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Daniel Guggenheim School of Aerospace Engineering

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https://hdl.handle.net/1853/70742

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College of Engineering

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Aerospace Design Group

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Aerospace Systems Design Laboratory (ASDL)

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Air Transportation Laboratory

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Cognitive Engineering Center

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Space Systems Design Laboratory (SSDL)

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https://finding-aids.library.gatech.edu/agents/corporate_entities/106

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Publication Search Results

Now showing 1 - 10 of 1432

Optimization-based methods for deterministic and stochastic control: Algorithmic development, analysis and applications on mechanical systems & fields

(Georgia Institute of Technology, 2019-12-17) Boutselis, Georgios

Developing efficient control algorithms for practical scenarios remains a key challenge for the scientific community. Towards this goal, optimal control theory has been widely employed over the past decades, with applications both in simulated and real environments. Unfortunately, standard model-based approaches become highly ineffective when modeling accuracy degrades. This may stem from erroneous estimates of physical parameters (e.g., friction coefficients, moments of inertia), or dynamics components which are inherently hard to model. System uncertainty should therefore be properly handled within control methodologies for both theoretical and practical purposes. Of equal importance are state and control constraints, which must be effectively handled for safety critical systems. To proceed, the majority of works in controls and reinforcement learning literature deals with systems lying in finite-dimensional Euclidean spaces. For many interesting applications in aerospace engineering, robotics and physics, however, we must often consider dynamics with more challenging configuration spaces. These include systems evolving on differentiable manifolds, as well as systems described by stochastic partial differential equations. Some problem examples of the former case are spacecraft attitude control, modeling of elastic beams and control of quantum spin systems. Regarding the latter, we have control of thermal/fluid flows, chemical reactors and advanced batteries. This work attempts to address the challenges mentioned above. We will develop numerical optimal control methods that explicitly incorporate modeling uncertainty, as well as deterministic and probabilistic constraints into prediction and decision making. Our iterative schemes provide scalability by relying on dynamic programming principles as well as sampling-based techniques. Depending upon different problem setups, we will handle uncertainty by employing suitable concepts from machine learning and uncertainty quantification theory. Moreover, we will show that well-known numerical control methods can be extended for mechanical systems evolving on manifolds, and dynamics described by stochastic partial differential equations. Our algorithmic derivations utilize key concepts from optimal control and optimization theory, and in some cases, theoretical results will be provided on the convergence properties of the proposed methods. The effectiveness and applicability of our approach are highlighted by substantial numerical results on simulated test cases.
Multi-mission sizing and selection methodology for space habitat subsystems

(Georgia Institute of Technology, 2019-12-11) Boutaud, Agathe Kathia

Future space missions aim to set up exploration missions in further space and establish settlements on other celestial bodies like the Moon or Mars. In this context, subsystem sizing and selection is crucial, not only because resource management is critical for the astronauts’ survival, but also because subsystems can account for more than 20% of the total mass of the habitat, so reducing their size can greatly impact the cost of the mission. A few tools already exist to size space habitat subsystems and assess their performance. However, these tools are either very high-fidelity and very slow or instantaneous but steady-state. Steady-state tools do not allow to take risks or mission variations into account and the dynamic, slower tools are less performing at helping stakeholders evaluate the impact of technology trade-offs because of their long running time. Faster sizing tools would also allow to implement additional capabilities, such as multi-mission sizing, which could be used to develop lunar or martian settlements. These tools are also used in the context of point-based design, which focuses on the development of one design throughout the process. Such approach can lead to a sub-optimal design because the selection of an alternative is made early in the design process, based on low-fidelity analyses. In addition, because the costs and design choices are committed early in the design process, requirements or design changes can have very significant cost consequences. This research proposes a new sizing capability, developed using HabNet [1], a dynamic space habitat simulation tool. It is faster than existing dynamic sizing tools and it allowed to develop a multi-mission sizing methodology using Design Space Exploration. Finally, leveraging the faster sizing tool developed to create surrogate models for the size of the elements in the habitat, it was shown that trade-off analyses can be used to support set-based design during the conceptual design phase. Consequently, the methodology proposed is faster than what is currently used to size and select space habitat subsystem technologies. It gives more insight to the user because it can perform instantaneous trade-offs. However, the quality of the surrogate models generated is not sufficient to validate the multi-mission sizing method and environment developed during this thesis. This methodology could be used as a basis for the development of a set-based design method for space habitats. Numerous capabilities, including the evaluation of the impact of disruptions or the level of uncertainty associated with the various alternatives considered, could be easily implemented and added to the existing tool.
X-ray Pulsar Navigation Instrument Performance and Scale Analysis

