Uncertainty Quantification in Aeroelasticity

Beran, Philip S.; Stanford, Bret; Schrock, Christopher R.

doi:10.1146/annurev-fluid-122414-034441

Cited by 54 publications

(14 citation statements)

References 104 publications

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“…The consistency of the flutter solutions with time-domain analysis has previously been established by the second author. We refer to [38] for a detailed discussion on aeroelasticity and uncertainty quantification, where the authors establish that non-uniqueness in the flutter solution can be modeled as bi-modal distributions.…”

Section: Problem Setupmentioning

confidence: 99%

Multifidelity Monte Carlo estimation for large-scale uncertainty propagation

Peherstorfer

Beran

Willcox

2018

2018 AIAA Non-Deterministic Approaches Conference

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One important task of uncertainty quantification is propagating input uncertainties through a system of interest to quantify the uncertainties' effects on the system outputs; however, numerical methods for uncertainty propagation are often based on Monte Carlo estimation, which can require large numbers of numerical simulations of the numerical model describing the system response to obtain estimates with acceptable accuracies. Thus, if the model is computationally expensive to evaluate, then Monte-Carlo-based uncertainty propagation methods can quickly become computationally intractable. We demonstrate that multifidelity methods can significantly speedup uncertainty propagation by leveraging low-cost low-fidelity models and establish accuracy guarantees by using occasional recourse to the expensive high-fidelity model. We focus on the multifidelity Monte Carlo method, which is a multifidelity approach that optimally distributes work among the models such that the mean-squared error of the multifidelity estimator is minimized for a given computational budget. The multifidelity Monte Carlo method is applicable to general types of low-fidelity models, including projection-based reduced models, data-fit surrogates, response surfaces, and simplified-physics models. We apply the multifidelity Monte Carlo method to a coupled aero-structural analysis of a wing and a flutter problem with a high-aspect-ratio wing. The low-fidelity models are data-fit surrogate models derived with standard procedures that are built in common software environments such as M and numpy/scipy. Our results demonstrate speedups of orders of magnitude compared to using the high-fidelity model alone.

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Section: Problem Setupmentioning

confidence: 99%

Multifidelity Monte Carlo estimation for large-scale uncertainty propagation

Peherstorfer

Beran

Willcox

2018

2018 AIAA Non-Deterministic Approaches Conference

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“…Pettit [11], Dai and Yang [12], and Beran et al [13] reviewed the uncertainty quantification in aeroelasticity, including both probabilistic and non-probabilistic methods. Typically, uncertainties in the aeroelastic systems could be divided into two commonly recognized categories: aleatory uncertainty and epistemic uncertainty [14].…”

Section: Introductionmentioning

confidence: 99%

A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

Zhang

Yang

2020

IEEE Access

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A two-phase Monte Carlo Simulation/Non-intrusive Polynomial Chaos (MCS/NIPC) method for quantification of margins and mixed uncertainties (aleatory and epistemic uncertainties) is proposed in this paper for the flutter speed boundary analysis. Compared with the traditional MCS/MCS method which needs lots of numerical simulations, the MCS/NIPC method can reduce the computational cost without losing accuracy due to the use of point collocation non-intrusive polynomial chaos in the inner loop. Based on the results of uncertainty quantification, a novel practical quantification of margins and mixed uncertainties (QMMU) framework is proposed considering both aleatory and epistemic uncertainties such as the parametric uncertainties in complicated models. A two-dimensional airfoil and a three-dimensional benchmark wing, the AGARD 445.6 wing, are both employed to illustrate the practical application of the proposed methods for flutter speed computation in the presence of mixed uncertainties arising from the material properties and flight conditions. Within the analysis, aleatory and mixed uncertainty quantification are conducted to prove the effectiveness and efficiency of the MCS/NIPC method. Then the QMMU metrics are accomplished for the flutter speed boundary analysis of the two airfoil models. The results demonstrate the potential of the proposed QMMU framework to analyze the stability of engineering systems. INDEX TERMS Flutter, non-intrusive polynomial chaos, probability bounds, quantification of margins and mixed uncertainties, uncertainty quantification

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“…UQ is generally addressed in a probabilistic framework, although the actual regulations do not rely on probabilities for certification but rather introduce the notion of risks related to undesirable (failure) scenarios. Recent reviews on the various issues raised by UQ in aeroelasticity are given in [2,4,15,46]. Applications to stability or optimization are described in [1,12,31,36,38,47,62] for example.…”

Section: Introductionmentioning

confidence: 99%

Sparse polynomial surrogates for non-intrusive, high-dimensional uncertainty quantification of aeroelastic computations

Savin

Hantrais-Gervois

2020

Probabilistic Engineering Mechanics

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This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and structural parameters (random inputs) on the drag performance and deformation (outputs) of a flexible wing in transonic regime, is assessed. Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques are favored. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are commonly considered in this respect. The polynomial expansion coefficients are constructed using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. In complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weakly on the multiple

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Uncertainty Quantification in Aeroelasticity

Cited by 54 publications

References 104 publications

Multifidelity Monte Carlo estimation for large-scale uncertainty propagation

Multifidelity Monte Carlo estimation for large-scale uncertainty propagation

A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

Sparse polynomial surrogates for non-intrusive, high-dimensional uncertainty quantification of aeroelastic computations

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