Assessment of uncertainty on structural dynamic responses with the short transformation method

Abstract

The predictive capability of finite element models is limited by their deterministic nature: typically, not all model parameters are exactly known, while even small deviations may have significant effects on the predicted response. Parameter uncertainty should therefore be taken into account, e.g. with fuzzy arithmetic. The absence of fuzzy solvers led to interval arithmetic as a numerical alternative. The Transformation Method (TM), presented by M. Hanss, replaces interval arithmetic with a set of deterministic computations: for each interval, all parameter extrema are combined in every possible way. In a Design of Experiments terminology, the TM is a so-called Full Factorial design. The TM is applicable if the output is monotonic in the inputs. Unlike interval arithmetic, it does not overestimate the response uncertainty, as only parameter combinations are evaluated that actually occur. In this paper, the TM has been applied to visualise uncertain frequency response functions (FRFs), obtained with modal superposition. This yields accurate results when validated against Monte Carlo data, but the computation time is rather high. The Short Transformation Method (STM) is proposed as an attractive alternative to the original TM. A full set of deterministic computations, combining all interval extrema, is only performed at the lowest interval. For higher levels, a smaller set is evaluated. This 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 clamped plate and a car front cradle with uncertain design parameters.