Forecasting the geomagnetic activity of the Dst index using multiscale radial basis function networks

The Dst index is a key parameter which characterises the disturbance of the geomagnetic field in magnetic storms. Modelling of the Dst index is thus very important for the analysis of the geomagnetic field. A data-based modelling approach, aimed at obtaining efficient models from limited input–output observational data, provides a powerful tool for analysing and forecasting geomagnetic activities including the prediction of the Dst index. In this study, the process of the Dst index is treated to be a structure-unknown system, where the solar wind parameter (VBs) and the solar wind dynamic pressure (P) are the system inputs, and the Dst index is the system output. A novel multiscale RBF (MSRBF) network is introduced to represent such a two-input and single-output system, where the Dst index is related to the solar wind parameter and the dynamic pressure, via a hybrid network model consisting of two submodels: a linear part that reflects the linear relationship between the output and the inputs, and a nonlinear part that captures the effect of the interacting contribution of past observations of the inputs and the output, on the current output. The proposed MSRBF network can easily be converted into a linear-in-the-parameters form and the training of the linear network model can easily be implemented using a forward orthogonal regression (FOR) algorithm. One advantage of the new MSRBF network, compared with traditional single scale RBF networks, is that the new network is more flexible for describing complex nonlinear dynamical systems.