System identification of strongly nonlinear dynamics

We provide a review of current efforts for developing a nonlinear system identification (NSI) methodology of broad applicability. We propose a methodology with analytical, computational and post-processing components, including slow flow constructions, empirical mode decompositions, and wavelet / Hilbert transforms. The proposed methodology accounts for the fact that typically nonlinear systems are energy- and initial condition-dependent, and has both global and local components. In the global aspect of NSI, the dynamics is represented in a frequency - energy plot (FEP), whereas in the local aspect sets of intrinsic modal oscillators are constructed to model specific nonlinear transitions on the FEP. Application to identification of the dynamics of a vibro-impacting beam is provided.