A Karhunen-Loeve decomposition-based Wiener modeling approach for nonlinear distributed parameter processes

The spatio-temporal modeling problem from the input and output measurements for distributed parameter processes under unknown circumstances is investigated. The traditional Wiener modeling is extended to nonlinear distributed parameter systems with the help of the Karhunen-Loeve (KL) decomposition. The input is a finite-dimensional temporal variable, whereas the spatio-temporal output of the system is measured at a finite number of spatial locations. First, the measured output is used to construct a finite dimensional approximation of the system output which is expanded in terms of KL spatial basis functions. Subsequently, the temporal coefficients are used to identify a Wiener model. The identification algorithm is based on the least-squares estimation and the instrumental variables method. The simulations for parabolic and hyperbolic systems are presented to show the effectiveness of this spatio-temporal modeling method.