Uncertainty Quantification Across Design Space Using Spatially Accurate Polynomial Chaos

Abstract

In the last decade, the demand for stochastic engineering results has increased substantially. Concurrently, improvements in computing hardware, access to large computing clusters, and efficient statistical methods have made uncertainty quantification studies feasible for complex, computationally expensive simulations such as computational fluid dynamics or finite element methods. In current practice, uncertainty may be quantified at particular locations within a flight envelope or design space, but an ongoing challenge remains to interpolate or extrapolate this information to predict the uncertainty at untested or unsimulated locations. The goal of this paper is to introduce a spatially accurate polynomial chaos method, which can interpolate both aleatory and epistemic uncertainty throughout a flight envelope or design space. An additive correction is also presented, which improves accuracy at a small additional sample cost. Interpolation of polynomial chaos expansion coefficients is achieved using established regression techniques, allowing for a spatially accurate uncertainty propagation method which is agnostic to the characterization of parametric input uncertainties. As a demonstration of the method, results are shown for an analytic test function and for simulations of the NASA Common Research Model. The results indicate that Spatially Accurate Polynomial Chaos and its additive correction can provide accurate interpolated estimates of uncertainty.