Uncertainty-based evaluation and coupling of mathematical and physical models

A procedure for coupling of mathematical and physical models is proposed in this paper. This process is based on a quantification of uncertainties in both models. The procedure allows to determine the influences of uncertainties in mathematical models, as well as in physical models. Moreover, the influences of scattering input parameters in the models are quantified. To assess a global model, the approach for evaluation of models based on the graph theory is applied. By comparing the quantitative model outputs of mathematical and physical models, the coincidence of model responses is shown and assessed. The evaluation of model responses allows a model selection for the coupling process. This process of coupling is based on weighting factors, which are directly related to the model uncertainties. Hence, the model coupling approach gives possibilities to verify the accuracy of used models, and to adopt the coupled model, to be more precise in predicting physical reality. The process of coupling is illustrated by an academic example of the fourth order partial differential equation for a cantilever beam. To create a synthetic model data of a virtual physical model and to validate obtained results, the analytical solution which is based on the Fourier method is used. As an example with real measurements, the model of a torsional loaded steel beam is considered.