Grey-box state-space identification of nonlinear mechanical vibrations
For engineers analyzing nonlinear mechanical vibrations, this work provides a practical grey-box identification approach that balances physical interpretability and data-driven flexibility.
The paper introduces a grey-box nonlinear state-space representation for identifying nonlinear mechanical vibrations, assuming localized nonlinearities. The method is validated on an electrical circuit and a geometrically nonlinear beam, achieving accurate identification.
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.