Finite-time invariant manifold detection from experimental phase space trajectories
Recent advances in the generalization of invariant manifold concepts to finite-time have provided a means for understanding the structure of complex flows. Existing methods for finite-time invariant manifold detection require knowledge of the flow field, which limits application of these methods in practical problems, such as experimental vibrations. This work explores finite-time invariant manifold detection when only experimentally determined phase space trajectories are available. Several existing (but modified) manifold detection methods and a new method based on the concept of Phase Space Warping are tested for detection ability, data requirements, and noise sensitivity on numerically simulated experimental data of the damped driven two-well Duffing equation. The findings are then confirmed on experimentally recorded data from Moon's beam. It is found that accurate manifold identification is possible when only phase space trajectory data is available. In addition, the new phase space warping method is shown to generalize the popular finite-time Lyapunov exponent method. It is our hope that these findings will open the field of experimental vibrations to finite-time invariant manifold analysis, which provides a means to better understand the underlying structure in dynamical systems, and provide new insight into the generalization of invariant manifold concepts to finite-time, via the phase space warping interpretation. ^
Joseph J Kuehl,
"Finite-time invariant manifold detection from experimental phase space trajectories"
Dissertations and Master's Theses (Campus Access).