A two-experiment approach to Wiener system identification

We propose a new methodology for identifying Wiener systems using the data acquired from two separate experiments. In the first experiment, we feed the system with a sinusoid at a prescribed frequency and use the steady state response of the system to estimate the static nonlinearity. In the second experiment, the estimated nonlinearity is used to identify a model of the linear block, feeding the system with a persistently exciting input. We discuss both parametric and nonparametric approaches to estimate the static nonlinearity. In the parametric case, we show that modeling the static nonlinearity as a polynomial results into a fast least-squares based estimation procedure. In the nonparametric case, least squares support vector machines (LS-SVM) are employed to obtain a flexible model. The effectiveness of the method is demonstrated through numerical experiments.