  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.