(Georgia Institute of Technology, 2019-12-06) Payne, Jacob Hurrell

This thesis investigates instruments for autonomous satellite navigation using measurements of X-ray emissions from millisecond pulsars. A manifestation of an instrument for this purpose, called the Neutron star Interior Composition Explorer (NICER), was launched to the International Space Station in 2017. The NICER instrument was designed to observe X-ray emissions from neutron stars for astrophysics research, and is out of scale in terms of volume, power consumption, mass and mechanical complexity to be useful for small satellite missions. This work surveys the range of existing X-ray observation missions to tabulate collecting areas, focal lengths, and optical configurations from milestone missions which describe the evolution of the state of the art in X-ray observatories. A navigation demonstration experiment, called the Station Explorer for X-ray Timing and Navigation Technology (SEXTANT), was conducted using the NICER instrument. The experimental performance observed from NICER through the SEXTANT navigation demonstration is compared to theoretical predictions established by existing formulations. It is concluded that SEXTANT benefits from soft band (0.3-4 keV) exposure to achieve better accuracy than predicted by theoretical lower bounds. Additionally, investigation is presented on the readiness of a navigation instrument for small satellites using compound refractive lensing (CRL) and derived designs. X-ray refraction achieves a much shorter focal length than grazing incidence optics at the expense of signal attenuation in the lens material. Performance estimates and previous experimental results are presented as a baseline for physical prototypes and hardware testing to support future development of a physical instrument. The technological hurdle that will enable this tool is manufacturing precise lenses on a 3-micron scale from materials like beryllium with low atomic mass. Recent X-ray concentrator concepts demonstrate progress towards an implementation that can support a CubeSat scale navigation instrument optimized for soft band (0.3-4 keV) X-rays.
Development of a Multidisciplinary Design Analysis Framework for Unmanned Electric Flying Wings

(Georgia Institute of Technology, 2019-12-03) Whitmore, William Valentin

Small-scale subsonic unmanned aerial vehicles have become common tools in both military and civil applications. A vehicle configuration of special interest is the flying wing (aka all-wing or tailless aircraft). This configuration can potentially reduce drag, increase structural efficiency, and decrease detectability. When combined with an electric propulsion system, it produces no observable emissions and possesses fewer maintenance issues. Unfortunately, strong couplings between disciplinary analyses hinder the design of unmanned electric flying wings. In particular, achieving adequate stability characteristics degrades the aerodynamic efficiency of the vehicle, and constrains the available volume in which subsystem components may be placed. Exploiting the potential advantages of electric flying wings therefore necessitates a multidisciplinary perspective. In order to overcome the identified challenges of unmanned electric flying wing design, a multidisciplinary design analysis framework was conceptualized, implemented, and evaluated. The Python-based framework synthesizes automated analysis modules that model geometry, weight distribution, electric propulsion, aerodynamics, stability, and performance. Virtual experiments demonstrated the framework’s utility in quickly exploring a wide design space and assessing design robustness. Two important stand-alone contributions developed for the framework are (1) an algorithm for densely packing battery cells within a wing shape and (2) a parametric electric propulsion analysis code. In short, the framework supports the design of small-scale (i.e. 0-55lb weight range) subsonic unmanned electric flying wings with a host of valuable capabilities that were previously unavailable within traditional design methods.
Identification of Instantaneous Anomalies in General Aviation Operations using Energy Metrics

(Georgia Institute of Technology, 2019-12) Puranik, Tejas G. ; Mavris, Dimitri N.

