Inverse Fuzzy Arithmetic for the Quality Assessment of Substructured Models

The dynamical analysis of complex structures often suffers from large computational efforts, so that the application of substructuring methods has gained increasing importance in the last years. Substructuring enables dividing large finite element models and reducing the resulting multiple bodies, yielding a reduction of, in this case, complex eigenvalue calculation time. This method is used to predict the appearance of friction-induced vibrations such as squeal in brake systems. Since the method is very sensitive to changes in parameter values, uncertainties influencing the results are included and identified. As uncertain parameters, standard coupling elements are considered and modeled by so-called fuzzy numbers, which are particularly well suited to represent epis- temic uncertainties of modeled physical phenomena. The influence of these uncertainties is transferred to undamped and damped eigenfrequencies of a substructured model by means of direct fuzzy analyses. An inverse fuzzy arithmetical approach is applied to identify the uncertain parameters that optimally cover the undamped reference eigenfrequencies of a non-substructured, full model. If a validity criteria is defined, a positive decision in favor of the most adequate model can be performed.