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Title: DEEP LEARNING IN ENGINEERING MECHANICS: WAVE PROPAGATION AND DYNAMICS IMPLEMENTATIONS
Creator: Finol Berrueta, David
Date: 2019
Description: With the advent of Artiﬁcial Intelligence research in the 1960s, the need for intelligent systems that are able to truly comprehend the...
Show moreWith the advent of Artiﬁcial Intelligence research in the 1960s, the need for intelligent systems that are able to truly comprehend the physical world around them became relevant. Signiﬁcant milestones in the realm of machine learning and, in particular, deep learning during the past decade have led to advanced data-driven models that are able to approximate complex functions from pure observations. When it comes to the application of physics-based scenarios, the vast majority of these models rely on statistical and optimization constructs, leaving minimal room in their development for the physics-driven frameworks that more traditional engineering and science ﬁelds have been developing for centuries. On the other hand, the more traditional engineering ﬁelds, such as mechanics, have evolved on a diﬀerent set of modeling tools that are mostly based on physics driven assumptions and equations, typically aided by statistical tools for uncertainty handling. Deep learning models can provide signiﬁcant implementation advantages in commercial systems over traditional engineering modeling tools in the current economies of scale, but they tend to lack the strong reliability their counterparts naturally allow. The work presented in this thesis is aimed at assessing the potential of deep learning tools, such as Convolutional Neural Networks and Long Short-Term Memory Networks, as data-driven models in engineering mechanics, with a major focus on vibration problems. In particular, two implementation cases are presented: a data driven surrogate model to a Phononic eigenvalue problem, and a physics-learning model in rigid-body dynamics scenario. Through the applications presented, this work that shows select deep learning architectures can appropriately approximate complex functions found in engineering mechanics from a system’s time history or state and generalize to set expectations outside training domains. In spatio-temporal systems, it is also that shown local learning windows along space and time can provide improved model reliability in their approximation and generalization performance
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Title: INTERACTIVE MULTIPLE MODEL ESTIMATION FOR UNMANNED AIRCRAFT SYSTEMS DETECT AND AVOID
Creator: Canolla, Adriano Carlos
Date: 2018
Description: This research presents new methods to apply safety standards to Detect and Avoid (DAA) functions for Unmanned Aircraft Systems (UAS), using...
Show moreThis research presents new methods to apply safety standards to Detect and Avoid (DAA) functions for Unmanned Aircraft Systems (UAS), using maneuvering target tracking and encounter models.Previous DAA research methods focused on predefined, linear encounter generation. The new estimation and prediction methods in this research are based on the target tracking of maneuvering intruders using Multiple Model Adaptive Estimation and a realistic random encounter generation based on an established encounter model.When tracking maneuvering intruders there is limited knowledge of changes in intruder behavior beyond the current measurement. The standard Kalman filter (KF) with a single motion model is limited in performance for such problems due to ineffective responses as the target maneuvers. In these cases, state estimation can be improved using MMAE. It is assumed that the current active dynamic model is one of a discrete set of models, each of which is the basis for a separate filter. These filters run in parallel to estimate the states of targets with changing dynamics. In practical applications of multiple model systems, one of the most popular algorithms for the MMAE is the Interacting Multiple Model (IMM) estimator. In the IMM, the regime switching is modeled by a finite state homogeneous Markov Chain. This is represented by a transition probability matrix characterizing the mode transitions. A Markov Chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the previous event.This research uses the hazard states estimates (which are derived from DAA standards) to analyze the IMM performance, and then presents a new method to predict the hazard states. To reduce the prediction error, this new method accounts for maneuvering intruders. The new prediction method uses the prediction phase in the IMM algorithm to predict the future intruder aircraft states based on the current and past sensor measurements. The estimation and prediction methods described in this thesis can help ensure safe encounters between UAS and manned aircraft in the National Airspace System through improvement of the trajectory estimation used to inform the DAA sensor certification process.
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Title: AN EXPERIMENTAL INVESTIGATION OF THE DYNAMICS OF AN INVERTED SERRATED FLAG
Creator: MURUGESAN PAZHANI, KAUSHIK
Date: 2018
Description: An experimental investigation of the role of leading-edge triangular serrations was conducted to understand the role of free leading edge in...
