期刊
PROBABILISTIC ENGINEERING MECHANICS
卷 66, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.probengmech.2021.103141
关键词
Non-Gaussian; Multivariate stochastic process; Stochastic harmonic function; Mehler's formula; Memoryless nonlinear transformation
资金
- National Key R&D Program of China [2018YFC0809400]
- National Natural Science Foundation of China [51678092, 51478064]
- Fundamental Research Funds for the Central Universities [2019CDXYTM0032]
A new model is proposed to represent and simulate Gaussian/non-Gaussian stochastic processes using stochastic harmonic functions and Mehler's formula. The model efficiently generates Gaussian/non-Gaussian processes and is demonstrated through numerical examples.
A new model is proposed to represent and simulate Gaussian/non-Gaussian stochastic processes. In the proposed model, stochastic harmonic function (SHF) is extended to represent multivariate Gaussian process firstly. Compared with the conventional spectral representation method (SRM), the SHF based model requires much fewer variables and Cholesky decompositions. Then, SHF based model is further extended to univariate/multivariate non-Gaussian stochastic process simulation. The target non-Gaussian process can be obtained from the corresponding underlying Gaussian processes by memoryless nonlinear transformation. For arbitrarily given marginal probability distribution function (PDF), the covariance function of the underlying multivariate Gaussian process can be determined easily by introducing the Mehler's formula. And when the incompatibility between the target non-Gaussian power spectral density (PSD) or PSD matrix and marginal PDF exists, the calibration of the target non-Gaussian spectrum will be required. Hence, the proposed model can be regarded as SRM to efficiently generate Gaussian/non-Gaussian processes. Finally, several numerical examples are addressed to show the effectiveness of the proposed method.
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