  A nonlinear model relating the imposed motion of a circular cylinder,
submerged in a fluid flow, to the transverse force coefficient is presented.
The nonlinear fluid system, featuring vortex shedding patterns, limit cycle
oscillations and synchronisation, is studied both for swept sine and multisine
excitation. A nonparametric nonlinear distortion analysis (FAST) is used to
distinguish odd from even nonlinear behaviour. The information which is
obtained from the nonlinear analysis is explicitly used in constructing a
nonlinear model of the polynomial nonlinear state-space (PNLSS) type. The
latter results in a reduction of the number of parameters and an increased
accuracy compared to the generic modelling approach where typically no such
information of the nonlinearity is used. The obtained model is able to
accurately simulate time series of the transverse force coefficient over a wide
range of the frequency-amplitude plane of imposed cylinder motion.
