Quantification of Uncertainty in Aerodynamic Heating of a  Reentry Vehicle due to Uncertain Wall and Freestream  Conditions

Bettis, Benjamin R.; Hosder, Serhat

doi:10.2514/6.2010-4642

Cited by 9 publications

(6 citation statements)

References 10 publications

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“…For the robust optimization methodology described in this paper, stochastic expansions obtained with the NIPC technique is used due to its computational efficiency and accuracy in uncertainty propagation as shown in the previous studies [10,11]. The stochastic expansions are used as response surfaces (i.e., surrogates of the response) in the optimization procedure and are used to approximate the stochastic objective function and the constraint functions.…”

Section: Stochastic Expansions For Surrogate Modelingmentioning

confidence: 99%

Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

Shah

Hosder

Koziel

et al. 2015

Aerospace Science and Technology

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Section: Stochastic Expansions For Surrogate Modelingmentioning

confidence: 99%

Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

Shah

Hosder

Koziel

et al. 2015

Aerospace Science and Technology

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“…4,11 While constructing the stochastic expansions, a combined expansion approach will be utilized, which will expand the polynomials as a function of both uncertain variables (aleatory and epistemic) and deterministic design variables. Below we give the description of the Point-Collocation NIPC, the combined expansion approach, and the utilization of the stochastic response surface in robust optimization.…”

Section: Robust Optimization With Stochastic Expansionsmentioning

confidence: 99%

Robust Airfoil Optimization Under Inherent and Model-Form Uncertainties Using Stochastic Expansions

Zhang

Hosder

Leifsson

et al. 2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The objective of this paper was to introduce a computationally efficient approach for robust aerodynamic optimization under aleatory (inherent) and epistemic (model-form) uncertainties using stochastic expansions that are based on Non-Intrusive Polynomial Chaos method. The stochastic surfaces were used as surrogates in the optimization process. To create the surrogates, a combined non-intrusive polynomial chaos expansion approach was utilized, which is a function of both the design and the uncertain variables. In this paper, two stochastic optimization formulations were given: (1) optimization under pure aleatory uncertainty and (2) optimization under mixed (aleatory and epistemic) uncertainty. The formulations were demonstrated for the drag minimization of NACA 4-digit airfoils described with three geometric design variables over the range of uncertainties at transonic flow conditions. The deterministic CFD simulations were performed to solve steady, 2-D, compressible, turbulent RANS equations. The pure aleatory uncertainty case included the Mach number as the uncertain variable. For the mixed uncertainty case, a k factor which is multiplied with the turbulent eddy-viscosity coefficient is introduced to the problem as the epistemic uncertain variable. The results of both optimization cases confirmed the effectiveness of the robust optimization approach with stochastic expansions by giving the optimum airfoil shape that has the minimum drag over the range of aleatory and epistemic uncertainties. The optimization under pure aleatory uncertainty case required 90 deterministic CFD evaluations, whereas the optimization under mixed uncertainty case required 126 CFD evaluations to create the stochastic response surfaces, which show the computational efficiency of the proposed stochastic optimization approach. The stochastic optimization methodology described in this paper is general in the sense that it can be applied to aerodynamic optimization problems that utilize different shape parameterization techniques.

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“…The procedure for calculating these bounds is shown in Bettis and Hosder. 10 The free-stream velocity was assumed to have a uniform distribution with a mean of 4167 m/s. 10 The lower and upper bounds were set at 3958.65 m/s and 4375.35 m/s respectively which correspond to a 5% uncertainty in the free-stream velocity.…”

Section: B Description Of the Stochastic Problemmentioning

confidence: 99%

“…10 The free-stream velocity was assumed to have a uniform distribution with a mean of 4167 m/s. 10 The lower and upper bounds were set at 3958.65 m/s and 4375.35 m/s respectively which correspond to a 5% uncertainty in the free-stream velocity. For comparison purposes, the free-stream velocity was also modeled as a normal random variable with a mean of 4167 m/s and a standard deviation of 100 m/s.…”

Section: B Description Of the Stochastic Problemmentioning

confidence: 99%

Efficient Uncertainty Quantification in Multidisciplinary Analysis of a Reusable Launch Vehicle

Hosder

Winter

Bettis

2011

17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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The objective of this study was to apply a recently developed uncertainty quantification framework to the multidisciplinary analysis of a reusable launch vehicle (RLV). This particular framework is capable of efficiently propagating mixed (inherent and epistemic) uncertainties through complex simulation codes. The goal of the analysis was to quantify uncertainty in various output parameters obtained from the RLV analysis, including the maximum dynamic pressure, cross-range, range, and vehicle takeoff gross weight. Three main uncertainty sources were treated in the simulations: (1) reentry angle of attack (inherent uncertainty), (2) altitude of the initial reentry point (inherent uncertainty), and (3) the Young's Modulus (epistemic uncertainty). The Second-Order Probability Theory utilizing a stochastic response surface obtained with Point-Collocation Non-Intrusive Polynomial Chaos was used for the propagation of the mixed uncertainties. This particular methodology was applied to the RLV analysis, and the uncertainty in the output parameters of interested was obtained in terms of intervals at various probability levels. The preliminary results have shown that there is a large amount of uncertainty associated withthe vehicle takeoff gross weight. Furthermore, the study has demonstrated the feasibility of the developed uncertainty quantification framework for efficient propagation of mixed uncertainties in the analysis of complex aerospace systems. Nomenclature C = Mass fraction h = Enthalpy (J/kg) Le = Lewis number n = Number of random variables p = Polynomial order of total expansion Pr = Prandtl number q = Maximum dynamic pressure R N = Radius of curvature (m) α = Reentry angle of attack µ = Mean ξ = Standard random variable a ξ r = Standard aleatory uncertain variable vector e ξ r = Standard epistemic uncertain variable vector ρ = Density (kg/m 3 ) σ = Standard deviation σ 2 = Statistical variance Ψ = Random basis function

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Quantification of Uncertainty in Aerodynamic Heating of a Reentry Vehicle due to Uncertain Wall and Freestream Conditions

Cited by 9 publications

References 10 publications

Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

Robust Airfoil Optimization Under Inherent and Model-Form Uncertainties Using Stochastic Expansions

Efficient Uncertainty Quantification in Multidisciplinary Analysis of a Reusable Launch Vehicle

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