Stochastic Up-Scaling of Discrete Fine-Scale Models Using Bayesian Updating

In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters f...

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Bibliographic Details
Main Authors: Muhammad Sadiq Sarfaraz, Bojana V. Rosić, Hermann G. Matthies
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Computation
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Online Access:https://www.mdpi.com/2079-3197/13/3/68
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Summary:In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters from fine-scale measurements, which is discrete and also inherently random (<i>aleatory</i> uncertainty) in nature. Owing to the completely dissimilar nature of models for the involved scales, the energy is used as the essential medium (i.e., the predictions of the coarse-scale model and measurements from the fine-scale model) of communication between them. This task is realized computationally using a generalized version of the Kalman filter, employing a functional approximation of the involved parameters. The approximations are obtained in a <i>non-intrusive</i> manner and are discussed in detail especially for the fine-scale measurements. The demonstrated numerical examples show the utility and generality of the presented approach in terms of obtaining calibrated coarse-scale models as reasonably accurate approximations of fine-scale ones and greater freedom to select widely different models on both scales, respectively.
ISSN:2079-3197