Quantification and improvement of safety is one of the most important objectives among the General Aviation community. In recent years, machine learning techniques have emerged as an important enabler in the data-driven safety enhancement of aviation operations with a number of techniques being applied to flight data to identify and isolate anomalous (and potentially unsafe) operations. Energy-based metrics provide measurable indications of the energy state of the aircraft and can be viewed as an objective currency to evaluate various safety-critical conditions across a heterogeneous fleet of aircraft and operations. In this paper, a novel method of identifying instantaneous anomalies for retrospective safety analysis in General Aviation using energy-based metrics is proposed. Each flight data record is processed by a sliding window across the multi-variate time series of evaluated metrics. A Gaussian Mixture Model using energy metrics and their variability within each window is fit in order to predict the probability of any instant during the flight being nominal. Instances during flights that deviate from the nominal are isolated to identify potential increased levels of risk. The identified anomalies are compared with traditional methods of safety assessment such as exceedance detection to highlight the benefits of the developed method. The methodology is demonstrated using flight data records from two representative aircraft for critical phases of flight.
An architecture model of the U.S. air transportation network

(Georgia Institute of Technology, 2019-11-26) Song, Kisun

For almost a century, the U.S. Air Transportation Network (ATN) has continuously and successfully adapted to its changing environment as if it were a living organism. Today, the complexity of the network encompasses various exogenous as well as endogenous factors: fuel price, socioeconomic and political climates, atmospheric conditions, varying interests of stakeholders, and growing dependence on technology, to name a few. Its sophisticated interactions among diverse factors affecting the ATN have captivated many network researchers. Some researchers have attempted to retrieve an order out of seemingly chaotic constructions, while others have analyzed historical variations in its properties to understand the ATN’s behavioral mechanisms. However, its mathematical representation led by the known components and rules is yet to be developed. Thus, this thesis develops an architecture model of the ATN that mathematically represents the components and rules with realism. In the model, the network evolves in a virtual environment comprising three time-variant components – demand, airport, and aircraft technology – built upon extensive realistic datasets. Then the network is constructed by the active agents – airlines – performing multi-tiered network evolutionary processes and evolves into a strong hub-and-spoke (H&S) structure network that mimics the function of its reference: real-world ATN. The validated model provides various opportunities to conduct extensive analyses and studies on the past, current, and future of the ATN. Finally, a case study has been performed: forecasting the future ATN disruption caused by the technological revolution of civil supersonic transports. It provided an opportunity to experience the exploratory and interpretative capability of the architecture model, which shed light on performing future researches with better realism.
Ignition, topology, and growth of turbulent premixed flames in supersonic flows

(Georgia Institute of Technology, 2019-11-12) Ochs, Bradley Alan

Supersonic combustion ramjets (scramjets) are currently the most efficient combustor technology for air breathing hypersonic flight, however, lack of fundamental understanding and numerous engineering challenges hinder regular deployment of these devices. This work addresses scramjet-relevant knowledge gaps in supersonic turbulent premixed combustion, including laser ignition, numerical modeling, and flame-compressibility interaction. One of the main contributions of this work is introduction of a new turbulent premixed flame arrangement where flame-compressibility interaction can be systematically explored: flame kernels in an expanding flow field. The scramjet flow path is replaced by a simplified channel geometry with a well characterized mean flow acceleration that mimics flow field expansion typically imposed on scramjet combustors to avoid thermal choking. Spherically expanding flames are created via laser ignition and subsequent flame growth and morphology are investigated using combined physical and numerical experiments. Pressure-density misalignment due to flame-compressibility interaction produces vorticity at the flame surface through baroclinic torque, i.e. flame-compressibility interaction acts like a turbulence source. The flame ultimately evolves into a reacting vortex ring that increases the flame speed and enhances reactant consumption. To explore the relative importance of turbulence and compressibility on flame dynamics, the Mach number (M=1.5,1.75,2), equivalence ratio (φ= 1.0,0.9,0.8,0.7), and root-mean-squared turbulent velocity (u'=3.98,4.14,4.45 m/s) are varied systematically. This work also introduces flame kernels in an expanding flow field as a canonical numerical validation test case for flame-compressibility interaction. Inaccuracies in simulation results are easily identified due to high flow velocity and simplicity of the problem. The numerical setup and models are scrutinized to minimize errors. Using the appropriately verified numerical models, simulation results show very reasonable agreement with experimental data. Validated simulations are instrumental in enhancing understanding of the underlying physics of supersonic flame kernels. Laser ignition studies in supersonic flows have historically focused on ignition of non-premixed fuels within cavity flame holders. This work introduces a far simpler and more tractable problem: laser ignition of a fully premixed supersonic gas. Ignition experiments with a range of laser settings are performed to determine supersonic breakdown and ignition probabilities, length of time the ignition event influences flame growth, and Mach number influence on the ignition process. The ignition event has a long-lasting effect on kernel growth, but the influence can be minimized by properly selecting the laser energy. Mach number has a minimal impact on the ignition process, but does affect the initial kernel shape due to flow field variations with Mach number. Kernel growth matches low speed studies closely at early times, but deviates at later times due to vortex ring topology. It is not obvious how the turbulent flame speed will scale for flows with mean compressibility. Therefore, the combined physical and numerical experiments are leveraged to explore this question. The vortex ring causes significant errors in the line of sight-measured burned volume, hence correction factors to convert from line of sight to volumetric measurements are presented. Conditions for displacement and consumption speed equivalency are shown to depend heavily on the particular diagnostic used; which progress variable isocontour is measured and where it is measured within the flame brush must be considered carefully during interpretation of experimental data. Scaling with the RMS turbulent velocity cannot collapse these flame speed data, i.e. previously established flame speed scalings are inappropriate for flames interacting with compressibility. Drawing motivation from vortex ring literature, a new flame speed scaling based on the ring propagation velocity is proposed. The proposed scaling collapses the data and produces a nearly linear scaling regime, which suggests turbulence plays a secondary role to the hydrodynamic instability created by flame-compressibility interaction. In summary, flame kernels are a new and effective canonical configuration for exploring flame-compressibility interactions in supersonic flows.
Using sample-based continuation techniques to efficiently compute subspace reachable sets and Pareto surfaces

