A New Methodology for Automatic Cluster-Based Kriging Using K-Nearest Neighbor and Genetic Algorithms

Abstract

Kriging is a geostatistical interpolation technique that performs the prediction of observations in unknown locations through previously collected data. The modelling of the variogram is an essential step of the kriging process because it drives the accuracy of the interpolation model. The conventional method of variogram modelling consists of using specialized knowledge and in-depth study to determine which parameters are suitable for the theoretical variogram. However, this situation is not always possible, and, in this case, it becomes interesting to use an automatic process. Thus, this work aims to propose a new methodology to automate the estimation of theoretical variogram parameters of the kriging process. The proposed methodology is based on preprocessing techniques, data clustering, genetic algorithms, and the K-Nearest Neighbor classifier (KNN). The performance of the methodology was evaluated using two databases, and it was compared to other optimization techniques widely used in the literature. The impacts of the clustering step on the stationary hypothesis were also investigated with and without trend removal techniques. The results showed that, in this automated proposal, the clustering process increases the accuracy of the kriging prediction. However, it generates groups that might not be stationary. Genetic algorithms are easily configurable with the proposed heuristic when setting the variable ranges in comparison to other optimization techniques, and the KNN method is satisfactory in solving some problems caused by the clustering task and allocating unknown points into previously determined clusters.