Adaptive sampling in higher dimensions for point-wise experimental measurement techniques

When performing point-wise measurements within a pre-defined domain, the experimentalist is faced with the problem of defining the spatial locations where to collect data based on an a priori unknown underlying signal. While structured sampling grids are most common, these are rarely optimal from a time-efficiency perspective. In this work an adaptive process is presented for point-wise measurement techniques to guide the spatial distribution of sampling locations in two-dimensions. Thin plate splines of varying degree of smoothing are utilised to iteratively obtain surrogate models of the spatial distribution of the quantities of interest. Adaptive sampling criteria reflecting typical human decisions are combined into a unique objective function, allowing the derivation of suitable measurement positions. The total number of sampling locations thus no longer requires to be pre-defined, as the sampling process is terminated automatically once the addition of measurements is deemed not to provide additional information. The overall implementation is elaborated and the methodology is assessed on the basis of numerical simulations and an experimental test case. Results support the new method's advocated superiority compared to traditional full-factorial sampling in terms of accuracy and reliability.