Integral estimation with the ordinary Kriging method using the Gaussian semivariogram function

Abstract

SUMMARYThis paper describes a detailed procedure for integral estimation of an unknown function using the ordinary Kriging method. This method estimates the definite integral of an approximated surface generated using the ordinary Kriging method. The integral of an approximated surface can be computed directly using a set of sampling data for a function value. One of the merits of the proposed method is that the integral can be estimated without iterative summation generally used in a conventional numerical integration technique. In addition to a continuous function, the proposed method enables to estimate the integral using a set of discrete sampling data.In this paper, a basic formulation for an integral estimation using the Kriging method, especially with the Gaussian-type semivariogram model, is introduced. An explicit form of the integral of the Gaussian function is approximated by Williams' method.As test problems, definite integrals of some elementary functions are estimated using the proposed method. In addition, as an engineering example, a flow in a pipe is estimated using the proposed method with less samples of the velocity of fluid. The numerical results illustrate the accuracy and efficiency of the proposed method.

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

“…In this study, types of semivariograms are from the Gaussian semivariogram model because the Gaussian semivariogram model generates a relatively smooth estimated surface [57]. It is widely used in the field of approximate optimization [58].…”