Show moreAn experimental investigation of the role of leading-edge triangular serrations was conducted to understand the role of free leading edge in large amplitude flapping of an inverted flag. The serrations are in the form of triangles arranged spanwise along the leading edge of the flag model. High – speed camera imaging experiment was conducted in open – loop wind tunnel at air – speeds ranging from 3.3m/s to 6.5m/s. For this velocity range, the non – dimensional bending stiffness (the ratio of bending force to the fluid inertial forces) ranges from 0.285 to 0.073. Flow visualization experiment using PIV technique was conducted for baseline flag and two serrated flags at flow velocity 4.8m/s (bending stiffness – 0.13). At a critical value of the velocity or bending stiffness, the flag oscillations transition from low amplitude asymmetric oscillations to symmetric high amplitude oscillations. This critical velocity is higher for the serrated flags indicating a reduction in the instantaneous lift force. The critical velocity was found to increase as serration height increased for a fixed number of serrations. The serrations create leading edge counter rotating eddy structures that interact with the primary tip vortex formation and breakdown process leading to changes in critical velocity, amplitude and frequency. The flapping amplitude and frequency were found to decrease as serration height increased for a fixed number of serrations. The “shallow” serrations have no effect of serrations while “tall” serrations decrease the non – dimensional flapping frequency and amplitude. The phase averaged velocity results show serrations delay leading edge vortex formations, and flow separation. This leads to decrease in pressure difference causing the serrated flag to deform less than baseline flag. Leading edge vortex formed in serrated flags were observed to be deformed compared to baseline flag leading edge vortex. Vortex deformation is due to serration induced three-dimensional flow effects. Serrated flags exhibit elongated vortical structures from flag tip instead of periodic vortex shedding in rebound phase. Streamlines used for qualitative analysis also shows, serrated flags lack periodic vortex formation and shedding during rebound phase. Using qualitative evidence from streamline plots and vorticity contour plots (elongated vortex structures) it could be stated due to change in leading edge geometry, serrated flags demonstrate a non – VIV flapping.
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Title: A Novel Remote Sensing System Using Reflected GNSS Signals
Creator: Parvizi, Roohollah
Date: 2020
Description: This dissertation presents a method to remotely sense freshwater surface ice and water using reflected signals from Global Navigation...
Show moreThis dissertation presents a method to remotely sense freshwater surface ice and water using reflected signals from Global Navigation Satellite Systems (GNSS). A portable ground-based sensor system is designed and built for collecting both scattered Global Positioning System (GPS) signals and independent validation data (lidar and camera) from the surface. GPS front-end signals are collected from both a direct receiving antenna facing upward and from a reflection-receiving antenna facing downward. Multiple data campaigns are conducted on the Lake Michigan waterfront in Chicago. A customized software receiver tests a new signal processing method to detect and acquire Global Navigation Satellite System (GNSS) signals reflected from the lake surface ice and collected by a downward-facing antenna. The method, modified differential coherent integration, multiplies time-shifted auto-correlation samples. The new method is evaluated against three conventional integration methods (coherent, incoherent, and differential integration) with signals from the direct antenna. With front-end samples from the reflection antenna, the new method is the only one of the four methods compared that acquires satellites in the reflected GPS signals, with three acquired using 10 ms of integration.The lidar surface scans are mapped with camera images and estimated reflection points to indicate the surface reflection type and to provide surface height relative to the sensors. For one satellite whose specular point is estimated to be on the ice surface, a Delay Doppler Map (DDM), signal-to-noise (SNR) ratio, and surface reflectivity (SR) are computed with the modified differential coherent integration method using the GPS. The DDM shows that, with modified differential integration, the satellite can be acquired in the reflected signal. For two satellites whose reflection points scan across ice and water over time the SNR and SR are computed over time. The SR is shown to be lower for liquid water than lake ice. This system concept may be used in the future for more complete mapping of phase changes in the cryosphere.
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Title: Modeling the Aerodynamic Response to Impulsive Active Flow Control
Creator: Asztalos, Katherine
Date: 2021
Description: In unsteady aerodynamics the response to external disturbances can depend significantly on the initial condition, and the extent to which this...
