Generation of initial estimates for Wiener-Hammerstein models via basis function expansions

Abstract

Block-oriented models are often used to model nonlinear systems. They consist of linear dynamic (L) and nonlinear static (N) sub-blocks. This paper proposes a method to generate initial values for a Wiener-Hammerstein model (LNL cascade). The method starts from the best linear approximation (BLA) of the system, which provides an estimate of the product of the transfer functions of the two linear dynamic sub-blocks. Next, the poles of the BLA are assigned to both linear dynamic sub-blocks. The linear dynamics are then parameterized in terms of rational orthonormal basis functions, while the nonlinear sub-block is parameterized by a polynomial. This allows to reformulate the model to the cascade of a parallel Wiener (with parallel LN structure) and a linear dynamic system, which is bilinear in its parameters. After a bilinear optimization, the parallel Wiener part is projected to a single-branch Wiener model. The approach is illustrated on a simulation example.