The Short Transformation Method to Predict the FRF of Dynamic Structures subject to Uncertainty

This paper aims to assess the effect of input uncertainty on FRF predictions obtained with Finite Element analysis. The Transformation Method (TM), presented by M. Hanss, uses a fuzzy approach based on interval arithmetic: the uncertain response is reconstructed from a set of deterministic responses, combining the extrema of each interval in every possible way. The TM is applicable if the output is monotonic in the inputs, otherwise an error is introduced. In this paper, the Short Transformation Method (STM) is proposed as an attractive alternative to the original TM, for dynamic analyses where the eigenfrequency values are monotonic in the uncertain inputs. A full set of deterministic responses is only performed at the lowest interval level. For higher levels, a smaller set is evaluated. The STM allows reconstructing the fuzzy FRF from a much lower number of deterministic computations, with only a small reduction in the accuracy of FRFs. Both methods are demonstrated on a car front cradle with uncertain design parameters.