Show moreIn unsteady aerodynamics the response to external disturbances can depend significantly on the initial condition, and the extent to which this impacts the ability to model the flowfield can vary. In this work, we look to develop a model that can capture and predict the long-time response to actuation, which we suspect to be sensitive to the instantaneous state. We investigate whether a physical understanding of the short-time response to impulsive actuation can be obtained, with the goal of understanding the observed physical phenomenon present in the immediate response to this type of actuation. We find that the response to impulsive actuation is sensitive to the instantaneous wake, and that the short-time response is directly proportional to the time rate of change of the actuation input. Computational simulations of a stalled NACA 0009 airfoil subject to leading-edge synthetic jet actuation were performed. Full state information, as well as force response measurements, were collected using an immersed boundary method (IBM) numerical code. The numerical simulations performed sought to characterize the response to actuation by varying the actuation parameters, such as the strength, direction, and phase at which the onset of actuation occurs. It was found that the long-time response to actuation can be sensitive to the instantaneous wake state at the onset of actuation. The ability to extract models that describe the complex behavior of the system provides additional insight into the dominant features governing the response of such systems, as well as achieves predictive capabilities of the systems' response. The data-driven models, which are identified using variants of dynamic mode decomposition, can capture both the short- and long-time response of the system to actuation. Predictive models are identified using multiple trajectories of data corresponding to varying the phase of vortex shedding at which the onset of actuation occurs. These models achieve accurate predictions for off-design cases as well. It is also shown that multiple control objectives with the same actuator can be achieved. Classical theory aids in understanding the physics governing unsteady aerodynamic motion and the response to disturbances. Theoretical models are developed using the assumptions from classical unsteady aerodynamic theory, which provide insight into the forms that the data-driven models take. The effect of short-duration momentum injection actuation is modeled through a combination of source/sink, doublet, and vortex elements. Regardless of the precise elements used in the theoretical model, the lift response is composed of a contribution directly proportional to the rate of change of actuation strength, and a contribution that persists after the actuation burst ends that arises due to the enforcement of the Kutta condition. Methodologies that retain the physics inherent to the system by projecting the governing equations of motion onto a well-suited basis are extremely valuable for gaining physical insight and understanding into the dynamics of the flowfield. A new methodology is proposed for extracting spectral content from systems with limited data available using projection-based modeling approaches. There are challenges associated with using modal decomposition-based modeling techniques for systems exhibiting large transient dynamics due to external inputs, which is applicable in this particular instance and for related systems. The methodology presented here shows how the dynamics of this system can be understood through analysis of optimal finite-time horizon transient energy growth, applied to reduced-order models identified using actuation response data with either data-driven or physics-based models. A novel methodology is proposed to guide future experimental actuation design to achieve maximal response by considering an optimal forcing mode, identified from considering the optimal perturbation of the full unactuated system, which maximizes a given output.
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Title: MULTIYEAR AUTOMATED ANALYSIS OF AURORAL IMAGES TO CATEGORIZE IONOSPHERE IRREGULARITY LAYER
Creator: Stuart, David Jacques
Date: 2020
Description: This thesis presents a method of automated analysis of auroral all-sky images (ASIs) to determine the ionospheric layer of plasma...
Show moreThis thesis presents a method of automated analysis of auroral all-sky images (ASIs) to determine the ionospheric layer of plasma irregularities. These irregularities can perturb radio signals in an effect called scintillation, degrading and at worst preventing signal reception. One key question about scintillation-causing irregularities is whether they occur in the E or F layer of the ionosphere, whose dynamics differ.Previous studies have shown Global Positioning System (GPS) scintillation to be correlated with aurorae. The Scintillation Auroral GPS Array (SAGA) at Poker Flat Research Range, Alaska, was used to detect thousands of GPS L1 and L2C scintillation events over 2014-2015. Collocated auroral images of emissions are recorded nightly by both a keogram spectrograph (measuring intensity along a single longitude vs time) and an ASI filtered at 630.0 nm (red), 557.7 nm (green), and 427.8 nm (blue) wavelengths.In this work scattering layers are hypothesized based on optical measurements, through automated filtering of keograms followed by spectral analysis of aurorae, which tend to occur with these irregularities. A cloud detection method using the North-South keogram is implemented, where a time-averaged, intensity-corrected characteristic snapshot of cloudy times was built as a baseline response, and used as the gain in a flat field correction-like step to normalize the cloudy sky appearance. The coefficient of variation Cv is used as the test statistic to determine cloudy times. Cloud-free ASIs have the location of scintillating PRNs identified, and the ratio of red oxygen 630 nm to blue nitrogen 428 nm emissions in that direction. With an auroral model of characteristic energy, ratios above 0.5 are categorized E-Layer and ratios below F-Layer.Multiyear ASI irregularity layer determinations are used to categorize 364 of the initial 4174 SAGA scintillation events. A 77% majority of the events are hypothesized to be F-Layer based on ASI spectral classification. This disagrees with prior PFISR categorizations, which found scintillation events to be majority E-layer. This presents an outstanding question as to the possible reasons for the difference.
