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Uncertainty Propagation Methods
An extensive review of various methods available for uncertainty
propagation by Huyse and Walters can be found here. This page summarises our
literature survey on these methods. Various methods have been proposed
in literature for uncertainty
propagation:
1. Monte Carlo Simulations:
Monte Carlo simulations are the most accurate method of uncertainty
propagation. In the priliminary design stage, when computationally
inexpensive fluid models (like inviscid flow with drag correction) are
used, Monte Carlo simulations may be used. In case of computationally
expensive simulations (3D RANS), a surrogate model can be generated for
various confidence levels and then the Monte Carlo simulations can be
performed. For a good introduction to these methods can be found in the
paper from ASDL, Gatech, here.
2. Moment Method:
The simplest and most commonly used method is the method of moments. A
good illustration of this method can be found in the work by
Putko et. al. here. This
method is computational much cheaper than the full non-linear Monte
Carlo simulations. Traditionally, only the first order moments are
available for full non-linear CFD calculations. The accuracy of the
method may be improved by using higher order derivatives. Calculation
of higher order derivatives is computationally expensive and no known
automatic differentiation packages can calculate more than first order
derivatives. Use of adjoints has been successfully demonstrated in
propagating first order derivatives by alekseev et. al.
3. Polynomial Chaos:
Polynomial chaos was first introduced to the field of fluid dynamics
early to model turbulence. But it is not found to the optimal method
for modelling turbulence. Lately, a great interest has been shown by
researchers all over the world in polynomial chaos to propagate
geometric uncertainties and fluid model uncertainties through fluid
mechanics simulations. We have not investigated this method at all. But
some good pointers are here.
A brief study on effectiveness of various propagation methods as found
in the literature was carried on simple non-linear functions. We have
investigated first order, second order and third order moment methods
compared with complete non-linear Monte-Carlo simulations. These
results
are further compared with the super-convergent functional estimates
using adjoint error correction.
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