Nonlinear model calibration through bifurcation curves

Nonlinear systems exhibit a plethora of complex dynamic behaviours that are difficult to model and predict accurately. This difficulty often arises from a lack of knowledge of the physics that induces the nonlinear behaviours and the strong sensitivity of the nonlinear dynamics to parameter variation. We introduce in this paper a methodology to carry out nonlinear model updating based on bifurcations. The proposed approach involves minimizing the distance between experimental and numerical bifurcation curves, which are key dynamic features that define stability boundaries and regions of multi-stability. For the model, bifurcation curves are computed via standard numerical bifurcation tracking analyses. In the experiment, we use control-based continuation to obtain the data. The approach is first demonstrated on a Duffing and a beam system using synthetic data, before being applied to experimental data collected on a base-excited energy harvester with magnetic nonlinearity.