Journal article
Higher-order moments of spline chaos expansion
Probabilistic engineering mechanics, Vol.77, 103666
07/2024
DOI: 10.1016/j.probengmech.2024.103666
Abstract
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.
Details
- Title: Subtitle
- Higher-order moments of spline chaos expansion
- Creators
- Sharif Rahman - College of Engineering, The University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Probabilistic engineering mechanics, Vol.77, 103666
- Publisher
- Elsevier Ltd
- DOI
- 10.1016/j.probengmech.2024.103666
- ISSN
- 0266-8920
- eISSN
- 1878-4275
- Grant note
- CMMI-2317172 / U.S. National Science Foundation P116S210005 / U.S. Department of Education
- Language
- English
- Date published
- 07/2024
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984687783902771
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