Least-Squares Support Vector Machines for the identification of Wiener–Hammerstein systems

This paper considers the identification of Wiener–Hammerstein systems using Least-Squares Support Vector Machines based models. The power of fully black-box NARX-type models is evaluated and compared with models incorporating information about the structure of the systems. For the NARX models it is shown how to extend the kernel-based estimator to large data sets. For the structured model the emphasis is on preserving the convexity of the estimation problem through a suitable relaxation of the original problem. To develop an empirical understanding of the implications of the different model design choices, all considered models are compared on an artificial system under a number of different experimental conditions. The obtained results are then validated on the Wiener–Hammerstein benchmark data set and the final models are presented. It is illustrated that black-box models are a suitable technique for the identification of Wiener–Hammerstein systems. The incorporation of structural information results in significant improvements in modeling performance.