The component mode transformation method: A fast implementation of fuzzy arithmetic for uncertainty management in structural dynamics

The study of mechanical systems with uncertain parameters is of increasing importance in the analysis and in the design of structures, because an adequate description of these uncertainties is necessary to provide a reliable forecasting model. In order to update or evaluate an uncertain model, different methods have been proposed, but many of these, such as the Monte Carlo simulation or the transformation method, require multiple sequential evaluations of the model. Moreover, to cover an adequate portion of the uncertain parameter space, the number of necessary evaluations of the model grows exponentially with the number of uncertain parameters, leading often to a large number of runs. The proposed methodology deals with uncertain parameters that are modeled by the use of fuzzy numbers, and the transformation method is applied to characterize the dynamic behavior of the structure. In order to reduce the order of magnitude of the computational time, a reduction of the model dimension, obtained through a component mode synthesis, is performed. Advantages and drawbacks of the proposed method are discussed together with an application to the study of the dynamics of a beam.