Advancements in Uncertainty Quantification with Stochastic Expansions Applied to Supersonic and Hypersonic Flows

Advancements in Uncertainty Quantification with Stochastic Expansions Applied to Supersonic and Hypersonic Flows
Author: Thomas Kelsey West (IV)
Publisher:
Total Pages: 153
Release: 2015
Genre: Aerodynamics, Hypersonic
ISBN:
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"The primary objective of this study was to develop improved methodologies for efficient and accurate uncertainty quantification with stochastic expansions and apply them to problems in supersonic and hypersonic flows. Methods introduced included approaches for efficient dimension reduction, sensitivity analysis, and sparse approximations. These methods and procedures were demonstrated on multiple stochastic models of hypersonic, planetary entry flows, which included high-fidelity, computational fluid dynamics models of radiative heating on the surface of hypersonic inflatable aerodynamic decelerators during Mars and Titan entry. For these stochastic problems, construction of an accurate surrogate model was achieved with as few as 10% of the number of model evaluations needed to construct a full dimension, total order expansion. Another objective of this work was to introduce methodologies used for further advancement of a quantification of margins and uncertainties framework. First, the use of stochastic expansions was introduced to efficiently quantify the uncertainty in system design performance metrics and performance boundaries. Then, procedures were defined to measure margin and uncertainty metrics for systems subject to multiple types of uncertainty in operating conditions and physical models. To demonstrate the new quantification of margins and uncertainties methodologies, two multi-system, multi-physics stochastic models were investigated: (1) a model for reentry dynamics, control, and convective heating and (2) a model of ground noise prediction of low-boom, supersonic aircraft configurations. Overall the methods and results of this work have outlined many effective approaches to uncertainty quantification of large-scale, high-dimension, aerospace problems containing both epistemic and inherent uncertainty. The methods presented showed significant improvement in the efficiency and accuracy of uncertainty analysis capability when stochastic expansions were used for uncertainty quantification."--Abstract, page iii.

Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling
Author: José Eduardo Souza De Cursi
Publisher: Springer Nature
Total Pages: 472
Release: 2020-08-19
Genre: Technology & Engineering
ISBN: 3030536696
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This proceedings book discusses state-of-the-art research on uncertainty quantification in mechanical engineering, including statistical data concerning the entries and parameters of a system to produce statistical data on the outputs of the system. It is based on papers presented at Uncertainties 2020, a workshop organized on behalf of the Scientific Committee on Uncertainty in Mechanics (Mécanique et Incertain) of the AFM (French Society of Mechanical Sciences), the Scientific Committee on Stochastic Modeling and Uncertainty Quantification of the ABCM (Brazilian Society of Mechanical Sciences) and the SBMAC (Brazilian Society of Applied Mathematics).

Uncertainty quantification for wave propagation and flow problems with random data

Uncertainty quantification for wave propagation and flow problems with random data
Author: Markus Wahlsten
Publisher: Linköping University Electronic Press
Total Pages: 45
Release: 2018-04-09
Genre:
ISBN: 917685339X
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In this thesis we study partial differential equations with random inputs. The effects that different boundary conditions with random data and uncertain geometries have on the solution are analyzed. Further, comparisons and couplings between different uncertainty quantification methods are performed. The numerical simulations are based on provably strongly stable finite difference formulations based on summation-by-parts operators and a weak implementation of boundary and interface conditions. The first part of this thesis treats the construction of variance reducing boundary conditions. It is shown how the variance of the solution can be manipulated by the choice of boundary conditions, and a close relation between the variance of the solution and the energy estimate is established. The technique is studied on both a purely hyperbolic system as well as an incompletely parabolic system of equations. The applications considered are the Euler, Maxwell's, and Navier--Stokes equations. The second part focuses on the effect of uncertain geometry on the solution. We consider a two-dimensional advection-diffusion equation with a stochastically varying boundary. We transform the problem to a fixed domain where comparisons can be made. Numerical results are performed on a problem in heat transfer, where the frequency and amplitude of the prescribed uncertainty are varied. The final part of the thesis is devoted to the comparison and coupling of different uncertainty quantification methods. An efficiency analysis is performed using the intrusive polynomial chaos expansion with stochastic Galerkin projection, and nonintrusive numerical integration. The techniques are compared using the non-linear viscous Burgers' equation. A provably stable coupling procedure for the two methods is also constructed. The general coupling procedure is exemplified using a hyperbolic system of equations.

New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems

New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems
Author: Parikshit Dutta
Publisher:
Total Pages:
Release: 2012
Genre:
ISBN:
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Recently there has been growing interest to characterize and reduce uncertainty in stochastic dynamical systems. This drive arises out of need to manage uncertainty in complex, high dimensional physical systems. Traditional techniques of uncertainty quantification (UQ) use local linearization of dynamics and assumes Gaussian probability evolution. But several difficulties arise when these UQ models are applied to real world problems, which, generally are nonlinear in nature. Hence, to improve performance, robust algorithms, which can work efficiently in a nonlinear non-Gaussian setting are desired. The main focus of this dissertation is to develop UQ algorithms for nonlinear systems, where uncertainty evolves in a non-Gaussian manner. The algorithms developed are then applied to state estimation of real-world systems. The first part of the dissertation focuses on using polynomial chaos (PC) for uncertainty propagation, and then achieving the estimation task by the use of higher order moment updates and Bayes rule. The second part mainly deals with Frobenius-Perron (FP) operator theory, how it can be used to propagate uncertainty in dynamical systems, and then using it to estimate states by the use of Bayesian update. Finally, a method to represent the process noise in a stochastic dynamical system using a nite term Karhunen-Loeve (KL) expansion is proposed. The uncertainty in the resulting approximated system is propagated using FP operator. The performance of the PC based estimation algorithms were compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF), and the FP operator based techniques were compared with particle filters, when applied to a duffing oscillator system and hypersonic reentry of a vehicle in the atmosphere of Mars. It was found that the accuracy of the PC based estimators is higher than EKF or UKF and the FP operator based estimators were computationally superior to the particle filtering algorithms.