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Title: Inviscid Shock Propagation within a Variable-Geometry Scramjet Inlet
Creator: Grybko, Maciej
Date: 2021
Description: The study concerns the propagation of shockwaves within an inlet of a scramjet engine and effect of inlet geometry variation on performance. A...
Show moreThe study concerns the propagation of shockwaves within an inlet of a scramjet engine and effect of inlet geometry variation on performance. A Python code was developed to simulate and visualize a flowfield within a scramjet inlet, based on inviscid oblique shock theory. The program was validated against NASA Shock software, and the results differed only by round-off error (0.05%). Subsequently a geometric sensitivity study was conducted, showing that throughout acceleration from Mach 5 to Mach 20 parameters like inlet height could be varied to ensure constant number of shocks within an inlet (preventing discontinuous changes of flowfield), whereas lower wedge angle could control compression required for optimal combustion. Correspondingly, a trajectory was determined with a constraint on static pressure entering combustion chamber (100 kPa). For an arbitrary baseline inlet geometry, it was established that beyond Mach 10 the scramjet would exceed structural load limit, despite delivering sufficient conditions for rapid combustion. Nevertheless, below Mach 10 it would operate efficiently, proving that hydrocarbon-fueled scramjets can have a fixed geometry. For higher speeds, a variable geometry is a necessity.
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Title: High-integrity modeling of non-stationary Kalman Filter input error processes and application to aircraft navigation
Creator: Gallon, Elisa
Date: 2023
Description: Most navigation applications nowadays rely heavily on Global Navigation Satellite Systems (GNSSs) and inertial sensors. Both of these systems...
Show moreMost navigation applications nowadays rely heavily on Global Navigation Satellite Systems (GNSSs) and inertial sensors. Both of these systems are known to be complementary, and as such, their outputs are very often combined in an extended Kalman Filter (KF) to provide a continuous navigation solution, resistant to poor satellite geometry, as well as radio frequency interference. Additionally, recent development in safety critical applications (such as aviation) revealed the performance limitations of current algorithms (Advance Receiver Autonomous Integrity Monitoring - ARAIM) to vertical guidance down to 200 feet above the runway (LPV-200). When nominal constellations are depleted, LPV-200 can only sparsely be achieved. Exploiting satellite motion in ARAIM (for instance using a KF) could help alleviate those limitations, but would require adequate modeling of the errors, including the error's time correlation.Power Spectral Density (PSD) bounding is a methodology that provides high integrity, time correlated error models, but this approach is currently limited to stationary errors (which is rarely the case with real data), and has never been applied to navigation errors. More generally, no high integrity, time correlated error models have ever been derived for navigation errors.As a result, in the first part of this thesis, a methodology for high integrity modeling of time correlated errors is introduced. The PSD bounding methodology is extended to both stationary and non-stationary errors. In the second part of this thesis, these methodologies are applied to the 3 main error sources impacting iono-free GNSS measurements (orbit and clock errors, tropospheric errors and multipath), as well as to inertial errors.The methodology introduced in this dissertation provides high integrity time correlated error models and is applicable to any type of applications where high integrity is required (e.g. Differential GNSS - DGNSS, Aircaft Based Augmentation System - ABAS, Ground Based Augmentation System - GBAS, Space Based Augmentation System - SBAS, etc...). Additionally, the error models derived here are not only limited to high integrity applications, but could also be used in applications were the correlation over time of the errors plays an important role (such as any KF integration).In the last part of this dissertation, we focus on a specific safety critical application: aviation, and in particular ARAIM. The dissertation is concluded with an assessment of the performance improvements provided by recursive ARAIM, using those bounding dynamic error models, with respect to those models, used for baseline snapshot ARAIM. Additionally, a sensitivity analysis is performed on each of the error model parameters to assess which of them impacts the KF performance (i.e. covariance) the most.
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Title: Quantifying Localization Safety for State-of-the-Art Mobile Robot Estimation Algorithms
Creator: Abdul Hafez, Osama Mutie Fahad
Date: 2023
Description: In mobile robotics, localization safety is quantified using covariance matrix or particle spread.However, such methods are insufficient for...
