Simulation of 4th-order non-Gaussian random processes by higher-order spectral representation method

In this study, a new higher-order spectral representation method (HOSRM) is derived to simulate fourth-order (kurtosis-order) non-Gaussian random processes. Applying the HOSRM allows fourth-order non-Gaussian random process (symmetric non-Gaussian) sample functions to be generated accurately. As the number of terms in the cosine function used in the HOSRM increases, the simulated non-Gaussian random process sample functions can more accurately reflect the second-order (variance) and fourth-order (kurtosis) statistical properties of the objective sample functions. In particular, if the number of terms tends to infinity, then the simulated sample function characteristics will be the same as the target value. Meanwhile, a reasonable three-dimensional Hermite interpolation method is proposed to improve the simulation efficiency of stochastic processes. Finally, two examples are provided to demonstrate the accuracy and effectiveness of the proposed HOSRM for generating fourth-order non-Gaussian random pro-cesses. The results show that the statistical properties (power spectral density, trispectrum, and kurtosis) of the simulated non-Gaussian random process are consistent with those of the target random process.

Automated summary

In this study, a new higher-order spectral representation method (HOSRM) is proposed to accurately simulate fourth-order non-Gaussian random processes. The HOSRM allows for the generation of sample functions that accurately reflect the statistical properties of the target sample functions. A three-dimensional Hermite interpolation method is also proposed to improve the simulation efficiency. The results demonstrate the accuracy and effectiveness of the HOSRM in generating fourth-order non-Gaussian random processes.