Stochastic Methods for Uncertainty Quantification in Radiation Transport

Stochastic Methods for Uncertainty Quantification in Radiation Transport
Author:
Publisher:
Total Pages:
Release: 2009
Genre:
ISBN:
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The use of generalized polynomial chaos (gPC) expansions is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables and is used to represent the uncertain input(s) and unknown(s). We assume a single uncertain input-the total macroscopic cross section-although this does not represent a limitation of the approaches considered here. Two solution methods are examined: The Stochastic Finite Element Method (SFEM) and the Stochastic Collocation Method (SCM). The SFEM entails taking Galerkin projections onto the orthogonal basis, which, for fixed source problems, yields a linear system of fully -coupled equations for the PC coefficients of the unknown. For k-eigenvalue calculations, the SFEM system is non-linear and a Newton-Krylov method is employed to solve it. The SCM utilizes a suitable quadrature rule to compute the moments or PC coefficients of the unknown(s), thus the SCM solution involves a series of independent deterministic transport solutions. The accuracy and efficiency of the two methods are compared and contrasted. The PC coefficients are used to compute the moments and probability density functions of the unknown(s), which are shown to be accurate by comparing with Monte Carlo results. Our work demonstrates that stochastic spectral expansions are a viable alternative to sampling-based uncertainty quantification techniques since both provide a complete characterization of the distribution of the flux and the k-eigenvalue. Furthermore, it is demonstrated that, unlike perturbation methods, SFEM and SCM can handle large parameter uncertainty.

Numerical Simulations of Inviscid Supersonic and Hypersonic Flows

Numerical Simulations of Inviscid Supersonic and Hypersonic Flows
Author: Ryan Mathew Han
Publisher:
Total Pages: 0
Release: 2020
Genre:
ISBN:
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With the always advancing aviation and space industries, supersonic and hypersonic flows are continually becoming more important to model and understand. Inviscid, compressible fluid mechanics are described by systems of hyperbolic partial differential equations, which are used in this thesis to model various supersonic and hypersonic flows. These flows include those through a converging-diverging nozzle, over a two dimensional wedge, over a cone, and over airfoils. Various flow phenomena such as normal, bow, oblique, and fishtail shocks are correctly modeled and shown. Through analysis of the results, it is found that each of the models in this paper demonstrate the correct qualitative flow characteristics for each set of boundary conditions. Accurate data for normal and attached shocks, including the shock position, shock angle, and post-shock flow conditions, as well as accurate expansion fan pressures are found and verified with various publications, all while using very simple numerical methods which are easy to implement and program.

An Empirical Chaos Expansion Method for Uncertainty Quantification

An Empirical Chaos Expansion Method for Uncertainty Quantification
Author: Gautam Andrew Wilkins
Publisher:
Total Pages: 162
Release: 2016
Genre:
ISBN:
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Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by uncertainty in their parameters. The polynomial chaos method is a computational approach to solve stochastic partial differential equations (SPDE) by projecting the solution onto a space of orthogonal polynomials of the stochastic variables and solving for the deterministic coefficients. Polynomial chaos can be more efficient than Monte Carlo methods when the number of stochastic variables is low, and the integration time is not too large. When performing long-term integration, however, achieving accurate solutions often requires the space of polynomial functions to become unacceptably large. This dissertation presents an alternative approach, where sets of empirical basis functions are constructed by examining the behavior of the solution for fixed values of the random variables. The empirical basis functions are evolved over time, which means that the total number can be kept small, even when performing long-term integration. We introduce this method of empirical chaos expansion, and apply it to a number of model equations, demonstrating that the computational time scales linearly with the final integration time. That is not the case for polynomial chaos in general, since achieving accuracy for long-term integration usually requires larger polynomial bases, causing a nonlinear scaling with the final integration time. We also present an analytical method that uses the dynamics of the SPDE to predict the evolution of the empirical basis functions and demonstrate how it can be applied to evolve the empirical basis functions without needing to resample realizations of the original SPDE.

Shock Wave-Boundary-Layer Interactions

Shock Wave-Boundary-Layer Interactions
Author: Holger Babinsky
Publisher: Cambridge University Press
Total Pages: 481
Release: 2011-09-12
Genre: Technology & Engineering
ISBN: 1139498649
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Shock wave-boundary-layer interaction (SBLI) is a fundamental phenomenon in gas dynamics that is observed in many practical situations, ranging from transonic aircraft wings to hypersonic vehicles and engines. SBLIs have the potential to pose serious problems in a flowfield; hence they often prove to be a critical - or even design limiting - issue for many aerospace applications. This is the first book devoted solely to a comprehensive, state-of-the-art explanation of this phenomenon. It includes a description of the basic fluid mechanics of SBLIs plus contributions from leading international experts who share their insight into their physics and the impact they have in practical flow situations. This book is for practitioners and graduate students in aerodynamics who wish to familiarize themselves with all aspects of SBLI flows. It is a valuable resource for specialists because it compiles experimental, computational and theoretical knowledge in one place.