Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems

A Wiener model is a fairly simple, well known, and often used nonlinear block-oriented black-box model. A possible generalization of the class of Wiener models lies in the parallel Wiener model class. This paper presents a method to estimate the linear time-invariant blocks of such parallel Wiener models from input/output data only. The proposed estimation method combines the knowledge obtained by estimating the best linear approximation of a nonlinear system with the MAVE dimension reduction method to estimate the linear time-invariant blocks present in the model. The estimation of the static nonlinearity boils down to a standard static nonlinearity estimation problem starting from input-output data once the linear blocks are known.