Show moreIn mobile robotics, localization safety is quantified using covariance matrix or particle spread.However, such methods are insufficient for mission or life-critical applications, like Autonomous Vehicles (AVs), because they only reflect nominal sensor noise without considering sensor measurement faults. Sensor faults are unknown deterministic errors that cannot be modeled using a zero mean Gaussian distribution. Ignoring sensor faults, in such applications, might result in large localization errors, which in turn deceives other reliant systems, like the controller, leading to catastrophic consequences, such as traffic accidents for AVs. Thus, other techniques need to be used to conservatively quantify pose safety.This thesis builds upon previous research in aviation safety, or what is referred to as \textit{integrity monitoring}, to quantify localization safety for mobile robots that use state-of-the-art state estimators (as localizers).Specifically, this thesis utilizes the localization \textit{integrity risk} metric, as a measure of localization safety, which is defined as the probability of the robot's pose estimate error to lie outside pre-determined acceptable limits while an alarm is not triggered. Unlike open-sky aviation applications, where Global Navigation Satellite Systems (GNSS) signals are available, mobile robots operate in GNSS-denied, or in the best case GNSS-degraded, environments, which demands utilizing more complex set of sensors to guarantee an acceptable level of localization safety. This thesis provides a conservative measure of localization safety by rigorously upper-bounding the integrity risk while accounting for both nominal lidar noise and unmodeled lidar measurement faults.The contributions of this thesis include the design and analysis of practical integrity monitoring and failure detection procedures for mobile robots utilizing map-based particle filtering, a recursive integrity monitoring method for mobile robots utilizing map-based fixed lag smoothing for both solution-separation and chi-squared as failure detectors, the synthesis of an integrity monitoring procedure for mobile robots utilizing Extended Kalman Filter-based Simultaneous Localization And Mapping (EKF-based SLAM), and a Model Predictive Control (MPC) framework that is capable of planning mobile robot's trajectory to follow a predefined robot path while maintaining a predefined minimum level of mobile robot localization safety. The proposed methodologies are validated using both simulation and experimental results conducted in real-world urban university campus environments.
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Title: Pressure Feedback Control on a UCAS Model in Random Gusts
Creator: He, Xiaowei
Date: 2021
Description: This research focuses on efficient active flow control (AFC) of the aerodynamic loads on a generic tailless delta wing in various flow/flight...
Show moreThis research focuses on efficient active flow control (AFC) of the aerodynamic loads on a generic tailless delta wing in various flow/flight conditions, such as, flying through atmosphere gusts, fast pitching, and other rapid maneuvers that would cause the aircraft to experience unsteady aerodynamic effects. A feedback control scheme that uses the surface pressure measurements to estimate the actual aerodynamic loads that act on the aircraft is put forward, with the hypothesis that a pressure surrogate can replace the inertia-based sensors to provide the controller with faster and/or more accurate feedback signals of the real-time aerodynamic load. The control performance of the AFC actuation and conventional elevons were evaluated. Results showed that the AFC with a momentum coefficient input of 2% was equivalent to 27-deg elevon deflection in terms of roll moment change and the control derivative of the AFC is at least doubled than that of the elevons.Streamwise and cross-flow gusts were simulated in the Andrew Fejer Unsteady Wind Tunnel at IIT. A spectral feedback approach was tested by generating the horizontal velocity components of the von Karman and the Dryden turbulence spectra. The velocity components in the test section were controlled temporally and spatially to generate transverse cross-flow gusts with designated wavelengths and frequencies. Sparse surface pressure measurements on the aircraft surface were used to develop lower-order models to estimate the instantaneous aerodynamic loads using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm. The pressure-based models acted as surrogates of the aerodynamic loads to provide feedback signals to the closed-loop controller to alleviate the gust effects on the wing. The control results showed that the pressure feedback scheme was sufficient to provide feedback signals to the controller to reduce the roll moment fluctuations caused by the dynamic perturbations down to 20% comparing to 30% to 50% in previous studies.
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Title: Carrier phase multipath characterization and frequency-domain bounding
Creator: Benz, Chloe
Date: 2022
Description: Safely relying on Global Navigation Satellite Systems (GNSS) measurements for position estimation using multi-sensor navigation algorithms,...