(Georgia Institute of Technology, 2019-11-11) Brew, Julian

For a given continuous-time dynamical system with control input constraints and prescribed state boundary conditions, one can compute the reachable set at a specified time horizon. Forward reachable sets contain all states that can be reached using a feasible control policy at the specified time horizon. Alternatively, backwards reachable sets contain all initial states that can reach the prescribed state boundary condition using a feasible control policy at the specified time horizon. The computation of reachable sets has been applied to many problems such as vehicle collision avoidance, operational safety planning, system capability demonstration, and even economic modeling and weather forecasting. However, computing reachable volumes for general nonlinear systems is very difficult to do both accurately and efficiently. The first contribution of this thesis investigates computational techniques for alleviating the curse of dimensionality by computing reachable sets on subspaces of the full state dimension and computing point solutions for the reachable set boundary. To compute these point solutions, optimal control problems are reduced to initial value problems using continuation methods and then solved. The sample-based continuation techniques are computationally efficient in that they are easily parallelizable. However, the distribution of samples on the reachable set boundary is not directly controlled. The second contribution presents necessary conditions for distributed computation convergence, as well as necessary conditions for curvature- or uniform coverage-based sampling methods. Solutions to multi-objective optimization problems are generally defined using a set of feasible solutions such that for any one objective to improve it is necessary for other objectives to degrade. This suggests there is a connection between the two fields with the potential of cross-fertilization of computational techniques and theory. The third contribution explores analytical connections between reachability theory and multi-objective optimization with investigation into properties, constraints, and special cases.
A reduced-order modeling methodology for the multidisciplinary design and analysis of boundary layer ingestion configurations

