Efficient functional representation of the structural mechanical response dependent on polymorphic uncertain parameters and uncertainties
The project focuses on the developement of efficient numerical procedures with the aim of obtaining accurate adaptive low-rank representations of uncertain parameters and their functionals describing reinforced concrete beam structures. For this purpose already existing computational procedures for the propagation, identification, and stochastic upscaling of probabilistic uncertainties through parametric models will be extended to deal with more general descriptions of uncertanties such as Dempster-Shafer belief functions and imprecise probabilities, which may reflect a modeler’s ignorance, evidence incompleteness, or conflict. In this respect three main goals are to be achieved in the project:
- Imprecise probability modelling and quantification:
The material model of concrete is to be parameterised by taking into consideration experts’ knowledge, which may be conflicting. Therefore, the imprecise probability models according to Walley — previsions, Dempster-Shafer theory (DST) belief functions and transferable belief models to name but a few — will be used to describe the prior information. These will be compared to a robust Bayesian approach in which the distribution parameters are assumed to be uncertain and modelled by distributions that describe the imprecise modeller’s belief. As a result parametrised model described by a minimal number of uncertain parameters in a low-rank approximation will be provided. The uncertainties will be further propagated through the mechanical model by using the data-driven approaches combined with the reduced order modelling. - Learning from experimental data:
to include the imprecise probabilities the classical Bayes’s rule will be extended to a robust Bayesian analysis for which the prior and likelihoods are assumed to be uncertain and described by hierarhical distributions. In addition, the estimation will be generalised to the Dempster’s rule of combination or the transfer belief rule in case of highly conflicting information. Both approaches will be considered in an adaptive low-rank and sparse setting. - Multiscale modelling:
Concrete as a highly heterogeneous material is characterised by a random micro/meso-scale, which has a large influence on the behaviour of reinforced concrete beams. Therefore, the reinforced concrete will be considered on two different scales: a fine scale which incorporates uncertainties and can be observed either as a discrete model or as a very finely refined continuum model, and a coarse scale taking the form of a continuum model based on a standard generalised material theory. The coupling of the two scales will be done in a generalised Bayesian framework by using the energy conservation principles.
Prof. Dr. Hermann G. Matthies
Prof. Dr. Herman G. Matthies
Institut für Wissenschaftliches Rechnen
Technische Universität Braunschweig
Dr. Bojana Rosić
Dr.-Ing. Bojana Rosić
Institut für Wissenschaftliches Rechnen
Technische Universität Braunschweig
Truong Vinh Hoang
Dr. Truong Vinh Hoang
Institute of Scientific Computing
Technische Universität Braunschweig