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On fractional moment estimation from polynomial chaos expansion

Author

Listed:
  • Novák, Lukáš
  • Valdebenito, Marcos
  • Faes, Matthias

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 Hölder’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.

Suggested Citation

  • Novák, Lukáš & Valdebenito, Marcos & Faes, Matthias, 2025. "On fractional moment estimation from polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    • Handle: RePEc:eee:reensy:v:254:y:2025:i:pa:s0951832024006653
    DOI: 10.1016/j.ress.2024.110594
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