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Daniel Guggenheim School of Aerospace Engineering
Daniel Guggenheim School of Aerospace Engineering
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ItemA Sliding-Window Matrix Pencil Method for Aeroelastic Design Optimization with Limit-Cycle Oscillation Constraints(Georgia Institute of Technology, 2023-12-15) Golla, TarunThis paper presents a new approach for constraining limit-cycle oscillations in aeroelastic design optimization. The approach builds on a gradient-oriented limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, bypassing the need for bifurcation diagrams. Previous work demonstrated the constraint using recovery rates approximated via a conservative approach. This work introduces a new approach to accurately evaluate recovery rates from transient simulations. The approach uses the matrix pencil method within a time window that slides along the time history for the quantity of interest, allowing this damping identification method to resolve amplitude-variant nonlinear effects. The new sliding-window matrix pencil method is verified with reference recovery rates from envelope finite differencing of the dynamic responses induced with a large initial perturbation of a typical aeroelastic section. Sensitivity analyses identify optimal parameters to obtain accurate recovery rates while minimizing computational costs. The new developments are then demonstrated by optimizing the typical section subject to the proposed limit-cycle oscillation constraint along with flutter and side constraints. The results are compared with previous work that solved the same optimization problem by evaluating the limit-cycle oscillation constraint using approximate recovery rates. The limit-cycle oscillation constraint based on the new sliding-window matrix pencil method allows the optimizer to achieve a less conservative design solution while satisfying the constraints. This methodology was additionally extended through the optimization of a more complex 3-variable optimization. The implementation was further ported into a modular framework within which results were verified, allowing for future extensions to this methodology. This work is anticipated to pave the way for larger-scale aeroelastic design optimizations subject to limit-cycle oscillation constraints.
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ItemA Sliding-Window Matrix Pencil Method for Aeroelastic Design Optimization with Limit-Cycle Oscillation Constraints(Georgia Institute of Technology, 2023-12-13) Golla, TarunThis thesis presents a new approach to constraining limit-cycle oscillations (LCOs) in aeroelastic design optimization. LCOs are self-excited oscillations that can develop in nonlinear aeroelastic systems experiencing flutter, and they must be avoided during operation to keep safety and performance. One approach to addressing this problem is to design the system using an optimization process that includes an LCO constraint. Previous efforts have proposed various LCO constraints for aeroelastic design optimization but have not addressed realistic design applications. This gap persists because existing LCO constraints are not oriented toward scalable gradient-based optimization algorithms. The proposed approach builds on a recent LCO constraint that bounds the recovery rate to equilibrium and is suited to gradient-based optimization. The new contribution from this thesis consists of introducing a new matrix pencil method for accurately evaluating the recovery rate within the LCO constraint using output data from transient responses. The amplitude-varying behavior of the recovery rate in the presence of dynamic nonlinearities is captured using a sliding time window along the transient response for a chosen quantity of interest. This new approach differs from the conventional matrix pencil method, which considers an entire transient response at once under linearized assumptions. Sensitivity studies are conducted to identify the optimal singular-value decomposition tolerance, sliding window size, stride size, output data sampling step, and aggregation parameters for obtaining accurate results. The new sliding-window matrix pencil method is then used to optimize a typical aeroelastic section model with a subcritical LCO behavior, enforcing no flutter or LCOs at chosen operation conditions. Optimization results are compared with previous work that used the same LCO constraint formulation combined with an approximate, conservative method to evaluate the recovery rate. The LCO constraint evaluated using the new sliding-window matrix pencil method allows the optimizer to completely suppress subcritical LCOs within the specified operating conditions while minimizing design changes, achieving a less conservative optimized solution. This work is a step toward constraining LCOs in large-scale aeroelastic design optimization to enable higher-performance designs while avoiding undesirable dynamics, such as subcritical LCOs. Future work includes formulating adjoint derivatives of the LCO constraint and demonstrating the methodology for aeroelastic models of increasing physical and computational complexity.
