On Fractional Moment Estimation from Polynomial Chaos Expansion
Lukáš Novák Marcos Valdebenito Matthias Faes
Fractional statistical moments are utilized for various tasks of uncertainty
quantification, including the estimation of probability distributions. However,
an estimation of fractional statistical moments of costly mathematical models
by statistical sampling is challenging since it is typically not possible to
create a large experimental design due to limitations in computing capacity.
This paper presents a novel approach for the analytical estimation of
fractional moments, directly from polynomial chaos expansions. Specifically,
the first four statistical moments obtained from the deterministic PCE
coefficients are used for an estimation of arbitrary fractional moments via
H\"{o}lder's inequality. The proposed approach is utilized for an estimation of
statistical moments and probability distributions in three numerical examples
of increasing complexity. Obtained results show that the proposed approach
achieves a superior performance in estimating the distribution of the response,
in comparison to a standard Latin hypercube sampling in the presented examples.