  Nonlinear state-space modelling is a very powerful black-box modelling
approach. However powerful, the resulting models tend to be complex, described
by a large number of parameters. In many cases interpretability is preferred
over complexity, making too complex models unfit or undesired. In this work,
the complexity of such models is reduced by retrieving a more structured,
parsimonious model from the data, without exploiting physical knowledge.
Essential to the method is a translation of all multivariate nonlinear
functions, typically found in nonlinear state-space models, into sets of
univariate nonlinear functions. The latter is computed from a tensor
decomposition. It is shown that typically an excess of degrees of freedom are
used in the description of the nonlinear system whereas reduced representations
can be found. The method yields highly structured state-space models where the
nonlinearity is contained in as little as a single univariate function, with
limited loss of performance. Results are illustrated on simulations and
experiments for: the forced Duffing oscillator, the forced Van der Pol
oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.
