Experimental Testing and Identification of Bistable Systems for Seismic Energy Dissipation

The identification of dynamic parameters in nonlinear systems is a challenging task, particularly when dealing with experimental measurements. If the nonlinearity is negligible for the response, one can rely on linear techniques without compromising the accuracy of the solution. However, if the nonlinear effects are significant, as frequently happens under strong excitations, these assumptions do not hold anymore, and one should refer to more sophisticated methods. This is the case of bistable systems, i.e., systems characterised by two stable equilibria and one unstable equilibrium point. In experimental settings, additional uncertainties may arise from the definition of boundary conditions, materials, and manufacturing. In this context, the need for a technique capable of instantaneously tracking the nonlinear parameters of systems exhibiting rapid changes, such as the bistable ones, is fundamental. This requirement is mainly linked to the ultimate purpose of these systems, namely the dissipation and/or absorption in terms of instantaneous energy, which is critical in real -world applications. This work describes a novel method for experimentally measuring and identifying dynamic parameters of bistable systems. An instantaneous probabilistic estimator, constructed using an unscented Kalman filter (UKF), is proposed for the identification of the parameters governing the bistable dynamics. The method is validated by employing experimental measurements achieved during a testing campaign carried out on a 3D-printed bistable sample, with the final goal of estimating the instantaneous energy dissipated under different external excitations. To this end, an ad hoc testing machine, composed of a pendulum actuator, was built to accurately simulate the single degree-of-freedom model employed in the identification task. The procedure proved robust and reliable.