A comparison of grey-box and black-box approaches in nonlinear state-space modelling and identification

In the present contribution, it is shown that, in the case of mechanical systems where nonlinearities are physically localised, the general structure of black-box nonlinear state-space models can be drastically simplified. A more parsimonious, grey-box state-space representation is derived, which is found to be compatible with Newton's second law of dynamics. For demonstration purposes, black-box and grey-box state-space models of the Silverbox benchmark, i.e. an electrical mimicry of a single-degree-of-freedom mechanical system with cubic nonlinearity, are identified using a maximum likelihood estimator. It is found that the grey-box approach allows to reduce markedly modelling errors with respect to a black-box model with a comparable number of parameters. It is also suggested that the greater accuracy of the grey-box model lends itself to the computation of reliable confidence bounds on the model parameters.