On fractional moment estimation from polynomial chaos expansion

IF 9.4 1区工程技术 Q1 ENGINEERING, INDUSTRIAL

Reliability Engineering & System Safety Pub Date : 2024-10-22 DOI:10.1016/j.ress.2024.110594

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引用次数: 0

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.

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从多项式混沌展开论分数矩估计

分数统计矩被用于各种不确定性量化任务，包括概率分布的估计。然而，由于计算能力的限制，通常无法创建大型实验设计，因此通过统计抽样估算高成本数学模型的分数统计矩具有挑战性。本文提出了一种直接从多项式混沌展开分析估计分数统计矩的新方法。具体来说，从多项式混沌展开的确定性系数中获得的前四个统计矩被用于通过荷尔德不等式估计任意分数矩。在四个复杂度不断增加的数值示例中，利用所提出的方法对统计矩和概率分布进行了估计。结果表明，与标准拉丁超立方采样相比，所提出的方法在估算响应分布方面具有更优越的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reliability Engineering & System Safety 管理科学-工程：工业

CiteScore

15.20

自引率

39.50%

发文量

621

审稿时长

67 days

期刊介绍： Elsevier publishes Reliability Engineering & System Safety in association with the European Safety and Reliability Association and the Safety Engineering and Risk Analysis Division. The international journal is devoted to developing and applying methods to enhance the safety and reliability of complex technological systems, like nuclear power plants, chemical plants, hazardous waste facilities, space systems, offshore and maritime systems, transportation systems, constructed infrastructure, and manufacturing plants. The journal normally publishes only articles that involve the analysis of substantive problems related to the reliability of complex systems or present techniques and/or theoretical results that have a discernable relationship to the solution of such problems. An important aim is to balance academic material and practical applications.