  Many real world systems exhibit a quasi linear or weakly nonlinear behavior
during normal operation, and a hard saturation effect for high peaks of the
input signal. In this paper, a methodology to identify a parsimonious
discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical
system with relatively short data record is proposed. The capability of the
NLSS model structure is demonstrated by introducing two different
initialisation schemes, one of them using multivariate polynomials. In
addition, a method using first-order information of the multivariate
polynomials and tensor decomposition is employed to obtain the parsimonious
decoupled representation of the set of multivariate real polynomials estimated
during the identification of NLSS model. Finally, the experimental verification
of the model structure is done on the cascaded water-benchmark identification
problem.
