Model-form and predictive uncertainty quantification in linear aeroelasticity

In this work, Bayesian techniques are employed to quantify model-form and predictive uncertainty in the linear behavior of an elastically mounted airfoil undergoing pitching and plunging motions. The Bayesian model averaging approach is used to construct an adjusted stochastic model from different model classes for time-harmonic incompressible flows. From a set of deterministic function approximations, we construct different stochastic models, whose uncertain coefficients are calibrated using Bayesian inference with regard to the critical flutter velocity. Results show substantial reductions in the predictive uncertainties of the critical flutter speed compared to non-calibrated stochastic simulations. In particular, it is shown that an efficient adjusted model can be derived by considering a possible bias in the random error term on the posterior predictive distributions of the flutter index

Quantification of Model-Form, Predictive, and Parametric Uncertainties in Simulation-Based Design

Traditional uncertainty quantification techniques in simulation-based analysis and design focus upon on the quantification of parametric uncertainties-inherent natural variations of the input variables. This is done by developing a representation of the uncertainties in the parameters and then efficiently propagating this information through the modeling process to develop distributions or metrics regarding the output responses of interest. However, in problems with complex or newer modeling methodologies, the variabilities induced by the modeling process itself-known collectively as model-form and predictive uncertainty-can become a significant, if not greater source of uncertainty to the problem. As such, for efficient and accurate uncertainty measurements, it is necessary to consider the effects of these two additional forms of uncertainty along with the inherent parametric uncertainty. However, current methods utilized for parametric uncertainty quantification are not necessarily viable or applicable to quantify model-form or predictive uncertainties. Additionally, the quantification of these two additional forms of uncertainty can require the introduction of additional data into the problem-such as experimental data-which might not be available for particular designs and configurations, especially in the early design-stage. As such, methods must be developed for the efficient quantification of uncertainties from all sources, as well as from all permutations of sources to handle problems where a full array of input data is unavailable. This work develops and applies methods for the quantification of these uncertainties with specific application to the simulation-based analysis of aeroelastic structures

On the calculation of dynamic derivatives using computational fluid dynamics

In this thesis, the exploitation of computational fluid dynamics (CFD) methods for the flight dynamics of manoeuvring aircraft is investigated. It is demonstrated that CFD can now be used in a reasonably routine fashion to generate stability and control databases. Different strategies to create CFD-derived simulation models across the flight envelope are explored, ranging from combined low-fidelity/high-fidelity methods to reduced-order modelling. For the representation of the unsteady aerodynamic loads, a model based on aerodynamic derivatives is considered. Static contributions are obtained from steady-state CFD calculations in a routine manner. To more fully account for the aircraft motion, dynamic derivatives are used to update the steady-state predictions with additional contributions. These terms are extracted from small-amplitude oscillatory tests. The numerical simulation of the flow around a moving airframe for the prediction of dynamic derivatives is a computationally expensive task. Results presented are in good agreement with available experimental data for complex geometries. A generic fighter configuration and a transonic cruiser wind tunnel model are the test cases. In the presence of aerodynamic non-linearities, dynamic derivatives exhibit significant dependency on flow and motion parameters, which cannot be reconciled with the model formulation. An approach to evaluate the sensitivity of the non-linear flight simulation model to variations in dynamic derivatives is described. The use of reduced models, based on the manipulation of the full-order model to reduce the cost of calculations, is discussed for the fast prediction of dynamic derivatives. A linearized solution of the unsteady problem, with an attendant loss of generality, is inadequate for studies of flight dynamics because the aircraft may experience large excursions from the reference point. The harmonic balance technique, which approximates the flow solution in a Fourier series sense, retains a more general validity. The model truncation, resolving only a small subset of frequencies typically restricted to include one Fourier mode at the frequency at which dynamic derivatives are desired, provides accurate predictions over a range of two- and three-dimensional test cases. While retaining the high fidelity of the full-order model, the cost of calculations is a fraction of the cost for solving the original unsteady problem. An important consideration is the limitation of the conventional model based on aerodynamic derivatives when applied to conditions of practical interest (transonic speeds and high angles of attack). There is a definite need for models with more realism to be used in flight dynamics. To address this demand, various reduced models based on system-identification methods are investigated for a model case. A non-linear model based on aerodynamic derivatives, a multi-input discrete-time Volterra model, a surrogate-based recurrence-framework model, linear indicial functions and radial basis functions trained with neural networks are evaluated. For the flow conditions considered, predictions based on the conventional model are the least accurate. While requiring similar computational resources, improved predictions are achieved using the alternative models investigated. Furthermore, an approach for the automatic generation of aerodynamic tables using CFD is described. To efficiently reduce the number of high-fidelity (physics-based) analyses required, a kriging-based surrogate model is used. The framework is applied to a variety of test cases, and it is illustrated that the approach proposed can handle changes in aircraft geometry. The aerodynamic tables can also be used in real-time to fly the aircraft through the database. This is representative of the role played by CFD simulations and the potential impact that high-fidelity analyses might have to reduce overall costs and design cycle tim

