System identification of nonlinear structures through a parametrically varying transfer function approach

Abstract

The current work presents a methodology for the identification of weakly nonlinear structures using a quasi-linearized description. Quasi-linearization, in this context, refers to the fact that it is possible to approximate weakly nonlinear systems as linear systems parameterized by some measure of their response amplitude. The paper formalizes this by describing the forced response by an amplitude-dependent transfer function written in a rational fraction polynomial form. The coefficients are estimated through a regularized iterative identification approach based on frequency-domain measurements. An $L_0$ regularization is used to promote sparsity/model simplicity, and a bi-objective optimization approach is developed for its tuning. Apart from serving to obtain an accuracy-sparsity trade-off, this procedure allows for a minimal realization of the transfer function that is also physically meaningful. Following analytical explorations on a Duffing oscillator, the developed framework is applied to three experimental benchmarks, encompassing geometrically nonlinear, frictional, and multi-physics interactions. The performance of the method is assessed in its ability to describe the fixed displacement forced response surfaces. Furthermore, the identified models are used to synthesize fixed excitation forced response and compared against measurements to obtain additional insights.