Parameter Estimation of Parallel Wiener-Hammerstein Systems by Decoupling their Volterra Representations

Abstract Nonlinear dynamic systems are often approximated by a Volterra series, which is a generalization of the Taylor series for systems with memory. However, the Volterra series lacks physical interpretation. To take advantage of the Volterra representation while aiming for an interpretable block-oriented model, we establish a link between the Volterra representation and the parallel Wiener-Hammerstein model, based on decoupling of multivariate polynomials. The true link is through a constrained decoupling model with (block-)Toeplitz structure on the factors and sets of identical internal branches. The solution of the modified decoupling problem then reveals directly the parameters of the parallel Wiener-Hammerstein model of the system. However, due to the uniqueness properies of the plain decoupling algorithm, even if the structure is not imposed, the method still leads to the true solution (in the exact case).