Hybrid neural networks for nonlinear system identification

The authors propose the use of single-layer network models, a special class of neural networks, for modelling and identification of nonlinear system dynamics. Several model representations can be cast into a single-layer network form, like Wiener models and parametric approximating functions. Wiener models suffer from the disadvantage of having large numbers of parameters, while approximating functions generally allow a quite modest model size. Certain radial basis type functions (RBF) for function approximation not only have effective modelling capacities, but provide stable models as well. The application of hybrid linear/RBF models appears to improve model optimisation and quality significantly. The orthogonal least squares selection algorithm has proved to be an effective and reliable optimisation tool for single-layer network type models of any representation, but it suffers from high calculation loads. In this paper a case study is described, in which the hybrid modelling of a fed-batch fermentor is demonstrated. The accuracy of the obtained model shows that the use of a hybrid model is a valid approach. Practical aspects of the hybrid modelling approach are discussed, concerning the dimension of the model and the accuracy which can be achieved.