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

Abstract

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.

Increasing evenness and stability in synthetic microbial consortia

“…Once an initial set of points were obtained, we switched to adaptive sampling method to select next training points in the solution space. Adaptive sampling technique generates points in regions of the parametric space with large prediction errors 47, 48 . Surrogates built from adaptive training points are better approximations while requiring fewer points and hence evaluations.…”

Efficiency of Sequential Spatial Adaptive Sampling Algorithm to Accelerate Multifrequency Near-Field Scanning Measurement

“…Then, the SSAS algorithm increases the meshing locally according to a selection criterion. A new sampling point is added when the neighbor measurement points are above the noise floor and if a sufficient field gradient is observed (5). Depending on the selection criterion, either the measurement time reduction or the accuracy of the field reconstruction is favored.…”

“…An effective method to reach this goal is to use a spatial adaptive sampling, which selects spatial sampling position only where a sufficient amount of information can be collected. Several approaches have been proposed for electromagnetic applications [3] [4] [5]. For a near-field scanning above a PCB, the approach described in [6] [7] [8], dedicated to adaptive sampling of planar surface, ensures a significant reduction of the number of samples.…”

Fast and Accurate Near-Field Measurement Method Using Sequential Spatial Adaptive Sampling (SSAS) Algorithm

“…11), most of the scanned points do not carry significant information about the radiated sources. For decades, several adaptive sampling approaches have been developed [2], [3] on the wave propagation application [4], [5] and for planar surface [6], [7]. The planar sampling is suited for electronic equipment scanning.…”