Simulation of parameterized random fields, Part II

This paper presents two numerical algorithms to simulate non-Gaussian random fields that are parameterized by random parameters. The simulation of such kind of random fields is very challenging due to their parameterized non-Gaussian properties. For each sample realization of the random parameters, the parameterized non-Gaussian random field degrades into a classical non-Gaussian random field. In the first algorithm, we present a sample-based iterative algorithm to simulate the obtained classical non-Gaussian random field. Initial random samples are first generated to meet the sampled marginal distribution, and an iterative procedure is adopted to change the ranking of the random samples to match the target sampled covariance function. However, this method is computationally expensive since we have to simulate a non-Gaussian random field for each sample realization of the random parameters. To avoid this issue, we develop a reformulation-based algorithm in the second method. Parameterized marginal distributions are reformulated as non-parameterized marginal distributions via a conditional probability integral, and parameterized covariance functions are reformulated as non-parameterized covariance functions via an expectation operation on random parameters. In this way, the original parameterized non-Gaussian random field is transformed into a classical non-Gaussian random field. The sample-based iterative algorithm is then used to simulate the obtained non-Gaussian random field. Moreover, a multi-fidelity approach is presented to further reduce the computational effort of the above iteration by taking advantage of the Karhunen-Loève expansion. Specifically, the expanded random variables in Karhunen-Loève expansion are calculated on a low-fidelity model and the deterministic functions in Karhunen-Loève expansion are calculated on a high-fidelity model. Thus, the method has low computational effort and high fidelity simultaneously. Two numerical examples, including one- and three-dimensional parameterized non-Gaussian random fields, are used to verify the effectiveness of the proposed methods.