The MS focuses on the process of modeling, quantifying and estimating the effects of uncertainties that characterize irreversible/dissipative material behavior in quasi-static and dynamic conditions. Particular examples of great significance include metal fatigue and concrete fracture analysis, as well as material aging of bone tissues. Moreover, special attention will be paid to the multi-scale and multi-fidelity nature of these problems, as well as to Bayesian analysis and corresponding design of experiments. Numerical tools to be discussed are low-rank functional approximations, Bayesian learning, optimization, stochastic Galerkin, polynomial chaos expansion, and stochastic homogenization, to name just a few.
08:30
Bayesian study of metallic fatigue data considering spatial Poisson processes
Marco Scavino | KAUST | Saudi Arabia
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Authors:
Marco Scavino | KAUST | Saudi Arabia
Ivo Babuska | ICES, University of Texas | United States
Barna Szabo | ESRD | United States
Zaid Sawlan | KAUST | Saudi Arabia
Raul F. Tempone | RWTH Aachen and KAUST | Germany
We analyze the performance of a proposed spatial Poisson model on data from fatigue experiments on notched and unnotched sheet specimens of 75S-T6 aluminium alloys. The model parameters are calibrated for the individual data sets and their combination. We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. Bayesian approach is applied to estimate the survival-probability function for any specimen tested under a prescribed fatigue experimental setup. Finally, cross-validation analysis is performed to predict the life of specimens with geometries not considered in the calibration stage.
09:00
A weighted least squares approach for Bayesian inversion
Philipp Trunschke | WIAS Berlin | Germany
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Philipp Trunschke | WIAS Berlin | Germany
Reinhold Schneider | TU Berlin | Germany
Martin Eigel | WIAS Berlin | Germany
We consider an explicit Bayesian inversion approach where the parameter distribution is determined in a functional form without requiring any sampling. This is possible if the forward model is already available in a functional representation. To obtain this with minimal computational effort, we derive an optimal sampling strategy for a weighted least squares method in hierarchical tensor formats, extending previous results from linear to nonlinear function spaces.
09:30
- CANCELED - Uncertainty Propagation in a reinforced concrete damage model with localised failure
Simona Dobrilla | TU Braunschweig | Germany
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Authors:
Simona Dobrilla | TU Braunschweig | Germany
Bojana Rosic | University of Twente | Netherlands
Hermann G. Matthies | TU Braunschweig | Germany
Adnan Ibrahimbegovic | IUF-Institute Universitaire de France | France
Uncertainty quantification and parameter estimation typically require numerous forward model simulations in order to accurately characterise uncertainties in model response. A major challenge in the application of sampling methods to UQ is the high computational cost due to the complexity of the forward model. To overcome this difficulty, one can construct a proxy model which approximates the model response at much lower computational cost without a significant loss of accuracy. In this regard, efficient uncertainty quantification can be achieved by representing the output by functional approximation. Another challenge which arises from the complexity of the numerical model are the nonlinearities in the model response. Namely, when forward model exhibits sharp gradients across a certain region in the parameter space, functional approximation of the global model response, which relies upon the assumption of smoothness of the input-output relationship, becomes extremely inaccurate. This calls for a novel approach which requires exploring smoothness of the integrand.
10:00
Stochastic material modelling and multifidelity uncertainty quantification of bone tissue
Sharana Kumar Shivanand | TU Braunschweig | Germany
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Authors:
Sharana Kumar Shivanand | TU Braunschweig | Germany
Bojana Rosic | University of Twente | Netherlands
Hermann G. Matthies | TU Braunschweig | Germany
Human bone tissue is a typical example of material which exhibits randomness in the mechanical response due to an uncertain heterogeneous micro-structure and uncertain directional dependency of material constants. By extending already existing deterministic models derived from the Helmholtz free energy, the objective of this talk is to develop an appropriate heterogeneous-anisotropic material description in a probabilistic framework. In this study, instead of performing stochastic parametric modelling of material constants belonging to a given material symmetry, the emphasis is given on building the entire positive-definite elasticity tensor as random. Due to essentially large number of parameters describing the material model, the process of obtaining the functional representation of the stochastic response is often proven to be computationally expensive. To relieve the computational demand, in this work will be considered multi-fidelity uncertainty quantification approaches.