network machine learning techniques to perform image classification of SAR imagery. The Moving and Stationary Target Acquisition and Recognition dataset from the Air Force Research Laboratory was used, which contained 2,987 total observations of the BMP-2, BTR-70, and T-72 vehicles. Using a 75%/25% train/test split, the classical model achieved an average multi-class image recognition accuracy of 70%, while a convolutional neural network was able to achieve a 97% accuracy with lower model …


Twisted Spatiotemporal Optical Vortex Random Fields, Milo W. Hyde Iv Apr 2021

Twisted Spatiotemporal Optical Vortex Random Fields, Milo W. Hyde Iv

Faculty Publications

We present twisted spatiotemporal optical vortex (STOV) beams, which are partially coherent light sources that possess a coherent optical vortex and a random twist coupling their space and time dimensions. These beams have controllable partial coherence and transverse orbital angular momentum (OAM), which distinguishes them from the more common spatial vortex and twisted beams (known to carry longitudinal OAM) in the literature and should ultimately make them useful in applications such as optical communications and optical tweezing. We present the mathematical analysis of twisted STOV beams, deriving the mutual coherence function and linear and angular momentum densities. We simulate the …


Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith Mar 2021

Temperature-Immune Self-Referencing Fabry–Pérot Cavity Sensors, Hengky Chandrahalim, Jonathan W. Smith

AFIT Patents

A passive microscopic Fabry-Pérot Interferometer (FPI) sensor an optical fiber a three-dimensional microscopic optical structure formed on a cleaved tip of an optical fighter that reflects a light signal back through the optical fiber. The reflected light is altered by refractive index changes in the three-dimensional structure that is subject to at least one of: (i) thermal radiation; and (ii) volatile organic compounds.


Optical Study Of 2-D Detonation Wave Stability, Eulaine T. Grodner Mar 2021

Optical Study Of 2-D Detonation Wave Stability, Eulaine T. Grodner

Theses and Dissertations

Fundamental optical detonation study of detonations constricted to a 2-d plane propagation, and detonations propagating around a curve. All images were processed using modern image processing techniques. The optical techniques used were shadowgraph, Schlieren, and chemiluminescence. In the 2-Dstraight channels, it was determined wave stability was a factor of cell size. It was also determined the detonation wave thickness (area between the combustion and shockwave) was a factor of how much heat available for the detonation. For the detonations propagating around a curve, it was determined the three main classifications of wave stability were stable, unstable, and detonation wave restart. …


Computational Electromagnetic Modeling Of Metasurface Optical Devices With Defect Study, Carlos D. Diaz Mar 2021

Computational Electromagnetic Modeling Of Metasurface Optical Devices With Defect Study, Carlos D. Diaz

Theses and Dissertations

One of the first fabricated metasurface optical devices, the in-plane V-antenna lenses, were plagued by a fundamental transmission limit (<25 >). Two distinct sets of Out-of-Plane phase elements were designed with improved transmission (~60 ). These were fabricated as beamsteerers and characterized in terms of their Bidirectional Transmittance Distribution Function measured as a function of scatter angle. Experimental data from the beamsteerers was analyzed via simulations using a finite element method (FEM). The measurements showed the designed beamsteering, but also a strong zero-order diffraction not present in the simulations, which motivated this study to understand what was causing these differences. …


Studying The Conditions For Magnetic Reconnection In Solar Flares With And Without Precursor Flares, Seth H. Garland Mar 2021

Studying The Conditions For Magnetic Reconnection In Solar Flares With And Without Precursor Flares, Seth H. Garland

Theses and Dissertations

Forecasting of solar flares remains a challenge due to the limited understanding of the triggering mechanisms associated with magnetic reconnection, the primary physical phenomenon connected to these events. Consequently, methods continue to rely on the climatology of solar flare events as opposed to the underlying physics principles. Models of magnetic reconnection in the solar atmosphere places the null point of the reconnection within the corona. Though as of now the coronal magnetic field cannot be directly measured, the field is tied to the photospheric magnetic field, which can be. This study utilized data from the Solar Dynamics Observatory Helioseismic and …


Indoor Navigation Using Convolutional Neural Networks And Floor Plans, Ricky D. Anderson Mar 2021

