Three‐stage non‐Gaussian homogeneous random field representation over manifolds

Abstract

AbstractRandom fields are widely used to characterize the inherent spatial uncertainty in engineering applications. However, for widely existing manifolds, few studies focus on the simulation of Gaussian/non‐Gaussian fields over manifolds due to the geometry complexity. Recently, we proposed a two‐stage method to simulate Gaussian fields over manifolds. In this study, we extend it to a three‐stage method for non‐Gaussian fields. In the first stage, the original manifold is dimensional reduced to a Euclidean domain by the isometric feature mapping. By this step, the geodesic distance is preserved to guarantee the correlation structure unchanged. In the second stage, conventional representations can be used to simulate the underlying Gaussian field over the Euclidean domain. In the third stage, an enhanced translation procedure is proposed to translate the underlying Gaussian field to the target non‐Gaussian field over the manifold. To explain the applicability and accuracy of the three‐stage method, two kinds of non‐Gaussian fields over three different manifolds are simulated. Then, a global error is proposed to evaluate the performance of the method, and the error analysis demonstrates the method is accurate enough. Finally, two engineering structures, that is, a compressed half‐cylinder and a Canopy shell with complex geometry, are investigated to illustrate the potential applications of the method.