  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.
