Geometric Uncertainty Analysis of Aerodynamic Shapes Using Multifidelity Monte Carlo Estimation

Uncertainty analysis is of great use both for calculating outputs that are more akin to real
flight, and for optimization to more robust shapes. However, implementation of uncertainty
has been a longstanding challenge in the field of aerodynamics due to the computational cost
of simulations. Geometric uncertainty in particular is often left unexplored in favor of uncer-
tainties in freestream parameters, turbulence models, or computational error. Therefore, this
work proposes a method of geometric uncertainty analysis for aerodynamic shapes that miti-
gates the barriers to its feasible computation. The process takes a two- or three-dimensional
shape and utilizes a combination of multifidelity meshes and Gaussian process regression
(GPR) surrogates in a multifidelity Monte Carlo (MFMC) algorithm. Multifidelity meshes
allow for finer sampling with a given budget, making the surrogates more accurate. GPR
surrogates are made practical to use by parameterizing major factors in geometric uncer-
tainty with only four variables in 2-D and five in 3-D. In both cases, two parameters control
the heights of steps that occur on the top and bottom of airfoils where leading and trailing
edge devices are attached. Two more parameters control the height and length of waves
that can occur in an ideally smooth shape during manufacturing. A fifth parameter controls
the depth of span-wise skin buckling waves along a 3-D wing. Parameters are defined to
be uniformly distributed with a maximum size of 0.4 mm and 0.15 mm for steps and waves
to remain within common manufacturing tolerances. The analysis chain is demonstrated
with two test cases. The first, the RAE2822 airfoil, uses transonic freestream parameters
set by the ADODG Benchmark Case 2. The results show a mean drag of nearly 10 counts
above the deterministic case with fixed lift, and a 2 count increase for a fixed angle of attack
version of the case. Each case also has small variations in lift and angle of attack of about
0.5 counts and 0.08◦, respectively. Variances for each of the three tracked outputs show that
more variability is possible, and even likely. The ONERA M6 transonic wing, popular due
to the extensive experimental data available for computational validation, is the second test
case. Variation is found to be less substantial here, with a mean drag increase of 0.5 counts,
and a mean lift increase of 0.1 counts. Furthermore, the MFMC algorithm enables accurate
results with only a few hours of wall time in addition to GPR training.