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

TL;DR

This paper introduces a grey-box state-space model for nonlinear mechanical vibrations that uses limited output data and a two-step identification process, demonstrated on a benchmark system.

Contribution

It presents a novel, parsimonious nonlinear state-space modeling approach with an integrated identification procedure for mechanical vibrations.

Findings

Effective modeling of nonlinear vibrations with limited measurements

Successful application to Silverbox benchmark

Combines subspace initialization with maximum likelihood optimization

Abstract

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 two-step identification procedure is derived for this grey-box model, integrating nonlinear subspace initialisation and maximum likelihood optimisation. The complete procedure is demonstrated on the Silverbox benchmark, which is an electrical mimicry of a single-degree-of-freedom mechanical system with one displacement-dependent nonlinearity.