Sparse polynomial chaos expansion for high-dimensional nonlinear damage mechanics

verfasst von: 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.
Organisationseinheit(en): Institut für Baumechanik und Numerische Mechanik
Typ: Artikel
Journal: Probabilistic Engineering Mechanics
Band: 75
Anzahl der Seiten: 12
ISSN: 0266-8920
Publikationsdatum: 01.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Statistische und nichtlineare Physik, Tief- und Ingenieurbau, Kernenergie und Kernkraftwerkstechnik, Physik der kondensierten Materie, Luft- und Raumfahrttechnik, Meerestechnik, Maschinenbau
Elektronische Version(en): https://doi.org/10.1016/j.probengmech.2023.103556 (Zugang: Geschlossen)

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.",
}