Characterization of a two-dimensional static wind field using Radial Basis Functions

Abstract

Radial Basis Functions are a modern way of creating a regression model of a multivariate function when sampled data points are not uniformly distributed in a perfect grid. Radial Basis Functions are well suited to atmospheric characterization when unmanned aerial vehicles (UAVs) are used to sample the given space. Multiple UAVs reduce the time for the Radial Basis Functions to yield a suitable solution to the measured data while data from all aircraft are aggregated and sent to Radial Basis Functions to fit the data. The research presented here focuses on the requirements for a high correlation value between the sampled data and the actual data. It is found that the number of centers is a large driver of the goodness of fit in the Radial Basis Function routine, much like aliasing is an issue in sampling a sinusoidal function. These centers act like a sampling rate for the spatially varying wind field. If the centers are dense enough to fully capture the spatial frequency of the wind field, the Radial Basis Functions will produce a suitable fit. This also requires the number of data points to be larger than the number of centers. The ratio between the number of centers and number of sampled data points declines as the number of centers increases. The results presented here are revealed using a two-dimensional Fourier series analysis coupled to a spatially varying atmospheric wind model and a Radial Basis Function regression model.