An iterative multi-fidelity scheme for simulating multi-dimensional non-Gaussian random fields

Abstract

This paper presents an efficient multi-fidelity scheme to simulate multi-dimensional non-Gaussian random fields that are specified by covariance functions and marginal probability distribution functions. To develop the multi-fidelity scheme, two numerical algorithms are proposed in turn. The first algorithm is used to simulate random samples of the random field. In this algorithm, initial random samples are first generated to meet the marginal distribution and an iterative procedure is adopted to change the ranking of the random samples to match the target covariance function. By using the above algorithm, random samples satisfying the target covariance function and the target marginal distribution are obtained, but it is computationally intensive and is not suitable to simulate large-scale random fields. By taking advantage of Karhunen–Loève expansion, a multi-fidelity algorithm is then proposed to reduce the computational effort. The random variables in Karhunen–Loève expansion are calculated via performing the first algorithm on the low-fidelity model and the deterministic functions in Karhunen–Loève expansion are solved on the high-fidelity model. In this way, the proposed method has low computational effort and a high fidelity simultaneously. Three numerical examples, including two- and three-dimensional non-Gaussian random fields, are used to verify the good performance of the proposed algorithms.