Indoor Navigation Using Convolutional Neural Networks And Floor Plans, Ricky D. Anderson

Theses and Dissertations

The goal of this thesis is to evaluate a new indoor navigation technique by incorporating floor plans along with monocular camera images into a CNN as a potential means for identifying camera position. Building floor plans are widely available and provide potential information for localizing within the building. This work sets out to determine if a CNN can learn the architectural features of a floor plan and use that information to determine a location. In this work, a simulated indoor data set is created and used to train two CNNs. A classification CNN, which breaks up the floor plan into …


Comparison Of Conic Ray Tracing For Occlusion Determination On 3d Point Cloud Data, Henry Cho Mar 2021

Comparison Of Conic Ray Tracing For Occlusion Determination On 3d Point Cloud Data, Henry Cho

Theses and Dissertations

The US Air Force has been increasing the use of automation in its weapon systems to include the remotely piloted aircraft (RPA) platforms. The RPA career field has had issues with poor pilot retention due to job stressors. For example, RPA operators spend a lot of time and attention surveilling a suspect on the ground for many hours, so adding automation to this activity could help improve pilot retention. The research problem in this thesis attempted to automate the process of observing a ground target. This thesis presents a method termed conic ray tracing for determining visibility and occlusion of …


Laser Illuminated Imaging: Beam And Scene Deconvolution Algorithm, Benjamin W. Davis Mar 2021

Laser Illuminated Imaging: Beam And Scene Deconvolution Algorithm, Benjamin W. Davis

Theses and Dissertations

Laser illuminated imaging systems deal with several physical challenges that must be overcome to achieve high-resolution images of the target. Noise sources like background noise, photon counting noise, and laser speckle noise will all greatly affect the imaging systems ability to produce a high-resolution image. An even bigger challenge to laser illuminated imaging systems is atmospheric turbulence and the effect that it will have on the imaging system. The illuminating beam will experience tilt, causing the beam to wander off the center of the target during propagation. The light returning to the detector will similarly be affected by turbulence, and …


The Wargaming Commodity Course Of Action Automated Analysis Method, William T. Deberry Mar 2021

The Wargaming Commodity Course Of Action Automated Analysis Method, William T. Deberry

Theses and Dissertations

This research presents the Wargaming Commodity Course of Action Automated Analysis Method (WCCAAM), a novel approach to assist wargame commanders in developing and analyzing courses of action (COAs) through semi-automation of the Military Decision Making Process (MDMP). MDMP is a seven-step iterative method that commanders and mission partners follow to build an operational course of action to achieve strategic objectives. MDMP requires time, resources, and coordination – all competing items the commander weighs to make the optimal decision. WCCAAM receives the MDMP's Mission Analysis phase as input, converts the wargame into a directed graph, processes a multi-commodity flow algorithm on …


On-Chip Silicon Photonic Controllable 2 × 2 Four-Mode Waveguide Switch, Cao Dung Truong, Duy Nguyen Thi Hang, Hengky Chandrahalim, Minh Tuan Trinh Jan 2021

On-Chip Silicon Photonic Controllable 2 × 2 Four-Mode Waveguide Switch, Cao Dung Truong, Duy Nguyen Thi Hang, Hengky Chandrahalim, Minh Tuan Trinh

Faculty Publications

Multimode optical switch is a key component of mode division multiplexing in modern high-speed optical signal processing. In this paper, we introduce for the first time a novel 2 × 2 multimode switch design and demonstrate in the proof-of-concept. The device composes of four Y-multijunctions and 2 × 2 multimode interference coupler using silicon-on-insulator material with four controllable phase shifters. The shifters operate using thermo-optic effects utilizing Ti heaters enabling simultaneous switching of the optical signal between the output ports on four quasi-transverse electric modes with the electric power consumption is in order of 22.5 mW and the switching time …


3-D Fabry–Pérot Cavities Sculpted On Fiber Tips Using A Multiphoton Polymerization Process, Jonathan W. Smith, Jeremiah C. Williams, Joseph S. Suelzer, Nicholas G. Usechak, Hengky Chandrahalim Dec 2020

