Development and Use of a Spatially Accurate Polynomial Chaos Method for Aerospace Applications

Uncertainty is prevalent throughout the design, analysis, and optimization of aerospace products. When scientific computing is used to support these tasks, sources of uncertainty may include the freestream flight conditions of a vehicle, physical modeling parameters, geometric fidelity, numerical error, and model-form uncertainty, among others. Moreover, while some uncertainties may be treated as probabilistic, aleatory sources, other uncertainties are non-probabilistic and epistemic due to a lack of knowledge, and cannot be rigorously treated using classical statistics or Bayesian approaches. An additional complication for propagating uncertainty is that many aerospace scientific computing tools may be computationally expensive; for example, a single high-fidelity computational fluid dynamics solution may require several days or even weeks to complete. It is therefore necessary to employ uncertainty propagation strategies that require as few solutions as possible.

The Non-Intrusive Polynomial Chaos (NIPC) method has grown in popularity in recent decades due to its ability to propagate both aleatory and epistemic parametric sources of uncertainty in a computationally efficient manner. While traditional Monte Carlo methods might require thousands to millions of function evaluations to achieve statistical convergence, NIPC typically requires tens to hundreds for problems with similar numbers of uncertain dimensions. Despite this efficiency, NIPC is limited in one important aspect: it can only propagate uncertainty at a particular point in a design space or flight envelope. For optimization or aerodynamic database problems that require uncertainty estimates at many more than one point, the use of NIPC quickly becomes computationally intractable.

This dissertation introduces a new method entitled Spatially Accurate Polynomial Chaos (SAPC) that extends the original NIPC approach for the spatial regression of aleatory and epistemic parametric sources of uncertainty. Throughout the dissertation, the SAPC method is applied to various aerospace problems of interest. These include the regression of aerodynamic force and moment uncertainties throughout the flight envelope of a commercial aircraft, the design under uncertainty of a two-stream propulsive mixer device, and the robust design of a low-boom supersonic demonstrator aircraft. Collectively the results suggest that SAPC may be useful for a large variety of engineering applications.