Efficient Uncertainty Quantification in Multidisciplinary Analysis of a Reusable Launch Vehicle

Abstract

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

Quantification of Margins and Uncertainties for Integrated Spacecraft Systems Models

“…In recent studies [11,12,14,16,17], the polynomial chaos method has been used as a means of UQ over traditional methods, such as Monte Carlo, for its computational efficiency. Polynomial chaos is a surrogate modeling technique based on the spectral representation of the uncertainty.…”

“…The first objective is to demonstrate the use of stochastic response surfaces based on nonintrusive polynomial chaos (NIPC) for efficient quantification of uncertainty in system performance metrics, as well as performance boundaries. Previous work by Hosder and Bettis [11] and Bettis et al [12], as well as Hosder et al [13,14], in the area of using stochastic expansions based on NIPC as a means of efficient uncertainty quantification (UQ) has been extensively investigated. These works included studies involving the propagation of both aleatory (inherent) and epistemic uncertainties through a variety of stochastic model problems.…”

Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

“…Recently, Eldred et al [31] have demonstrated mixed UQ using different methods like interval optimization, second-order probability [19,28,30,32] and DSTE. They investigated the use of nested sampling for mixed UQ, where each sample taken from the epistemic distributions at the outer loop results in an inner loop sampling over the aleatory probability distributions.…”

“…In this work, we focus on generalized polynomial chaos using the Wiener-Askey scheme, which is explained in detail by Xiu and Karniadakis [44]. In previous years, many researchers have utilized polynomial chaos theory in stochastic computations [26][27][28]35,45,46]. In non-intrusive polynomial chaos expansion (PCE), simulations are used as black boxes and the calculation of chaos expansion coefficients is based on a set of simulation response evaluations.…”

“…A sampling based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory was introduced by Helton et al [15] to reduce the computational cost of crude Monte Carlo method. In the present paper, a stochastic response surface constructed using point-collocation NIPC [26][27][28][29][30] has been implemented as a response surrogate in uncertainty analysis in order to reduce the computational cost.…”