A multi-channel spatio-temporal Hammerstein modeling approach for nonlinear distributed parameter processes

Modeling of distributed parameter processes is a challenging problem because of their complex spatio-temporal nature, nonlinearities and uncertainties. In this study, a spatio-temporal Hammerstein modeling approach is proposed for nonlinear distributed parameter processes. Firstly, the static nonlinear and the distributed dynamical linear parts of the Hammerstein model are expanded onto a set of spatial and temporal basis functions. In order to reduce the parametric complexity, the Karhunen–Loève decomposition is used to find the dominant spatial bases with Laguerre polynomials selected as the temporal bases. Then, using the Galerkin method, the spatio-temporal modeling will be reduced to a traditional temporal modeling problem. Finally, the unknown parameters can be easily estimated using the least squares estimation and the singular value decomposition. In the presence of unmodeled dynamics, a multi-channel modeling framework is proposed to further improve the modeling performance. The convergence of the modeling can be guaranteed under certain conditions. The simulations are presented to show the effectiveness of this modeling method and its potential to a wide range of distributed processes.