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ItemMechanical Metamaterial Lattices via Direct Methods(Georgia Institute of Technology, 2023-08-23) Gloyd, James ToddDiscrete lattices use individually manufactured unit cell building blocks, which are then assembled to form large lattice structures, the quality of which is not significantly influenced by the scale of the structure. Furthermore, the size of the final structure is not bounded by the footprint of the manufacturing equipment. Tuning the elastic behavior of materials and structures provides the possibility for significant improvements to overall performance, as demonstrated by structural and topology optimization studies. Similar improvements can be made in discrete lattice applications, as shown by the Coded Structures Laboratory at NASA. Improvements made to performance of discrete lattice structures are, so far, limited by the lack of a systematic, direct method to dictate the behavior---that is, prescribe the deformation---of the final structure. Here we present a direct method of prescribed structural behavior integrating structural and topology optimization, for both discrete lattice structures and general structures. Also presented are formulas and methods for calculating the determinant and inverse of a linear combination of matrices, which originally stemmed from the development of prescribed behavior methods however, while applicable to prescribed deformation problems, are much more useful in other situations. The direct methods of prescribed deformation presented here automatically produce dictated behavior from the candidate structure when possible and produce an approximation when the desired behavior is impossible. These methods are shown to move towards a minimizer with quadratic convergence, with improved results in situations with fewer limits on the prescribed behavior. Additionally, the presented formula for calculation of the determinant of a linear combination of matrices provides exact results in as little as one tenth of the time of traditional approximation methods, and the exact inverse of the linear combination is calculated in as little as one quarter of the time of traditional exact methods. We show these formulas provide significant computational and conceptual improvement to current methods and provide unmatched performance in parallel computing settings.
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ItemA Framework for Integrating Advanced Air Mobility Vehicle Development, Safety and Certification(Georgia Institute of Technology, 2022-04-28) Markov, AlexanderAs urbanization continues to grow world wide, cities are experiencing challenges dealing with the increases in pollution, congestion, and availability of public transportation. A new market in aviation, Advanced Air Mobility, has emerged to address these challenges by engineering novel aircraft that are all electric and meant to transport people within and between cities quickly and efficiently. The scale of this market and the associated operations means that vehicles will need to fly with increased autonomy. The lack of highly trained and skilled pilots, along with the increased work load for novel aircraft makes piloted aircraft infeasible at the scale intended or Advanced Air Mobility. While a variety of concepts have been created to meet the performance needs of such operations, the safety and certification requirements of these aircraft remain unclear. The paradigm shift from conventional aircraft to novel, highly integrated, and autonomous aircraft presents many challenges which motivate this work. An emphasis is placed on the safety assessment and the gaps between current regulations and the needs for Advanced Air Mobility. The research objective of this work is to develop a framework for the development and safety assessment of autonomous Advanced Air Mobility aircraft by first examining the existing methods, techniques, and regulations. In doing so, several gaps are identified pertaining to the hazard analysis, reliability analysis of Integrated Modular Avionics systems, and the inclusion of a Run-Time Assurance architecture for vehicle control. An improved hazard analysis approach is developed to capture functional failures as well as systematic areas that can lead to unsafe system behavior. The Systems-Theoretic Process Analysis is supplemented to the Continuous Functional Hazard Assessment so that system behavior and component interactions can be captured. Unsafe system and component actions are identified and used to develop loss scenarios which provide context to the specific conditions that lead to loss of critical vehicle functionality. This information is traced back to identified hazards and used to establish constraints to mitigate unsafe behavior. The Functional Hazard Assessment is then applied to applicable scenarios to provide severity and risk information so that quantitative metrics can be used in additional to qualitative ones. The improved approach develops requirements and determines component and system constraints so that requirements can be refined. It also develops a control structure of the system and assigns traceable items at each step to track how unsafe actions, losses, hazards, and constraints are linked. To improve the reliability modeling of complex modular avionics systems utilizing Multi-Core Processing, a Dynamic Bayesian Network modeling method is developed. This method first utilizes the existing methods defined in ARP 4761 for reliability analysis, namely the Fault Tree Analysis. A mapping is identified for converting fault trees to Bayesian networks, before a Dynamic Bayesian Network is developed by defining how component reliability changes with time. The capability to model reliability of these kinds