Show moreSafely relying on Global Navigation Satellite Systems (GNSS) measurements for position estimation using multi-sensor navigation algorithms, especially in critical phases of flight – such as takeoff or landing – requires precise knowledge of the errors affecting position estimates and their extrema values at any time. This work investigates a method for characterization and power-spectral density (PSD) bounding of GNSS carrier phase multipath error intended for use in sensor fusion for aircraft navigation. In this dissertation, two methods of GNSS carrier phase multipath characterization are explored: single frequency dual antenna (DA) and single antenna dual frequency (DF). However, since not all aircraft are equipped with multiple GNSS antennas, because the DA method entails a meticulous tracking of the lever arm between the two antennas, and as multipath seen by two antennas in a short baseline configuration may cancel out, the DF method is preferred and is the main emphasis of this work. By subtracting carrier phase measurements collected by a receiver overtwo distinct frequencies, a composite measurement containing ionospheric delay and carrier phase multipath is obtained. The ionospheric delay has slower dynamics than multipath, so it is removed using a high pass filter. The filter cutoff frequency is carefully picked based on a study of ionospheric delay dynamics. The DF method is validated on a rooftop GPS carrier phase dataset, and finally, directions and considerations for its ultimate intended use on airborne collected GNSS carrier phase data are provided.
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Title: GLOBAL ESTIMATION AND ANALYSIS OF IONOSPHERIC DRIVERS WITH A DATA ASSIMILATION ALGORITHM
Creator: López Rubio, Aurora
Date: 2022
Description: This dissertation studies a data assimilation algorithm that estimates the drivers of the ionosphere-thermosphere (IT) region of the Earth....
Show moreThis dissertation studies a data assimilation algorithm that estimates the drivers of the ionosphere-thermosphere (IT) region of the Earth. The algorithm, EMPIRE (Estimating Model Parameters from Ionospheric Reverse Engineering) can estimate 2 main drivers of the ionospheric behavior: neutral winds and electric potential by ingesting mainly ionospheric densities obtained through Global Satellite System (GNSS) measurements. Additionally, the algorithm can ingest FPI (Fabry-Perot interferometer) neutral wind measurements. The contributions include 1) Vector spherical harmonic basis function for neutral wind estimation, 2) Quantification of the representation error of the estimations of the algorithm EMPIRE, 3) Analysis of Nighttime Ionospheric Localized density Enhancement (NILE) events and 4) Ingestion of global ICON (Ionospheric Connection Explorer) neutral winds measurements. The IT region in the atmosphere is characterized by having a large concentration of free ions and electrons, electromagnetic radiation and Earth's magnetic field. The behavior of the region is dominated by the solar activity, that ionizes the free electrons of the region, forming ionospheric plasma and determining its density. Unusual solar activity or any atmospheric disturbance affects the distribution of the ionospheric plasma and the behavior of the IT region. The redistribution of the ionospheric density impacts technology widely used such as telecommunication or satellite navigation, so it is increasingly important to study the IT system response. The IT behavior can be characterized by what drives its changes. Two drivers that play a key role, the ones we focus on this dissertation, are electric potential, that directly affects the charged ions in the system, and neutral winds, that refers to the velocity of the neutral particles that form the thermosphere. To quantify these drivers, measurements and climate models are available. Measurements are limited as the IT region is vast and covers the entire globe. Climate models can provide information in all the region, but they are usually not as reliable during the unusual solar activity conditions or disturbances. In this dissertation we use a data assimilation algorithm, EMPIRE, that combines both sources of data, measurements and models, to estimate the IT drivers, neutral winds and electric potential. EMPIRE ingests measurements of the plasma density rate and models the physics of the region with the ion continuity equation. The drivers are represented with basis functions and their coefficients are estimated by fitting the expansions with a Kalman filter. In previous work and use of the algorithm, the neutral winds were expanded using power series basis function for each of the components of the vector. The first contribution of the dissertation is to use a vector spherical harmonic expansion to describe the winds, allowing a continuous expansion around the globe and self-consistent components of the vector. Before, EMPIRE estimated the correction of the drivers with respect climate model values. In this work, EMPIRE is also modified to directly estimate the drivers. Then, a study of the representation error, which is the discrepancy between the true physics and the discrete model that represents the physics of EMPIRE and its quantification is done. Next, EMPIRE is used to analyze two NILE events, using the global estimation of both winds, from the first contribution, and the electric potential, derived in previous work. Finally, global estimation of winds allows us to implement the ingestion of ICON global winds in EMPIRE, in addition to the plasma density rate measurements.
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Title: Non-Hermitian Phononics
Creator: Mokhtari, Amir Ashkan
Date: 2021
Description: Non-Hermitian and open systems are those that interact with their environment by the ﬂows of energy, particles, and information. These systems...
