Identification of Wiener Models in the Presence of Structural Disturbances

In empirical system identification, non-stationary structural disturbances, such as trends and outliers, can have a negative effect on the estimation of the system parameters. As it not possible to determine a priori which parts of the measured data stem from structural disturbances and which are due to the system dynamics, the identification of structural disturbances and system model should be done simultaneously. In this study, a method for output error identification of nonlinear Wiener models in the case when the measurement is affected by trends and outliers is presented. The Wiener model can be described by a dynamic linear block followed by an static nonlinear block. In the proposed method the dynamic block is expanded using orthonormal basis functions, while the static nonlinear block is modeled by a kernel model. The kernel parameters and structural disturbances are estimated simultaneously by using sparse optimization, which is solved using l₁-regularization and iterative reweighting. The feasibility of the proposed method is demonstrated on a simulated example.