Model-less forecasting of Hopf bifurcations in fluid-structural systems

Predicting critical transitions and post-transition dynamics of complex systems is a unique challenge. In this paper, a novel approach is introduced to forecast Hopf bifurcations and the post-bifurcation dynamics of nonlinear fluid-structural systems. The forecasting method is model-less and uses measurements of the system response collected only in the pre-bifurcation regime. To demonstrate the method, it is applied to a cantilever high aspect ratio wing exposed to gust loads as perturbations. To generate surrogate measurements required for forecasting bifurcations in this large-dimensional complex system, a nonlinear strain-based finite element formulation coupled with unsteady aerodynamics is used to model the fluid-structure interaction. Results show that the method successfully forecasts the linear flutter speed and the amplitude of the limit cycle oscillations that occur in the post-bifurcation regime. The procedure is shown to be time efficient, model-less, and to require only few measurements, which makes the proposed forecasting method a unique tool for nonlinear analysis of complex systems.