3-D Fabry–Pérot Cavities Sculpted On Fiber Tips Using A Multiphoton Polymerization Process, Jonathan W. Smith, Jeremiah C. Williams, Joseph S. Suelzer, Nicholas G. Usechak, Hengky Chandrahalim

Faculty Publications

This paper presents 3-D Fabry–Pérot (FP) cavities fabricated directly onto cleaved ends of low-loss optical fibers by a two-photon polymerization (2PP) process. This fabrication technique is quick, simple, and inexpensive compared to planar microfabrication processes, which enables rapid prototyping and the ability to adapt to new requirements. These devices also utilize true 3-D design freedom, facilitating the realization of microscale optical elements with challenging geometries. Three different device types were fabricated and evaluated: an unreleased single-cavity device, a released dual-cavity device, and a released hemispherical mirror dual-cavity device. Each iteration improved the quality of the FP cavity's reflection spectrum. The …


Deep Learning-Based, Passive Fault Tolerant Control Facilitated By A Taxonomy Of Cyber-Attack Effects, Dean C. Wardell Dec 2020

Deep Learning-Based, Passive Fault Tolerant Control Facilitated By A Taxonomy Of Cyber-Attack Effects, Dean C. Wardell

Theses and Dissertations

In the interest of improving the resilience of cyber-physical control systems to better operate in the presence of various cyber-attacks and/or faults, this dissertation presents a novel controller design based on deep-learning networks. This research lays out a controller design that does not rely on fault or cyber-attack detection. Being passive, the controller’s routine operating process is to take in data from the various components of the physical system, holistically assess the state of the physical system using deep-learning networks and decide the subsequent round of commands from the controller. This use of deep-learning methods in passive fault tolerant control …


Improving Closely Spaced Dim Object Detection Through Improved Multiframe Blind Deconvolution, Ronald M. Aung Sep 2020

Improving Closely Spaced Dim Object Detection Through Improved Multiframe Blind Deconvolution, Ronald M. Aung

Theses and Dissertations

This dissertation focuses on improving the ability to detect dim stellar objects that are in close proximity to a bright one, through statistical image processing using short exposure images. The goal is to improve the space domain awareness capabilities with the existing infrastructure. Two new algorithms are developed. The first one is through the Neighborhood System Blind Deconvolution where the data functions are separated into the bright object, the neighborhood system, and the background functions. The second one is through the Dimension Reduction Blind Deconvolution, where the object function is represented by the product of two matrices. Both are designed …


Autoassociative-Heteroassociative Neural Network, Claudia V. Kropas-Hughes, Steven K. Rogers, Mark E. Oxley, Matthew Kabrisky Jun 2020

Autoassociative-Heteroassociative Neural Network, Claudia V. Kropas-Hughes, Steven K. Rogers, Mark E. Oxley, Matthew Kabrisky

AFIT Patents

An efficient neural network computing technique capable of synthesizing two sets of output signal data from a single input signal data set. The method and device of the invention involves a unique integration of autoassociative and heteroassociative neural network mappings, the autoassociative neural network mapping enabling a quality metric for assessing the generalization or prediction accuracy of the heteroassociative neural network mapping.


Statistical Photo-Calibration Of Photo-Detectors For Radiometry Without Calibrated Light Sources Comprising An Arithmetic Unit To Determine A Gain And A Bias From Mean Values And Variance Values, Adrian M. Catarius, Nicholas Yielding, Stephen C. Cain, Michael D. Seal Jun 2020

Statistical Photo-Calibration Of Photo-Detectors For Radiometry Without Calibrated Light Sources Comprising An Arithmetic Unit To Determine A Gain And A Bias From Mean Values And Variance Values, Adrian M. Catarius, Nicholas Yielding, Stephen C. Cain, Michael D. Seal

AFIT Patents

Calibration of a radiometry system uses a readout circuit of a photo-detector to provide first and second measurements collected over first and second integration times, respectively, where the first and second measurements are related to a photonic input to the photo-detector by a gain and a bias. First mean and variance values are computed for a plurality of first measurements. Second mean and variance values are computed for a plurality of second measurements. The gain and bias are determined from the first and second mean values and the first and second variance values without the use of a calibrated source. …


