Dynamic shape reconstruction of a notched beam by proportional observer and multi-resolution analysis

A novel virtual sensing technique aimed at reconstructing the displacement field throughout the structure from pointwise measurements is here exploited for dynamic shape reconstruction of a notched beam. This estimator is a proportional observer that exploits a linear, frequency independent, relation between the estimated state-space vector and the measurements. To improve its accuracy, this concept is augmented to the definition of a sequence of proportional observers, each one acting on a signal decomposition provided by wavelet multi-resolution analysis. The considered experimental test case is a straight, uniform beam with an unmodeled stiffness and mass reduction. The strain data are provided by strain gauges positioned on the top face of the beam, whereas the estimated state variables are the time dependent coordinates of the modal expansion of the vertical displacement along the beam elastic axis. An optimization solver, which minimizes the estimation error, is employed to get the optimal gain matrix of the proposed observer.