Sparse polynomial chaos expansion for high-dimensional nonlinear damage mechanics

authored by: Esther dos Santos Oliveira, Udo Nackenhorst
Abstract: Finite Element Simulations in solid mechanics are nowadays common practice in engineering. However, considering uncertainties based on this powerful method remains a challenging task, especially when nonlinearities and high stochastic dimensions have to be taken into account. Although Monte Carlo Simulation (MCS) is a robust method, the computational burden is high, especially when a nonlinear finite element analysis has to be performed behind each sample. To overcome this burden, several “model-order reduction” techniques have been discussed in the literature. Often, these studies are limited to quite smooth responses (linear or smooth nonlinear models and moderate stochastic dimensions). This paper presents systematic studies of the promising Sparse Polynomial Chaos Expansion (SPCE) method to investigate the capabilities and limitations of this approach using MCS as a benchmark. A nonlinear damage mechanics problem serves as a reference, which involves random fields of material properties. By this, a clear limitation of SPCE with respect to the stochastic dimensionality could be shown, where, as expected, the advantage over MCS disappears. As part of these investigations, options to optimise SPCE have been studied, such as different error measures and optimisation algorithms. Furthermore, we have found that combining SPCEs with sensitivity analysis to reduce the stochastic dimension improves accuracy in many cases at low computational cost.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: Probabilistic Engineering Mechanics
Volume: 75
No. of pages: 12
ISSN: 0266-8920
Publication date: 01.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Civil and Structural Engineering, Nuclear Energy and Engineering, Condensed Matter Physics, Aerospace Engineering, Ocean Engineering, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.probengmech.2023.103556 (Access: Closed)

BibTeX

@article{6ac935f337664eaa88c817da2a9151b0,
title = "Sparse polynomial chaos expansion for high-dimensional nonlinear damage mechanics",
abstract = "Finite Element Simulations in solid mechanics are nowadays common practice in engineering. However, considering uncertainties based on this powerful method remains a challenging task, especially when nonlinearities and high stochastic dimensions have to be taken into account. Although Monte Carlo Simulation (MCS) is a robust method, the computational burden is high, especially when a nonlinear finite element analysis has to be performed behind each sample. To overcome this burden, several “model-order reduction” techniques have been discussed in the literature. Often, these studies are limited to quite smooth responses (linear or smooth nonlinear models and moderate stochastic dimensions). This paper presents systematic studies of the promising Sparse Polynomial Chaos Expansion (SPCE) method to investigate the capabilities and limitations of this approach using MCS as a benchmark. A nonlinear damage mechanics problem serves as a reference, which involves random fields of material properties. By this, a clear limitation of SPCE with respect to the stochastic dimensionality could be shown, where, as expected, the advantage over MCS disappears. As part of these investigations, options to optimise SPCE have been studied, such as different error measures and optimisation algorithms. Furthermore, we have found that combining SPCEs with sensitivity analysis to reduce the stochastic dimension improves accuracy in many cases at low computational cost.",
keywords = "Damage modelling, Effective sampling, High-dimensional, Random field, Sparse polynomial chaos expansion",
author = "{dos Santos Oliveira}, Esther and Udo Nackenhorst",
year = "2024",
month = jan,
doi = "10.1016/j.probengmech.2023.103556",
language = "English",
volume = "75",
journal = "Probabilistic Engineering Mechanics",
issn = "0266-8920",
publisher = "Elsevier Ltd.",
}