State estimation of geometrically non-linear systems using reduced-order models

Slender structures with high stiffness-to-weight ratio form the main bearing element of modern engineering. This renders geometrical non-linear effects a key feature to be considered throughout the whole life-time of diverse structural components, such as Wind Turbine (WT) blades. Although the Finite Element (FE) method constitutes a well-established tool for the analysis of such systems, the resulting models are often prohibitively expensive in terms of computational resources and thus cannot be implemented in the design. The problem of state estimation for condition diagnostics and control applications is therefore rendered a challenging and intricate task when it comes to systems experiencing geometrical non-linearities. This is firstly due to the computationally demanding FE models associated with such systems and, secondly, to the requirement that estimation methods must consider non-linear phenomena. The problem is further pronounced in online applications, where real-time performance is required, as is commonly the case in structural health monitoring (SHM). Within this context, the focus is on computationally efficient models that operate on subspaces of significantly smaller size as compared to the full-order problem and which can be tailored to the framework of non-linear state estimation. This study proposes the implementation of physics-based reduced-order models (ROMs) for response prediction of systems featuring geometrically non-linear effects. In so doing, the concept of modal derivatives is adopted and combined with a flexible multibody approach in order to capture second-order effects, e.g. twist-bend coupling, that arise as the system departs from the linear regime. In identifying the vibration response of such structures, the ROMs are compounded with the unscented Kalman filter (UKF) for the non-linear state estimation. The outlined approach is tested on the real-time response prediction of a WT blade, assuming that a limited number of artificial vibration measurements is available. The effectiveness of the scheme is assessed as a tool for online SHM and vibration control.