Kernel based modelling of friction dynamics

The accurate modelling of friction dynamics remains an obstacle to the identification of a number of processes. Typically models are derived based on a detailed physical understanding of the underlying process. However, this can often be time consuming and, in any case, the models must be tailored to the particular process being studied. Alternatively, we can model friction dynamics using only observations of the process. In this paper a comparison is presented of the relative value of incorporating differing levels of prior knowledge into the modelling of friction dynamics. A new approach to data-driven modelling is presented, the generalised Fock space nonlinear autoregressive with exogeneous inputs (GFSNARX) model. This model allows Volterra and polynomial NARX models of arbitrary degree to be estimated using finite data. The results of modelling friction dynamics using the GFSNARX model are compared to the DNLR Maxwell slip and AVDNN models. It is shown that, whilst the incorporation of a priori physical knowledge results in a definite improvement in model performance, appropriate data driven models can achieve comparable performance without the effort of physical modelling. However, these results depend on the friction regime being modelled. Those models incorporating prior knowledge achieved good results for all regimes whilst the GFSNARX model was best suited to the pre-sliding regime.