Development and Analysis of Methods for the Identification of Correlated Parameters in Multifield Problems

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The evaluation of the safety of buildings, which suffer from hydrological, temperature and mechanical loads, e.g., dams, is a highly demanding problem due to the interaction effects of the different fields.The estimation of the lifetime of such building is often linked to the question of the current state of damage.For existing structures the question arises, how existent cracks or damages can be identified with a high precision in a model-based approach. A possible scenario might be, that for a newly constructed building a validated and calibrated model has been derived. After some years of usage, and in particular after extreme events like earthquakes, cracks or damages might have occurred inside the structures.Those shall be identified by measurements of a relatively short time interval (e.g. one month) and the comparison with the existing model. The goal of the proposed project is the develop and analyze methods, which can consider during identification procedures possible correlations of main parameters (e.g. those to model damage) in a multi-field system. For example, in case of a damage in a dam one can expect in parallel a local increase of the hydraulic permeability and a local reduction of the mechanical stiffness.Such correlations can be considered explicitly during an inverse analysis, in order to improve the confidence in the detected quantities. For the proposed problem, the damage identification, cracks and damages will be described with the eXtended Finite Element Methode (XFEM). XFEM has established as a useful tool, in particular for inverse problems, as during the identification routines no re-meshing of the domain is necessary.The method to develop is of general character and might be applied to several multi-field identification problems in engineering and natural sciences, where correlations between the input parameters are known or can at least be estimated, e.g. piezoelectricity, magneto-electronics or thermo-mechanics. The proposed research project includes the development and analysis of mathematical models for the identification of parameters in a multi-field context and the validation of the derived methods with existing measurements of real buildings.