of systems overtime alone is useful for developing and evaluating maintenance schedules. Additionally, it can handle degradable and repairable components and has the capability to infer failure probabilities using observed evidence. This is useful for identifying weak areas of the system that may be the most likely to cause an overall system failure. A secondary capability is the modeling of uncertainty and the reliability impacts of Multi-Core Processing factors. Subject Matter Expert input and test data can be used to develop conditional dependencies between factors like Worst-Case Execution time, complexity, and partitioning of multi-core systems and their impact on the reliability of the Real-Time Operating System. The added safety challenges of interference and system complexity can be modeled earlier in the design process and can quickly be updated as more information becomes available. Finally, the safe inclusion of autonomy is addressed. To do so, a Simplex architecture is chosen for the development and testing of complex controllers. These controllers are non0deterministic in nature and would otherwise not be certifiable as a result. The Simplex architecture uses an assured back up controller that is triggered when a monitor senses that some predefined safety threshold is breached and gives control back once the system is back to nominal operations. This architecture enables the use of complex control and functionality while also enabling the overall system to be certified. A model predictive control algorithm is developed using a recursive neural network and a receding horizon control scheme that allows a simple system to be controlled quickly and accurately. A PID controller is used as the assured back up controller and the monitoring and triggering capability is demonstrated. The architecture successfully triggers the back up when a threshold is exceeded and hands control back over to the complex controller when the system is brought back to nominal conditions. The main contribution of this dissertation is the development of a modified development assurance and safety management framework that is applicable to Advanced Air Mobility aircraft. The modifications made are specifically targeted at the challenges of applying the existing framework to novel, integrated, complex, and autonomous aircraft. This supports the objective of this research and provides guidance for how existing well understood and trusted methods can be modified for novel applications.
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ItemA DATA-DRIVEN METHODOLOGY TO ANALYZE AIR TRAFFIC MANAGEMENT SYSTEM OPERATIONS WITHIN THE TERMINAL AIRSPACE(Georgia Institute of Technology, 2021-12-10) Corrado, Samantha JaneAir Traffic Management (ATM) systems are the systems responsible for managing the operations of all aircraft within an airspace. In the past two decades, global modernization efforts have been underway to increase ATM system capacity and efficiency, while maintaining safety. Gaining a comprehensive understanding of both flight-level and airspace-level operations enables ATM system operators, planners, and decision-makers to make better-informed and more robust decisions related to the implementation of future operational concepts. The increased availability of operational data, including widely-accessible ADS-B trajectory data, and advances in modern machine learning techniques provide the basis for offline data-driven methods to be applied to analyze ATM system operations. Further, analysis of ATM system operations of arriving aircraft within the terminal airspace has the highest potential to impact safety, capacity, and efficiency levels due to the highest rate of accidents and incidents occurring during the arrival flight phases. Therefore, motivating this research is the question of how offline data-driven methods may be applied to ADS-B trajectory data to analyze ATM system operations at both the flight and airspace levels for arriving aircraft within the terminal airspace to extract novel insights relevant to ATM system operators, planners, and decision-makers. An offline data-driven methodology to analyze ATM system operations is proposed involving the following three steps: (i) Air Traffic Flow Identification, (ii) Anomaly Detection, and (iii) Airspace-Level Analysis. The proposed methodology is implemented considering ADS-B trajectory data that was extracted, cleaned, processed, and augmented for aircraft arriving at San Francisco International Airport (KSFO) during the full year of 2019 as well as the corresponding extracted and processed ASOS weather data. The Air Traffic Flow Identification step contributes a method to more reliably identify air traffic flows for arriving aircraft trajectories through a novel implementation of the HDBSCAN clustering algorithm with a weighted Euclidean distance function. The Anomaly Detection step contributes the novel distinction between spatial and energy anomalies in ADS-B trajectory data and provides key insights into the relationship between the two types of anomalies. Spatial anomalies are detected leveraging the aforementioned air traffic flow identification method, whereas energy anomalies are detected leveraging the DBSCAN clustering algorithm. Finally, the Airspace-Level Analysis step contributes a novel method to identify operational patterns and characterize operational states of aircraft arriving within the terminal airspace during specified time intervals leveraging the UMAP dimensionality reduction technique and DBSCAN clustering algorithm. Additionally, the ability to predict, in advance, a time interval’s operational pattern using metrics derived from the ASOS weather data as input and training a gradient-boosted decision tree (XGBoost) algorithm is provided.
