Numerical Assessment of Polynomial Nonlinear State-Space and Nonlinear-Mode Models for Near-Resonant Vibrations

Identification of nonlinear systems using Polynomial Nonlinear State Space models

Grey-box nonlinear state-space modelling for mechanical vibrations identification

In the present paper, a flexible and parsimonious model of the vibrations of nonlinear mechanical systems is introduced in the form of state-space equations. It is shown that the nonlinear model terms can be formed using a limited number of output measurements. A twostep identification procedure is derived for this grey-box model, integrating nonlinear subspace initialisation and maximum likeli...

System identification of nonlinear state-space models

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the st...

Bayesian Learning in Nonlinear State-Space Models

We describe Bayesian learning in nonlinear state-space models (NSSMs). NSSMs are a general method for the probabilistic modelling of sequences and time-series. They take the form of iterated maps on continuous state-spaces, and can have either discrete or continuous valued output functions. They are generalizations of the more well known state-space models such as Hidden Markov models (HMMs), a...

Hysteresis Identification using Nonlinear State-Space Models

Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinea...