Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

Zhiheng Wang, Philippe Hawi, Sami Masri, Venkat Aitharaju and Roger Ghanem

Reliability Engineering and System Safety, 2023, vol. 235, issue C

Abstract: This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ†. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. A robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

Keywords: Multiscale modeling; Uncertainty quantification; Extended polynomial chaos expansion; Model error; Statistical error; Sensitivity (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:235:y:2023:i:c:s095183202300128x

DOI: 10.1016/j.ress.2023.109213

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