An algorithm to simulate nonstationary and non-Gaussian stochastic processes

• Published in: Journal of infrastructure preservation and resilience Vol. 2; no. 1; p. 17
• Main Authors: Hong, H. P., Cui, X. Z., Qiao, D.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 21-06-2021; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Amplitudes; Civil Engineering; Continuous wavelet transform; Continuous wavelet transforms; Distribution functions; Domains; Engineering; Fourier transforms; Gaussian process; Hypotheses; Hypothesis testing; Iterative methods; Nonstationary and non-Gaussian process; Power spectral density; Probability distribution; Probability distribution functions; S-transform; Seismic ground motions; Simulation; Spectral density function; Stochastic models; Stochastic processes; Stochasticity; Wavelet transforms; Wind; Wind velocity; Wind velocity; Continuous wavelet transforms; Simulation; Nonstationary and non-Gaussian process; Seismic ground motions; S-transform
• ISSN: 2662-2521; 2662-2521
• DOI: 10.1186/s43065-021-00030-5

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.