An algorithm to simulate nonstationary and non-Gaussian stochastic processes

H P Hong; X Z Cui; D Qiao

doi:10.1186/s43065-021-00030-5

An algorithm to simulate nonstationary and non-Gaussian stochastic processes

J Infrastruct Preserv Resil. 2021;2(1):17. doi: 10.1186/s43065-021-00030-5. Epub 2021 Jun 21.

Authors

H P Hong¹, X Z Cui¹, D Qiao²

Affiliations

¹ Department of Civil and Environmental Engineering, University of Western Ontario, London, N6A 5B9 Canada.
² China Construction Eighth Engineering Division Corp, LTD., Shanghai, China.

Abstract

We proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Keywords: Continuous wavelet transforms; Nonstationary and non-Gaussian process; S-transform; Seismic ground motions; Simulation; Wind velocity.