Improving aircraft performance using machine learning: a review

This review covers the new developments in machine learning (ML) that are impacting the multi-disciplinary area of aerospace engineering, including fundamental fluid dynamics (experimental and numerical), aerodynamics, acoustics, combustion and structural health monitoring. We review the state of the art, gathering the advantages and challenges of ML methods across different aerospace disciplines and provide our view on future opportunities. The basic concepts and the most relevant strategies for ML are presented together with the most relevant applications in aerospace engineering, revealing that ML is improving aircraft performance and that these techniques will have a large impact in the near future

Dissecting the Flow Physics of Aeroelastic Oscillations and Vortex-Dominated Flows: Computational and Data-Driven Methods

Fluid flows interact with flexible and moving bodies in a wide range of natural and engineering applications. These problems are often characterized by highly non-linear flow physics due to the generation and shedding of several vortices, their interactions, and the forces they induce on surfaces within the flow. However, our current understanding of the force producing mechanisms in these flows and our ability to accurately quantify their influence remains limited. As a result, the dynamics of many such vortex-dominated problems involving fluid-structure interactions and unsteady aerodynamics are notoriously hard to predict. In this work, we use computational modeling in conjunction with data-driven techniques to analyze the flow physics of these problems. We particularly focus on the flow-induced oscillation of wings and cylindrical bluff-bodies at low Reynolds numbers. Using simulations based on a sharp-interface immersed boundary method, we demonstrate the large range of oscillation responses and parametric dependencies that these systems exhibit. We propose an energy-based tool to analyze, predict and control the non-linear, and often non-intuitive, oscillation responses observed. We show that ``energy maps'' identify all possible flow-induced oscillation response branches and bifurcations in a system, thus allowing their use in the prediction and control of pitching oscillations for wings interacting with incoming gusts. Furthermore, we also formulate and demonstrate a novel extension to Dynamic Mode Decomposition for the analysis of such flows involving moving boundaries. A second focus of this work is on disentangling the various mechanisms at play in the generation of loads on surfaces within vortex-dominated flows. To this end, we develop a force and moment partitioning method which allows us to rigorously quantify the influence of distinct physical mechanisms as well as individual flow features in force/moment production. This method is combined with data-driven techniques to estimate the influence of each individual vortex in a flow-field, while also tracking and categorizing these vortices as they evolve with the flow. We utilize these tools to reveal new insights into fundamental phenomena in aerodynamics and flow-induced oscillations -- such as the mechanisms that drive the flow-induced oscillation of cylinders and the production of lift during dynamic stall and on three-dimensional wings

Model reduction for nonlinear dynamical systems with parametric uncertainties

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 113-120).Nonlinear dynamical systems are known to be sensitive to input parameters. In this thesis, we apply model order reduction to an important class of such systems -- one which exhibits limit cycle oscillations (LCOs) and Hopf-bifurcations. Highfidelity simulations for systems with LCOs are computationally intensive, precluding probabilistic analyses of these systems with uncertainties in the input parameters. In this thesis, we employ a projection-based model reduction approach, in which the proper orthogonal decomposition (POD) is used to derive the reduced basis while the discrete empirical interpolation method (DEIM) is employed to approximate the nonlinear term such that the repeated online evaluations of the reduced-order model (ROM) is independent of the full-order model (FOM) dimension. In problems where vastly different magnitudes exist in the unknowns variables, the original POD-DEIM approach results in large error in the smaller variables. In unsteady simulations, such error quickly accumulates over time, significantly reducing the accuracy of the ROM. The interpolatory nature of the DEIM also limits its accuracy in approximating highly oscillatory nonlinear terms. In this work, modifications to the existing methodology are proposed whereby scalar-valued POD modes are used in each variable of the state and the nonlinear term, and the pure interpolation of the DEIM approximation is also replaced by a regression via over-sampling of the nonlinear term. The modified methodology is applied to two nonlinear dynamical problems: a reacting flow model of a tubular reactor and an aeroelastic model of a cantilevered plate, both of which exhibit LCO and Hopf-bifurcation. Results indicate that in situations where the efficiency of the original POD-DEIM ROM is compromised by disparate magnitudes in unknown variables or by the need to include large sets of interpolation points, the modified POD-DEIM ROM accurately predicts the system responses in a small fraction of the FOM computational time.by Yuxiang Beckett Zhou.S.M

Aeronautical engineering: A continuing bibliography with indexes (supplement 254)

This bibliography lists 538 reports, articles, and other documents introduced into the NASA scientific and technical information system in June 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 233)

This bibliography lists 637 reports, articles, and other documents introduced into the NASA scientific and technical information system in November, 1988. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics