Efficient functional representation of the structural mechanical response dependent on polymorphic uncertain parameters and uncertaintiesx

• Applicant: Professor Dr. Hermann Georg Matthies
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 341531955

The purpose of this project is to build an efficient computationalframework for the treatment of various polymorphic uncertainty descriptions for large scale structural problems characterized by a large number of uncertain parameters. Our main goal is to find efficient ways to produce accurate functional approximations (meta-, proxy-, surrogate-models, response surface) in these parameters which will support different uncertainty descriptions, such as probabilistic, belief functions, and imprecise probabilities. This will be achieved by a suitable optimal re-parametrization of uncertainties to the forms which are consistent with the observation data and adherent to the physical laws, and are most suitable for separable low-rank tensor approximations. Together with the adaptive functional approximation algorithms such representations will enable fast surrogate models easily tuned to the particular structural problem.Once found, parameterised models can be combined with low-rank procedures for the purpose of reducing uncertainty in the model, or for upscaling from a fine to a coarse model in a later project phase. In addition, the solution of both the forward and inverse problems can be considered as one whole adaptive process.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1886: Polymorphic uncertainty modelling for the numerical design of structures
• Co-Investigator: Dr.-Ing. Bojana Rosic