Detail publikačního výsledku

On fractional moment estimation from polynomial chaos expansion

NOVÁK, L.; VALDEBENITO, M.; FAES, M.

Originální název

On fractional moment estimation from polynomial chaos expansion

Anglický název

On fractional moment estimation from polynomial chaos expansion

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

NOVÁK, L.; VALDEBENITO, M.; FAES, M.

Rok RIV

2026

Vydáno

01.02.2025

Nakladatel

ELSEVIER SCI LTD

Místo

London

ISSN

0951-8320

Periodikum

RELIABILITY ENGINEERING & SYSTEM SAFETY

Svazek

254

Číslo

February

Stát

Spojené království Velké Británie a Severního Irska

Strany počet

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"
}