The practical calculation method of the high-order moment spectra of quadratic Gaussian stochastic processes

Abstract

In the frequency-domain analysis of structures under non-Gaussian excitations, the determination of high-order moment spectra of excitations remains a substantial challenge due to the complexity and inaccuracy of the existing estimation method. This paper proposes the practical calculation method of the high-order moment spectra models for quadratic Gaussian stochastic processes. Firstly, the expressions of the first four moment spectra of quadratic Gaussian stochastic processes are derived based on the relation between the high-order cumulant function of Gaussian stochastic processes and high-order moment function. Secondly, a practical calculation method of the high-order moment spectra is presented by the ratio of the corresponding component moment functions. Finally, two numerical examples are investigated to validate the efficiency and accuracy of the practical calculation method of the high-order moment spectra for quadratic Gaussian stochastic processes.