Model selection for system identification by means of artificial neural networks

System identification is one main task in modern deformation analysis. If the physical structure of the monitoring object is unknown or not accessible the system identification is performed in a behavioural framework. Therein the relations between input and output signals are formulated on the basis of regression models. Artificial neural networks (ANN) are a very flexible tool for modelling especially non-linear relationships between the input and the output measures. The universal approximation theorem ensures that every continuous relation can be modelled with this approach. However, some structural aspects of the ANN-based models, like the number of hidden nodes or the number of data needed to obtain a good generalisation, remain unspecified in the theorem. Therefore, one faces a model selection problem. In this article the methodology of modelling the deformations of a lock occurring due to water level and temperature changes is described. We emphasise the aspect of model selection, by presenting and discussing the results of various approaches for the determination of the number of hidden nodes. The first one is cross-validation. The second one is a weight deletion technique based on the exact computation of the Hessian matrix. Finally, the third method has a rigorous theoretical background and is based on the capacity concept of a model structure.