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ItemStress-Based Topology Optimization for Steady-State and Transient Thermoelastic Design(Georgia Institute of Technology, 2021-08-02) Leader, Mark K.Topology optimization is a powerful design tool, benefiting from a broadened design space that can be efficiently navigated with gradient-based optimization algorithms. Complex design problems which often involve coupled multidisciplinary domains may require the use of gradient-based optimization techniques to satisfy demanding design requirements. In addition to multiphysics analysis, structural optimization problem formulations must consider design stresses in order to produce feasible designs. Popular alternative formulations may produce overly stiff designs which do not consider areas of stress concentration. Current topology optimization methods use physics modeling which is too simplistic for many design scenarios, and many do not consider design stress within the problem formulation. Finally, designs generated using topology optimization should be finely refined to achieve a smooth and detailed design. This thesis increases the scope of physics-modeling available for topology optimization, while also considering critical design stress limits. First, due to the high-vibration environments that are common with aerospace structures, unwanted frequency response of the structure must be avoided. To address the high computational cost of eigenvalue problems, the natural frequency problem is solved using a Jacobi–Davidson eigenvalue solution method that is compatible with iterative solution techniques. Second, many aerospace vehicles require structures that operate at high temperatures while simultaneously being subjected to mechanical loads. In this thesis, thermoelastic physics with both steady-state and transient heat transfer analysis are developed for topology optimization. Each of these modeling domains requires significant computational cost. The work in this thesis presents a novel adaptive mesh refinement technique which both increases the resolution of the design while reducing computational cost, making these modeling approaches more viable for topology optimization design.
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ItemAdjoint based design optimization of systems with time dependent physics and probabilistically modeled uncertainties(Georgia Institute of Technology, 2020-07-28) Boopathy, KomahanFor aerospace structures, failure can occur not only because of static adversities like divergence, but also due to time dependent issues like flutter and large vibrations. Therefore, the consideration of time-domain physics becomes essential during design. The physics-based design of aerospace systems involves solving partial differential equations to obtain metrics of interest that guide the design process. These differential equations contain unknown parameters that are sometimes difficult to be characterized as a deterministic value. The uncertainties in input parameters have a direct impact on the output metrics of interest which guide the system design process. To this end, optimization under uncertainty has evolved as a field that accounts for the effect of uncertainties, by propagating the effect of uncertainties through physics simulations. For numerical optimization, the algorithms that do not use gradient information become computationally intractable as the number of design variables increases. Moreover, the numerical approximations of the gradients through the finite-difference or the complex-step methods are inefficient, for their lack of scalability with respect to the number of design variables. Therefore, efficient gradient evaluation techniques such as the adjoint method are needed for solving large scale optimization problems with practical turnaround times. However, because of the inclusion of time dependent physics, the corresponding time dependent adjoint equations needs to be formulated and implemented. Furthermore, the uncertainties need to be propagated through the time dependent physics and the adjoint sensitivity analysis framework. Due to the inherent complexities in the development of time domain physics and adjoint sensitivities analysis capabilities, the sampling-based methods are widely used for the propagation of uncertainties while the projection-based methods are less used. This work presents enhanced implicit time marching methods for flexible multibody dynamics, to analyze the time dependent behavior of aerospace structures, and formulates the corresponding time dependent adjoint sensitivity analysis equations, to efficiently optimize designs using gradient based methods. The adjoint-based design capabilities are demonstrated with the structural optimization of a rotorcraft hub system. A newly developed semi-intrusive approach for projection is shown to fully reuse the underlying time-domain analysis and adjoint sensitivity analysis capabilities, for the projection-based propagation of uncertainties. Using this method, the stochastic residuals and Jacobians are formed implicitly from the deterministic counterparts that have been implemented apriori. The application of the semi-intrusive projection method is shown using a flexible robotic manipulator system modeled after the Canadarm. In the presence of uncertainties in the payloads, the Canadarm system experiences stresses that have a large variability. This work demonstrates the use of uncertainty quantification as a valuable tool for assessing the risk associated with such operating conditions.
