A novel general method for simulating a one dimensional random field based on the active learning Kriging model

Abstract

Random fields are widely used to represent the uncertainty of some parameters in engineering, and numerous simulation approaches have been developed for Gaussian and non-Gaussian random fields. However, the unified methods among them suffer from low computational accuracy and efficiency or discontinuities in the simulated random fields. Therefore, an easy-to-implement general simulation method based on the active learning Kriging model is proposed for a one dimensional(1D) Gaussian or non-Gaussian random field in this paper. In the proposed method, there are two stages. One stage, called the inner loop, is to construct the Kriging approximation of a random field sample with enough accuracy by some samples of the random variables at some discretized locations, in which an active learning strategy based on the error estimation for the Kriging model is introduced to select adaptively the added locations, and a fast sampling method is presented to determine efficiently the samples at the added locations. In the other stage, called the outer loop, some random field samples are represented accurately by their corresponding Kriging approximations through training iteratively. Furthermore, several numerical examples are presented to show the accuracy, effectiveness and generality of the proposed method for 1D Gaussian and non-Gaussian random fields by comparing with the Karhunen–Loève(KL) expansion method. Meanwhile, the effects of the types of correlation function and the scales of fluctuation on the simulation results are analyzed.