Robust uncertainty quantification in structural dynamics under scarse experimental modal data: A Bayesian-interval approach

The accurate prediction of the dynamic behaviour of a complex component or system is often difficult due to uncertainty or scatter on the physical parameters in the underlying numerical models. Over the past years, several non-deterministic techniques have been developed to account for these model inaccuracies, supporting an objective assessment of the effect of these uncertainties on the dynamic behaviour. Still, also these methods require a realistic quantification of the scatter in the uncertain model properties in order to have any predictive value. In practice, this information is typically inferred from experiments. This uncertainty quantification is especially challenging in case only fragmentative or scarce experimental data are available, as is often the case when using modal data sets. This work therefore studies the application of these limited data sets for this purpose, and focuses more specifically on the quantification of interval uncertainty based on limited information on experimentally obtained eigenfrequencies. The interval approach, which is deemed to be the most robust against data insufficiency, typically starts from bounding the data using the extreme values in the limited data set. This intuitive approach, while of course representing the experiments, in general yields highly unconservative interval estimates, as the extreme realisations are typically not present in the limited data set. This work introduces a completely new approach for quantifying the bounds on the dynamic properties under scarce modal data. It is based on considering a complete set of parametrized probability density functions to determine likelihood functions, which can then be used in a Bayesian framework. To illustrate the practical applicability of the proposed techniques, the methodology is applied to the well-known DLR AIRMOD test case where in a first step, the bounds on the experimental eigenfrequencies are estimated. Then, based on a calibrated finite element model of the structure, bounds on the frequency response functions are estimated. It is illustrated that the method allows for a largely objective estimation of conservative interval bounds under scarce data.