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ItemDesign and manufacturing of conformal ablative heatshields(Georgia Institute of Technology, 2019-06-10) Sidor, Adam ThomasConformal ablators, first introduced in the early 2000s under the NASA Hypersonics Project, are a type of rigid ablative thermal protection system that uses flexible, rather than rigid, fibrous substrates. These materials are impregnated with resin in a mold to yield a part that is close to the final geometry and requires little post-process machining (a near net shape part). The lack of fiber connectivity through the thickness enables the TPS to tolerate larger strains than comparable rigid substrate ablators facilitating larger tiles and installation on most aeroshells without strain isolation. Reduced part count and simplified integration drive reductions in labor, cost and complexity –advancements which are enabling for planetary and human missions. Conformal ablators are currently fabricated using an open liquid impregnation process adapted from a technique developed for Lightweight Ceramic Ablators, such as Phenolic Impregnated Carbon Ablator, which leads to design and manufacturing inefficiencies. This work advanced a new manufacturing technique for conformal ablators, vacuum infusion processing, that reduces resin consumption and streamlines clean up. The closed process also eliminates an expensive atmosphere-controlled oven or vacuum chamber. A design methodology, centered around a simulation of the mold filling process, was developed to tailor a conformal ablative heatshield to vacuum infusion processing. A constitutive model, combining properties of individual components, was formulated to estimate the properties of the composite TPS material. The methodology leverages this model, integrated with material selection, tile layout, and the mold filling simulation, to automate a conceptual conformal heatshield design. The approach allows rapid iteration on TPS composition and manufacturing constraints.
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ItemMulti-physics high resolution topology optimization for aerospace structures(Georgia Institute of Technology, 2019-03-28) Chin, Ting WeiAdvancements in multimaterial additive manufacturing have the potential to enable the creation of topology optimized structures with both shape and material tailoring. These are extremely useful in creating designs for multi-physics applications where engineering experience may be lacking. These include designing aerospace structures that are subjected to elevated temperature environment, where mechanical and thermal loads are present or designing structures for strength and avoiding low natural frequency resonance. Multi-physics analysis and multimaterial design parametrization present additional complexity and technical challenges to overcome for large-scale designs. Design and analysis using large-scale uniform meshes is computationally expensive due to the large number of degrees of freedom (DOFs). The same mesh resolution can be created through adaptive mesh refinement such that it has fewer DOFs. However, due to the complexity in creating these adaptive meshes, especially for higher order 3D designs, they are mostly confined to 2D topology optimization. Large-scale multimaterial design through Discrete Material Optimization (DMO) also results in numerous partition of unity constraints and a multimaterial design space that has more local minima than an equivalent single material design space. This work presents new techniques for obtaining large-scale 3D multimaterial, multi-physics designs. Adaptive mesh refinement and higher order design parametrization are introduced to obtain smooth features. The multi-physics capabilities of the method are demonstration in the form of thermoelastic topology optimization. Multimaterial designs using adaptive mesh refinement as well as higher order design parametrization with steady-state thermoelastic topology optimization are presented. Novel technique to accelerate large-scale natural frequency-constrained topology optimization design is also presented.
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ItemAdjoint-based aeroelastic optimization with high-fidelity time-accurate analysis(Georgia Institute of Technology, 2018-12-18) Jacobson, Kevin EdwardA methodology is proposed for adjoint-based sensitivities of steady and time-accurate aeroelastic analysis with high-fidelity models based on computational fluid dynamics and structural finite element modeling. The proposed methodology allows for aerodynamic, structural, and aeroelastic constraints to be formulated, and expressions for sensitivities with respect to aerodynamic, structural, and geometric design variables are derived and verified. Additionally, two types of explicit aeroelastic constraints are presented: flutter constraints based on the matrix pencil method and gust response constraints based on the field velocity method. Optimizations based on the proposed methodology and explicit aeroelastic constraints are demonstrated with two-dimensional and three-dimensional aerospace problems.