A modified straightforward spectral representation method for accurate and efficient simulation of the stationary non-Gaussian stochastic wave

Abstract

The widely used spectral representation method for simulation of stationary non-Gaussian stochastic wave needs the iterative procedure to handle the incompatibility between the power spectral density (PSD) and cumulative density function (CDF) of the stochastic process, and the accuracy and efficiency of the method should be improved. In this paper, a modified straightforward spectral representation method is developed for accurately and efficiently simulating the non-Gaussian stochastic wave based on the specified PSD and target kurtosis and skewness. In the proposed method, the stationary non-Gaussian stochastic wave is first generated based on the specified PSD, and then transformed into the non-Gaussian stochastic wave with a modified analytical translation model. The transformed non-Gaussian stochastic wave is further decomposed into random phase angles and amplitudes, and the target non-Gaussian stochastic wave is finally reconstructed with the random phase angles extracted from the transformed non-Gaussian stochastic wave and the amplitudes discretized from the specified PSD. The key feature of the proposed method is that the CDF of the non-Gaussian stochastic wave can be explicitly constructed by the modified translation model, and the PSD distortion caused by nonlinear transformation can be eliminated with the stochastic wave decomposition and reconstruction procedure. The proposed method therefore possesses advantages of immune to incompatibility between the PSD and CDF, and the non-Gaussian stochastic wave can be simulated in a straightforward manner without any need for iterations. The effectiveness of the proposed method in representing the non-Gaussian stochastic wave is investigated with a series of case studies. Numerical results indicate that the proposed method is robust, efficient and accurate within engineering expectations. It may have a wide range of applicability to engineering problems involving stochastic wave where the Gaussian assumption is not appropriate.