#### Date of Award

9-2004

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Department of Aeronautics and Astronautics

#### First Advisor

Paul I. King, PhD

#### Abstract

There is a growing interest in understanding how uncertainties in flight conditions and structural parameters affect the character of a limit cycle oscillation (LCO) response, leading to failure of an aeroelastic system. Uncertainty quantification of a stochastic system (parametric uncertainty) with stochastic inputs (initial condition uncertainty) has traditionally been analyzed with Monte Carlo simulations (MCS). Probability density functions (PDF) of the LCO response are obtained from the MCS to estimate the probability of failure. A candidate approach to efficiently estimate the PDF of an LCO response is the stochastic projection method. The objective of this research is to extend the stochastic projection method to include the construction of B-spline surfaces in the stochastic domain. The multivariate B-spline problem is solved to estimate the LCO response surface. An MCS is performed on this response surface to estimate the PDF of the LCO response. The probability of failure is then computed from the PDF. This method is applied to the problem of estimating the PDF of a subcritical LCO response of a nonlinear airfoil in inviscid transonic flow. The stochastic algorithm provides a conservative estimate of the probability of failure of this aeroelastic system two orders of magnitude more efficiently than performing an MCS on the governing equations.

#### AFIT Designator

AFIT-DS-ENY-04-03

#### DTIC Accession Number

ADA426657

#### Recommended Citation

Millman, Daniel R., "Quantifying Initial Condition and Parametric Uncertainties in a Nonlinear Aeroelastic System with an Efficient Stochastic Algorithm" (2004). *Theses and Dissertations*. 3904.

https://scholar.afit.edu/etd/3904

#### Included in

Aerodynamics and Fluid Mechanics Commons, Design of Experiments and Sample Surveys Commons