Nonlinear system identification through backbone curves and Bayesian inference

Abstract

Nonlinear structures exhibit complex behaviors that can be predicted and analyzed once a mathematical model of the structure is available. Obtaining such a model is a challenge. Several works in the literature suggest different methods for the identification of nonlinear structures. Some of the methods only address the question of whether the system is linear or not, others are more suitable for localizing the source of nonlinearity in the structure, only a few suggest some quantification of the nonlinear terms. Despite the effort made in this field, there are several limits in the identification methods suggested so far, especially when the identification of a multi-degree of freedom (MDOF) nonlinear structure is required. This work presents a novel method for the identification of nonlinear structures. The method is based on estimating backbone curves and the relation between backbone curves and the response of the system in the frequency domain. Using a Bayesian framework alongside Markov chain Monte Carlo (MCMC) methods, nonlinear model parameters were inferred from the backbone curves of the response and the Second Order Nonlinear Normal Forms which gives a relationship between the model and the backbone curve. The potential advantage of this method is that it is both efficient from a computation and from an experimental point of view.