样条混沌扩展的高阶矩

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
Sharif Rahman
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引用次数: 0

摘要

样条混沌展开(简称 SCE)是用输入随机变量和确定系数中的量纲一致的正交样条来表示输出随机变量的有限序列。本文报告了对 SCE 在计算输出随机变量的高阶矩(如果存在的话)时的近似质量进行评估的新结果。本文提供了一个新颖的数学证明,证明随着最大元素尺寸的减小,任意阶 SCE 的矩在任何程度的花键上都会收敛到精确矩。还进行了补充性数值分析,结果与理论结论一致。本文列举了一系列简单而相关的例子,以评定 SCE 与著名的多项式混沌扩展(PCE)的逼近质量。这些示例的结果表明,在本研究考虑的所有情况下,使用 SCE 计算的高阶矩都是收敛的。相比之下,大于两阶的 PCE 时刻可能收敛,也可能不收敛,这取决于输出函数的规则性或输入随机变量的概率度量。此外,当 SCE 和 PCE 产生的时刻都收敛时,在非光滑函数或输入随机变量的无界域存在的情况下,前者的收敛速度明显快于后者。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Higher-order moments of spline chaos expansion

Spline chaos expansion, referred to as SCE, is a finite series representation of an output random variable in terms of measure-consistent orthonormal splines in input random variables and deterministic coefficients. This paper reports new results from an assessment of SCE’s approximation quality in calculating higher-order moments, if they exist, of the output random variable. A novel mathematical proof is provided to demonstrate that the moment of SCE of an arbitrary order converges to the exact moment for any degree of splines as the largest element size decreases. Complementary numerical analyses have been conducted, producing results consistent with theoretical findings. A collection of simple yet relevant examples is presented to grade the approximation quality of SCE with that of the well-known polynomial chaos expansion (PCE). The results from these examples indicate that higher-order moments calculated using SCE converge for all cases considered in this study. In contrast, the moments of PCE of an order larger than two may or may not converge, depending on the regularity of the output function or the probability measure of input random variables. Moreover, when both SCE- and PCE-generated moments converge, the convergence rate of the former is markedly faster than the latter in the presence of nonsmooth functions or unbounded domains of input random variables.

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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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