Show moreNon-Hermitian and open systems are those that interact with their environment by the ﬂows of energy, particles, and information. These systems show rich physical behaviors such as unidirectional wave reflection, enhanced transmission, and enhanced sensitivity to external perturbations comparing to a Hermitian system. To study non-Hermitian and open systems, we first present key concepts and required mathematical tools such as the theory of linear operators, linear algebra, biorthogonality, and exceptional points. We first consider the operator properties of various phononic eigenvalue problems. The aim is to answer some fundamental questions about the eigenvalues and eigenvectors of phononic operators. These include questions about the potential real and complex nature of the eigenvalues, whether the eigenvectors form a complete basis, what are the right orthogonality relationships, and how to create a complete basis when none may exist at the outset. In doing so we present a unified understanding of the properties of the phononic eigenvalues and eigenvectors which would emerge from any numerical method employed to compute such quantities. Next, we apply the mentioned theories on the phononic operators to the problem of scattering of in-plane waves at an interface between a homogeneous medium and a layered composite. This problem is an example of a non self-adjoint operator with biorthogonal eigenvectors and a complex spectrum. Since this problem is non self-adjoint, the degeneracies in the spectrum generally represent a coalescing of both the eigenvalues and eigenvectors (exceptional points). These degeneracies appear in both the complex and real domains of the wavevector. After calculating the eigenvalues and eigenvectors, we then calculate the scattered fields through a novel application of the Betti-Rayleigh reciprocity theorem. Several numerical examples showing rich scattering phenomena are presented afterward. We also prove that energy flux conservation is a restatement of the biorthogonality relationship of the non self-adjoint operators. Finally, we discuss open elastodynamics as a subset of non-Hermitian systems. A basic concept in open systems is effective Hamiltonian. It is a Hamiltonian that acts in the space of reduced set of degrees of freedom in a system and describes only a part of the eigenvalue spectrum of the total Hamiltonian. We present the Feshbach projection operator formalism -- traditionally used for calculating effective Hamiltonians of subsystems in quantum systems -- in the context of mechanical wave propagation problems. The formalism allows for the direct formal representation of effective Hamiltonians of finite systems which are interacting with their environment. This results in a smaller set of equations which isolate the dynamics of the system from the rest of the larger problem that is usually infinite size. We then present the procedure to calculate the Green's function of effective Hamiltonian. Finally we solve the scattering problem in 1D discrete systems using the Green's function method.
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Title: REDUCED-ORDER MODELING OF UNSTEADY FLOW OVER TWO COLLINEAR PLATES AT LOW REYNOLDS NUMBERS
Creator: Almashjary, Abdulrahman N
Date: 2021
Description: Wakes of bluff bodies that exhibit unsteady behavior are a topic of great interest in the study of fluid dynamics. Vortex formation in these...
Show moreWakes of bluff bodies that exhibit unsteady behavior are a topic of great interest in the study of fluid dynamics. Vortex formation in these wakes depends significantly on the Reynolds number and the arrangement of the bluff bodies in the computation domain. To attain a comprehensive understanding of the unsteady wakes of adjacent bodies, we examine the emerged flow patterns in the wake of two bodies when subjected to different flow regimes and geometric configurations. This work aims to develop a reduced-order model that can capture the dynamics and predict the time evolution of specific parameters in the flowfield. Investigations including direct numerical simulations of two collinear plates normal to the flow were performed. Flowfield data and forces exerted on the plates were collected using a numerical code of an immersed boundary projection method (IBPM). The conducted numerical simulations pursued classifying the flow patterns by systematically varying the Reynolds number and the gap between the two plates. It was found that at small gap spacings, a typical von Karman vortex street is observed. Whereas at larger gap spacings, both a biased and a flip-flopping gap flow are detected. Prevalent coherent structures present in various flow regimes can be extracted via data-driven modeling techniques. The proper orthogonal decomposition (POD) method is used in this framework, from which projection-based reduced-order models are developed utilizing the governing equations of fluid flows. Single and broadband spectra are observed in the unsteady wake of the two-plate configuration. The amplitude and frequency of the time-evolution of the true POD modes and the predicted models are assessed using the spectral proper orthogonal decomposition (SPOD), an empirical method to extract coherent structures one frequency at a time from fluid flows. It was found that these reduced-order models are able to recover the frequency content from non-time resolved data.
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Title: Improvement and Validation of Multiyear Auroral Analysis to Categorize Scintillation Event Layer
Creator: English, Breanna R.
Date: 2022
Description: Ionospheric irregularities scintillate electromagnetic waves, such as Global Positioning System (GPS) signals, as they pass through the...
