Simulating Nonhomogeneous Non-Gaussian Field by Using Iterative Rank-Dependent Reordering versus Translation Process-Based Procedure

We compare two commonly used procedures, namely, the iterative rank-dependent reordering (IRDR) procedure and the translation process based procedure, for simulating homogeneous/nonhomogeneous non-Gaussian fields. We identify the limitations and the implicit assumptions of the procedures. We provide a new interpretation of the IRDR procedure, point out that there is no guarantee that the algorithm converges, and suggest modifications in terms of the initial samples, iteration involving decomposition, and convergence requirement to the IRDR procedure for it to become more efficient and robust. The numerical results show that, depending on the prescribed marginal probability distribution, the use of the IRDR procedure may not achieve a prescribed correlation function, a feature that is well-known if the translation process (i.e., Nataf translation system) based procedure is employed. It is shown that the performance of the modified IRDR procedure is comparable to that of the translation process based procedures in terms of limitations and matching the prescribed correlation function. The numerical results also show that the suggested modifications to IRDR in the present study make the algorithm more efficient and robust.