A General Framework for Uncertainty Propagation Based on Point Estimate Methods

René Schenkendorf
Submission Type: 
Full Paper
phmce_14_073.pdf436.59 KBMay 29, 2014 - 9:52am

A general framework to approach the challenge of uncertainty
propagation in model based prognostics is presented in this
work. It is shown how the so-called Point Estimate Methods
(PEMs) are ideally suited for this purpose because of the
following reasons: 1) A credible propagation and representation
of Gaussian (normally distributed) uncertainty can be
done with a minimum of computational effort for non-linear
applications. 2) Also non-Gaussian uncertainties can be propagated
by evaluating suitable transfer functions inherently.
3) Confidence intervals of simulation results can be derived
which do not have to be symmetrically distributed around
the mean value by applying PEM in conjunction with the
Cornish-Fisher expansion. 4) Moreover, the entire probability
function of simulation results can be reconstructed efficiently
by the proposed framework. The joint evaluation of PEM
with the Polynomial Chaos expansion methodology is likely
to provide good approximation results. Thus, non-Gaussian
probability density functions can be derived as well. 5) The
presented framework of uncertainty propagation is derivativefree,
i.e. even non-smooth (non-differentiable) propagation
problems can be tackled in principle. 6) Although the PEM
is sample-based the overall method is deterministic. Computational
results are reproducible which might be important to
safety critical applications. - Consequently, the proposed approach
may play an essential part in contributing to render the
prognostic health management into a more credible process.
A given study of a generic uncertainty propagation problem
supports this issue illustratively.

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Submission Keywords: 
uncertainty propagation
RUL uncertainty
unscented transform
point estimate method
Submission Topic Areas: 
Uncertainty Quantification and Management in PHM
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