Show moreIonospheric irregularities scintillate electromagnetic waves, such as Global Positioning System (GPS) signals, as they pass through the ionosphere, especially in auroral zones. A previous method was developed to determine which layer of the ionosphere these scintillation events occurred in by analyzing optical all sky images (ASI). The results of determining the ionospheric scattering layer using the ratio of 630 nm (red) intensity to 428 nm (blue) intensity were compared to a radar-based method of determining the scintillation layer, and it was found that the results disagreed. In this work, the ASI method is critically analyzed to identify possible errors or sensitivities in the original method that might resolve the discrepancy. This is done by improving and validating the nighttime auroral cloud detection method by comparing to National Oceanic and Atmospheric Administration (NOAA) satellite cloud data. Then a sensitivity analysis is performed on the ASI method to determine which parameters of the method the results are sensitive to. The keogram cloud detection method is improved by automating the selection of the keogram time points that are used to calculate a flat-field gain correction, and by calculating the flat field gain for each year rather than calculatingit once and using it for all years of the study. Keogram cloud detection using the coefficient of variation is verified by comparing the keogram results to true sky conditions based on NOAA cloud mask data, and using detection theory to determine the optimal coefficient of variation threshold. We find that the ideal keogram threshold was 0.37 producing a disagreement rate of 22.4%. The ASI image analysis criteria tested are: the ASI azimuth and elevation mapping files, the magnetic zenith limit, the number of pixels of the ASI that are being analyzed, the duration of the scintillation event that is analyzed, and the red-to-blue ratio threshold. It is found that only changing the red-to-blue ratio threshold has a significant effect on the ASI method, with the red-to-blue ratio that minimizes the number of misattributed layers found to be 1.43.
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Title: High-latitude plasma drift structuring from a first principles ionospheric model
Creator: Kim, Heejin
Date: 2020
Description: In the high-latitude ionosphere dense plasma formations called polar cap patches are sometimes observed. These patches are often associated...
Show moreIn the high-latitude ionosphere dense plasma formations called polar cap patches are sometimes observed. These patches are often associated with ionospheric scintillation, a rapid fluctuation in the amplitude and phase of a radio signal that degrades communications and navigation systems. Predicting polar cap patch movement across the polar cap is an important subject for enabling forecasting of the scintillation.Lagrangian coherent structures (LCSs) are ridges indicating regions of maximum fluid separation in a time-varying flow. In previous studies, the Ionosphere-Thermosphere Algorithm for Lagrangian Coherent Structures (ITALCS) predicted the location of LCSs. These LCSs were shown to constrain polar cap patch source and transport regions for flow assumed to due to $\vec{E} \times \vec{B}$ plasma drift. The LCSs were predicted based on an empirical model of the high-latitude electric field for $\vec{E}$. In this thesis, the LCSs are generated using the first principles ionospheric model SAMI3 (SAMI3 is Another Model of the Ionosphere) as the model for electric field. The work relies on an understanding of various magnetic coordinate systems in space science, and includes three different approaches for attempting to generate the $\vec{E} \times \vec{B}$ drift as the flow fields that are to input to ITALCS. Finally, a representative LCS result is obtained with SAMI3 and shown to be at the high latitudes on the dayside, similar to prior work, but spanning a shorter longitudinal range.
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Title: Analysis of High-Fidelity Experiments and Simulations of the Flow in Simplified Urban Environments
Creator: Stuck, Maxime
Date: 2020
Description: The mean ﬂow and turbulence statistics of the ﬂow through a simpliﬁed urban environment, which is an active research area in order to improve...
Show moreThe mean ﬂow and turbulence statistics of the ﬂow through a simpliﬁed urban environment, which is an active research area in order to improve the knowledge of turbulent ﬂow in cities, is investigated. This is useful for civil engineering, pedestrian comfort and for health concerns caused by pollutant spreading. In this work, we provide analysis of the turbulence statistics obtained both from highly-quality stereoscopic particle image-velocimetry (SPIV) measurements (from Monnier et al.) and well-resolved large eddy simulations (LES) by Torres et al. A detailed comparison of both databases reveals the impact of the geometry of the urban array on the ﬂow characteristics and provides for a good description of the turbulent features of the ﬂow around a simpliﬁed urban environment. The most prominent features of this complex ﬂow include coherent vortical structures such as the so-called arch vortex, the horseshoe vortex, or the roof vortex. These structures of the ﬂow have been identiﬁed by an analysis of the turbulence statistics. The inﬂuence of the geometry of the urban environment (and particularly the street width and the building height) on the overall ﬂow behavior has also been studied.
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