  The flow-induced vibration of bluff bodies is an important problem of many
marine, civil, or mechanical engineers. In the design phase of such structures,
it is vital to obtain good predictions of the fluid forces acting on the
structure. Current methods rely on computational fluid dynamic simulations
(CFD), with a too high computational cost to be effectively used in the design
phase or for control applications. Alternative methods use heuristic
mathematical models of the fluid forces, but these lack the accuracy (they
often assume the system to be linear) or flexibility to be useful over a wide
operating range.
  In this work we show that it is possible to build an accurate, flexible and
low-computational-cost mathematical model using nonlinear system identification
techniques. This model is data driven: it is trained over a user-defined region
of interest using data obtained from experiments or simulations, or both. Here
we use a Van der Pol oscillator as well as CFD simulations of an oscillating
circular cylinder to generate the training data. Then a discrete-time
polynomial nonlinear state-space model is fit to the data. This model relates
the oscillation of the cylinder to the force that the fluid exerts on the
cylinder. The model is finally validated over a wide range of oscillation
frequencies and amplitudes, both inside and outside the so-called lock-in
region. We show that forces simulated by the model are in good agreement with
the data obtained from CFD.
