Numerical simulation of non-Gaussian stochastic process with time-varying power spectrum

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (2) : 204-209.

LI Jin-hua1, 2, WU Chun-peng2, CHEN Shui-sheng2, LI Jian-feng2 YU Wei-guang2

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Abstract

In order to simulate effectively a non-stationary non-Gaussian stochastic process possessing a given time-varying power spectrum and probability density function, a nonlinear translation relationship to achieve mutual conversion between non-Gaussian and Gaussian random processes was established, the conversion relationship between power spectrum or correlation function of a non-Gaussian stochastic process and that of a Gaussian stochastic process was also established. Then, a non-stationary non-Gaussian stochastic process was converted through these relationships into a non-stationary Gaussian stochastic process to be simulated. A non-stationary Gaussian stochastic process was effectively simulated with the spectral representation. In order to verify the effectiveness of this method, the simulation of a fluctuating wind velocity possessing target non-stationary non-Gaussian characteristics was performed. The simulation results showed that the simulated fluctuating wind speed sample’s power spectrum has time-varying characteristics, meanwhile its instantaneous power spectrum and correlation function match those of the target; the probability density function (PDF) of the fluctuating wind velocity sample at any time matches the target’s PDF possessing non-Gaussian characteristics; therefore, the simulated random samples not only have the non-stationary features of target time-varying power spectrum, but also have the non-Gaussian features of target probability density function, the effectiveness of the proposed method to simulate a non-stationary non-Gaussian random process is verified.

Key words

time-varying power spectrum / probability density function / non-Gaussian stochastic process / non-stationary feature / fluctuating wind velocity.

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LI Jin-hua1, 2, WU Chun-peng2, CHEN Shui-sheng2, LI Jian-feng2 YU Wei-guang2. Numerical simulation of non-Gaussian stochastic process with time-varying power spectrum[J]. Journal of Vibration and Shock, 2018, 37(2): 204-209

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