Uncertainty Quantification in the Prediction of
Nonlinear Aeroelasticity
Chris L. Pettit, Ph.D., P.E.
Aerospace Engineering Dept.
United States Naval Academy
Annapolis, MD 21402
pettitcl@usna.edu
Basic probabilistic methods for linear systems have been employed in gust
analysis for several decades, but probabilistic study of aeroelastic stability is
a more recent development. Standard gust analysis methods assume
variability only in an idealized freestream gust velocity and depend on linear
structural dynamics to develop equivalent static design loads; thus, gust
analysis forces an inherently probabilistic process to conform to our
deterministic engineering philosophy. In contrast, recent research is the
outgrowth of a more holistic perspective on the role of uncertain system and
environment properties in establishing the probability of aeroelastic stability.
This approach can produce insight in all aeroelastic stability studies, but the
payoff likely will be greatest in analyzing the time-dependent behavior of
nonlinear systems owing to their generally higher sensitivity.
The presentation will describe current and anticipated prediction problems in
the movement toward a high-fidelity approach to aeroelastic design.
Although the presentation will be centered on aeronautical applications, the
underlying concepts should be relevant to many fluid-structure interaction
problems, especially in offshore structures and long-span bridges. Some
critical prediction difficulties have been uncovered through our efforts to
employ stochastic expansion methods to the study of limit cycles in an
elementary aeroelastic system. Practical issues that motivate these studies
will be summarized along with the underlying theory of Hermite expansions.
Our work has demonstrated that limit cycles cannot be represented in a timeaccurate manner through global Hermite expansions; however, we have
recently shown that a wavelet-based Hermite expansion substantially
eliminates the shortcomings of the global approach. The presentation will
conclude with some discussion of the need to develop new modeling and
design frameworks to enable the design of revolutionary aerospace vehicles.