Towards Development of Nonparametric System Identification Base Based on Slow-Flow Dynamics, with Application to Damage Detection and Uncertainty Quantification

A theoretical framework for a new nonlinear system identification NSI method was developed. An equivalence between analytical slow-flows of the dynamics, derived from complexification and averaging, and empirical slow-flows, obtained directly from data as the intrinsic mode functions resulting from empirical mode decomposition, was rigorously demonstrated. The NSI method was then formulated based on multiscale dynamic partitions and direct analysis of measured time series, with no presumptions regarding the type and strength of the system nonlinearity. In fact, the method is applicable to time-varianttime-invariant, linearnonlinear, and smoothnon-smooth dynamical systems. The method systematically leads to reduced order models of strongly nonlinear transitions in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. The method identifies not only the dominant time scales of the dynamics but also the nonlinear interactions across the scales of the dynamics.