Conditional Simulation of Multivariate Stationary Non-Gaussian Processes Based on an Improved Iterative Translation Approximation Method

The simulation of multivariate stationary non-Gaussian stochastic processes, based on translation process theory, is widely used in fields like structural wind engineering due to its high accuracy and strong applicability. However, existing studies focus primarily on unconditional simulation, and often struggle to computational efficiency and accuracy, limiting their applications in engineering. To address these issues, this paper proposes an efficient and high-accuracy conditional simulation method for multivariate stationary non-Gaussian stochastic processes, based on translation process theory. The proposed method iteratively determines the underlying Gaussian cross-spectral density matrix (CSDM) corresponding to any prescribed target non-Gaussian CSDM. Based on this, the Spectral Representation Method (SRM) and a marginal distribution transformation function are used to generate non-Gaussian samples. The method is then extended to enable conditional simulation. The effectiveness of the proposed approach is demonstrated through two numerical examples. Results indicate that the method is applicable to non-Gaussian stochastic processes with both weak and strong incompatibility, achieving higher computational efficiency and accuracy compared to existing methods.