Nonlinear system identification: Finding structure in nonlinear black-box models

The use of black-box models is wide-spread in signal processing and system identification applications. However, often such models possess a large number of parameters, and obfuscate their inner workings, as there are cross-connections between all inputs and all outputs (and possibly all internal states) of the model. Although black-box models have proven their success and wide applicability, there is a need to shed a light on what goes on inside the model. We have developed a tensor-based method that aims at pinpointing the nonlinearities of a given nonlinear model into a small number of univariate nonlinear mappings, with the advantageous side-effect of reducing the parametric complexity. In this contribution we will discuss how the method is conceived, and how it can be applied to the task of finding structure in blackbox models. We have found that the tensor-based decoupling method is able to reconstruct up to high accuracy a given blackbox nonlinear model, while reducing the parametric complexity and revealing some of the inner operation of the model. Due to their universal use, we will focus the presentation on the use of nonlinear state-space models, but the method is also suitable for other model structures. We validate the method on a case study in nonlinear system identification.