Monte Carlo Tree Search Applied To A Modified Pursuit/Evasion Scotland Yard Game With Rendezvous Spaceflight Operation Applications, Joshua A. Daughtery Jun 2020

Monte Carlo Tree Search Applied To A Modified Pursuit/Evasion Scotland Yard Game With Rendezvous Spaceflight Operation Applications, Joshua A. Daughtery

Theses and Dissertations

This thesis takes the Scotland Yard board game and modifies its rules to mimic important aspects of space in order to facilitate the creation of artificial intelligence for space asset pursuit/evasion scenarios. Space has become a physical warfighting domain. To combat threats, an understanding of the tactics, techniques, and procedures must be captured and studied. Games and simulations are effective tools to capture data lacking historical context. Artificial intelligence and machine learning models can use simulations to develop proper defensive and offensive tactics, techniques, and procedures capable of protecting systems against potential threats. Monte Carlo Tree Search is a bandit-based …


Securing Photovoltaic (Pv) System Deployments With Data Diodes, Robert D. Larkin, Torrey J. Wagner, Barry E. Mullins Jun 2020

Securing Photovoltaic (Pv) System Deployments With Data Diodes, Robert D. Larkin, Torrey J. Wagner, Barry E. Mullins

Faculty Publications

A survey of a typical photovoltaic (PV) system with and without the cybersecurity protections of a data diode is explored. This survey includes a brief overview of Industrial Control Systems (ICS) and their relationship to the Internet of Things (IoT), Industrial Internet of Things (IIoT), and Industry 4.0 terminology. The cybersecurity features of eight data diodes are compared, and the cyber attack surface, attack scenarios, and mitigations of a typical PV system are discussed. After assessing cybersecurity, the economic considerations to purchase a data diode are considered. At 13.19 cents/kWh, the sale of 227,445 kWh is needed to fund one …


Machine Learning Modeling Of Horizontal Photovoltaics Using Weather And Location Data, Christil Pasion, Torrey J. Wagner, Clay Koschnick, Steven J. Schuldt, Jada B. Williams, Kevin Hallinan May 2020

Machine Learning Modeling Of Horizontal Photovoltaics Using Weather And Location Data, Christil Pasion, Torrey J. Wagner, Clay Koschnick, Steven J. Schuldt, Jada B. Williams, Kevin Hallinan

Faculty Publications

Solar energy is a key renewable energy source; however, its intermittent nature and potential for use in distributed systems make power prediction an important aspect of grid integration. This research analyzed a variety of machine learning techniques to predict power output for horizontal solar panels using 14 months of data collected from 12 northern-hemisphere locations. We performed our data collection and analysis in the absence of irradiation data—an approach not commonly found in prior literature. Using latitude, month, hour, ambient temperature, pressure, humidity, wind speed, and cloud ceiling as independent variables, a distributed random forest regression algorithm modeled the combined …


Learning Set Representations For Lwir In-Scene Atmospheric Compensation, Nicholas M. Westing [*], Kevin C. Gross, Brett J. Borghetti, Jacob A. Martin, Joseph Meola Apr 2020

Learning Set Representations For Lwir In-Scene Atmospheric Compensation, Nicholas M. Westing [*], Kevin C. Gross, Brett J. Borghetti, Jacob A. Martin, Joseph Meola

Faculty Publications

Atmospheric compensation of long-wave infrared (LWIR) hyperspectral imagery is investigated in this article using set representations learned by a neural network. This approach relies on synthetic at-sensor radiance data derived from collected radiosondes and a diverse database of measured emissivity spectra sampled at a range of surface temperatures. The network loss function relies on LWIR radiative transfer equations to update model parameters. Atmospheric predictions are made on a set of diverse pixels extracted from the scene, without knowledge of blackbody pixels or pixel temperatures. The network architecture utilizes permutation-invariant layers to predict a set representation, similar to the work performed …


Single-Pulse, Kerr-Effect Mueller Matrix Lidar Polarimeter, Keyser, Christian K., Richard K. Martin, Helena Lopez-Aviles, Khanh Nguyen, Arielle M. Adams, Demetrios Christodoulides Apr 2020

