A Computational Intelligence Technique for the Identification of Non-Linear Non-Stationary Systems

This paper addresses nonlinear nonstationary system identification from stimulus-response data, a problem concerning a large variety of applications, in dynamic control as well as in signal processing, communications, physiological system modelling and so on. Among the different methods suggested in the vast literature for nonlinear system modelling, the ones based on the Volterra series and the Neural Networks are the most commonly used. However, a strong limitation for the applicability of these methods lies in the necessary property of stationarity, an assumption that cannot be considered as valid in general and strongly affecting the validity of results. Another weakness of the approaches currently used is that they refer to differential systems, thus being unsuitable to model systems described by integral equations. A computational intelligence technique that exploits the potentialities of both the Karhunen-Loeve Transform (KLT) and Neural Networks (NNs) representation and without any of the limitations of the previous approaches is suggested in this paper. The technique is suitable for modelling the wide class of systems described by nonlinear nonstationary functionals, thus including both differential and integral systems. It takes advantage of the KLT separable kernel representation that is able to separate the dynamic and static behaviours of the system as two distinct components, and the approximation property of NNs for the identification of the nonlinear no-memory component. To validate the suggested technique comparisons with experimental results on both nonlinear nonstationary differential and integral systems are reported.