Non-linear System Identification Using the Hilbert-Huang Transform and Complex Non-linear Modal Analysis

Modal analysis is a well-established method for analysis of linear dynamic structures, but its extension to non-linear structures has proven to be much more problematic. A number of viewpoints on non-linear modal analysis as well as a range of different non-linear system identification techniques have emerged in the past, each of which tries to preserve a subset of properties of the original linear theory. The objective of this paper is to discuss how the Hilbert-Huang transform can be used for detection and characterization of non-linearity, and to present an optimization framework which combines the Hilbert-Huang transform and complex non-linear modal analysis for quantification of the selected model. It is argued that the complex non-linear modes relate to the intrinsic mode functions through the reduced order model of slow-flow dynamics. The method is demonstrated on simulated data from a system with cubic non-linearity.