Stochastic finite element model updating and its application in aeroelasticity

Knowledge in the field of modelling and predicting the dynamic responses of structures is constantly developing. Modelling of uncertainty is considered as one of the tools that increases confidence by providing extra information. This information may then be useful in planning physical tests. However, the complexity of structures together with uncertainty-based methods leads inevitably to increased computation; therefore deterministic approaches are preferred by industry and a safety factor is incorporated to account for uncertainties. However, the selection of a proper safety factor relies on engineering insight. Hence, there has been much interest in developing efficient uncertainty-based methods with a good degree of accuracy. This thesis focuses on the uncertainty propagation methods; namely Monte Carlo Simulation, first-order and second-order perturbation, asymptotic integral, interval analysis, fuzzy-logic analysis and meta-models. The feasibility of using these methods (in terms of computational time) to propagate structural model variability to linear and Computational Fluid Dynamic (CFD) based aeroelastic stability is investigated. In this work only the uncertainty associated with the structural model is addressed, but the approaches developed can be also used for other types of non-structural uncertainties. Whichever propagation method is used, an issue of very practical significance is the initial estimation of the parameter uncertainty to be propagated particularly when the uncertain parameters cannot be measured, such as damping and stiffness terms in mechanical joints or material-property variability. What can be measured is the variability in dynamic behaviour as represented by natural frequencies, mode shapes, or frequency response functions. The inverse problem then becomes one of inferring the parameter uncertainty from statistical mea-