Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling

•A method to reduce nonlinear state-space models.•A revision of the approach to decouple multivariate polynomials into univariate polynomials.•Additional reshaping and reduction of the decoupled polynomial functions when used in nonlinear state-space models.•Successful application to a number of both numerical and experimental case studies.