Grey-box state-space identification of nonlinear mechanical vibrations

TL;DR

This paper introduces a grey-box nonlinear state-space model for mechanical vibrations, utilizing limited measured outputs to identify localized nonlinearities, and demonstrates its effectiveness on electrical and mechanical systems.

Contribution

It presents a novel semi-physical identification method for nonlinear vibrations using a limited output-based state-space representation.

Findings

Effective identification of nonlinearities in mechanical systems

Successful application to electrical circuit and beam structure

Improved accuracy over purely black-box models

Abstract

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.