Development of Nonlinear Black Box Models using Orthonormal Basis Filters: A Review*

Over the last two decades, there has been a growing interest in the use of orthonormal basis filters (OBF) for developing dynamic black box models. When compared with the conventional approach, a substantial dimensionality reduction can be achieved through OBF parameterization. Moreover, the orthonormal filters, because of their similarity to the Padé approximation, can model systems that exhibit long time delays. Due to these advantages, several authors have recently resorted to OBF based parameterization of block oriented nonlinear black box models. This paper presents a review of nonlinear output error (NOE) and nonlinear ARX (NARX) model development using OBF. To begin with, the linear time series modelling using OBF parameterization is briefly reviewed. The methods available in the literature for the development of models with Wiener, Hammerstein and Wiener-Hammerstein structures are presented next. Features and properties of different model structures are examined in the light of their abilities to model the unmeasured disturbances and to capture complex nonlinear behaviour, such as input and output multiplicities.