In many engineering applications the dynamics may significantly be affected by nonlinear effects, which must be accounted for in order to accurately understand and robustly model the dynamics. From a practical point of view, it is very important to solve the inverse problem related to system identification and output prediction. In this paper the recently developed Nonlinear Subspace Identification (NSI) method is presented and applied to an oscillator described by the Duffing equation, with different types of excitation including random forces, which are demonstrated to be very suitable for the identification process. The estimates of system parameters are excellent and, as a consequence, the behaviour of the system, including the jump phenomena, is reconstructed to a high level of fidelity. In addition, the possible memory limitations affecting the method are overcome by the development of a novel algorithm, based on a specific computation of the QR factorisation.
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