Simulation of stationary non-Gaussian stochastic vector processes using an eigenvalue-based iterative translation approximation method

Abstract

The simulation of stationary non-Gaussian stochastic vector processes is of great importance in the time-domain response analysis of structures under non-Gaussian excitations. When incompatibility between the target cross power spectral density matrix and the marginal probabilistic density function of the stochastic vector process occurs in the sense of translation processes, an iterative simulation scheme must be required. Currently, the Cholesky decomposition-based iterative translation approximation method is widely utilized. However, the use of this method still encounters some difficulties. First, it requires performing Cholesky decompositions three times at each iteration and is therefore cumbersome. Second, a complicated random shuffling procedure is necessary, which renders the final iteration result non-unique. Third, it is very difficult for this method to handle cases with complex-valued spectral matrices. Lastly, it can generally be used to simulate stochastic vector processes with very limited components. To overcome these difficulties, an eigenvalue-based iterative translation approximation method is proposed in this study. This method can not only avoid the cumbersome Cholesky decomposition and complex random shuffling, but can also handle cases with complex-valued and large spectral matrices more easily. Four numerical examples with no incompatibility, significant incompatibility, complex-valued coherence and a large number of component processes are respectively employed to demonstrate the effectiveness of the proposed method. The results show that the proposed method has similar accuracy to the Cholesky decomposition-based iterative method in the first two examples. For the last two examples, the simulation accuracy is also satisfactory. The above results verify that the proposed method is superior to the Cholesky decomposition-based iterative translation approximation method overall.