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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Computation |
| Subjects: | |
| 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. |
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| ISSN: | 2079-3197 |