Qualitative validation of radial basis function networks

In system identification applications of neural networks, the aim is usually to obtain a dynamically valid model of the system which can be used for system analysis and for controller design. In the present study, a cell to a cell mapping procedure is adopted for the global analysis of non-linear systems and the qualitative validation of radial basis function networks. The method is used to graphically display the dynamic properties of non-linear systems in a cell state space, including the fixed points, periodic and aperiodic solutions or chaotic behaviour and the corresponding stability properties. The orthogonal least-squares algorithm (OLS) is then used to train a radial basis function network and the trained network is analysed using the cell mapping framework. In this way, the dynamical properties of the trained network can be qualitatively compared with those of the original system. The effects of overparametrisation and output noise on the dynamic properties of the trained network are investigated using cell map analysis. (C) 1999 Academic Press.