Quantification of Margins and Uncertainties for Integrated Spacecraft Systems Models

Abstract

The objective of this study was to introduce an efficient and accurate approach to the quantification of margins and uncertainties for integrated spacecraft systems models. In this study, stochastic expansions, based on nonintrusive polynomial chaos, were used for efficient representation of uncertainty both in design metrics and associated performance limits of a system. Additionally, procedures were outlined for analyzing systems that contain different uncertainty types between the performance metrics and performance limits. These methodologies were demonstrated on two model problems, each possessing mixed (epistemic and aleatory) uncertainty, which was propagated through the models using second-order probability. The first was a complex system model of highly nonlinear analytical functions. The second was a coupled multisystem, physics-based model for spacecraft reentry. The performance metrics consisted of two systems used to determine the maximum g load, the necessary bank angle correction, and maximum convective heat load along a reentry trajectory. Overall, the methodologies and examples of this work have detailed an efficient approach for measuring the reliability of complex spacecraft systems models, as well as the importance of quantifying margins and uncertainties for the design of reliable systems. Nomenclature c i = mass fraction of species i F = performance metric FL, FU = lower and upper performance limit h = enthalpy or altitude, km h D = enthalpy of diffusion, J∕kg h 0 = total enthalpy, J∕kg h 0 f = heat of formation, J∕k mol Le = Lewis number M LW , M UP = lower and upper performance gate margin m = mass, kg N s = number of samples N t = number of terms in a total-order polynomial chaos expansion n = number of random dimensions P = pressure, Pa Pr = Prandtl number p = order of polynomial expansion _ q = heat flux, W∕cm 2 r = orbital radius, km S = reference area, m 2 s = downrange distance, km T = temperature, K U = velocity, m∕s U F = performance metric uncertainty U FL , U FU = lower and upper performance limit uncertainty U LW , U UP = lower and upper performance gate uncertainty α = deterministic coefficient in the polynomial chaos expansion α = generic uncertain function β = confidence level γ = flight-path angle, deg ϵ = wall emissivity θ = longitude, deg μ = dynamic viscosity, kg∕m · s ξ = standard input random variable ρ = density, kg∕m 3 σ = Stefan-Boltzmann constant, 5.67 × 10 −8 W∕ m 2 -K 4 , or bank angle, deg ϕ = latitude, deg Ψ = random basis function or heading angle, deg ω = planetary body rotation rate, rad∕s Subscripts c = conduction d = diffusion e = boundary-layer edge condition r = radiation w = wall condition ∞ = freestream condition

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

“…Recently, there has been many discussions of the QMU application in many engineering problems such as radiative shock system [34], radioactive waste disposal [35], satellite power system evaluation [36], and missile reliability [37]. Thomas et al [38] presented a practical QMU for complex spacecraft systems in which uncertainty exists in both the operating region and the performance requirement. Harsheel et al [30] implemented Dempster-Shafer Theory of Evidence in the presence of mixed uncertainties in the reliability and performance assessment of complex engineering systems through the use of the QMU methodology.…”