Journal article
Toward uncertainty quantification with arbitrarily dependent probability distributions of random input
Computer methods in applied mechanics and engineering, Vol.454, 118845
06/01/2026
DOI: 10.1016/j.cma.2026.118845
Abstract
This paper puts forward a novel and practical adaptation of generalized polynomial dimensional decomposition (GPDD) for uncertainty quantification (UQ) in the presence of dependent input random variables with arbitrary, non-product-type probability distributions. Instead of relying on a Rodrigues-type formula, which exists only for select probability measures, a new four-step computational algorithm is introduced to generate approximate, measure-consistent multivariate orthogonal polynomials in subsets of input variables. Unlike generalized polynomial chaos expansion (GPCE), which requires the full joint input distribution to construct its orthogonal polynomial basis, GPDD operates using only low-variate marginal distributions, allowing efficient dimensionwise construction even when the joint distribution is unknown. For high-dimensional stochastic problems characterized by strongly nonlinear output but weak input interactions, GPDD is expected to deliver substantial computational advantages over GPCE due to its hierarchical, dimensionwise structure. Numerical experiments involving both Gaussian and non-Gaussian probability measures on rectangular and non-rectangular domains show that the proposed algorithm produces highly accurate orthogonal polynomials. Results from representative mathematical and structural examples demonstrate that GPDD provides accurate and computationally efficient estimates of statistical moments and reliability, while an engineering application involving stochastic stress analysis of a vehicle suspension control arm with 34 random variables further highlights GPDD’s practical effectiveness for high-dimensional UQ problems.
Details
- Title: Subtitle
- Toward uncertainty quantification with arbitrarily dependent probability distributions of random input
- Creators
- Md Rashel Talukdar - University of IowaSharif Rahman - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Computer methods in applied mechanics and engineering, Vol.454, 118845
- DOI
- 10.1016/j.cma.2026.118845
- ISSN
- 0045-7825
- eISSN
- 1879-2138
- Publisher
- Elsevier B.V
- Grant note
- U.S. National Science Foundation: CMMI-2317172
U.S. National Science Foundation (Grant No. CMMI-2317172) .
- Language
- English
- Electronic publication date
- 02/26/2026
- Date published
- 06/01/2026
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9985141873102771
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