Comparison of Uncertainty Propagation / Response Surface Techniques for Two Aeroelastic Systems

Uncertainty has always been an important consideration when designing, analyzing and testing engineered systems, but computational investigations of the effects of uncertainty are only now beginning to become feasible. Often the limiting factor is the computational expense required to assess the influence of uncertainty on the system. This work provides an overview of techniques that seek to reduce this expense. Sampling methods such as Monte Carlo Simulation (MCS), Latin Hypercube Sampling (LHS) and Low-Discrepancy Sequences will be discussed, as well as reliability methods such as MV, AVM, FORM and SORM. Response surface approximations such as Kriging and Polynomial Chaos will also be discussed, highlighting the fact that all of these uncertainty quantification techniques can be understood in the context of a response surface. The strengths and weaknesses of these uncertainty propagation techniques will be discussed and they will be compared by applying them to two loworder aerospace problems. The examples illustrate a case where most of the methods are not so satisfactory, and another where almost any would perform surprisingly well. Most of these methods are implemented in the Design Analysis Kit for Optimization and Terascale Applications or DAKOTA package, an open source design and optimization toolkit that was created by Sandia National Laboratories beginning in 2001, which was used to perform many of the analyses discussed in the paper.