Single-Pulse, Kerr-Effect Mueller Matrix Lidar Polarimeter, Keyser, Christian K., Richard K. Martin, Helena Lopez-Aviles, Khanh Nguyen, Arielle M. Adams, Demetrios Christodoulides

Faculty Publications

We present a novel light detection and ranging (LiDAR) polarimeter that enables measurement of 12 of 16 sample Mueller matrix elements in a single, 10 ns pulse. The new polarization state generator (PSG) leverages Kerr phase modulation in a birefringent optical fiber, creating a probe pulse characterized by temporally varying polarization. Theoretical expressions for the Polarization State Generator (PSG) Stokes vector are derived for birefringent walk-off and no walk-off and incorporated into a time-dependent polarimeter signal model employing multiple polarization state analyzers (PSA). Polarimeter modeling compares the Kerr effect and electro-optic phase modulator–based PSG using a single Polarization State Analyzer …


Object Detection With Deep Learning To Accelerate Pose Estimation For Automated Aerial Refueling, Andrew T. Lee Mar 2020

Object Detection With Deep Learning To Accelerate Pose Estimation For Automated Aerial Refueling, Andrew T. Lee

Theses and Dissertations

Remotely piloted aircraft (RPAs) cannot currently refuel during flight because the latency between the pilot and the aircraft is too great to safely perform aerial refueling maneuvers. However, an AAR system removes this limitation by allowing the tanker to directly control the RP A. The tanker quickly finding the relative position and orientation (pose) of the approaching aircraft is the first step to create an AAR system. Previous work at AFIT demonstrates that stereo camera systems provide robust pose estimation capability. This thesis first extends that work by examining the effects of the cameras' resolution on the quality of pose …


Extracting Range Data From Images Using Focus Error, Erik M. Madden Mar 2020

Extracting Range Data From Images Using Focus Error, Erik M. Madden

Theses and Dissertations

Air-to-air refueling (AAR) has become a staple when performing long missions with aircraft. With modern technology, however, people have begun to research how to perform this task autonomously. Automated air-to-air refueling (A3R) is this exact concept. Combining many different systems, the idea is to allow computers on the aircraft to link up via the refueling boom, refuel, and detach before resuming pilot control. This document lays out one of the systems that is needed to perform A3R, namely, the system that extracts range data. While stereo cameras perform such tasks, there is interest in finding other ways of accomplishing the …


One-Dimensional Multi-Frame Blind Deconvolution Using Astronomical Data For Spatially Separable Objects, Marc R. Brown Mar 2020

One-Dimensional Multi-Frame Blind Deconvolution Using Astronomical Data For Spatially Separable Objects, Marc R. Brown

Theses and Dissertations

Blind deconvolution is used to complete missions to detect adversary assets in space and to defend the nation's assets. A new algorithm was developed to perform blind deconvolution for objects that are spatially separable using multiple frames of data. This new one-dimensional approach uses the expectation-maximization algorithm to blindly deconvolve spatially separable objects. This object separation reduces the size of the object matrix from an NxN matrix to two singular vectors of length N. With limited knowledge of the object and point spread function the one-dimensional algorithm successfully deconvolved the objects in both simulated and laboratory data.


Comparison Of Visual Simultaneous Localization And Mapping Methods For Fixed-Wing Aircraft Using Slambench2, Patrick R. Latcham Mar 2020

Comparison Of Visual Simultaneous Localization And Mapping Methods For Fixed-Wing Aircraft Using Slambench2, Patrick R. Latcham

Theses and Dissertations

Visual Simultaneous Localization and Mapping (VSLAM) algorithms have evolved rapidly in the last few years, however there has been little research evaluating current algorithm's effectiveness and limitations when applied to tracking the position of a fixed-wing aerial vehicle. This research looks to evaluate current monocular VSLAM algorithms' performance on aerial vehicle datasets using the SLAMBench2 benchmarking suite. The algorithms tested are MonoSLAM, PTAM, OKVIS, LSDSLAM, ORB-SLAM2, and SVO, all of which are built into the SLAMBench2 software. The algorithms' performance is evaluated using simulated datasets generated in the AftrBurner Engine. The datasets were designed to test the quality of each …