Initializing Wiener-Hammerstein models based on partitioning of the best linear approximation

This paper describes a new algorithm for initializing and estimating WienerHammerstein models. The algorithm makes use of the best linear model of the system which is split in all possible ways into two linear sub-models. For all possible splits, a WienerHammerstein model is initialized which means that a nonlinearity is introduced in between the two sub-models. The linear parameters of this nonlinearity can be estimated using leastsquares. All initialized models can then be ranked with respect to their fit. Typically, one is only interested in the best one, for which all parameters are fitted using prediction error minimization. The paper explains the algorithm and the consistency of the initialization is stated. Computational aspects are investigated, showing that in most realistic cases, the number of splits of the initial linear model remains low enough to make the algorithm useful. The algorithm is illustrated on an example where it is shown that the initialization is a tool to avoid many local minima.