(Georgia Institute of Technology, 2019-11-08) Bozeman, Michael Dwain

In response to the increasingly stringent requirements for subsonic transport aircraft, NASA has established aggressive goals for the noise, emissions, and fuel burn of the next generations of aircraft. This has led to the investigation of a variety of unconventional configurations and new technologies. Boundary Layer Ingestion (BLI) propulsion has been identified as a promising technology to reduce fuel burn. Preliminary studies show that BLI propulsion can offer 3-12% reduction in fuel burn, depending on the configuration. Traditionally, the design and analysis of the airframe and propulsion system has been performed in a decoupled manner. For BLI configurations, the propulsion system is tightly integrated into the airframe resulting in strong interactions between the airframe aerodynamics and propulsion system performance. As a result, the design and analysis of BLI configurations requires coupled multidisciplinary analysis (MDA) consisting of an aerodynamic analysis in an iterative loop with a propulsion system analysis. This is a very expensive analysis considering the requirement for high-fidelity models. Additionally, the design of highly-coupled configurations cannot rely solely on intuition to make design decisions. Advanced methods including Multidisciplinary Analysis and Optimization (MDAO) and design space exploration are needed to allow for the design decisions to be made based directly on a system-level objective (e.g., fuel burn) and to allow for design studies to provide insight into the multidisciplinary trades associated with BLI configurations. However, MDAO and design space exploration using coupled, high-fidelity analysis models are not practical. In this work, reduced-order modeling (ROM) is proposed as a potential solution to reduce the computational cost associated with the coupled MDA of BLI configurations and to enable these advanced design methods. An interpolation-based POD ROM is developed based on the CFD analysis to allow for predictions of the aerodynamics over a range of propulsor operating conditions for a simplified tail-cone thruster (TCT) configuration. The resulting ROM is then coupled to a propulsion model to perform ROM-based, coupled MDA. Finally, the ROM-based, coupled MDA approach is employed for coupled MDAO to assess the performance benefit offered relative to equivalent CFD- and adjoint-based approaches. The results show that the ROM-based, coupled MDA approach offers an improvement in performance relative to the current state of the art. Relative to the equivalent CFD-based approach, the ROM-based, coupled MDA method demonstrated significant computational savings for even a single optimization. However, the ROM-based approach requires multiple optimizations to offer a computational benefit over the adjoint-based approach. This result highlights the benefit of the proposed approach for optimization studies and design space exploration.
Optimal covariance steering: Theory and its application to autonomous driving

(Georgia Institute of Technology, 2019-11-08) Okamoto, Kazuhide

Optimal control under uncertainty has been one of the central research topics in the control community for decades. While a number of theories have been developed to control a single state from an initial state to a target state, in some situations, it is preferable to simultaneously compute control commands for multiple states that start from an initial distribution and converge to a target distribution. This dissertation aims to develop a stochastic optimal control theory that, in addition to the mean, explicitly steers the state covariance. Specifically, we focus on the control of linear time-varying (LTV) systems with additive Gaussian noise. The task is to steer a Gaussian-distributed initial system state distribution to a target Gaussian distribution, while minimizing a state and control expectation-dependent quadratic cost under probabilistic state constraints. Notice that, in such systems, the system state keeps being Gaussian distributed. Because Gaussian distributions can be fully described by the first two moments, the proposed optimal covariance steering (OCS) theory allows us to control the whole distribution of the state and quantify the effect of uncertainty without conducting Monte-Carlo simulations. We propose to use a control policy that is an affine function of filtered disturbances, which utilizes the results of convex optimization theory and efficiently finds the solution. After the OCS theory for LTV systems is introduced, we extend the theory to vehicle path planning problems. While several path planning algorithms have been proposed, many of them have dealt with deterministic dynamics or stochastic dynamics with open-loop un- certainty, i.e., the uncertainty of the system state is not controlled and, typically, increases with time due to exogenous disturbances, which may lead to the design of potentially conservative nominal paths. A typical approach to deal with disturbances is to use a lower-level local feedback controller after the nominal path is computed. This unidirectional dependence of the feedback controller on the path planner makes the nominal path unnecessarily conservative. The path-planning approach we develop based on the OCS theory computes the nominal path based on the closed-loop evolution of the system uncertainty by simultaneously optimizing the feedforward and feedback control commands. We validate the performance using numerical simulations with single and multiple vehicle path planning problems. Furthermore, we introduce an optimal covariance steering controller for linear systems with input hard constraints. As many real-world systems have input constraints (e.g., air- craft and spacecraft have minimum/maximum thrust), this problem formulation will allow us to deal with realistic scenarios. In order to incorporate input hard constraints in the OCS theory framework, we use element-wise saturation functions and limit the effect of disturbance to the control commands. We prove that this problem formulation leads to a convex programming problem and demonstrate the effectiveness using simple numerical examples. Finally, we develop the OCS-based stochastic model predictive control (CS-SMPC) theory for stochastic linear time-invariant (LTI) systems with additive Gaussian noise subject to state and control constraints. In addition to the conventional terminal cost and terminal mean constraints, we introduce terminal covariance constraints in the stochastic model predictive control theory. The OCS theory efficiently computes the control commands that satisfy the terminal covariance constraints. The key benefit of the CS-SMPC algorithm is its ability to ensure stability and recursive feasibility of the controlled system. In addition, thanks to the efficient OCS theory, the proposed CS-SMPC theory is computationally less demanding than previous SMPC approaches. In order to verify the effectiveness, the CS-SMPC approach is also applied to the problem of self-driving vehicle control under uncertainty.