Publication detail

On fractional moment estimation from polynomial chaos expansion

NOVÁK, L. VALDEBENITO, M. FAES, M.

Original Title

On fractional moment estimation from polynomial chaos expansion

Type

journal article in Web of Science

Language

English

Original Abstract

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 coefficients of polynomial chaos expansion are used for an estimation of arbitrary fractional moments via H & ouml;lder's inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in four 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.

Keywords

Polynomial chaos expansion; Fractional moments; Statistical analysis; H & ouml;lder's inequality

Authors

NOVÁK, L.; VALDEBENITO, M.; FAES, M.

Released

1. 2. 2025

Publisher

ELSEVIER SCI LTD

Location

London

ISBN

0951-8320

Periodical

RELIABILITY ENGINEERING & SYSTEM SAFETY

Year of study

254

Number

February

State

United Kingdom of Great Britain and Northern Ireland

Pages count

12

URL

https://www.sciencedirect.com/science/article/pii/S0951832024006653

BibTex

@article{BUT191345,
  author="Lukáš {Novák} and Marcos {Valdebenito} and Matthias {Faes}",
  title="On fractional moment estimation from polynomial chaos expansion",
  journal="RELIABILITY ENGINEERING & SYSTEM SAFETY",
  year="2025",
  volume="254",
  number="February",
  pages="12",
  doi="10.1016/j.ress.2024.110594",
  issn="0951-8320",
  url="https://www.sciencedirect.com/science/article/pii/S0951832024006653"
}