Towards Multi-scale Nonlinear (and Linear) System Identification in Structural Dynamics

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental oscillatory components, termed the intrinsic mode functions (IMFs). In this presentation, we describe a combination of methods involving numerical integral transforms and theoretical analysis that cumulate to a new nonparametric method for nonlinear system identification based on multiple slow-fast partitions of the dynamics. This method can find wide applicability to linear and (weakly or strongly) nonlinear systems with various damping and/or stiffness nonlinearities. Moreover, through this method we can systematically examine transient resonance captures in the responses of dynamically interacting nonlinear structures, hence, decomposing and identifying the underlying multimodal nonlinear modal interactions that give rise to complex phenomena.