Model order reduction in space and parameter dimension - towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability

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The evaluation of robustness and reliability of realistic structures in the presence of polymorphic uncertainty involves numerical simulations with a very high number of degrees-of-freedom as well as parameters. Some of these parameters are certain in the way that they are a priori known. However, the second group of parameters is imprecise, vague, uncertain or based on incomplete information. In this group are many parameters which crucially influence the damage and failure behavior and as such have a strong influence on the load bearing capacity of a structure. It is of pivotal importance to include their uncertainty and fuzziness into the modelling. The main goal of the project is to develop a modeling framework for this purpose which uses extended model order reduction and hierarchical tensor approximation, together with a recently developed method of data-driven mechanics to significantly reduce the computational effort. The idea is to combine an adaptive method of proper orthogonal decomposition with hierarchical tensor approximation and intelligent data mechanics in such a way that the uncertain or fuzzy quantities of interest can be computed by simple functional evaluation. Quantities of interest are e.g. certain stress or deformation levels which shall not be exceeded. It is also conceivable to require the damage level going below a certain prescribed value.Although the focus of the project is on civil engineering structures, it is intended to make the method relatively generally applicable and in this way generate multiple cooperation possibilities within the priority program 1886. Therefore, the new combined tool of model reduction and hierarchical tensor approximation shall be open to several material models, various types of geometry description and finally also different notions of uncertainty and fuzziness. The flexibility with respect to the latter aspect is firstly given by the possibility to set up the original parameter space in many different ways. Secondly the evaluation of uncertainty or fuzziness is majorly simplified by the functional representation of the quantities of interest.